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Dynare: Reference Manual Version 4

1. 22 15 4 3 1 2 Outside the model 15 4 3 2 Operators sin distants its wt pia Pede era hibeded Ya esa pas 15 43 9 Functions 2smamma a one cae bag eee ND Gone ok en ERU le iie sere pt 16 4 8 3 1 Built in Functions 232043206 6c cede Rad eR Ras ere EE y ERR RE etes 16 4 3 3 2 External Functions 22220 17 4 3 4 A few words of warning in stochastic context 18 4 4 Parameter initialization 2 220 18 4 5 Model declaration 4 222 18 46 Auxiliary variables seen ae e bee ER RR RR dd ac deep E CR Tot d 21 4 7 Initial and terminal conditions 2222 22 4 8 Shocks on exogenous variables 20 DT 4 9 Other general declarations 4 22 30 4 10 Steady State soccer ke und nu ain Peas a EE PIDE ERA PNE D eer RS 30 4 10 1 Finding the steady state with Dynare nonlinear solver 30 4 10 2 Using a steady state file 33 4 10 3 Replace some equations during steady state computations 35 4 11 Getting information about the model
2. 114 ED same wise necem eese obs ende ed ais 114 H hiStval ice aen desea wai e Dresses dubakud 26 homotopy setup etr re mpeg 32 horZcat o5eraew E wists create 115 125 HPEYCLE mue E ba he Rubr Eee lh dra ens 126 hptrend ii rl E RR GR E 127 I identification pce fb Ree eR vain ue 86 ADP ose dagegen E M Xr du E USC 14 init plamnu ssLseresgveree dee otal cee er ERT EA 73 Mas Wie aie Ste ae ead decuit ns is 22 oy es f 8 Lt GUMMI 2T BAS LE e E EL EE 4 RDEST UN EE E Ts 128 internals eiczadceugeuernbrr4d m dise arava s 148 intersect nisse spe d queer Racers dd dealer s 115 isempty gehe ek a peste ER 116 128 Command and Function Index lag E A SEP EAT DECR SN ER E end 129 mc 116 Tead i eroe his dehell gi sisi 130 length 16b persie arai ror e pedra ere 116 An E E E E dr Ra RU E ER Pu E 16 load_params_and_steady_state 105 HRe A Qance teeters 16 131 log trend V in Les shine dentaires 14 TU MH TEC 16 tisse E Sa Ca ks em en 117 markov Switching isiseececueivouk Wesen do 8T ro 16 IIT Herg l lilnizeuesiiedl d ege hair ane 131 nih ReibbReUebgwe REPSRPEeWeR Degd apes edu 16 117 MANUS ET SH aule cre he ed e ade did ENG E Y TIT 132 mod l MP Tnm 18 nodel comparison e e i e Ee mes 67 model diagnostiCsS eo ete ror pr pen 36 model info i2o err amas Tn PT des 36 MPOWED segt irtir eee Aeg pud ED Net Visio 133 Inrdlivid
3. 36 4 12 Deterministic simulation 3T 4 13 Stochastic solution and simulation 39 4 13 1 Computing the stochastic solution 40 4 13 2 Typology and ordering of variables 46 4 13 3 First order approximation 47 4 13 4 Second order approximation 47 4 13 5 Third order approximation 48 AAA CO Re nee Ee mee adeeseibu E oben Reus aab PP IDE 48 45 borecast ng cdesesebteeetuuaebhe ree ner ERE EREECE E fo cen RE RERBA a 69 4 160 Optimal policy sed rd Lesser e pb ERR CERA E bre ARR aie 75 4 17 Sensitivity and identification analysis 79 417 1 Sampin Esa ienr o aden Lie PR shee ee dune REIN eG Poe ee 79 4 17 2 Stability Mapping 44 2242 4 79 4 17 3 Reduced Form Mapping 4 28 80 47 4 RMSE ni rs an re Rb dam eR CE ie lande lier 80 4 17 5 Screening Analysis esee upper ane dos RARE a ee tae ent 82 4 17 6 Identification Analysis 82 4 17 7 Performing Sensitivity and Identification Analysis
4. 82 4 18 Markov switching SBVAR 22 87 4 19 Displaying and saving results 97 4 20 Macro processing language 98 4 20 1 Macro EXPr SSIONS 2 32 22 4 0 dansante Pea eee ee Reda une nets pat 98 4 20 2 Macro directives 444 e4eeeee 99 4 20 8 Typical usages ex tiiri RR xe E CDS naine diet desde 101 420 3 1 Modularizatio n ie25c I ego seine dt iiei ana bide bin at 101 4 20 3 2 Indexed sums or products 101 4 20 3 3 Multi country models 102 4 20 3 4 Endogeneizing parameters 102 4 20 4 MATLAB Octave loops versus macro processor loops 103 4 21 Verbatim inclusion 4 4444 eee 104 4 22 Mise commands c ERE a autos deat raat Pa to aegre d tie etes 104 5 The Configuration File 106 5 1 Dynare Configuration 4 42444 24 106 5 2 Parallel Configuration 244222 107 6 Time Sees ETE 110 OL Dates RE qc NRA de eee cine eA Uu ete ee pe eee 110 6 1 1 dates in a mod file dee e eee RR AR deeded R
5. 3 2 1 Software requirements 4 3 2 2 Installation of Dynare issue eher et hante E EA E et 3 22 On WiIndOWS s cerxxed Upper de ey evexit en lapse tud bella 3 2 2 2 On Debian GNU Linux and Ubuntu i22 249 9o eR eCECHER ARRAY UR Pee 3 2 2 3 On Mac OS Xavier E com RR E E CR ER eA Deka 4 22A For other Systems uds ss dissident a annee Uere ber 4 2 9 Configuration 22252 na dde E E he Race EE edite Visa Rig ER ee este 4 2 3 1 For MATLAB eese tbe UR EK YT RR DR OCC Geb ER gd e oed 4 2 32 For GNU Octave esee teer ssh nets de Mapa ce 4 2 3 3 Some words of warning 5 Running DNHATS xi aap ood anions a Rd Rd awh AU a CU UAR IN c ws 6 Sel Dynare mnvocati n ii inieseneuenessecriesedcwe9lpORUEE porteur added detente 6 3 2 Dyn are hooks 2 41 gan eo ME NUR E p deren C SAS os Det 9 3 3 Understanding Preprocessor Error Messages 9 The Model Heus cosvpa shes Wise Wine a narration 10 Al CONVENTIONS rss dass een Re pee ere CRURA qu pea ERR RR D ICE eris 10 4 2 Variable declarations 44 2222 10 4 9 EXpresslOlSascisqoccReitbtebshrte IR Gc ORG RE SER PES PENPXGUORRLECOULEPRMPREE Soa LENS 14 4 3 1 Parameters and variables 2 15 4 3 1 1 Inside the model
6. Mean Mean of the posterior forecast distribution HPDinf HPDsup Upper lower bound of the 90 HPD interval taking into account only parameter uncertainty HPDTotalinf HPDTotalsup Upper lower bound of the 9096 HPD interval taking into account both parameter and future shock uncertainty VARIABLE NAME contains a matrix of the following size number of time periods for which forecasts are requested using the nobs INTEGER1 INTEGER2 option times the number of forecast horizons requested by the forecast option Le the row indicates the period at which the forecast is performed and the column the respective k step ahead forecast The starting periods are sorted in ascending order not in declaration order oo_ convergence geweke MATLAB Octave variable Variable set by the convergence diagnostics of the estimation command when used with mh nblocks page 54 1 option see mh nblocks page 54 Fields are of the form oo convergence geweke VARIABLE NAME DIAGNOSTIC OBJECT where DIAGNOSTIC OBJECT is one of the following posteriormean Mean of the posterior parameter distribution 5 See forecast page 60 for more information Chapter 4 The Model file 67 posteriorstd Standard deviation of the posterior parameter distribution nse iid Numerical standard error NSE under the assumption of iid draws rne iid Relative numerical efficiency RNE under the assumption of iid draws nse x Numerical standard error NSE when using an
7. 4 5 Model declaration The model is declared inside a model block model Block model OPTIONS Block Description The equations of the model are written in a block delimited by model and end keywords There must be as many equations as there are endogenous variables in the model except when computing the unconstrained optimal policy with ramsey_policy or discretionary_policy The syntax of equations must follow the conventions for MODEL_EXPRESSION as described in Section 4 3 Expressions page 14 Each equation must be terminated by a semicolon A normal equation looks like MODEL_EXPRESSION MODEL_EXPRESSION When the equations are written in homogenous form it is possible to omit the 0 part and write only the left hand side of the equation A homogenous equation looks like Chapter 4 The Model file 19 MODEL EXPRESSION Inside the model block Dynare allows the creation of model local variables which constitute a simple way to share a common expression between several equations The syntax consists of a pound sign s followed by the name of the new model local variable which must not be declared as in Section 4 2 Variable declarations page 10 an equal sign and the expression for which this new variable will stand Later on every time this variable appears in the model Dynare will substitute it by the expression assigned to the variable Note that the scope of this variable is restrict
8. Options periods INTEGER Number of periods to be plotted Default equal to periods in conditional forecast The number of periods declared in plot conditional forecast cannot be greater than the one declared in conditional forecast bvar forecast Command This command computes out of sample forecasts for an estimated BVAR model using Min nesota priors See bvar a la sims pdf which comes with Dynare distribution for more information on this command If the model contains strong non linearities or if some perfectly expected shocks are considered the forecasts and the conditional forecasts can be computed using an extended path method The forecast scenario describing the shocks and or the constrained paths on some endogenous variables should be build The first step is the forecast scenario initialization using the function init plan HANDLE init plan DATES MATLAB Octave command Creates a new forecast scenario for a forecast period indicated as a dates class see dates class members page 111 This function return a handle on the new forecast scenario The forecast scenario can contain some simple shocks on the exogenous variables This shocks are described using the function basic plan HANDLE basic plan HANDLE VARIABLE NAME MATLAB Octave command SHOCK_TYPE DATES MATLAB VECTOR OF DOUBLE DOUBLE EXPRESSION DOUBLE EXPRESSION Adds to the forecast scenario a shock on the exogenou
9. Command simul OPTIONS Command Description Triggers the computation of a deterministic simulation of the model for the number of periods set in the option periods Options periods INTEGER Number of periods of the simulation maxit INTEGER Determines the maximum number of iterations used in the non linear solver The default value of maxit is 10 The maxit option is shared with the steady command So a change in maxit in a simul command will also be considered in the following steady commands Stack solve algo INTEGER Algorithm used for computing the solution Possible values are 0 Newton method to solve simultaneously all the equations for every pe riod using sparse matrices Default 1 Use a Newton algorithm with a sparse LU solver at each iteration re quires bytecode and or block option see Section 4 5 Model declara tion page 18 2 Use a Newton algorithm with a Generalized Minimal Residual GM RES solver at each iteration requires bytecode and or block option see Section 4 5 Model declaration page 18 not available under Octave 3 Use a Newton algorithm with a Stabilized Bi Conjugate Gradient BICGSTAB solver at each iteration requires bytecode and or block option see Section 4 5 Model declaration page 18 4 Use a Newton algorithm with a optimal path length at each iteration requires bytecode and or block option see Section 4 5 Model decla ration page 18 Chapter 4 The Mod
10. dseries Chapter 6 Time Series 132 C minus 4 B dseries Overloads the minus operator for dseries objects element by element subtraction If both A and B are dseries objects they do not need to be defined over the same time ranges If A and B are dseries objects with T4 and Tg observations and N4 and Np variables then N4 must be equal to Ng or 1 and Ng must be equal to Ny or 1 If Ta Tg isequal A init B init returns 1 and N4 Ng then the minus operator will compute for each couple t n with 1 lt t lt T and1 n N4 C data t n A data t n B data t n If Ng is equal to 1 and N4 gt 1 the smaller dseries object B is broadcast across the larger dseries A so that they have compatible shapes the minus operator will subtract the variable defined in B from each variable in A If B is a double scalar then the method minus will subtract B from all the observations variables in A If B is a row vector of length N4 then the minus method will subtract B i from all the observations of variable i for i 1 N4 If B is a column vector of length T4 then the minus method will subtract B from all the variables Example gt gt ts0 dseries rand 3 2 gt gt tsi tsO Variable_2 gt gt tsO tsi ans is a dseries object minus Variable_1 Variable_2 0 48853 0 50535 3Y 0 32063 minus Variable_2 Variable_2 N e KK gt gt tsi tsi is a dseries object Var
11. dseries Overloads the Matlab Octave save function and saves dseries object A to disk Possible formats are csv this is the default m Matlab Octave script and mat Matlab binary data file The name of the file without extension is specified by basename Example gt gt tsO dseries ones 2 2 gt gt tsO save ts0 The last command will create a file ts0 csv with the following content Variable_1 Variable_2 1Y 1 1 2Y 1 1 To create a Matlab octave script the following command gt gt tsO save ts0 m will produce a file ts0 m with the following content File created on 14 Nov 2013 12 08 52 FREQ 1 INIT 1Y NAMES Variable 1 Variable 27 TEX__ Variable 1 Variable_ 2 Variable 1 1 1 Variable_2 1 1 The generated csv m or mat files can be loaded when instantiating a dseries object as explained above B set names A s1 s2 dseries Renames variables in dseries object and returns a dseries object B with new names s1 s2 s3 The number of input arguments after the first one dseries object A must be equal to A vobs the number of variables in A s1 will be the name of the first variable in B s2 the name of the second variable in B and so on Example gt gt tsO dseries ones 1 3 gt gt tsi ts0 set_names Barbibul Barbouille tsi is a dseries object Barbibul Varia
12. 1 1 sigma u2 c2 1 1 sigma 1 1 sigma end Example 3 a linear model model linear x a x 1 bxy 1 e x y dxy 1 e_y end Chapter 4 The Model file 21 Dynare has the ability to output the list of model equations to a TFX file using the write latex dynamic model command The static model can also be written with the write latex static model command write latex dynamic model Command Description This command creates a IATEX file containing the dynamic model If your mod file is FILENAME mod then Dynare will create a file called FILENAME dynamic tex containing the list of all the dynamic model equations If TEX names were given for variables and parameters see Section 4 2 Variable declarations page 10 then those will be used otherwise the plain text names will be used Time subscripts t t 1 t 1 will be appended to the variable names as IATEX subscripts Note that the model written in the TEX file will differ from the model declared by the user in the following dimensions e the timing convention of predetermined variables see predetermined variables page 13 will have been changed to the default Dynare timing convention in other words variables declared as predetermined will be lagged on period back e the expectation operators see expectation page 15 will have been removed replaced by auxiliary variables and new equations as explained in the documentation of the o
13. FILENAME See file_tag page 93 output_file_tag FILENAME See output file tag page 93 simulation file tag FILENAME See simulation file tag page 94 horizon INTEGER See horizon page 95 filtered probabilities See filtered probabilities page 95 no error bands Do not output percentile error bands i e compute mean Default off i e output error bands error band percentiles DOUBLE1 See error band percentiles page 95 Shock draws INTEGER See shock draws page 95 Shocks per parameter INTEGER See shocks per parameter page 95 thinning factor INTEGER See thinning factor page 95 free parameters NUMERICAL VECTOR See free parameters page 95 parameter uncertainty See parameter uncertainty page 95 regime INTEGER See regime page 95 regimes See regimes page 96 4 19 Displaying and saving results Dynare has comments to plot the results of a simulation and to save the results rplot VARIABLE NAME Command Plots the simulated path of one or several variables as stored in oo endo simul by either simul see Section 4 12 Deterministic simulation page 37 or stoch_simul with option periods see Section 4 13 1 Computing the stochastic solution page 40 The variables are plotted in levels dynatype FILENAME VARIABLE NAME Command This command prints the listed variables in a text file named FILENAME If no VARI ABLE NAME
14. The variable is assumed to have a multiplicative growth trend For an additive growth trend use log_trend_var instead Trend variables are required if the user wants to be able to write a nonstationary model in the model block The trend_var command must appear before the var command that references the trend variable trend_var commands can appear several times in the file and Dynare will concatenate them If the model is nonstationary and is to be written as such in the model block Dynare will need the growth factor of every trend variable in order to stationarize the model The growth factor must be provided within the declaration of the trend variable using the growth_factor keyword All endogenous variables and parameters referenced in MODEL_EXPRESSION must already have been declared by the var and parameters commands Example trend_var growth_factor gA A log_trend_var log_growth_factor MODEL_EXPRESSION VARIABLE_NAME Command LATEX NAMES Description Same as trend var except that the variable is supposed to have an additive trend or to put it otherwise to be equal to the log of a variable with a multiplicative trend 4 3 Expressions Dynare distinguishes between two types of mathematical expressions those that are used to de scribe the model and those that are used outside the model block e g for initializing parameters or variables or as command options In this manual those two types of expressions a
15. This is the tolerance criterion for convergence and refers to changes in the objective function value It should be rather loose since it will gradually be tightened during estimation Default 1e 3 convergence ending value DOUBLE The convergence criterion ending value Values much smaller than square root machine epsilon are probably overkill Default 1e 6 convergence increment value DOUBLE Determines how quickly the convergence criterion moves from the starting value to the ending value Default 0 1 Chapter 4 The Model file 92 max_iterations_starting_value INTEGER This is the maximum number of iterations allowed in the hill climbing optimiza tion routine and should be rather small since it will gradually be increased during estimation Default 50 max iterations increment value DOUBLE Determines how quickly the maximum number of iterations is increased Default 2 max block iterations INTEGER The parameters are divided into blocks and optimization proceeds over each block After a set of blockwise optimizations are performed the convergence criterion is checked and the blockwise optimizations are repeated if the criterion is violated This controls the maximum number of times the blockwise optimization can be performed Note that after the blockwise optimizations have converged a single optimization over all the parameters is performed before updating the convergence value and maximum number of iterations Default
16. di lt dates 1950Q1 1950Q2 1959Q3 1959Q4 gt d2 dates 195001 195002 1969Q3 1969Q4 Chapter 6 Time Series 116 B isempty 4 dates Overloads the Matlab Octave isempty function for dates object Example gt gt A dates 1950Q1 dates 195104 gt gt A isempty ans C isequal 4 B dates Overloads the Matlab Octave isequal function for dates objects Example gt gt A dates 195001 dates 195104 gt gt isequal A A ans C le 4 B dates Overloads the Matlab Octave le less or equal lt operator dates objects A and B must have the same number of elements say n The returned argument is a n by 1 vector of zeros and ones The i th element of C is equal to 1 if and only if the date A i is not posterior to the date B i Example gt gt A dates 1950Q1 1951Q2 gt gt B dates 195001 19500Q2 gt gt A lt B ans B length 4 dates Overloads the Matlab Octave length function Returns the number of dates in dates object A B is a scalar integer Example gt gt A dates 7195001 195102 gt gt A length ans Chapter 6 Time Series 117 C D 1t A B dates Overloads the Matlab Octave 1t less than lt operator dates objects and B must have the same number of elements say n The returned argument is a n by 1 vector of zeros and ones The i th element of C is equal to 1 if and only
17. Default VARIABLE NAME Example var c gnp qi q2 var deflator A i b var c C long name Consumption varexo VARIABLE NAME LATEX NAMES long name QUOTED_STRING Command Description This optional command declares the exogenous variables in the model See Section 4 1 Conven tions page 10 for the syntax of VARIABLE_NAME Optionally it is possible to give a ATEX name to the variable Exogenous variables are required if the user wants to be able to apply shocks to her model varexo commands can appear several times in the file and Dynare will concatenate them Options long name QUOTED STRING Like long_name page 11 but value stored in M exo names long Example Varexo m gov varexo det VARIABLE NAME LATEX NAMES Command long_name QUOTED_STRING Description This optional command declares exogenous deterministic variables in a stochastic model See Section 4 1 Conventions page 10 for the syntax of VARIABLE_NAME Optionally it is possible to give a IATEX name to the variable Chapter 4 The Model file 12 It is possible to mix deterministic and stochastic shocks to build models where agents know from the start of the simulation about future exogenous changes In that case stoch simul will compute the rational expectation solution adding future information to the state space nothing is shown in the output of stoch simul and forecast will compute a simulation conditional on ini
18. Description This command runs Bayesian or maximum likelihood estimation The following information will be displayed by the command e results from posterior optimization also for maximum likelihood e marginal log data density e posterior mean and highest posterior density interval shortest credible set from posterior simulation e Metropolis Hastings convergence graphs that still need to be documented e graphs with prior posterior and mode e graphs of smoothed shocks smoothed observation errors smoothed and historical variables Also during the MCMC Bayesian estimation with mh_replic gt 0 a graphical or text waiting bar is displayed showing the progress of the Monte Carlo and the current value of the acceptance ratio Note that if the load mh file option is used see below the reported acceptance ratio does not take into account the draws from the previous MCMC In the literature there is a general agreement for saying that the acceptance ratio should be close to one third or one quarter If this not the case you can stop the MCMC Ctr1 C and change the value of option mh jscale see below Note that by default Dynare generates random numbers using the algorithm mt199937ar ie Mersenne Twister method with a seed set equal to 0 Consequently the MCMCs in Dynare are deterministic one will get exactly the same results across different Dynare runs ceteris paribus For instance the posterior moments or posterior densities w
19. Each member is private one can display the content of a member but cannot change its value Chapter 6 Time Series 112 gt gt d dates 200902 gt gt d time ans 2009 2 gt gt Note that it is not possible to mix frequencies in a dates object all the elements must have common frequency The dates class has five constructors dates dates dates FREQ dates Returns an empty dates object with a given frequency if the constructor is called with one input argument FREQ is a character equal to Y or A for annual dates Q for quarterly dates M for monthly dates or W for weekly dates Note that FREQ is not case sensitive so that for instance q is also allowed for quarterly dates The frequency can also be set with an integer scalar equal to 1 annual 4 quarterly 12 monthly or 52 weekly The instantiation of empty objects can be used to rename the dates class For instance if one only works with quarterly dates he can create qq as qq dates Q and a dates object holding the date 2009Q2 dO qq 2009 2 which is much simpler if dates objects have to be defined programmatically dates STRING dates dates STRING STRING dates Returns a dates object that represents a date as given by the string STRING This string has to be interpretable as a date only strings of the following forms are admitted 1990Y 1990A 1990Q1 1990M2 1990W5 the r
20. If equal to 1 load previous RMSE analysis If equal to 0 make a new RMSE analysis Default O lik only INTEGER If equal to 1 compute only likelihood and posterior If equal to 0 compute RMSE s for all observed series Default 0 var rmse VARIABLE NAME List of observed series to be considered indicates all observed variables Default varobs Chapter 4 The Model file 85 pfilt_rmse DOUBLE Filtering threshold for RMSE s Default 0 1 istart rmse INTEGER Value at which to start computing RMSE s use 2 to avoid big intitial error De fault presample 1 alpha rmse DOUBLE Critical value for Smirnov statistics d plot parameters with d gt alpha rmse De fault 0 002 alpha2_rmse DOUBLE Critical value for correlation p plot couples of parmaters with p alpha2_rmse Default 1 0 datafile FILENAME See datafile page 53 INTEGER INTEGER1 INTEGER2 See nobs page 53 first obs INTEGER See first obs page 53 nobs nobs prefilter INTEGER See prefilter page 53 presample INTEGER See presample page 53 nograph See nograph page 41 nodisplay See nodisplay page 41 graph format FORMAT graph format FORMAT FORMAT See graph format page 41 conf sig DOUBLE See conf_sig page 69 loglinear See loglinear page 53 mode file FILENAME See mode file page 55 kalman algo INTEGER See kalman_algo page 60 Identif
21. Journal of Economic Dynamics and Control 19 711 734 Brooks Stephen P and Andrew Gelman 1998 General methods for monitoring convergence of iterative simulations Journal of computational and graphical statistics T pp 434 455 Cardoso Margarida F R L Salcedo and S Feyo de Azevedo 1996 The simplex simulated annealing approach to continuous non linear optimization Computers chem Engng 20 9 1065 1080 Collard Fabrice 2001 Stochastic simulations with Dynare A practical guide Collard Fabrice and Michel Juillard 2001a Accuracy of stochastic perturbation methods The case of asset pricing models Journal of Economic Dynamics and Control 25 979 999 Collard Fabrice and Michel Juillard 2001b A Higher Order Taylor Expansion Approach to Simulation of Stochastic Forward Looking Models with an Application to a Non Linear Phillips Curve Computational Economics 17 125 139 Christiano Lawrence J Mathias Trabandt and Karl Walentin 2011 Introducing financial frictions and unemployment into a small open economy model Journal of Economic Dynamics and Control 35 12 1999 2041 Del Negro Marco and Franck Schorfheide 2004 Priors from General Equilibrium Models for VARS International Economic Review 45 2 643 673 Dennis Richard 2007 Optimal Policy In Rational Expectations Models New Solution Algorithms Macroeconomic Dynamics 11 1 31 55 Durbin J and S J Koopman 2012 Time S
22. MOMENT NAME This field can take the following values HPDinf Lower bound of a 90 HPD interval HPDsup Upper bound of a 9096 HPD interval Mean Mean of the posterior distribution Median Median of the posterior distribution Std Standard deviation of the posterior distribution Variance Variance of the posterior distribution deciles Deciles of the distribution density Nonparametric estimate of the posterior density First and second columns are respectively abscissa and ordinate coordinates ESTIMATED OBJECT This field can take the following values measurement errors corr Correlation between two measurement errors measurement errors std Standard deviation of measurement errors parameters Parameters 3 See option conf sig page 69 to change the size of the HPD interval Chapter 4 The Model file 64 shocks_corr Correlation between two structural shocks shocks_std Standard deviation of structural shocks oo MarginalDensity LaplaceApproximation MATLAB Octave variable Variable set by the estimation command oo MarginalDensity ModifiedHarmonicMean MATLAB Octave variable Variable set by the estimation command if it is used with mh replic gt O or load mh file option oo FilteredVariables MATLAB Octave variable Variable set by the estimation command if it is used with the filtered_vars option After an estimation without Metropolis fields are of the form oo FilteredVariables VARIABLE NAME Afte
23. O 1 mh replic thinning factor thinning factor INTEGER The total number of draws is equal to thinning factor mh replic drop Default 1 adaptive mh draws INTEGER Tuning period for Metropolis Hastings draws Default 30 000 save draws Save all elements of A At Q and to a file named draws file tag out with each draw on a separate line A file that describes how these matrices are laid out is contained in draws header file tag out A file called load_ flat file m is provided to simplify loading the saved files into the corresponding variables AO Aplus Q and Zeta in your MATLAB Octave workspace Default off Example ms simulation file tag second run ms simulation file tag third run mh replic 5000 thinning factor 3 Chapter 4 The Model file 94 ms_compute_mdd Command ms_compute_mdd OPTIONS Command Description Computes the marginal data density of a Markov switching SBVAR model from the posterior draws At the end of the run the Muller and Bridged log marginal densities are contained in the oo ms structure Options file tag FILENAME See file tag page 93 output file tag FILENAME See output file tag page 93 simulation file tag FILENAME The portion of the filename associated with the simulation run Default file tag proposal type INTEGER The proposal type 1 Gaussian 2 Power 3 Truncated Power 4 Step 5 Truncated Gaussian Default 3
24. a simplex based optimization routine available un der MATLAB if the optimization toolbox is installed available under Octave if the optim package from Octave Forge is installed Chapter 4 The Model file 56 8 Uses Dynare implementation of the Nelder Mead simplex based opti mization routine generally more efficient than the MATLAB or Octave implementation available with mode compute 7 9 Uses the CMA ES Covariance Matrix Adaptation Evolution Strategy algorithm an evolutionary algorithm for difficult non linear non convex optimization 10 Uses the simpsa algorithm based on the combination of the non linear simplex and simulated annealing algorithms and proposed by Cardoso Salcedo and Feyo de Azevedo 1996 FUNCTION NAME It is also possible to give a FUNCTION NAME to this option instead of an INTEGER In that case Dynare takes the return value of that function as the posterior mode Default value is 4 mcmc jumping covariance hessian prior variancelidentity matrix FILENAME Tells Dynare which covariance to use for the proposal density of the MCMC sampler mcmc jumping covariance can be one of the following hessian Uses the Hessian matrix computed at the mode prior_variance Uses the prior variances No infinite prior variances are allowed in this case identity_matrix Uses an identity matrix FILENAME Loads an arbitrary user specified covariance matrix from FILENAME mat The covariance matrix must be saved i
25. comprised of an analysis for the linearized rational expectation model as well as the associated reduced form solution Further performs a brute force search of the groups of parameters best reproducing the behavior of each single parameter The maximum dimension of the group searched is triggered by max dim cova group Default 0 max dim cova group INTEGER In the brute force search performed when advanced 1 this option sets the maxi mum dimension of groups of parameters that best reproduce the behavior of each single model parameter Default 2 periods INTEGER When the analytic Hessian is not available i e with missing values or diffuse Kalman filter or univariate Kalman filter this triggers the length of stochastic simulation to compute Simulated Moments Uncertainty Default 300 replic INTEGER When the analytic Hessian is not available this triggers the number of replicas to compute Simulated Moments Uncertainty Default 100 Chapter 4 The Model file 87 gsa_sample_file INTEGER If equal to 0 do not use sample file If equal to 1 triggers gsa prior sample If equal to 2 triggers gsa Monte Carlo sample i e loads a sample corresponding to pprior 0 and ppost 0 in the dynare sensitivity options Default 0 gsa sample file FILENAME Uses the provided path to a specific user defined sample file Default 0 parameter set calibration prior mode prior mean posterior mode posterior mean posterior median
26. filtered vars Triggers the computation of filtered variables See filtered vars page 60 for more details filter step ahead INTEGER1 INTEGER2 See filter step ahead page 60 Chapter 4 The Model file 69 4 15 Forecasting On a calibrated model forecasting is done using the forecast command On an estimated model use the forecast option of estimation command It is also possible to compute forecasts on a calibrated or estimated model for a given constrained path of the future endogenous variables This is done from the reduced form representation of the DSGE model by finding the structural shocks that are needed to match the restricted paths Use conditional forecast conditional forecast paths and plot conditional forecast for that purpose Finally it is possible to do forecasting with a Bayesian VAR using the bvar forecast command forecast VARIABLE NAME Command forecast OPTIONS VARIABLE NAME Command Description This command computes a simulation of a stochastic model from an arbitrary initial point When the model also contains deterministic exogenous shocks the simulation is computed con ditionally to the agents knowing the future values of the deterministic exogenous variables forecast must be called after stoch simul forecast plots the trajectory of endogenous variables When a list of variable names follows the command only those variables are plotted A 9096 confidence interval
27. proposal lower bound DOUBLE The lower cutoff in terms of probability Not used for proposal type in 1 2 Required for all other proposal types Default 0 1 proposal upper bound DOUBLE The upper cutoff in terms of probability Not used for proposal type equal to 1 Required for all other proposal types Default 0 9 mdd proposal draws INTEGER The number of proposal draws Default 100 000 mdd use mean center Use the posterior mean as center Default off ms compute probabilities Command ms compute probabilities OPTIONS Command Description Computes smoothed regime probabilities of a Markov switching SBVAR model Output eps files are contained in output file tag utput Probabilities Options file tag FILENAME See file tag page 93 Chapter 4 The Model file 95 output_file_tag FILENAME See output file tag page 93 filtered probabilities Filtered probabilities are computed instead of smoothed Default off real time smoothed Smoothed probabilities are computed based on time t information for 0 t lt nobs Default off ms irf Command ms irf OPTIONS Command Description Computes impulse response functions for a Markov switching SBVAR model Output eps files are contained in output file tag utput IRF while data files are contained in output file tag IRF Options file tag FILENAME See file tag page 93 output file tag FILENAME See out
28. q diag flat prior ncsk nstd ninv indxparr indxovr aband indxap apband indximf indxfore foreband indxgforhat indxgimfhat indxestima indxgdls eq ms cms ncms eq cms tlindx tlnumber cnum forecast coefficients prior hyperparameters svar identification Block Description This block is terminated by end and contains lines of the form UPPER_CHOLESKY LOWER_CHOLESKY EXCLUSION CONSTANTS EXCLUSION LAG INTEGER VARIABLE NAME VARIABLE NAME EXCLUSION LAG INTEGER EQUATION INTEGER VARIABLE NAME VARIABLE NAME RESTRICTION EQUATION INTEGER EXPRESSION EXPRESSION To be documented For now see the wiki http www dynare org DynareWiki MarkovSwitchingInterface Chapter 4 The Model file 90 ms estimation OPTIONS Command Description Triggers the creation of an initialization file for and the estimation of a Markov switching SBVAR model At the end of the run the A At Q and matrices are contained in the oo ms structure Options General Options file tag FILENAME The portion of the filename associated with this run This will create the model initialization file init file tag dat Default mod file output file tag FILENAME The portion of the output filename that will be assigned to this run This will cre ate among other files est final output file tag out est intermediate output file tag out Default file tag no
29. rho rhos i stoch simul order 1 CHendfor This is very similar to previous example except that the loop is unrolled The macro processor manages the loop index but not the data array rhos With a macro processor loop case 2 for rho val in 0 8 0 9 1 Chapter 4 The Model file 104 rho rho_val stoch_simul order 1 endfor The advantage of this method is that it uses a shorter syntax since list of values directly given in the loop construct Note that values are given as character strings the macro processor does not know floating point values The inconvenient is that you can not reuse an array stored in a MATLAB Octave variable 4 21 Verbatim inclusion Pass everything contained within the verbatim block to the mod file m file verbatim Block Description By default whenever Dynare encounters code that is not understood by the parser it is directly passed to the preprocessor output In order to force this behavior you can use the verbatim block This is useful when the code you want passed to the lt mod_file gt m file contains tokens recognized by the Dynare preprocessor Example verbatim Anything contained in this block will be passed directly to the lt modfile gt m file including comments var 1 end 4 22 Misc commands set_dynare_seed INTEGER Command set_dynare_seed default Command set_dynare_seed clock Command set_dynare_seed reset Comm
30. ts2 tsO tsi gt gt ts2 ts2 is a dseries object nifnif noufnouf nafnaf 195001 0 17404 0 71431 NaN 1950Q2 0 62741 0 90704 NaN 195003 0 84189 0 21854 0 83666 195004 0 51008 0 87096 0 8593 195101 0 16576 0 21184 0 52338 1951Q2 NaN NaN 0 47736 195103 NaN NaN 0 88988 1951Q4 NaN NaN 0 065076 195201 NaN NaN 0 50946 hpcycle A 1ambda dseries Extracts the cycle component from a dseries A object using Hodrick Prescott 1997 filter and returns a dseries object B The default value for lambda the smoothing parameter is 1600 Example Simulate a component model stochastic trend deterministic trend and a stationary autoregressive process e 2 randn 200 1 u randn 200 1 stochastic trend cumsum e deterministic trend 1 transpose 1 200 x zeros 200 1 for i 2 200 x i 75 x i 1 e i end y x stochastic_trend deterministic_trend Instantiates time series objects tsO dseries y 1950Q1 tsi dseries x 1950Q1 stationary component Apply the HP filter ts2 tsO hpcycleO Plot the filtered time series plot tsi ts2 dates data k Plot of the stationary component hold on plot ts2 data r 4 Plot of the filtered y hold off axis tight id get gca XTick set gca XTickLabel strings ts dates id Chapter 6 Time Series 127 The previous code should produce somethi
31. 1 x 1 Chapter 4 The Model file 16 is equal to the expected value of variable x at next period using the information set available at the previous period See Section 4 6 Auxiliary variables page 21 for an explanation of how this operator is handled internally and how this affects the output 4 3 3 Functions 4 3 3 1 Built in Functions The following standard functions are supported internally for both MODEL EXPRESSION and EXPRESSION exp x Function Natural exponential log x Function ln x Function Natural logarithm logi0 x Function Base 10 logarithm sqrt x Function Square root abs x Function Absolute value Note that this function is not differentiable at x 0 However for facilitating convergence of Newton type methods Dynare assumes that the derivative at x 0 is equal to 0 this assumption comes from the observation that the derivative of abs x is equal to sign x for x Z 0 and from the convention for the derivative of sign x at x 0 sign x Function Signum function Note that this function is not differentiable at x 0 However for facilitating convergence of Newton type methods Dynare assumes that the derivative at x 0 is equal to 0 this assumption comes from the observation that both the right and left derivatives at this point exist and are equal to 0 sin x Function cos x Function tan x Function asin x Function acos x Function atan x Function
32. 100 max repeated optimization runs INTEGER The entire process described by max block iterations page 92 is repeated until improvement has stopped This is the maximum number of times the process is allowed to repeat Set this to O to not allow repetitions Default 10 function convergence criterion DOUBLE The convergence criterion for the objective function when max repeated optimizations runs is positive Default 0 1 parameter convergence criterion DOUBLE The convergence criterion for parameter values when max repeated optimizations runs is positive Default 0 1 number of large perturbations INTEGER The entire process described by max block iterations page 92 is repeated with random starting values drawn from the posterior This specifies the number of random starting values used Set this to O to not use random starting values A larger number should be specified to ensure that the entire parameter space has been covered Default 5 number of small perturbations INTEGER The number of small perturbations to make after the large perturbations have stopped improving Setting this number much above 10 is probably overkill De fault 5 number of posterior draws after perturbation INTEGER The number of consecutive posterior draws to make when producing a small per turbation Because the posterior draws are serially correlated a small number will result in a small perturbation Default 1 max number of s
33. 123 dseries Sanity check of dseries object A Returns 1 if there is an error 0 otherwise The second output argument is a string giving brief informations about the error cumsum Al d v Overloads the Matlab Octave cumsum function for dseries objects The cumulated sum cannot be computed if the variables in dseries object A has NaNs If a dates object d is provided as a second argument then the method computes the cumulated sum with the additional constraint that the variables in the dseries object B are zero in period d If a single observation dseries object v is provided as a third argument the cumulated sum in B is such that B d matches v dseries objects A and v must have the same number of variables Example gt gt tsi dseries ones 10 1 gt gt ts2 tsi cumsum gt gt ts2 ts2 is a dseries object cumsum Variable_1 1Y 2Y 3Y AY 5Y 6Y 7Y 8Y 9Y J OO O1 amp NN H m o gt gt ts3 cumsum dates 3Y gt gt ts3 dseries Chapter 6 Time Series 124 ts3 is a dseries object cumsum Variable_1 1Y 2Y 3Y 4Y 5Y 6Y 7Y 8Y 9Y gt gt ts4 ts i cumsum dates 3Y dseries pi gt gt ts4 ts4 is a dseries object cumsum Variable 1 1Y 1 1416 2Y 2 1416 3Y 3 1416 4Y 4 1416 5Y 5 1416 6Y 6 1416 7Y 7 1416 8Y 8 1416 9Y 9 1416 10Y 10 1416 C eq A B dseries Overloads
34. Linux should install the package for MEX file compilation under Debian or Ubuntu it is called liboctave dev If you are using Octave or MATLAB under Mac OS X you should install the latest version of XCode see instructions on the Dynare wiki Mac OS X Octave users will also need to install gnuplot if they want graphing capabilities Users of MATLAB under Linux and Mac OS X and users of Octave under Windows normally need to do nothing since a working compilation environment is available by default 2 2 Installation of Dynare After installation Dynare can be used in any directory on your computer It is best practice to keep your model files in directories different from the one containing the Dynare toolbox That way you can upgrade Dynare and discard the previous version without having to worry about your own files 2 2 1 On Windows Execute the automated installer called dynare 4 x y win exe where 4 x y is the version number and follow the instructions The default installation directory is c NdynareM x y After installation this directory will contain several sub directories among which are matlab mex and doc The installer will also add an entry in your Start Menu with a shortcut to the documentation files and uninstaller Note that you can have several versions of Dynare coexisting for example in c Ndynare as long as you correctly adjust your path settings see Section 2 3 3 Some words of warning page 5 2 2 2
35. NAME DSGE PRIOR WEIGHT INITIAL VALUE LOWER BOUND UPPER BOUND PRIOR SHAPE PRIOR MEAN PRIOR STANDARD ERROR PRIOR S3RD PARAMETER PRIOR 4TH PARAMETER SCALE PARAMETER The first part of the line consists of one of the three following alternatives Chapter 4 The Model file 50 stderr VARIABLE NAME Indicates that the standard error of the exogenous variable VARIABLE NAME or of the observation error measurement errors associated with endogenous observed variable VARIABLE NAME is to be estimated corr VARIABLE NAME1 VARIABLE NAME2 Indicates that the correlation between the exogenous variables VARIABLE NAME and VARIABLE NAME J or the correlation of the observation errors measurement errors associated with endogenous observed variables VARIABLE NAMEI and VARIABLE NAME2 is to be estimated Note that correlations set by previous shocks blocks or estimation commands are kept at their value set prior to estima tion if they are not estimated again subsequently Thus the treatment is the same as in the case of deep parameters set during model calibration and not estimated PARAMETER NAME The name of a model parameter to be estimated DSGE PRIOR WEIGHT The rest of the line consists of the following fields some of them being optional INITIAL VALUE Specifies a starting value for the posterior mode optimizer or the maximum likelihood estimation If unset defaults to the prior mean LOWER BOUND Specifies a
36. Time Series 120 6 2 dseries class The Matlab Octave dseries class handles time series data As any Matlab Octave statements this class can be used in a Dynare s mod file dseries object has eight members nobs A scalar integer the number of observations vobs A scalar integer the number of variables name cell of strings the names of the variables tex A cell of strings the tex names of the variables freq scalar integer equal to 1 4 12 or 52 the frequency of the dataset init single element dates object the initial date of the sample dates dates object with nobs element the dates of the sample data nobs by vobs array of doubles the data freq nobs vobs data name tex are private members The following constructors are available dseries dseries dseries INITIAL_DATE dseries Instantiates an empty dseries object with if defined an initial date given by the single element dates object INITIAL_DATE the frequency is then set accordingly dseries FILENAME dseries Instantiates and populates a dseries object with a data file specified by FILENAME a string passed as input Valid file types are m file mat file csv file and xls file A typical m file will have the following form INIT__ 1994Q3 NAMES__ azert yuiop TEX__ azert yuiop azert randn 100 1 yuiop randn 100 1 If a mat file is used instead it should provide the same in
37. a An implementation could consist of the following files modeqs mod This file contains variable declarations and model equations The code for the decla ration of and lab_rat would look like if steady var alpha parameter lab_rat Qitelse parameter alpha var lab rat Qitendif steady mod This file computes the steady state It begins with define steady 1 include modeqs mod Then it initializes parameters including lab rat excluding a computes the steady state using guess values for endogenous including a then saves values of parameters and endogenous at steady state in a file using the save params and steady state command simul mod This file computes the simulation It begins with define steady 0 include modeqs mod Then it loads values of parameters and endogenous at steady state from file using the load_params_and_steady_state command and computes the simulations 4 20 4 MATLAB Octave loops versus macro processor loops Suppose you have a model with a parameter p and you want to make simulations for three values p 0 8 0 9 1 There are several ways of doing this With a MATLAB Octave loop rhos 0 8 0 9 1 for i 1 length rhos rho rhos i stoch_simul order 1 end Here the loop is not unrolled MATLAB Octave manages the iterations This is inter esting when there are a lot of iterations With a macro processor loop case 1 rhos 0 8 0 9 1 Qifor i in 1 3
38. are passed differently than those to Dynare commands They take the form of named options to Matlab functions where the arguments come in pairs e g function name option 1 name option 1 value option 2 name option 2 value where option X name is the name of the option while option X value is the value assigned to that option The ordering of the option pairs matters only in the unusual case when an option is provided twice probably erroneously In this case the last value passed is the one that is used Below you will see a list of methods available for the Report class and a clarifying example report compiler showDate filename margin marginUnit orientation Method on Report paper title Instantiates a Report object Options compiler FILENAME The full path to the ATEX compiler on your system If this option is not provided Dynare will try to find the appropriate program to compile IXTEX on your system Default is system dependent Windows the result of findtexmf file type exe pdflatex Mac OS X and Linux the result of which pdflatex showDate BOOLEAN Display the date and time when the report was compiled Default true filename FILENAME The filename to use when saving this report Default report tex margin DOUBLE The margin size Default 2 5 marginUnit cm in Units associated with the margin Default cm orientation landscape portrait Paper orie
39. be larger than 1200 Default 20000 sub draws INTEGER number of draws from the Metropolis iterations that are used to compute poste rior distribution of various objects smoothed variable smoothed shocks forecast moments IRF sub draws should be smaller than the total number of Metropolis draws available Default min 1200 0 25 Total number of draws mh nblocks INTEGER Number of parallel chains for Metropolis Hastings algorithm Default 2 mh drop DOUBLE The fraction of initially generated parameter vectors to be dropped as a burnin before using posterior simulations Default 0 5 Chapter 4 The Model file 55 mh jscale DOUBLE The scale parameter of the jumping distribution s covariance matrix Metropolis Hastings algorithm The default value is rarely satisfactory This option must be tuned to obtain ideally an acceptance ratio of 2596 3396 in the Metropolis Hastings algorithm Basically the idea is to increase the variance of the jumping distribution if the acceptance ratio is too high and decrease the same variance if the acceptance ratio is too low In some situations in may help to consider parameter specific values for this scale parameter this can be done in the estimated params page 49 block Default 0 2 mh init scale DOUBLE The scale to be used for drawing the initial value of the Metropolis Hastings chain Default 2 mh scale mh recover Attempts to recover a Metropolis Hastings simulation that
40. block has only one equation If several equation appears in the block x is equal to COMPLETE Options static Prints out the block decomposition of the static model Without static option model_info displays the block decomposition of the dynamic model incidence Displays the gross incidence matrix and the reordered incidence matrix of the block decomposed model print_bytecode_dynamic_model Command Prints the equations and the Jacobian matrix of the dynamic model stored in the bytecode binary format file Can only be used in conjunction with the bytecode option of the model block print_bytecode_static_model Command Prints the equations and the Jacobian matrix of the static model stored in the bytecode binary format file Can only be used in conjunction with the bytecode option of the model block 4 12 Deterministic simulation When the framework is deterministic Dynare can be used for models with the assumption of per fect foresight Typically the system is supposed to be in a state of equilibrium before a period 1 when the news of a contemporaneous or of a future shock is learned by the agents in the model The purpose of the simulation is to describe the reaction in anticipation of then in reaction to Chapter 4 The Model file 38 the shock until the system returns to the old or to a new state of equilibrium In most models this return to equilibrium is only an asymptotic phenomenon which one m
41. block permits to specify different historical initial values for different periods This block is terminated by end and contains lines of the form VARIABLE_NAME INTEGER EXPRESSION EXPRESSION is any valid expression returning a numerical value and can contain already initialized variable names By convention in Dynare period 1 is the first period of the simulation Going backward in time the first period before the start of the simulation is period 0 then period 1 and so on If your lagged variables are linked by identities be careful to satisfy these identities when you set historical initial values Variables not initialized in the histval block are assumed to have a value of zero at period 0 and before Note that this behavior differs from the case where there is no histval block where all variables are initialized at their steady state value at period 0 and before except when a steady command doesn t follow an initval block In a stochastic simulation context In the context of stochastic simulations histval allows setting the starting point of those sim ulations in the state space it does not affect the starting point for impulse response functions As for the case of perfect foresight simulations all not explicitly specified variables are set to 0 Moreover as only states enter the recursive policy functions all values specified for control variables will be ignored Example var x yj varexo e model x
42. current directory the full path has to be given gt gt internals test matlab fr ROUTINENAME Prints on screen the internal documentation of ROUTINENAME if this routine exists and if this routine has a texinfo internal documentation header The path to ROUTINENAME has to be provided if the routine is not in the current directory Example internals doc matlab fr ROUTINENAME At this time will work properly for only a small number of routines At the top of the available Matlab Octave routines a commented block for the internal documenta tion is written in the GNU texinfo documentation format This block is processed by calling texinfo from MATLAB Consequently texinfo has to be installed on your machine display mh history Displays information about the previously saved MCMC draws generated by a mod file named MODFILENAME This file must be in the current directory Example gt gt internals display mh history MODFILENAME load mh history Loads into the Matlab Octave s workspace informations about the previously saved MCMC draws generated by a mod file named MODFILENAME Example gt gt internals load mh history MODFILENAME This will create a structure called mcmc informations in the workspace with the following fields Nblck The number of MCMC chains InitialParameters A Nblck n where n is the number of estimated parameters array of doubles Initial state of the MCMC LastParameters A Nb
43. equal to 0 do not prepare Monte Carlo sample of reduced form matrices Default 0 load redform INTEGER If equal to 1 load previously estimated mapping If equal to 0 estimate the mapping of the reduced form model Default 0 logtrans_redform INTEGER If equal to 1 use log transformed entries If equal to 0 use raw entries Default 0 threshold redform DOUBLE DOUBLE The range over which the filtered Monte Carlo entries of the reduced form coefficients should be analyzed The first number is the lower bound and the second is the upper bound An empty vector indicates that these entries will not be filtered Default empty ksstat redform DOUBLE Critical value for Smirnov statistics d when reduced form entries are filtered De fault 0 1 alpha2 redform DOUBLE Critical value for correlations p when reduced form entries are filtered Default 0 3 namendo VARIABLE NAME List of endogenous variables indicates all endogenous variables Default empty namlagendo VARIABLE NAME List of lagged endogenous variables indicates all lagged endogenous variables Analyze entries namendoxnamlagendo Default empty tet namexo VARIABLE NAME List of exogenous variables indicates all exogenous variables Analyze entries namendo xnamexo Default empty EV RMSE Options rmse INTEGER If equal to 1 perform RMSE analysis If equal to 0 do not perform RMSE analysis Default 0 load rmse INTEGER
44. example The steady state file generated by Dynare will be called FILENAME steadystate2 m e You can write the corresponding MATLAB function by hand If your MOD file is called FILENAME mod the steady state file must be called FILENAME steadystate m See NK baseline steadystate m in the examples directory for an example This option gives a bit more flexibility at the expense of a heavier programming burden and a lesser efficiency Note that both files allow to update parameters in each call of the function This allows for example to calibrate a model to a labor supply of 0 2 in steady state by setting the labor disutility parameter to a corresponding value see NK baseline steadystate m in the examples directory They can also be used in estimation where some parameter may be a function of an estimated parameter and needs to be updated for every parameter draw For example one might want to set the capital utilization cost parameter as a function of the discount rate to ensure that capacity utilization is 1 in steady state Treating both parameters as independent or not updating one as a function of the other would lead to wrong results But this also means that care is required Do not accidentally overwrite your parameters with new values as it will lead to wrong results Steady state model Block Description When the analytical solution of the model is known this command can be used to help Dynare find the steady state in a more e
45. file 71 conditional forecast OPTIONS VARIABLE NAME Command Description This command computes forecasts on an estimated or calibrated model for a given constrained path of some future endogenous variables This is done using the reduced form first order state space representation of the DSGE model by finding the structural shocks that are needed to match the restricted paths Consider the an augmented state space representation that stacks both predetermined and non predetermined variables into a vector y Ye Tyi Re Both y and e are split up into controlled and uncontrolled ones to get wy contr vars Tw 4 contr vars R contr_vars uncontr shocks e uncontr shocks R contr_vars contr shocks e contr shocks which can be solved algebraically for e contr shocks Using these controlled shocks the state space representation can be used for forecasting A few things need to be noted First it is assumed that controlled exogenous variables are fully under control of the policy maker for all forecast periods and not just for the periods where the endogenous variables are controlled For all uncontrolled periods the controlled exogenous variables are assumed to be 0 This implies that there is no forecast uncertainty arising from these exogenous variables in uncontrolled periods Second by making use of the first order state space solution even if a higher order approximation was performed the conditional forec
46. in the following periods This function first computes a random path for the exogenous variables stored in oo exo simul see oo_ exo_simul page 39 and then computes the corresponding path for endogenous Chapter 4 The Model file 46 variables taking the steady state as starting point The result of the simulation is stored in oo endo simul see oo endo simul page 39 Note that this simulation approach does not solve for the policy and transition equations but for paths for the endogenous variables Options periods INTEGER The number of periods for which the simulation is to be computed No default value mandatory option solver periods INTEGER The number of periods used to compute the solution of the perfect foresight at every iteration of the algorithm Default 200 order INTEGER If order is greater than 0 Dynare uses a gaussian quadrature to take into account the effects of future uncertainty If order S then the time series for the endogenous variables are generated by assuming that the agents believe that there will no more shocks after period t S This is an experimental feature and can be quite slow Default 0 hybrid Use the constant of the second order perturbation reduced form to correct the paths generated by the stochastic extended path algorithm 4 13 2 Typology and ordering of variables Dynare distinguishes four types of endogenous variables Purely backward or purely predetermined va
47. is plotted around the mean trajectory Use option conf sig to change the level of the confidence interval Options periods INTEGER Number of periods of the forecast Default 5 conf sig DOUBLE Level of significance for confidence interval Default 0 90 nograph See nograph page 41 nodisplay See nodisplay page 41 graph format FORMAT graph format FORMAT FORMAT See graph format page 41 Initial Values forecast computes the forecast taking as initial values the values specified in histval see Section 4 7 Initial and terminal conditions page 22 When no histval block is present the initial values are the one stated in initval When initval is followed by command steady the initial values are the steady state see Section 4 10 Steady state page 30 Output The results are stored in oo forecast which is described below Example varexo_det tau varexo e Chapter 4 The Model file 70 shocks var e stderr 0 01 var tau periods 1 9 values 0 15 end stoch_simul irf 0 forecast oo_ forecast MATLAB Octave variable Variable set by the forecast command or by the estimation command if used with the forecast option and if no Metropolis Hastings has been computed in that case the forecast is computed for the posterior mode Fields are of the form oo_ forecast FORECAST_MOMENT VARIABLE NAME where FORECAST MOMENT is one of the following HPDinf Lower bound of
48. jumpers and to the explosive eigenvalues must have full rank Options solve algo INTEGER See solve algo page 31 for the possible values and their meaning qz zero threshold DOUBLE Value used to test if a generalized eigenvalue is 0 0 in the generalized Schur de composition in which case the model does not admit a unique solution Default 1e 6 Output check returns the eigenvalues in the global variable oo dr eigval oo_ dr eigval MATLAB Octave variable Contains the eigenvalues of the model as computed by the check command model_diagnostics Command This command performs various sanity checks on the model and prints a message if a problem is detected missing variables at current period invalid steady state singular Jacobian of static model model info Command model info OPTIONS Command Description This command provides information about e the normalization of the model an endogenous variable is attributed to each equation of the model e the block structure of the model for each block model info indicates its type the equations number and endogenous variables belonging to this block Chapter 4 The Model file 37 This command can only be used in conjunction with the block option of the model block There are five different types of blocks depending on the simulation method used EVALUATE FORWARD In this case the block contains only equations where endogenous variabl
49. lesse 120 FREQ 222223144114 reims sde 142 ERE 52d ui MS rie RES ue 1412 CINITIAL DATE iiis iacu eh ba rdgays 120 STRING eser mener lire V HE 112 STRING i reseau pe mrate rages eur 112 Qidefin oc cee aie te hate aise Goa Xa ear eR dues 99 OH ChO 552 same seid eda menampeneatentares 101 Qfelse lldxelciegaeweqexug dan deg e ua rennes 100 QfendfOr due be te ane aue dure X qr a aded ev eos 100 CH NAT 2 25 pds ceres REDE I emma 100 Q GTIOP 2l vogue abra IPSA PE aa a qa 101 ORL OE Surnom RE Pad feda redu aie ate eii Bees 100 QUII i Leere bread buhe ted que e durer meh inm dor 100 QRL def Sie e PP panier eus ee waded 100 Qiifndef vested xau re bweUWedu gut epe 100 Qfincl de eigo iw ECRANS 99 cluster 2 2 f dE x P PES REN P 107 hookS ll ie reed an er om cam P iE 106 node rb e ras ini 108 A l e1 EE EA E pU Sheet beet I tI Sura tae LUE 16 Lir tp TE 16 addGraph On Report iileea edad Rep 141 addPage on Report 141 addSection on Report 141 addSeries on Report 143 addT ble n Report c ilem Re EIER 142 addVspace on Report 144 AE ET nn entendeur 121 append lb ied bee DR aver ETE 113 CRIME 16 QUA sgsr e erre wd Roses la ue aa P ate X T ECLIPSE 16 B basic plan em sine ERbRC OPER EAR EE E 73 baxter king filter o2 niara e ern 122 byar density ien eh ree ets w
50. lower bound for the parameter value in maximum likelihood estimation UPPER BOUND Specifies an upper bound for the parameter value in maximum likelihood estimation PRIOR SHAPE A keyword specifying the shape of the prior density The possible values are beta pdf gamma pdf normal pdf uniform pdf inv gamma pdf inv gamma pdf inv gamma2 pdf Note that inv gamma pdf is equivalent to inv gammai pdf PRIOR MEAN The mean of the prior distribution PRIOR STANDARD ERROR The standard error of the prior distribution PRIOR SRD PARAMETER A third parameter of the prior used for generalized beta distribution generalized gamma and for the uniform distribution Default 0 PRIOR 4TH PARAMETER A fourth parameter of the prior used for generalized beta distribution and for the uniform distribution Default 1 SCALE PARAMETER parameter specific scale parameter for the jumping distribution s covariance ma trix of the Metropolis Hasting algorithm Note that INITIAL VALUE LOWER_BOUND UPPER BOUND PRIOR MEAN PRIOR STANDARD ERROR PRIOR 3RD PARAMETER PRIOR 4TH PARAMETER and SCALE PARAMETER can be any valid EXPRESSION Some of them can be empty in which Dynare will select a default value depending on the context and the prior shape As one uses options more towards the end of the list all previous options must be filled for example if you want to specifn SCALE PARAMETER you must specify Chapter 4 The Model file 51 PRIOR_3R
51. objects A and B must have the same number of elements say n or one of the inputs must be a single element dates object The returned argument is a n by 1 vector of zeros and ones The i th element of C is equal to 1 if and only if the dates A i and B i are different Example gt gt A dates 1950Q1 1951Q2 gt gt B dates 1950Q1 1950Q2 gt gt A B C plus A B dates Overloads the Matlab Octave plus operator If both input arguments are dates objects then the method combines A and B without removing repetitions If B is a vector of integers the plus operator shifts the dates object by B periods forward Example gt gt di dates 1950Q1 1950Q2 dates 1960Q1 gt gt d2 dates 1950Q1 1950Q2 2 dates 1960Q1 gt gt ee d2 di ee 2 2 0 gt gt ditee ans dates 195003 195004 1960Q1 gt C pop A dates C pop A B dates Pop method for dates class If only one input is provided the method removes the last element of a dates object If a second input argument is provided a scalar integer between 1 and A length the method removes element number B from dates object A Example gt gt di dates 1950Q1 1950Q2 gt gt di popO ans lt dates 1950Q1 gt Chapter 6 Time Series 119 gt gt di pop 1 ans dates 1950Q2 gt B sort 4 dates B uminus 4 D union A B C
52. of oo UpdatedVariables which contains the estimation of the expected value of variables given the information available at the current date E y See below for a description of all these variables forecast INTEGER Computes the posterior distribution of a forecast on INTEGER periods after the end of the sample used in estimation If no Metropolis Hastings is computed the result is stored in variable oo_ forecast and corresponds to the forecast at the posterior mode If a Metropolis Hastings is computed the distribution of forecasts is stored in variables oo PointForecast and oo MeanForecast See Section 4 15 Forecasting page 69 for a description of these variables tex Requests the printing of results and graphs in TEX tables and graphics that can be later directly included in IATEX files not yet implemented kalman algo INTEGER 0 Automatically use the Multivariate Kalman Filter for stationary models and the Multivariate Diffuse Kalman Filter for non stationary models 1 Use the Multivariate Kalman Filter 2 Use the Univariate Kalman Filter 3 Use the Multivariate Diffuse Kalman Filter 4 Use the Univariate Diffuse Kalman Filter Default value is 0 In case of missing observations of single or all series Dynare treats those missing values as unobserved states and uses the Kalman filter to infer their value see e g Durbin and Koopman 2012 Ch 4 10 kalman tol DOUBLE Numerical tolerance for determining the singula
53. on policy and transition functions but isn t used in the computation of moments and of Impulse Response Functions Setting a variance to zero is an easy way of removing an exogenous shock Chapter 4 The Model file 28 shocks Block In deterministic context For deterministic simulations the shocks block specifies temporary changes in the value of exogenous variables For permanent shocks use an endval block The block should contain one or more occurrences of the following group of three lines var VARIABLE_NAME periods INTEGER INTEGER INTEGER INTEGER values DOUBLE EXPRESSION DOUBLE EXPRESSION It is possible to specify shocks which last several periods and which can vary over time The periods keyword accepts a list of several dates or date ranges which must be matched by as many shock values in the values keyword Note that a range in the periods keyword can be matched by only one value in the values keyword If values represents a scalar the same value applies to the whole range If values represents a vector it must have as many elements as there are periods in the range Note that shock values are not restricted to numerical constants arbitrary expressions are also allowed but you have to enclose them inside parentheses Here is an example shocks var ej periods 1 values 0 5 var uj periods 4 5 values 0 var vj periods 4 5 6 7 9 values 1 1 1 0 9 var w periods 1
54. one More precisely if the model contains x 41 then a variable AUX_DIFF_ VAR will be created such that AUX DIFF VAR x x 1 and x 1 will be replaced with x AUX_DIFF_VAR 1 The transformation is applied to all endogenous variables with a lead if the option is given without a list of variables If there is a list the transformation is restricted to endogenous with a lead that also appear in the list This option can useful for some deterministic simulations where convergence is hard to obtain Bad values for terminal conditions in the case of very persistent dynamics or permanent shocks can hinder correct solutions or any convergence The new dif ferentiated variables have obvious zero terminal conditions if the terminal condition is a steady state and this in many cases helps convergence of simulations parallel local files FILENAME FILENAME Declares a list of extra files that should be transferred to slave nodes when doing a parallel computation see Section 5 2 Parallel Configuration page 107 Example 1 elementary RBC model var c K varexo X parameters aa alph bet delt gam model c k aa x k 1 alph 1 delt k 1 c gam aa alph x 1 k alph 1 1 delt c 1 gam 1 bet end Example 2 use of model local variables The following program model gamma 1 1 sigma ui ci gamma gamma u2 c2 gamma gamma end is formally equivalent to model ui ci 1 1 sigma
55. significant amount Dynare issues a warning if the maximum relative difference between the sum of the contribution of each shock and aggregate variance is larger than 0 0196 The covariance matrix of the shocks is specified with the shocks command see Section 4 8 Shocks on exogenous variables page 27 When a list of VARIABLE NAME is specified results are displayed only for these variables The stoch simul command with a first order approximation can benefit from the block decom position of the model see block page 19 Options ar INTEGER Order of autocorrelation coefficients to compute and to print Default 5 drop INTEGER Number of points burnin dropped at the beginning of simulation before computing the summary statistics Note that this option does not affect the simulated series stored in oo_ endo_simul and the workspace Here no periods are dropped Default 100 hp filter DOUBLE Uses HP filter with DOUBLE before computing moments Default no filter hp ngrid INTEGER Number of points in the grid for the discrete Inverse Fast Fourier Transform used in the HP filter computation It may be necessary to increase it for highly autocor related processes Default 512 Chapter 4 The Model file 41 irf INTEGER Number of periods on which to compute the IRFs Setting irf 0 suppresses the plotting of IRFs Default 40 irf shocks VARIABLE NAME VARIABLE NAME The exogenous variables
56. simul solves a stochastic i e rational expectations model using perturbation tech niques More precisely stoch simul computes a Taylor approximation of the decision and transition functions for the model Using this it computes impulse response functions and various descrip tive statistics moments variance decomposition correlation and autocorrelation coefficients For correlated shocks the variance decomposition is computed as in the VAR literature through a Cholesky decomposition of the covariance matrix of the exogenous variables When the shocks are correlated the variance decomposition depends upon the order of the variables in the varexo command The Taylor approximation is computed around the steady state see Section 4 10 Steady state page 30 The IRFs are computed as the difference between the trajectory of a variable following a shock at the beginning of period 1 and its steady state value More details on the computation of IRFs can be found on the DynareWiki Variance decomposition correlation autocorrelation are only displayed for variables with strictly positive variance Impulse response functions are only plotted for variables with response larger than 10 9 Variance decomposition is computed relative to the sum of the contribution of each shock Normally this is of course equal to aggregate variance but if a model generates very large variances it may happen that due to numerical error the two differ by a
57. state calibration typically a separate model file is used for calibration which includes the list of variable declarations with the macro processor and flips some variable Example Chapter 4 The Model file 13 var y W parameters alpha bet change type var alpha bet change type parameters y w Here in the whole model file alpha and beta will be endogenous and y and w will be parameters predetermined variables VARIABLE NAME Command Description In Dynare the default convention is that the timing of a variable reflects when this variable is decided The typical example is for capital stock since the capital stock used at current period is actually decided at the previous period then the capital stock entering the production function is k 1 and the law of motion of capital must be written k i 1 delta k 1 Put another way for stock variables the default in Dynare is to use a stock at the end of the period concept instead of a stock at the beginning of the period convention The predetermined variables is used to change that convention The endogenous variables declared as predetermined variables are supposed to be decided one period ahead of all other endogenous variables For stock variables they are supposed to follow a stock at the beginning of the period convention Note that Dynare internally always uses the stock at the end of the period concept even when the model has been ente
58. taken from the preceeding initval block necessary condition for a successful homotopy is that Dynare must be able to solve the steady state for the initial parameters exogenous without additional help using the guess values given in the initval block If the homotopy fails a possible solution is to increase the number of steps given in homotopy_ steps option of steady Example In the following example Dynare will first compute the steady state for the initial values gam 0 5 and x 1 and then subdivide the problem into 50 smaller problems to find the steady state for the final values gam 2 and x 2 var c K varexo x parameters alph gam delt bet aa alph 0 5 delt 0 02 aa 0 5 bet 0 05 model C k aa x k 1 alph 1 delt k 1 c gam 1 bet 1 aa alph x 1 k alph 1 1 delt c 1 gam end initval xc k delt bet aa x alph 1 alph 1 c aax x k alph delt k end homotopy setup gam 0 5 2 X 2 end steady homotopy mode 1 homotopy_steps 50 4 10 2 Using a steady state file If you know how to compute the steady state for your model you can provide a MATLAB Octave function doing the computation instead of using steady Again there are two options for doing that Chapter 4 The Model file 34 e The easiest way is to write a steady state model block which is described below in more details See also s2000 mod in the examples directory for an
59. the Matlab Octave eq equal operator dseries objects A and B must have the same number of observations say T and variables N The returned argument is a T by N matrix of zeros and ones Element i j of C is equal to 1 if and only if observation i for variable j in and B are the same Example gt gt tsO dseries 2 ones 3 1 gt gt tsi dseries 2 0 2 gt gt tsO ts1 B exp A dseries Overloads the Matlab Octave exp function for dseries objects Chapter 6 Time Series 125 Example gt gt tsO dseries rand 10 1 gt gt tsi ts0 exp C extract A Bl dseries Extracts some variables from a dseries object A and returns a dseries object C The input arguments following are strings representing the variables to be selected in the new dseries object C To simplify the creation of sub objects the dseries class overloads the curly braces D extract A B C is equivalent to D A B C and allows implicit loops defined between a pair of symbol see examples below or Matlab Octave s regular expressions introduced by square brackets Examples The following selections are equivalent gt gt tsO dseries ones 100 10 gt gt tsi ts0 Variable_1 Variable_2 Variable_3 gt gt ts2 ts0 Variable_ 1 2 3 gt gt ts3 ts0 Variable_ 1 3 gt gt isequal ts1 ts2 amp amp isequal ts1 ts3 ans 1 It is possible to use up to two implic
60. the dynare command see Section 3 1 Dynare invocation page 6 The macro processor is invoked by placing macro directives in the mod file Directives begin with an at sign followed by a pound sign They produce no output but give instructions to the macro processor In most cases directives occupy exactly one line of text In case of need two anti slashes NX at the end of the line indicates that the directive is continued on the next line The main directives are e include for file inclusion e define for defining a macro processor variable e Qtif CHifdef CHifndef G else CHendif for conditional statements e for endfor for constructing loops The macro processor maintains its own list of variables distinct of model variables and of MATLAB Octave variables These macro variables are assigned using the define directive and can be of four types integer character string array of integers array of strings 4 20 1 Macro expressions It is possible to construct macro expressions which can be assigned to macro variables or used within a macro directive The expressions are constructed using literals of the four basic types integers strings arrays of strings arrays of integers macro variables names and standard operators String literals have to be enclosed between double quotes like name Arrays are enclosed within brackets and their elements are separated by commas like 1 2 3 or US EA N
61. this case they are used to represent the Lagrange multipliers when first order conditions of the Ramsey problem are computed The new variables take the form MULT i where i represents the constraint with which the multiplier is associated counted from the order of declaration in the model block The last type of auxiliary variables is introduced by the differentiate forward vars option of the model block The new variables take the form AUX DIFF FWRD i and are equal to x x 1 for some endogenous variable x Once created all auxiliary variables are included in the set of endogenous variables The output of decision rules see below is such that auxiliary variable names are replaced by the original variables they refer to The number of endogenous variables before the creation of auxiliary variables is stored in M orig endo nbr and the number of endogenous variables after the creation of auxiliary variables is stored in M endo nbr See Dynare Wiki for more technical details on auxiliary variables 4 7 Initial and terminal conditions For most simulation exercises it is necessary to provide initial and possibly terminal conditions It is also necessary to provide initial guess values for non linear solvers This section describes the statements used for those purposes In many contexts deterministic or stochastic it is necessary to compute the steady state of a non linear model initval then specifies numerical initial va
62. to span multiple lines and hence the parser cannot know that the second line will not have a semicolon on it until it gets there Once the parser begins parsing the second line it realizes that it has encountered a keyword parameters which it did not expect Hence it throws an error of the form ERROR lt lt file mod gt gt line 2 cols 0 9 syntax error unexpected PARAMETERS In this case you would simply place a semicolon at the end of line one and the parser would continue processing Chapter 4 The Model file 10 4 The Model file 4 1 Conventions A model file contains a list of commands and of blocks Each command and each element of a block is terminated by a semicolon Blocks are terminated by end Most Dynare commands have arguments and several accept options indicated in parentheses after the command keyword Several options are separated by commas In the description of Dynare commands the following conventions are observed e optional arguments or options are indicated between square brackets e repreated arguments are indicated by ellipses e mutually exclusive arguments are separated by vertical bars e INTEGER indicates an integer number e DOUBLE indicates a double precision number The following syntaxes are valid 1 1e3 1 1E3 1 1d3 1 1D3 In some places infinite values Inf and Inf are also allowed e NUMERICAL VECTOR indicates a vector of numbers separated by spaces enclosed by s
63. user interven tion 4 17 4 RMSE The RMSE analysis can be performed with different types of sampling options 1 When pprior 1 and ppost 0 the toolbox analyzes the RMSEs for the Monte Carlo sample obtained by sampling parameters from their prior distributions or prior ranges this analysis provides some hints about what parameter drives the fit of which observed series prior to the full estimation Chapter 4 The Model file 81 2 3 When pprior 0 and ppost 0 the toolbox analyzes the RMSEs for a multivariate normal Monte Carlo sample with covariance matrix based on the inverse Hessian at the optimum this analysis is useful when maximum likelihood estimation is done i e no Bayesian estimation When ppost 1 the toolbox analyzes the RMSEs for the posterior sample obtained by Dynare s Metropolis procedure The use of cases 2 and 3 requires an estimation step beforehand To facilitate the sensitivity analysis after estimation the dynare sensitivity command also allows you to indicate some options of the estimation command These are datafile nobs first obs prefilter presample nograph nodisplay graph format conf sig loglinear mode file Binary files produced my RMSE analysis are mod file prior mat these files store the filtered and smoothed variables for the prior Monte Carlo sample generated when doing RMSE analysis pprior 1 and ppost 0 mode file mc mat these files store the filtered an
64. will be used It is required even if you are only invoking multiple processes on one computer Options Name CLUSTER_NAME The reference name of this cluster Chapter 5 The Configuration File 108 Members NODE NAME WEIGHT NODE NAME WEIGHT list of nodes that comprise the cluster with an optional computing weight specified for that node The computing weight indicates how much more powerful one node is with respect to the others e g n1 2 n2 1 n3 3 means that n1 is two times more powerful than n2 whereas n3 is three times more powerful than n2 Each node is separated by at least one space and the weights are in parenthesis with no spaces separating them from their node Example cluster Name ci Members ni n2 n3 cluster Name c2 Members n1 4 n2 n3 node Configuration block Description When working in parallel node is required for every computer that will be used The options that are required differ depending on the underlying operating system and whether you are working locally or remotely Options Name NODE NAME The reference name of this node CPUnbr INTEGER INTEGER INTEGER If just one integer is passed the number of processors to use If a range of integers is passed the specific processors to use processor counting is defined to begin at one as opposed to zero Note that using specific processors is only possible under Windows under Linux and Mac OS X if a range
65. y 1 alpha y 2 1 alpha te end initval steady histval y 0 1 1 Chapter 4 The Model file 27 y 1 0 9 end resid Command This command will display the residuals of the static equations of the model using the values given for the endogenous in the last initval or endval block or the steady state file if you provided one see Section 4 10 Steady state page 30 initval file filename FILENAME Command Description In a deterministic setup this command is used to specify a path for all endogenous and exogenous variables The length of these paths must be equal to the number of simulation periods plus the number of leads and the number of lags of the model for example with 50 simulation periods in a model with 2 lags and 1 lead the paths must have a length of 53 Note that these paths cover two different things e the constraints of the problem which are given by the path for exogenous and the initial and terminal values for endogenous e the initial guess for the non linear solver which is given by the path for endogenous variables for the simulation periods excluding initial and terminal conditions The command accepts three file formats e M file extension m for each endogenous and exogenous variable the file must contain a row vector of the same name e MAT file extension mat same as for M files e Excel file extension xls or xlsx for each endogenous and exogenou
66. 2 values 1 p exp z end second example with a vector of values xx 1 2 1 3 1 shocks var periods 1 3 values xx end In stochastic context For stochastic simulations the shocks block specifies the non zero elements of the covariance matrix of the shocks of exogenous variables You can use the following types of entries in the block var VARIABLE_NAME stderr EXPRESSION Specifies the standard error of a variable var VARIABLE_NAME EXPRESSION Specifies the variance error of a variable Chapter 4 The Model file 29 var VARIABLE NAME VARIABLE NAME EXPRESSION Specifies the covariance of two variables corr VARIABLE NAME VARIABLE NAME EXPRESSION Specifies the correlation of two variables In an estimation context it is also possible to specify variances and covariances on endogenous variables in that case these values are interpreted as the calibration of the measurement errors on these variables This requires the var obs command to be specified before the shocks block Here is an example Shocks var e 0 000081 var u stderr 0 009 corre u 0 8 var v w 2 end Mixing deterministic and stochastic shocks It is possible to mix deterministic and stochastic shocks to build models where agents know from the start of the simulation about future exogenous changes In that case stoch_simul will compute the rational expectation solution adding future information to the st
67. 4 The Model file 91 initial subperiod INTEGER The first period of data i e for quarterly data an integer in 1 4 Default 1 final year INTEGER The last year of data Default Set to encompass entire dataset final subperiod INTEGER The final period of data i e for monthly data an integer in 1 12 Default When final_year is also missing set to encompass entire dataset when final year is indicated set to the maximum number of subperiods given the frequency i e 4 for quarterly data 12 for monthly datafile FILENAME See datafile page 53 xls sheet NAME See xls sheet page 53 xls_range RANGE See xls range page 53 nlags INTEGER The number of lags in the model Default 1 cross restrictions Use cross A and At restrictions Default off contemp reduced form Use contemporaneous recursive reduced form Default off no bayesian prior Do not use Bayesian prior Default off i e use Bayesian prior alpha INTEGER Alpha value for squared time varying structural shock lambda Default 1 beta INTEGER Beta value for squared time varying structural shock lambda Default 1 gsig2 lmdm INTEGER The variance for each independent A parameter under SimsZha restrictions Default 5072 Specification sims zha none This controls how restrictions are imposed to reduce the number of parameters Default Random Walk Estimation Options convergence starting value DOUBLE
68. 5 Default off ms forecast Command ms forecast OPTIONS Command Description Generates forecasts for a Markov switching SBVAR model Output eps files are contained in output file tag utput Forecast while data files are contained in output file tag Forecast gt Options file_tag FILENAME See file tag page 93 output_file_tag FILENAME See output_file_tag page 93 simulation_file_tag FILENAME See simulation_file_tag page 94 data_obs_nbr INTEGER The number of data points included in the output Default 0 error_band_percentiles DOUBLE1 See error_band_percentiles page 95 shock_draws INTEGER See shock_draws page 95 shocks_per_parameter INTEGER See shocks_per_parameter page 95 thinning factor INTEGER See thinning factor page 95 free_parameters NUMERICAL_VECTOR See free parameters page 95 parameter_uncertainty See parameter_uncertainty page 95 regime INTEGER See regime page 95 regimes See regimes page 96 median See median page 96 ms_variance_decomposition Command ms variance decomposition OPTIONS Command Description Computes the variance decomposition for a Markov switching SBVAR model Output eps files are contained in output file tag utput Variance Decomposition while data files are contained in output file tag Variance Decomposition Chapter 4 The Model file 97 Options file_tag
69. 7 Reporting 143 data dseries See data page 141 showHlines BOOLEAN Whether or not to show horizontal lines separating the rows Default false precision INTEGER The number of decimal places to report in the table data Default 1 range dates The date range of the data to be displayed Default a11 seriesToUse CELL ARRAY STRINGS See series ToUse page 142 title STRING Title for the table Default none titleSize STRING IXTEX string representing the size of the table title Default large vlineAfter dates CELL ARRAY DATES Show a vertical line after the specified date or dates if a cell array of dates is passed Default empty vlineAfterEndOfPeriod BOOLEAN Show a vertical line after the end of every period i e after every year after the fourth quarter etc Default false showVlines BOOLEAN Whether or not to show vertical lines separating the columns Default false addSeries data graphLineColor graphLineStyle graphLineWidth Method on Report graphMarker graphMarkerEdgeColor graphMarkerFaceColor graphMarkerSize tableDataRhs tableRowColor tableShowMarkers tableAlignRight tableNegColor tablePosColor tableSubSectionHeader zerotol Adds a Series to a Graph or a Table Options data dseries See data page 141 graphLineColor MATLAB_COLOR Color to use for the series in a graph Default k graphLineStyle none e f Line style for this series in a gr
70. B Sort method for dates objects Returns a dates object with elements sorted by increasing order Example gt gt dd dates 1945Q3 193804 178903 gt gt dd sort ans lt dates 178903 193804 194503 gt dates Overloads the Matlab Octave unary minus operator Returns a dates object with elements shifted one period backward Example gt gt dd dates 1945Q3 193804 1973Q1 gt gt dd ans dates 194502 193803 1972Q4 gt dates Overloads the Matlab Octave union function Returns a dates object with elements sorted by increasing order repetitions are removed to keep the repetitions use the horzcat or plus operators Example gt gt di dates 1945Q3 1973Q1 193804 gt gt d2 dates 1973Q1 1976Q1 gt gt union di d2 ans lt dates 193804 194503 1973Q1 1976Q1 gt unique A dates Overloads the Matlab Octave unique function Returns a dates object with repetitions re moved only the last occurence of a date is kept Example gt gt di dates 1945Q3 1973Q1 1945Q3 gt gt di unique ans lt dates 1973Q1 194503 gt uplus A dates Overloads the Matlab Octave unary plus operator Returns a dates object with elements shifted one period ahead Example gt gt dd dates 1945Q3 7193804 197301 gt gt dd ans dates 194504 193901 1973Q2 gt Chapter 6
71. D_PARAMETER and PRIOR 4TH_PARAMETER Use empty values if these parameters don t apply Example The following line corr eps_1 eps 2 0 5 beta pdf 0 0 3 1 1 sets a generalized beta prior for the correlation between eps 1 and eps 2 with mean 0 and variance 0 3 By setting PRIOR 3RD PARAMETER to 1 and PRIOR 4TH PARAMETER to 1 the standard beta distribution with support 0 1 is changed to a generalized beta with support 1 1 Note that LOWER BOUND and UPPER BOUND are left empty and thus default to 1 and 1 respectively The initial value is set to 0 5 Similarly the following line corr eps 1 eps 2 0 5 0 5 1 beta pdf 0 0 3 1 1 sets the same generalized beta distribution as before but now truncates this distribution to 0 5 1 through the use of LOWER BOUND and UPPER BOUND Hence the prior does not integrate to 1 anymore Parameter transformation Sometimes it is desirable to estimate a transformation of a parameter appearing in the model rather than the parameter itself It is of course possible to replace the original parameter by a function of the estimated parameter everywhere is the model but it is often unpractical In such a case it is possible to declare the parameter to be estimated in the parameters statement and to define the transformation using a pound sign expression see Section 4 5 Model declaration page 18 Example parameters bet model sig 1 bet c sig c 1 m
72. Dynare Working Papers Series http www dynare org wp Dynare Reference Manual Version 4 St phane Adjemian Houtan Bastani Fr deric Karam Michel Juillard Junior Maih Ferhat Mihoubi George Perendia Johannes Pfeifer Marco Ratto S bastien Villemot Working Paper no 1 Initial revision April 2011 This revision July 2014 CEPREMAP CENTRE POUR LA RECHERCHE ECONOMIQUE ET SES APPLICATIONS 142 rue du Chevaleret 75013 Paris France http www cepremap fr Dynare Reference Manual version 4 4 3 St phane Adjemian Houtan Bastani Fr d ric Karam Michel Juillard Junior Maih Ferhat Mihoubi George Perendia Johannes Pfeifer Marco Ratto S bastien Villemot Copyright 1996 2014 Dynare Team Permission is granted to copy distribute and or modify this document under the terms of the GNU Free Documentation License Version 1 3 or any later version published by the Free Software Foundation with no Invariant Sections no Front Cover Texts and no Back Cover Texts A copy of the license can be found at http www gnu org licenses fdl txt Table of Contents 1 Irt bodi LIDEES sa ruote AC ripe une deed ka a dtd aride 1 1i Whatis Dyn re 1 23 A se RR he Fei eA E RU Uc LR ERREUR RUE dela il 1 2 Documentation sources 0 6 cee eee I ehh 2 1 3 Citing Dynare in your research 22 2 Installation and configuration
73. E X X Ur RR REP 110 6 1 2 dates Classi decedat aa Renters Eau e Agde denr es 111 6 2 dseries class as osse P IURE sean eh da ee DOE Ea E nee 120 T Reportin EE a ol 140 B Examples uu a oe otc a ees on 147 9 Dynare misc commands 148 10 Bibl grapby o aser on ER ad EE t HRS E TL iaceo 150 Command and Function Index 152 Chapter 1 Introduction 1 1 Introduction 1 1 What is Dynare Dynare is a software platform for handling a wide class of economic models in particular dynamic stochastic general equilibrium DSGE and overlapping generations OLG models The models solved by Dynare include those relying on the rational expectations hypothesis wherein agents form their expectations about the future in a way consistent with the model But Dynare is also able to handle models where expectations are formed differently on one extreme models where agents perfectly anticipate the future on the other extreme models where agents have limited rationality or imperfect knowledge of the state of the economy and hence form their expectations through a learning process In terms of types of agents models solved by Dynare can incorporate consumers productive firms governments monetary authorities investors and financial intermediaries Some degree of heterogeneity can be achieved by including several distinct classes of agents in each of the aforementioned agent catego
74. Lo Le A E ea nii cn hsepS ers DH Pepe esee ques 47 00 HOT x PIU nn eE Eaa ie REE ERENS 47 005 Ne 1E ssec ze pucbSUpPSd Ede EE 47 OO AT ABhXU rise uh cepa Meee sep 47 00 5dr BhXX pe a ehe gewep pe Rene 47 155 OO0 dr inv order var i i siseuhete ee ses 46 o0_ dr order_var 46 GOAL VS Lise bh PRA ORPLR IRR UR RISE san Boe 47 48 o0_ endo_simul 39 41 06 sexo simul v oeseemyeeadGana e pResr S WI Have tre 39 oo Filtered Variables X step ahead 64 o0o_ FilteredVariables 64 oo FilteredVariablesKStep Ahead 64 oo FilteredVariablesKStepAheadVariances 64 00 forecast lc 9era evel E RP ra e 70 00 gama Ye ste metastatic DIE Ebtaxtet id e 45 OO UTE Sid ht hil BE deeem Rada sentent 45 oo_ MarginalDensity LaplaceApproximation 64 oo_ MarginalDensity ModifiedHarmonicMean 64 OO_ MCAN eee e en 44 o0o_ MeanForecast 70 oo_ osr objective_function 77 oo_ planner_objective_value 78 o00_ PointForecast 70 o0_ posterior_density 65 oo_ posterior_hpdinf 65 o0_ posterior_hpdsup 65 oo posterior Mean 4 ssmssuerrennsess amet 66 O00 posterior mode cene reprae asu sgerdrs ss 66 go posterior std m ur eru er es 66 oo_ Poste
75. MENT NAME VARIABLE NAME SHOCK NAME oo SmoothedMeasurementErrors MATLAB Octave variable Variable set by the estimation command if it is used with the smoother option Fields are of the form oo SmoothedMeasurementErrors VARIABLE NAME oo SmoothedShocks MATLAB Octave variable Variable set by the estimation command if used with the smoother option or by the calib_ smoother command After an estimation without Metropolis or if computed by calib_smoother fields are of the form oo SmoothedShocks VARIABLE NAME After an estimation with Metropolis fields are of the form oo SmoothedShocks MOMENT NAME VARIABLE NAME Chapter 4 The Model file 65 oo SmoothedVariables MATLAB Octave variable Variable set by the estimation command if used with the smoother option or by the calib_ smoother command After an estimation without Metropolis or if computed by calib_smoother fields are of the form oo_ SmoothedVariables VARIABLE NAME After an estimation with Metropolis fields are of the form oo SmoothedVariables MOMENT NAME VARIABLE NAME oo UpdatedVariables MATLAB Octave variable Variable set by the estimation command if used with the smoother option or by the calib_ smoother command Contains the estimation of the expected value of variables given the infor mation available at the current date After an estimation without Metropolis or if computed by calib smoother fields are of the form oo UpdatedVa
76. Ng variables then N4 must be equal to Ng or 1 and Ng must be equal to Ny or 1 If T4 Tg isequal A init B init returns 1 and N4 Np then the mtimes operator will compute for each couple t n with 1 t T4 and 1 n M1 C data t n A data t n B data t n If Ng is equal to 1 and Ny gt 1 the smaller dseries object B is broadcast across the larger dseries A so that they have compatible shapes mtimes operator will multiply each variable defined in A by the variable in B observation per observation If B is a double scalar then the method mtimes will multiply all the observa tions variables in A by B If B is a row vector of length N4 then the mtimes method will multiply all the observations of variable i by B i for i 1 Na If B is a column vector of length T4 then the mtimes method will perform a multiplication of all the variables by B element by element ne A B dseries Overloads the Matlab Octave ne equal operator dseries objects A and B must have the same number of observations say T and variables N The returned argument is a T by N matrix of zeros and ones Element i j of C is equal to 1 if and only if observation i for variable j in A and B are not equal Example gt gt tsO dseries 2 ones 3 1 gt gt tsi dseries 2 0 2 gt gt tsO tsi ans 0 1 0 plot A dseries plot A B dseries plot Al dseries plot A B dseries
77. O gamma y gamma inf lN delta 0 44 kappa 0 18 alpha 0 48 sigma 0 06 gammarr 0 gammaxO 0 2 gammacO 1 5 gamma_y_ 8 gamma_inf_ 3 model linear y delta y 1 1 delta y 1 sigma r inflation 1 y_ inflation alpha inflation 1 1 alpha inflation 1 kappaxy inf l r gammaxO y 1 gammacO inflation 1 gamma y y gamma inf inf end shocks var y_ stderr 0 63 var inf_ stderr 0 4 end optim_weights inflation 1 y 1 y inflation 0 5 end Chapter 4 The Model file 77 osr_params gammaxO gammacO gamma y gamma inf osr y oo osr objective function MATLAB Octave variable After an execution of the osr command this variable contains the value of the objective under optimal policy ramsey model OPTIONS Command y Description This command computes the First Order Conditions for maximizing the policy maker objective function subject to the constraints provided by the equilibrium path of the economy The planner objective must be declared with the planner_objective command This command only creates the expanded model it doesn t perform any computations It needs to be followed by other instructions to actually perfrom desired computations Note that it is the only way to perform perfect foresight simulation of the Ramsey policy problem See Section 4 6 Auxiliary variables page 21 for an explanation of how Lagrange multipli
78. On Debian GNU Linux and Ubuntu Please refer to the Dynare Wiki for detailed instructions Dynare will be installed under usr share dynare and usr lib dynare Documentation will be under usr share doc dynare Chapter 2 Installation and configuration 4 2 2 3 On Mac OS X Execute the automated installer called dynare 4 x y pkg where 4 x y is the version number and follow the instructions The default installation directory is Applications Dynare 4 x y Please refer to the Dynare Wiki for detailed instructions After installation this directory will contain several sub directories among which are matlab mex and doc Note that you can have several versions of Dynare coexisting for example in Applications Dynare as long as you correctly adjust your path settings see Section 2 3 3 Some words of warning page 5 2 2 4 For other systems You need to download Dynare source code from the Dynare website and unpack it somewhere Then you will need to recompile the pre processor and the dynamic loadable libraries Please refer to README md 2 3 Configuration 2 3 1 For MATLAB You need to add the matlab subdirectory of your Dynare installation to MATLAB path You have two options for doing that e Using the addpath command in the MATLAB command window Under Windows assuming that you have installed Dynare in the standard location and re placing 4 x y with the correct version number type addpath c dynare 4 x y matl
79. Overloads Matlab Octave s plot function for dseries objects Returns a Matlab Octave plot handle that can be used to modify the properties of the plotted time series If only one dseries Chapter 6 Time Series 135 object is passed as argument then the plot function will put the associated dates on the x abscissa If this dseries object contains only one variable additional arguments can be passed to modify the properties of the plot as one would do with the Matlab Octave s version of the plot function If dseries object A contains more than one variable it is not possible to pass these additional arguments and the properties of the plotted time series must be modify using the returned plot handle and the Matlab Octave set function see example below If two dseries objects and B are passed as input arguments the plot function will plot the variables in A against the variables in B the number of variables in each object must be the same otherwise an error is issued Again if each object contains only one variable additional arguments can be passed to modify the properties of the plotted time series otherwise the Matlab Octave set command has to be used Examples Define a dseries object with two variables named by default Variable_1 and Variable_2 gt gt ts dseries randn 100 2 1950Q1 The following command will plot the first variable in ts gt gt plot ts Variable_1 k linewidth 2 The next co
80. Section 2 1 Software requirements page 3 This option is only available under Windows and is used in conjunction with use d11 parallel CLUSTER_NAME Tells Dynare to perform computations in parallel If CLUSTER NAME is passed Dynare will use the specified cluster to perform parallel computations Otherwise Dynare will use the first cluster specified in the configuration file See Chapter 5 The Configuration File page 106 for more information about the configuration file conffile FILENAME Specifies the location of the configuration file if it differs from the default See Chapter 5 The Configuration File page 106 for more information about the con figuration file and its default location parallel slave open mode Instructs Dynare to leave the connection to the slave node open after computation is complete closing this connection only when Dynare finishes processing parallel test Tests the parallel setup specified in the configuration file without executing the mod file See Chapter 5 The Configuration File page 106 for more information about the configuration file DMACRO VARIABLE MACRO EXPRESSION Defines a macro variable from the command line the same effect as using the Macro directive define in a model file see Section 4 20 Macro processing language page 98 nostrict Allows Dynare to issue a warning and continue processing when 1 there are more endogenous variables than equations 2 an undeclared
81. Specify the parameter set to use Default prior mean lik init INTEGER See lik init page 54 kalman algo INTEGER See kalman_algo page 60 nograph See nograph page 41 nodisplay See nodisplay page 41 graph format FORMAT graph format FORMAT FORMAT See graph format page 41 4 18 Markov switching SBVAR Given a list of variables observed variables and a data file Dynare can be used to solve a Markov switching SBVAR model according to Sims Waggoner and Zha 2008 Having done this you can create forecasts and compute the marginal data density regime probabilities IRFs and variance decomposition of the model The commands have been modularized allowing for multiple calls to the same command within a mod file mod file The default is to use mod file to tag the input output files used produced by the program Thus to call any command more than once within a mod file mod file you must use the tag options described below markov switching OPTIONS Command Description Declares the Markov state variable information of a Markov switching SBVAR model Options chain INTEGER The Markov chain Default none state INTEGER This state has duration equal to duration Exactly one of state and number_of_ states must be passed Default none number_of_states INTEGER Total number of states Implies that all states have the same duration Exactly one of stat
82. Trigonometric functions max a b Function min a b Function Maximum and minimum of two reals Note that these functions are differentiable everywhere except on a line of the 2 dimensional real plane defined by a b However for facilitating convergence of Newton type methods Dynare assumes that at the points of non differentiability the partial derivative of these functions with respect to the first resp the second argument is equal to 1 resp to 0 i e the derivatives at the kink are equal to the derivatives observed on the half plane where the function is equal to its first argument Chapter 4 The Model file 17 normcdf x Function normcdf x mu sigma Function Gaussian cumulative density function with mean mu and standard deviation sigma Note that normcdf x is equivalent to normcdf x 0 1 normpdf x Function normpdf x mu sigma Function Gaussian probability density function with mean mu and standard deviation sigma Note that normpdf x is equivalent to normpdf x 0 1 erf x Function Gauss error function 4 3 3 2 External Functions Any other user defined or built in MATLAB or Octave function may be used in both a MODEL EXPRESSION and an EXPRESSION provided that this function has a scalar argu ment as a return value To use an external function in MODEL EXPRESSION one must declare the function us ing the external function statement This is not necessary for external f
83. W write on Report cine menage names nus 144 write_latex_definitions 105 write_latex_dynamic_model 21 write_latex_static_model 21 Command and Function Index Variable Index Variable Index F forecasts CON og su saumon da Rede RA T2 forecasts controlled_variables 72 forecasts graphs 72 forecasts instruments 72 forecasts unc nd tb ep mean e dus 12 M M a as a de tt ea nn 8 M endo nDEr c kc be eb dae ee 22 M_ lead_lag_incidence 6 M MOG rs eee aies ere cetes 46 M ndyna miC n Rr e ERR munis es 47 M OUfWEQ Gai i e 4cG ew oue NP CE SY Ka Ne qu 46 M HpEGd uere I dois een dese e 46 M MS VEd none eeu eeu Pe EA RES 47 M nspred circa tel iti en titine st 47 M mnstatiC i c la v eive A a UepPPRER tie 46 M orig endo nbr c eec odd er eere dada 22 M patas 5e nent nas ns 18 63 M Bigma e e re 9sex tetas Ree EF EP EFT Ra dag 63 O OO RR AE A EE A NEE 9 O0_ autOCONT 0 eee cece ee eee eee eee e nes 44 oo_ conditional_variance_decomposition 45 o0_ convergence geweke 66 00 df 618val 5 semsrsrinuslisssenmniauesslisse 36 OO AT BOL ane ee eee eee 48 00 drtg 1 oe doce aera ane eee saieba E 48 00 4dE V8 2 E qM Depp IT duse 48 00 OTE dose ce inne redes uten AH dae 48 00 df Eh82 5 E AR PIRE DE ER ii es 47
84. a end and if variables C A and K are defined as dseries objects then by writting Residuals 1 C beta C 1 exp A 1 K alpha 1 1 delta outside of the model block we create a new dseries object called Residuals for the residuals of the Euler equation the conditional expectation of the equation defined in the model block is zero but the residuals are non zero Chapter 6 Time Series B log 4 Overloads the Matlab Octave log function for dseries objects Example gt gt tsO gt gt tsi C merge A B Merges two dseries objects and B in dseries object C Objects A and B need to have common frequency but can be defined on different time ranges If a variable say x is defined both in dseries objects A and B then the merge will select the variable x as defined in the second input argument B Example gt gt tsO tsO is 1950Q1 195002 1950Q3 gt gt tsi tsi is 195002 195003 1950Q4 a dseries rand 10 1 ts0 logO dseries rand 3 2 1950Q1 7 A1 A2 dseries object A1 0 4 0 6 0 0 2448 0726 70764 A2 0 92477 0 64208 0 1045 dseries rand 3 1 1950Q2 A1 dseries object A1 0 7 0 3 0 0 0023 958 84905 gt gt merge ts0 ts1 ans is a dseries object 1950Q1 1950Q2 1950Q3 1950Q4 gt gt merge tsi ts0 ans is a dseries object 1950Q1 1950Q2 1950Q3 195004 A2 0 92477 0 64208 0 1045 NaN 131 dseries
85. a 9096 HPD interval of forecast due to parameter uncertainty HPDsup Lower bound of a 9096 HPD interval due to parameter uncertainty HPDTotalinf Lower bound of a 9096 HPD interval of forecast due to parameter uncertainty and future shocks only with the estimation command HPDTotalsup Lower bound of a 9096 HPD interval due to parameter uncertainty and future shocks only with the estimation command Mean Mean of the posterior distribution of forecasts Median Median of the posterior distribution of forecasts Std Standard deviation of the posterior distribution of forecasts oo PointForecast MATLAB Octave variable Set by the estimation command if it is used with the forecast option and if either mh_replic gt 0 or load mh file option is used Contains the distribution of forecasts taking into account the uncertainty about both parameters and shocks Fields are of the form oo PointForecast MOMENT NAME VARIABLE NAME oo MeanForecast MATLAB Octave variable Set by the estimation command if it is used with the forecast option and if either mh_replic gt 0 or load mh file option is used Contains the distribution of forecasts where the uncertainty about shocks is averaged out The distribution of forecasts therefore only represents the uncertainty about parameters Fields are of the form oo MeanForecast MOMENT NAME VARIABLE NAME See option conf sig page 69 to change the size of the HPD interval Chapter 4 The Model
86. a double ans 1950 00 1950 25 1950 50 1950 75 C eq A B dates Overloads the Matlab Octave eq equal operator dates objects A and B must have the same number of elements say n The returned argument is a n by 1 vector of zeros and ones The i th element of C is equal to 1 if and only if the dates A i and B i are the same Example gt gt A dates 1950Q1 1951Q2 gt gt B dates 1950Q1 1950Q2 ans C ge A B dates Overloads the Matlab Octave ge greater or equal gt operator dates objects A and B must have the same number of elements say n The returned argument is a n by 1 vector of zeros and ones The i th element of C is equal to 1 if and only if the date A i is posterior or equal to the date B i Example gt gt A dates 1950Q1 1951Q2 gt gt B dates 1950Q1 1950Q2 gt gt A gt B ans C gt A B dates Overloads the Matlab Octave gt greater than gt operator dates objects A and B must have the same number of elements say n The returned argument is a n by 1 vector of zeros and ones The i th element of C is equal to 1 if and only if the date A i is posterior to the date B i Example Chapter 6 Time Series 115 gt gt A dates 1950Q1 1951Q2 gt gt B dates 1950Q1 1950Q2 gt gt A gt B ans D horzcat A B C dates C Overloads the Matlab Octave ho
87. ab Under Debian GNU Linux or Ubuntu type addpath usr share dynare matlab Under Mac OS X assuming that you have installed Dynare in the standard location and replacing 4 x y with the correct version number type addpath Applications Dynare 4 x y matlab MATLAB will not remember this setting next time you run it and you will have to do it again e Via the menu entries Select the Set Path entry in the File menu then click on Add Folder and select the matlab subdirectory of your Dynare installation Note that you should not use Add with Subfolders Apply the settings by clicking on Save Note that MATLAB will remember this setting next time you run it 2 3 2 For GNU Octave You need to add the matlab subdirectory of your Dynare installation to Octave path using the addpath at the Octave command prompt Under Windows assuming that you have installed Dynare in the standard location and replac ing 4 x y with the correct version number type addpath c dynare 4 x y matlab Under Debian GNU Linux or Ubuntu there is no need to use the addpath command the packaging does it for you Under Mac OS X assuming that you have installed Dynare in the standard location and replacing 4 x y with the correct version number type Chapter 2 Installation and configuration 5 addpath Applications Dynare 4 x y matlab If you don t want to type this command every time you run Octave you can pu
88. ables in the columns is stored in M lead lag incidence The rows of this matrix represent time periods the first row denotes a lagged time t 1 variable the second row a contemporaneous time t variable and the third row a leaded time t 1 vari able The columns of the matrix represent the endogenous variables in their order of declaration zero in the matrix means that this endogenous does not appear in the model in this time period The value in the M 1ead lag incidence matrix corresponds to the column of that variable in the Jacobian of the dynamic model Example Let the second declared variable be c and the 3 2 entry of M_ lead_ lag incidence be 15 Then the 15th column of the Jacobian is the derivative with respect to y 41 FILENAME static m Contains the long run static model equations Note that Dynare might introduce auxiliary equations and variables see Section 4 6 Auxiliary variables page 21 Outputs are the residuals of the static model equations in the order the equations were declared and the Jacobian of the static equations Entry i j ofthe Jacobian represents the derivative of the ith static model equation with respect to the jth model variable in declaration order These files may be looked at to understand errors reported at the simulation stage dynare will then run the computing tasks by executing FILENAME m Chapter 3 Running Dynare 7 few words of warning is warranted here the filename of the m
89. actual computations start The pre and or post dynare preprocessor hooks are executed if and only if the aforementioned scripts are detected in the same folder as the the model file FILENAME mod 3 3 Understanding Preprocessor Error Messages If the preprocessor runs into an error while processing your mod file it will issue an error Due to the way that a parser works sometimes these errors can be misleading Here we aim to demystify these error messages The preprocessor issues error messages of the form 1 ERROR lt lt file mod gt gt line A col B error message 2 ERROR lt lt file mod gt gt line A cols B C lt lt error message 3 ERROR lt lt file mod gt gt line A col B line C col D lt lt error message The first two errors occur on a single line with error two spanning multiple columns Error three spans multiple rows Often the line and column numbers are precise leading you directly to the offending syntax Infrequently however because of the way the parser works this is not the case The most common example of misleading line and column numbers and error message for that matter is the case of a missing semicolon as seen in the following example varexo a b parameters c In this case the parser doesn t know a semicolon is missing at the end of the varexo command until it begins parsing the second line and bumps into the parameters command This is be cause we allow commands
90. ady state is solved analytically using the steady state model block see steady state model page 34 fs2000 mod A cash in advance model estimated by Schorfheide 2000 The file shows how to use Dynare for estimation fs2000 nonstationary mod The same model than fs2000 mod but written in non stationary form Detrending of the equations is done by Dynare bkk mod Multi country RBC model with time to build presented in Backus Kehoe and Kydland 1992 The file shows how to use Dynare s macro processor agtrend mod Small open economy RBC model with shocks to the growth trend presented in Aguiar and Gopinath 2004 NK baseline mod Baseline New Keynesian Model estimated in Fern ndez Villaverde 2010 It demon strates how to use an explicit steady state file to update parameters and call a numerical solver Chapter 9 Dynare misc commands 148 9 Dynare misc commands internals FLAG ROUTINENAME m MODFILENAME MATLAB Octave command Depending on the value of FLAG the internals command can be used to run unitary tests spe cific to a Matlab Octave routine if available to display documentation about a Matlab Octave routine or to extract some informations about the state of Dynare Flags test info Performs the unitary test associated to ROUTINENAME if this routine exists and if the matalab octave m file has unitary test sections Example gt gt internals test ROUTINENAME if routine m is not in the
91. ady state to Dynare using a steady_state_ model block or writing a steady state file if a closed form solution is available see steady_state_model page 34 or specify some constraints on the steady state see equation_tag_for_conditional_steady_state page 35 so that Dynare computes the steady state conditionally on some predefined levels for the non stationary variables In both cases the idea is to use dummy values for the steady state level of the exogenous non stationary variables Note that the nonstationary variables in the model must be integrated processes their first difference or k difference must be stationary selected_variables_only Only run the smoother on the variables listed just after the estimation command Default run the smoother on all the declared endogenous variables cova_compute INTEGER When 0 the covariance matrix of estimated parameters is not computed after the computation of posterior mode or maximum likelihood This increases speed of computation in large models during development when this information is not al ways necessary Of course it will break all successive computations that would require this covariance matrix Otherwise if this option is equal to 1 the covari ance matrix is computed and stored in variable hh of MODEL_FILENAME_mode mat Default is 1 solve_algo INTEGER See solve_algo page 31 order INTEGER Order of approximation either 1 or 2 When equal to 2 the likeliho
92. al research network for DSGE modeling The Dynare project also received funding through the Seventh Framework Programme for Research FP7 of the European Commission s Socio economic Sciences and Humanities SSH Program from October 2008 to September 2011 under grant agreement SSH CT 2009 225149 Chapter 1 Introduction 2 Interaction between developers and users of Dynare is central to the project web forum is available for users who have questions about the usage of Dynare or who want to report bugs Training sessions are given through the Dynare Summer School which is organized every year and is attended by about 40 people Finally priorities in terms of future developments and features to be added are decided in cooperation with the institutions providing financial support 1 2 Documentation sources The present document is the reference manual for Dynare It documents all commands and features in a systematic fashion New users should rather begin with Dynare User Guide Mancini 2007 distributed with Dynare and also available from the official Dynare web site Other useful sources of information include the Dynare wiki and the Dynare forums 1 3 Citing Dynare in your research If you would like to refer to Dynare in a research article the recommended way is to cite the present manual as follows St phane Adjemian Houtan Bastani Michel Juillard Fr d ric Karam Ferhat Mi houbi George Perendia Johannes Pfeifer Marc
93. all the periods preceeding the first simulation period unless some of these initial values are modified by histval Second in the absence of an endval block it sets the terminal conditions for all the periods succeeding the last simulation period Third in the absence of an endval block it provides initial guess values at all simulation dates for the non linear solver implemented in simul For this last reason it necessary to provide values for all the endogenous variables in an initval block even though theoretically initial conditions are only necessary for lagged variables If some variables endogenous or exogenous are not mentioned in the initval block a zero value is assumed Note that if the initval block is immediately followed by a steady command its semantics is changed The steady command will compute the steady state of the model for all the endogenous variables assuming that exogenous variables are kept constant to the value declared in the initval block and using the values declared for the endogenous as initial guess values for the non linear solver An initval block followed by steady is formally equivalent to an initval block with the same values for the exogenous and with the associated steady state values for the endogenous In a stochastic model The main purpose of initval is to provide initial guess values for the non linear solver in the steady state computation Note that if the initval block is not follow
94. amsey policy or discretionary policy You need to give the one period objective not the discounted lifetime objective The discount factor is given by the planner discount option of ramsey policy and discretionary policy The objective function can only contain current endogenous variables and no exogenous ones This limitation is easily circumvented by defining an appropriate auxiliary variable in the model With ramsey policy you are not limited to quadratic objectives you can give any arbitrary nonlinear expression With discretionary policy the objective function must be quadratic 4 17 Sensitivity and identification analysis Dynare provides an interface to the global sensitivity analysis GSA toolbox developed by the Joint Research Center JRC of the European Commission which is now part of the official Dynare distribution The GSA toolbox can be used to answer the following questions 1 What is the domain of structural coefficients assuring the stability and determinacy of a DSGE model 2 Which parameters mostly drive the fit of e g GDP and which the fit of inflation Is there any conflict between the optimal fit of one observed series versus another 3 How to represent in a direct albeit approximated form the relationship between structural parameters and the reduced form of a rational expectations model The discussion of the methodologies and their application is described in Ratto 2008 With respect to t
95. and set_dynare_seed ALGORITHM INTEGER Command Sets the seed used for random number generation It is possible to set a given integer value to use a default value or to use the clock by using the latter one will therefore get different results across different Dynare runs The reset option serves to reset the seed to the value set by the last set_dynare_seed command On MATLAB 7 8 or above it is also possible to choose a specific algorithm for random number generation accepted values are mcg16807 m1fg6331 64 mrg32k3a mt19937ar the default shr3cong and swb2712 save_params_and_steady_state FILENAME Command For all parameters endogenous and exogenous variables stores their value in a text file using a simple name value associative table e for parameters the value is taken from the last parameter initialization e for exogenous the value is taken from the last initval block e for endogenous the value is taken from the last steady state computation or if no steady state has been computed from the last initval block Note that no variable type is stored in the file so that the values can be reloaded with load_ params_and_steady_state in a setup where the variable types are different Chapter 4 The Model file 105 The typical usage of this function is to compute the steady state of a model by calibrating the steady state value of some endogenous variables which implies that some parameters must be endogeneize
96. andling of minimum feedback set of endogenous variables Only avail able with option block Possible values 0 All the endogenous variables are considered as feedback variables De fault 1 The endogenous variables assigned to equation naturally normalized i e of the form x f Y where x does not appear in Y are potentially recursive variables All the other variables are forced to belong to the set of feedback variables 2 In addition of variables with mfs 1 the endogenous variables related to linear equations which could be normalized are potential recursive variables All the other variables are forced to belong to the set of feedback variables 3 In addition of variables with mfs 2 the endogenous variables related to non linear equations which could be normalized are potential recursive variables All the other variables are forced to belong to the set of feedback variables In particular for big models the compilation step can be very time consuming and use of this option may be counter productive in those cases Chapter 4 The Model file 20 no_static Don t create the static model file This can be useful for models which don t have a steady state differentiate forward vars differentiate forward vars VARIABLE NAME VARIABLE NAME Tells Dynare to create a new auxiliary variable for each endogenous variable that appears with a lead such that the new variable is the time differentiate of the original
97. aph Default graphLineWidth DOUBLE Line width for this series in a graph Default 0 5 graphMarker fo x fs square d diamond v t lt p pentagram h hexagram none The Marker to use on this series in a graph Default none graphMarkerEdgeColor MATLAB_COLOR The edge color of the graph marker Default auto graphMarkerFaceColor MATLAB_COLOR The face color of the graph marker Default auto Chapter 7 Reporting 144 graphMarkerSize DOUBLE The size of the graph marker Default 6 tableDataRhs dseries series to be added to the right of the current series Usefull for displaying aggregate data for a series e g if the series is quarterly tableDataRhs could point to the yearly averages of the quarterly series This would cause quarterly data to be displayed followed by annual data Default empty tableRowColor STRING The color that you want the row to be Predefined values include LightCyan and Gray Default white tableShowMarkers BOOLEAN In a Table if true surround each cell with brackets and color it according to tableNegColor page 144 and tablePosColor page 144 No effect for graphs Default false tableAlignRight BOOLEAN Whether or not to align the series name to the right of the cell Default false tableMarkerLimit DOUBLE For values less than 1 tableMarkerLimit mark the cell
98. approximation Acceptable values are 1 2 and 3 Note that for third order k_order_solver option is implied and only empirical moments are available you must provide a value for periods option Default 2 except af ter an estimation command in which case the default is the value used for the estimation k_order_solver Use a k order solver implemented in C instead of the default Dynare solver This option is not yet compatible with the bytecode option see Section 4 5 Model declaration page 18 Default disabled for order 1 and 2 enabled otherwise periods INTEGER If different from zero empirical moments will be computed instead of theoretical moments The value of the option specifies the number of periods to use in the simulations Values of the initval block possibly recomputed by steady will be used as starting point for the simulation The simulated endogenous variables are Chapter 4 The Model file 42 made available to the user in a vector for each variable and in the global matrix oo endo simul see oo endo simul page 39 The simulated exogenous variables are made available in oo exo simul see oo_ exo_simul page 39 Default 0 qz_criterium DOUBLE Value used to split stable from unstable eigenvalues in reordering the Generalized Schur decomposition used for solving 1 st order problems Default 1 000001 ex cept when estimating with lik init option equal to 1 the default is 0 999999 in that case s
99. ariables used in a MODEL EXPRESSION denote current period values when neither a lead or a lag is given A lead or a lag can be given by enclosing an integer between parenthesis just after the variable name a positive integer means a lead a negative one means a lag Leads or lags of more than one period are allowed For example if c is an endogenous variable then c 1 is the variable one period ahead and c 2 is the variable two periods before When specifying the leads and lags of endogenous variables it is important to respect the following convention in Dynare the timing of a variable reflects when that variable is decided A control variable which by definition is decided in the current period must have no lead A predetermined variable which by definition has been decided in a previous period must have a lag A consequence of this is that all stock variables must use the stock at the end of the period convention Please refer to Mancini Griffoli 2007 for more details and concrete examples Leads and lags are primarily used for endogenous variables but can be used for exogenous variables They have no effect on parameters and are forbidden for local model variables see Section 4 5 Model declaration page 18 4 3 1 2 Outside the model When used in an expression outside the model block a parameter or a variable simply refers to the last value given to that variable More precisely for a parameter it refers to
100. asts will be based on a first order approximation Third although controlled exogenous variables are taken as instruments perfectly under the control of the policy maker they are nevertheless random and unforeseen shocks from the perspective of the households That is households are in each period surprised by the realization of a shock that keeps the controlled endogenous variables at their respective level Fourth keep in mind that if the structural innovations are correlated because the calibrated or estimated covariance matrix has non zero off diagonal elements the results of the conditional forecasts will depend on the ordering of the innovations as declared after varexo As in VAR models a Cholesky decomposition is used to factorize the covariance matrix and identify orthogonal impulses It is preferable to declare the correlations in the model block explicitly imposing the identification restrictions unless you are satisfied with the implicit identification restrictions implied by the Cholesky decomposition This command has to be called after estimation or stoch simul Use conditional forecast paths block to give the list of constrained endogenous and their constrained future path Option controlled varexo is used to specify the structural shocks which will be matched to generate the constrained path Use plot conditional forecast to graph the results Options parameter set calibration prior mode prior mean posterio
101. at is ignored when computing bounds for the parameters Default 1e 32 load_mh_file Tells Dynare to add to previous Metropolis Hastings simulations instead of starting from scratch Shouldn t be used together with mh_recover optim NAME VALUE A list of NAME and VALUE pairs Can be used to set options for the optimization routines The set of available options depends on the selected optimization routine ie on the value of option mode compute page 55 1 3 7 Available options are given in the documentation of the MATLAB op timization toolbox or in Octave s documentation 4 Available options are MaxIter Maximum number of iterations Default 1000 NumgradAlgorithm Possible values are 2 3 and 5 respectively corresponding to the two three and five points formula used to compute the gradient of the objective function see Abramowitz and Stegun 1964 Values 13 and 15 are more experimental If perturbations on the right and the left increase the value of the objective function we minimize this function then we force the corresponding element of the gradient to be zero The idea is to temporarily reduce the size of the op timization problem Default 2 NumgradEpsilon Size of the perturbation used to compute numerically the gradient of the objective function Default 1e 6 TolFun Stopping criteria Default 1e 7 gt InitialInverseHessian Initial approximation for the inverse of the H
102. ate space nothing is shown in the output of stoch_simul and forecast will compute a simulation conditional on initial conditions and future information Here is an example varexo det tau varexo e shocks var e stderr 0 01 var tau periods 1 9 values 0 15 end stoch_simul irf 0 forecast mshocks Block The purpose of this block is similar to that of the shocks block for deterministic shocks except that the numeric values given will be interpreted in a multiplicative way For example if a value of 1 05 is given as shock value for some exogenous at some date it means 5 above its steady state value as given by the last initval or endval block The syntax is the same than shocks in a deterministic context This command is only meaningful in two situations e on exogenous variables with a non zero steady state in a deterministic setup e on deterministic exogenous variables with a non zero steady state in a stochastic setup Sigma_e Special variable Warning Chapter 4 The Model file 30 The use of this special variable is deprecated and is strongly discouraged You should use a shocks block instead Description This special variable specifies directly the covariance matrix of the stochastic shocks as an upper or lower triangular matrix Dynare builds the corresponding symmetric matrix Each row of the triangular matrix except the last one must be terminated by a semi colon For a given e
103. ates the valid name of a server e g localhost server cepremap org or an IP address DRIVE NAME Indicates a valid drive name in Windows without the trailing colon e g C PATH Indicates a valid path in the underlying operating system e g home user dynare matlab PATH_AND_FILE Indicates a valid path to a file in the underlying operating system e g usr local MATLAB R2010b bin matlab BOOLEAN Is true or false 5 1 Dynare Configuration This section explains how to configure Dynare for general processing Currently there is only one option available hooks Configuration block Description The hooks block can be used to specify configuration options that will be used when running Dynare Options GlobalInitFile PATH AND FILE The location of the global initialization file to be run at the end of global initialization m Chapter 5 The Configuration File 107 Example hooks GlobalInitFile home usern dynare myInitFile m 5 2 Parallel Configuration This section explains how to configure Dynare for parallelizing some tasks which require very little inter process communication The parallelization is done by running several MATLAB or Octave processes either on local or on remote machines Communication between master and slave processes are done through SMB on Windows and SSH on UNIX Input and output data and also some short status messages are exchanged through network filesystems Currently t
104. ations with a period of length ranging between hf high frequency to If low frequency using a symmetric moving average smoother with 2K 1 points so that K observations at the beginning and at the end of the sample are lost in the computation of the filter T he default value for hf is 6 for If is 32 and for K is 12 Example Simulate a component model stochastic trend deterministic trend and a stationary autoregressive process e 2 randn 200 1 u randn 200 1 stochastic trend cumsum e deterministic trend 1 transpose 1 200 x 7 zeros 200 1 for i 2 200 x i 75 x i 1 e i end y x stochastic trend deterministic trend Instantiates time series objects tsO dseries y 1950Q1 tsi dseries x 1950Q1 stationary component Apply the Baxter King filter ts2 ts0 baxter_king_filter Plot the filtered time series plot tsi ts2 dates data k 4 Plot of the stationary component hold on plot ts2 data r 4 Plot of the filtered y hold off axis tight id get gca XTick set gca XTickLabel strings ts dates id Chapter 6 Time Series error flag message B The previous code should produce something like 0 6F 04fF 0 2 f 0 8 F I I Stationary component of y Filtered y 11 1 1 1967Q4 1972Q4 1977Q4 1 1962Q4 L 1957Q4 check A L 1982Q4 1 1987Q4 L 1992Q4
105. ault 0 5 Example See Section 4 7 Initial and terminal conditions page 22 After computation the steady state is available in the following variable oo Steady state MATLAB Octave variable Contains the computed steady state Endogenous variables are ordered in order of declaration used in var command which is also the order used in M_ endo_names homotopy_setup Block Description This block is used to declare initial and final values when using a homotopy method It is used in conjunction with the option homotopy mode of the steady command The idea of homotopy also called divide and conquer by some authors is to subdivide the problem of finding the steady state into smaller problems It assumes that you know how to compute the steady state for a given set of parameters and it helps you finding the steady state for another set of parameters by incrementally moving from one to another set of parameters Chapter 4 The Model file 33 The purpose of the homotopy_setup block is to declare the final and possibly also the initial values for the parameters or exogenous that will be changed during the homotopy It should contain lines of the form VARIABLE NAME EXPRESSION EXPRESSION This syntax specifies the initial and final values of a given parameter exogenous There is an alternative syntax VARIABLE NAME EXPRESSION Here only the final value is specified for a given parameter exogenous the initial value is
106. ble 2 Barbouille 1Y 1 1 1 Chapter 6 Time Series 138 T N size Al dim dseries Overloads the Matlab Octave s size function Returns the number of observations in dseries object A ie A nobs and the number of variables ie A vobs If a second input argument is passed the size function returns the number of observations if dim 1 or the number of variables if dim 2 for all other values of dim an error is issued Example gt gt tsO dseries ones 1 3 gt gt ts0 size B tex rename 4 name newtexname dseries Redefines the tex name of variable name to newtexname in dseries object A Returns a dseries object B uminus 4 dseries Overloads uminus unary minus for dseries object Example gt gt tsO dseries 1 tsO is a dseries object Variable_1 1Y 1 gt gt tsi ts0 tsi is a dseries object Variable 1 1Y 1 D vertcat A B dseries Overloads the vertcat Matlab Octave method for dseries objects This method is used to append more observations to a dseries object Returns a dseries object D containing the variables in dseries objects passed as inputs All the input arguments must be dseries objects with the same variables defined on different time ranges Example gt gt tsO dseries rand 2 2 1950Q1 nifnif noufnouf gt gt tsi dseries rand 2 2 1950Q3 nifnif noufnouf gt gt ts2 ts0 tsi
107. c ele vehebeis duos demo 133 MS_COMpUte mdd eris terrce tarp En een SEREN 94 ms_compute_probabilities 94 ms_estimation 90 MSL OTECAST 24 2er de wh da wns en un due MERE NUN 96 IS EE oriieerodewe ee Dicer eid AP aie DIS ten acai 95 ms simulation i cd epePUOPUP ERR QCPODE 93 ms_variance_decomposition 96 IiShOCES sis Si ar eaoat tuae sine ROSEO RU ste alee aon 3268 29 lupi ROREM 134 HA ne dents he dent wade ox desde einen 14 n MI p 118 134 MOLMCOL 0 sydd e Ern wind bane Riana hd icu bunte 17 normpdf 5 55 pirates arcade oor ET Na 17 O observation_trends 49 optim weights ere ebneri eee eee resa 76 OST E E EE E ET EE E andhaeba ad a T5 OS paramS cecee i tesehk se AR ODD Fa dur 76 parameters ass denis sr Rad ER Mettre 12 PerTOdS suce ses als oe ee nens ai aAa E nTa ais 30 planner_objective 79 PLOCs UM 134 plot conditional forecast 73 PUS Lens ed patag nini NEE ae vas seen 118 135 POP ss 52e de Chae eee eee Re Cie 118 135 predetermined_variables 13 print bytecode dynamic model 3T print bytecode static model 3T 153 Q CDU MNT TRO ERE 136 iau T E 136 R ramsey model rem Meer EORR ERES UT ramsey policy sce otic rantino ETE nET bokeh eed 77 rename sis de de ead soins poe
108. ce decomposition page 45 The variance decomposition is only conducted if theoretical moments are requested i e using the periods 0 option In case of order 2 Dynare provides a second order accurate approximation to the true second moments based on the linear terms of the second order solution see Kim Kim Schaumburg and Sims 2008 Note that the unconditional variance decomposition i e at horizon infinity is automatically conducted if theoretical moments are requested see oo variance decomposition page 45 pruning Discard higher order terms when iteratively computing simulations of the solution At second order Dynare uses the algorithm of Kim Kim Schaumburg and Sims 2008 while at third order its generalization by Andreasen Fern ndez Villaverde and Rubio Ramirez 2013 is used partial_information Computes the solution of the model under partial information along the lines of Pearlman Currie and Levine 1986 Agents are supposed to observe only some Chapter 4 The Model file 43 variables of the economy The set of observed variables is declared using the varobs command Note that if varobs is not present or contains all endogenous variables then this is the full information case and this option has no effect More references can be found at http www dynare org DynareWiki PartialInformation sylvester OPTION Determines the algorithm used to solve the Sylvester equation for block decomposed model Possible va
109. cedure These variables must be available in the data file see estimation cmd page 52 Alternatively this command is also used in conjunction with the partial information option of stoch simul for declaring the set of observed variables when solving the model under partial information Only one instance of varobs is allowed in a model file If one needs to declare observed variables in a loop the macro processor can be used as shown in the second example below Simple example varobs C y rr Example with a loop varobs for co in countries GDP_ co endfor 3 observation trends Block Description This block specifies linear trends for observed variables as functions of model parameters Each line inside of the block should be of the form VARIABLE_NAME EXPRESSION In most cases variables shouldn t be centered when observation_trends is used Example observation_trends Y eta P mu eta end estimated params Block Description This block lists all parameters to be estimated and specifies bounds and priors as necessary Each line corresponds to an estimated parameter In a maximum likelihood estimation each line follows this syntax stderr VARIABLE NAME corr VARIABLE NAME 1 VARIABLE NAME 2 PARAMETER NAMEN INITIAL VALUE LOWER BOUND UPPER BOUND In a Bayesian estimation each line follows this syntax stderr VARIABLE NAME corr VARIABLE NAME 1 VARIABLE NAME 2 PARAMETER
110. crashed prematurely Shouldn t be used together with load mh file mh mode INTEGER mode file FILENAME Name of the file containing previous value for the mode When computing the mode Dynare stores the mode xparami and the hessian hh only if cova_compute 1 in a file called MUDEL FILENAME mode mat mode compute INTEGER FUNCTION NAME Specifies the optimizer for the mode computation 0 The mode isn t computed When mode file option is specified the mode is simply read from that file When mode file option is not specified Dynare reports the value of the log posterior log likelihood evaluated at the initial value of the parameters When mode file option is not specified and there is no estimated params block but the smoother option is used it is a roundabout way to compute the smoothed value of the variables of a model with calibrated parameters 1 Uses fmincon optimization routine available under MATLAB if the optimization toolbox is installed not available under Octave 2 Value no longer used 3 Uses fminunc optimization routine available under MATLAB if the optimization toolbox is installed available under Octave if the optim package from Octave Forge is installed 4 Uses Chris Sims s csminwel 5 Uses Marco Ratto s newrat This value is not compatible with non linear filters or DSGE VAR models 6 Uses a Monte Carlo based optimization routine see Dynare wiki for more details 7 Uses fminsearch
111. create init Do not create an initialization file for the model Passing this option will cause the Initialization Options to be ignored Further the model will be generated from the output files associated with the previous estimation run i e est final lt file_tag gt out est intermediate file tag out or init file tag dat searched for in sequential order This functionality can be useful for continuing a previous estimation run to ensure convergence was reached or for reusing an initial ization file NB If this option is not passed the files from the previous estimation run will be overwritten Default off i e create initialization file Initialization Options coefficients prior hyperparameters DOUBLE1 DOUBLE2 DOUBLE3 DOUBLE4 DOUBLES DOUBLE6 Sets the hyper parameters for the model The six elements of the argument vector have the following interpretations Position Interpretation 1 Overall tightness for A and A 2 Relative tightness for A 3 Relative tightness for the constant term 4 Tightness on lag decay range 1 2 1 5 a faster decay produces better inflation process 5 Weight on nvar sums of coeffs dummy observations unit roots 6 Weight on single dummy initial observation including constant Default 1 0 1 0 0 1 1 2 1 0 1 0 freq INTEGER monthly quarterly yearly Frequency of the data e g monthly 12 Default 4 initial year INTEGER The first year of data Default none Chapter
112. d during the steady state computation You would then write a first mod file which computes the steady state and saves the result of the computation at the end of the file using save params and steady state In a second file designed to perform the actual simulations you would use load params and Steady state just after your variable declarations in order to load the steady state previously computed including the parameters which had been endogeneized during the steady state com putation The need for two separate mod files arises from the fact that the variable declarations differ between the files for steady state calibration and for simulation the set of endogenous and parameters differ between the two this leads to different var and parameters statements Also note that you can take advantage of the include directive to share the model equations between the two files see Section 4 20 Macro processing language page 98 load params and steady state FILENAME Command For all parameters endogenous and exogenous variables loads their value from a file created with save params and steady state e for parameters their value will be initialized as if they had been calibrated in the mod file e for endogenous and exogenous their value will be initialized as they would have been from an initval block This function is used in conjunction with save params and steady state see the documen tation of that funct
113. d smoothed variables for the multi variate normal Monte Carlo sample generated when doing RMSE analysis pprior 0 and ppost 0 Figure files lt mod_file gt _rmse_ fig store results for the RMSE analysis mod file rmse prior fig save results for the analysis using prior Monte Carlo samples mod file rmse mc fig save results for the analysis using multivariate normal Monte Carlo samples mod file rmse post fig save results for the analysis using Metropolis posterior samples The following types of figures are saved we show prior sample to fix ideas but the same conventions are used for multivariate normal and posterior mod file rmse prior fig for each parameter plots the cdfs corresponding to the best 1096 RMSEs of each observed series mod file rmse prior dens fig for each parameter plots the pdfs corresponding to the best 10 RMESs of each observed series mod file rmse prior name of observedseries gt _corr_ fig for each observed series plots the bi dimensional projections of samples with the best 10 RMSEs when the correlation is significant mod file rmse prior lnlik fig for each observed series plots in red the cdf of the log likelihood corresponding to the best 10 RMSEs in green the cdf of the rest of the sample and in blue the cdf of the full sample this allows one to see the presence of some idiosyncratic behavior mod file rmse prior lnpost fig for each
114. dseries The dseries that provides the data for the graph Default none figname STRING The name to use when saving this figure Default tempname tex figDirName STRING The name of the folder in which to store this figure Default tmpFigDir graphSize NUMERICAL VECTOR The width and height to be passed to the third and fourth elements of the array passed to the Position option of Matlab s figure command passed as a vector of size 2 Default Matlab sets width and height showGrid BOOLEAN Whether or not to display the minor grid on the graph Default true showLegend BOOLEAN Whether or not to display the legend Default false Chapter 7 Reporting 142 showLegendBox BOOLEAN Whether or not to display a box around the legend Default false legendLocation North South East West NorthEast SouthEast NorthWest SouthWest NorthOutside SouthOutside EastOutside WestOutside NorthEastOutside SouthEastOutside NorthWestOutside SouthWest utside Best BestOutside Where to place the legend in the graph NB some of these are not available under Octave Default SouthEast legendOrientation vertical horizontal Orientation of the legend Default horizontal legendFontSize DOUBLE The font size for legend entries Default 8 seriesToUse CELL_ARRAY_STRINGS The names of the seri
115. e models to be compared do not need to be nested However as the computation of posterior odds ratios is a Bayesian technique the comparison of models estimated with maximum likelihood is not supported Example model comparison my model 0 7 alt model 0 3 This example attributes a 70 prior over my model and 30 prior over alt model shock decomposition VARIABLE NAME Command shock decomposition OPTIONS VARIABLE NAME Command Description This command computes and displays shock decomposition according to the model for a given sample Note that this command must come after either estimation in case of an estimated model or Stoch simul in case of a calibrated model Options Chapter 4 The Model file 68 parameter_set PARAMETER_SET Specify the parameter set to use for running the smoother The PARAM ETER SET can take one of the following five values calibration prior mode prior mean posterior mode posterior mean posterior median De fault value posterior mean if Metropolis has been run else posterior mode datafile FILENAME See datafile page 53 Useful when computing the shock decomposition on a cali brated model The results are stored in the field oo shock decomposition which is a three dimensional array The first dimension contains the endogenous variables for which the shock decomposition has been requested The second dimension stores in the first M exo nbr columns the con
116. e Ea RAE 68 bvar forecast less uebep Rp eue 73 C Calib_smoother 68 change TY Pes odvincediada jede xu pude e eut 12 Check ice sexu sin nanas ns OPE amet 36 123 Cono Pr T13 152 compile on Report sise wb dr ER 144 conditional forecast 71 conditional_forecast_paths 73 GCOS ab 25 aide te mena rene mers nine E ad 16 CUMSUM conie Bs acne Re Saxe race aimes 123 D det_cond_forecast 74 discretionary_policy 78 double 2521 14 Ainsi delta qu 113 dsample Lb 2b eoni insien a insider 30 dynare 2 etece3ceuebicud sek DRE LE dede see 6 dynare_sensitivity 82 dynare version ss re err saone eee 105 dynaSave sus ads exe f ad EVODeLOEUURROPRPI E RU 97 dynatype siennes sense sense 97 E endyal fssusense eee donnee dere di etes 24 Te ACH de p MD RR UR 114 124 a EM TR Mm 17 estimated params cscs chiens re E ene e bees 49 estimated_params_bounds 52 estimated_params_init 51 eSt3matl nDz lites ee E EEE EEEE 52 ORD it cute E E E Ed atus Diane 16 124 EXPECTATION ses tramen Ries m N ee 6 15 extended path ss issen G more hard niet 45 external_function 17 nier PUEDE 125 F flip plan e idum e RIT tase eee eke PT ees 74 forecast ue beue ins aad deck YR arque 69 G
117. e and number_of_states must be passed Default none duration DOUBLE inf The duration of the state or states Default none Chapter 4 The Model file 88 svar OPTIONS Command Description Each Makov chain can control the switching of a set of parameters We allow the parameters to be divided equation by equation and by variance or slope and intercept Options coefficients Specifies that only the slope and intercept in the given equations are controlled by the given chain One but not both of coefficients or variances must appear Default none variances Specifies that only variances in the given equations are controlled by the given chain One but not both of coefficients or variances must appear Default none equations Defines the equation controlled by the given chain If not specified then all equations are controlled by chain Default none chain INTEGER Specifies a Markov chain defined by markov_switching page 87 Default none sbvar OPTIONS Command Description To be documented For now see the wiki http www dynare org DynareWiki Sbvar ptions Options datafile freq initial year initial subperiod final year final subperiod data vlist vlistlog vlistper restriction fname nlags cross restrictions contemp reduced form real pseudo forecast no bayesian prior dummy obs nstates indxscalesstates alpha Chapter 4 The Model file 89 beta gsig2 lmdm
118. e attributed to the equation appears currently on the left hand side and where no forward looking endogenous variables appear The block has the form yj fj Yt Yi 1 Ye x EVALUATE BACKWARD The block contains only equations where endogenous variable attributed to the equation appears currently on the left hand side and where no backward looking endogenous variables appear The block has the form yj fj Yr yiii Yt k SOLVE FORWARD x The block contains only equations where endogenous variable attributed to the equa tion does not appear currently on the left hand side and where no forward looking endogenous variables appear The block has the form 9 Yj Yt Ye 1 Yi x 0 x is equal to SIMPLE if the block has only one equation If several equation appears in the block x is equal to COMPLETE SOLVE FORWARD x The block contains only equations where endogenous variable attributed to the equa tion does not appear currently on the left hand side and where no backward looking endogenous variables appear The block has the form g y 4 Ye Yer Yt k 0 x is equal to SIMPLE if the block has only one equation If several equation appears in the block x is equal to COMPLETE SOLVE TWO BOUNDARIES x The block contains equations depending on both forward and backward variables The block looks like 9 Yj Ye Vii Yt k Yes Yt 1 sss Vk 0 x is equal to SIMPLE if the
119. e can easily create subsamples from a dseries object using the overloaded parenthesis operator If ds is a dseries object with T observations and d is a dates object with S T elements such that min d is not smaller than the date associated to the first observation in ds and max d is not greater than the date associated to the last observation then ds d instantiates a new dseries object containing the subsample defined by d list of the available methods by alphabetical order is given below A B align A B dseries If dseries objects A and B are defined on different time ranges this function extends A and or B with NaNs so that they are defined on the same time range Note that both dseries objects must have the same frequency Example gt gt tsO gt gt tsi gt gt tsO gt gt tsO tsO is 200001 200002 200003 200004 2001Q1 2001Q2 gt gt tsi tsi is 2000Q1 2000Q2 200003 200004 2001Q1 2001Q2 dseries rand 5 1 dates 2000Q1 2000Q1 gt 200101 dseries rand 3 1 dates 2000Q4 2000Q4 gt 2001Q2 tsi align tsO ts1 2000Q1 gt 200192 dseries object Variable_1 0 81472 0 90579 0 12699 0 91338 0 63236 NaN dseries object Variable 1 NaN NaN Chapter 6 Time Series 122 B baxter_king_filter A hf 1f K dseries Implementation of the Baxter and King 1999 band pass filter for dseries objects This filter isolates business cycle fluctu
120. e integer scalars in I must take values between 1 and A length 1 and refers to A s column numbers The dseries objects and B need not to be defined over the same time ranges but it is assumed that they have common frequency Example gt gt tsO dseries ones 2 4 1950Q1 Sly Gobbo Sneaky Stealthy gt gt tsi dseries pi ones 2 1 1950Q1 Noddy gt gt ts2 tsO insert ts1 3 ts2 is a dseries object Sly Gobbo Noddy Sneaky Stealthy 195001 1 1 3 1416 1 4 195002 1 1 3 1416 1 1 gt gt ts3 dseries pi ones 2 1 sqrt pi ones 2 1 1950Q1 Noddy Tessie Bear gt gt ts4 tsO insert tsi 3 4 ts4 is a dseries object Sly Gobbo Noddy Sneaky Tessie Bear Stealthy 1950Q1 1 1 3 1416 1 1 7725 1 1950Q2 1 1 3 1416 1 1 7725 1 B isempty A dseries Overloads the Matlab octave s isempty function Returns 1 if dseries object A is empty O otherwise Chapter 6 Time Series C isequal A B Overloads the Matlab octave s isequal function Returns 1 if dseries objects and B are identical O otherwise B lag Al pl Returns lagged time series Default value of p the number of lags is 1 Examples gt gt ts0 tsO is 1950Q1 1950Q2 1950Q3 195004 gt gt tsi tsi is 1950Q1 1950Q2 1950Q3 195004 gt gt ts2 ts2 is 1950Q1 1950Q2 1950Q3 195004 dser
121. e mrdivide operator will compute for each couple t n with 1 lt t T4 and 1 n Nag C data t n A data t n B data t n If Ng is equal to 1 and Ny gt 1 the smaller dseries object B is broadcast across the larger dseries A so that they have compatible shapes In this case the mrdivides operator will divide each variable defined in A by the variable in B observation per observation If B is a double scalar then mrdivide will divide all the observations variables in A by B If B is a row vector of length N4 then mrdivide will divide all the observations of variable i by B i for i 1 N4 If B is a column vector of length TA then mrdivide will perform a division of all the variables by B element by element Example gt gt tsO dseries rand 3 2 tsO is a dseries object Variable 1 Variable 2 1Y 0 72918 0 90307 2Y 0 93756 0 21819 3Y 0 51725 0 87322 Chapter 6 Time Series 134 C bbb gt gt tsi tsO Variable 27 gt gt ts0 tsi ans is a dseries object divide Variable_1 Variable_2 divide Variable 2 Variable 2 1Y 0 80745 ka 2Y 4 2969 1 3Y 0 59235 1 mtimes A B dseries Overloads the mtimes operator for dseries objects and the Hadammard product the Matlab Octave operator If both A and B are dseries objects they do not need to be defined over the same time ranges If and B are dseries objects with T4 and Tg ob servations and N4 and
122. e user provides an analytical solution for the steady state in steady_state_model block or ina _steadystate m file In this case it is necessary to provide a steady state solution CONDITIONAL on the value of the instruments in the optimal policy problem and declared with option instruments Note that choosing the instruments is partly a matter of interpretation and you can choose instruments that are handy from a mathematical point of view but different from the instruments you would refer to in the analysis of the paper A typical example is choosing inflation or nominal interest rate as an instrument discretionary_policy VARIABLE NAME Command discretionary policy OPTIONS VARIABLE NAME Command Description This command computes an approximation of the optimal policy under discretion The algo rithm implemented is essentially an LQ solver and is described by Dennis 2007 You should ensure that your model is linear and your objective is quadratic Also you should set the linear option of the model block Options This command accepts the same options than ramsey policy plus discretionary tol NON NEGATIVE DOUBLE Sets the tolerance level used to assess convergence of the solution algorithm Default 1e 7 maxit INTEGER Maximum number of iterations Default 3000 Chapter 4 The Model file 79 planner objective MODEL EXPRESSION Command This command declares the policy maker objective for use with r
123. ed by steady the steady state computation will still be triggered by subsequent commands stoch simul estimation It is not necessary to declare O as initial value for exogenous stochastic variables since it is the only possible value This steady state will be used as the initial condition at all the periods preceeding the first simulation period for the two possible types of simulations in stochastic mode e in stoch simul if the periods options is specified e in forecast in this case note that it is still possible to modify some of these initial values with histval Options all values required Issues an error and stops processing the mod file if there is at least one endogenous or exogenous variable that has not been set in the initval block Example initval c 1 2 k 12 kil Chapter 4 The Model file 24 end steady endval Block endval OPTIONS Block Description This block is terminated by end and contains lines of the form VARIABLE NAME EXPRESSION The endval block makes only sense in a deterministic model and serves two purposes First it sets the terminal conditions for all the periods succeeding the last simulation period Second it provides initial guess values at all the simulation dates for the non linear solver implemented in simul For this last reason it necessary to provide values for all the endogenous variables in an endval block even though theoretically termi
124. ed to the model block it cannot be used outside A model local variable declaration looks like VARIABLE NAME MODEL EXPRESSION Options linear Declares the model as being linear It spares oneself from having to declare initial values for computing the steady state of a stationary linear model This options can t be used with non linear models it will NOT trigger linearization of the model use dll Instructs the preprocessor to create dynamic loadable libraries DLL containing the model equations and derivatives instead of writing those in M files You need a working compilation environment i e a working mex command see Section 2 1 Software requirements page 3 for more details Using this option can result in faster simulations or estimations at the expense of some initial compilation time block Perform the block decomposition of the model and exploit it in computations steady state deterministic simulation stochastic simulation with first order ap proximation and estimation See Dynare wiki for details on the algorithms used in deterministic simulation and steady state computation bytecode Instead of M files use a bytecode representation of the model i e a binary file containing a compact representation of all the equations cutoff DOUBLE Threshold under which a jacobian element is considered as null during the model normalization Only available with option block Default 1e 15 mfs INTEGER Controls the h
125. ee Section 4 14 Estimation page 48 qz zero threshold DOUBLE See az zero threshold page 36 replic INTEGER Number of simulated series used to compute the IRFs Default 1 if order 1 and 50 otherwise simul replic INTEGER Number of series to simulate when empirical moments are requested i e periods 0 Note that if this option is greater than 1 the additional series will not be used for computing the empirical moments but will simply be saved in binary form to the file FILENAME simul Default 1 solve algo INTEGER See solve_algo page 31 for the possible values and their meaning aim solver Use the Anderson Moore Algorithm AIM to compute the decision rules instead of using Dynare s default method based on a generalized Schur decomposition This option is only valid for first order approximation See AIM website for more details on the algorithm conditional variance decomposition INTEGER See below conditional variance decomposition INTEGER1 INTEGER2 See below conditional variance decomposition INTEGER1 INTEGER2 Computes a conditional variance decomposition for the specified period s The periods must be strictly positive Conditional variances are given by var y 4 t For period 1 the conditional variance decomposition provides the decomposition of the effects of shocks upon impact The results are stored in oo conditional variance decomposition see oo conditional varian
126. el file 39 5 Use a Newton algorithm with a sparse Gaussian elimination SPE solver at each iteration requires bytecode option see Section 4 5 Model declaration page 18 6 Use the historical algorithm proposed in Juillard 1996 it is slower than stack solve algo 0 but may be less memory consuming on big models not available with bytecode and or block options markowitz DOUBLE Value of the Markowitz criterion used to select the pivot Only used when stack_ solve algo 5 Default 0 5 minimal_solving_periods INTEGER Specify the minimal number of periods where the model has to be solved before using a constant set of operations for the remaining periods Only used when stack_ solve algo 5 Default 1 datafile FILENAME If the variables of the model are not constant over time their initial values stored in a text file could be loaded using that option as initial values before a deterministic simulation Output The simulated endogenous variables are available in global matrix oo endo simul oo endo simul MATLAB Octave variable This variable stores the result of a deterministic simulation computed by simul or of a stochas tic simulation computed by stoch simul with the periods option or by extended path The variables are arranged row by row in order of declaration as in M endo names Note that this variable also contains initial and terminal conditions so it has more columns than the va
127. endogenous variables namendo versus lagged endogenous variables namlagendo suffix log indicates the results for log transformed entries e mod file redform endo name vs shocks fig shows bar charts of the sensitivity in dices for the ten most important parameters driving the reduced form coefficients of the selected endogenous variables namendo versus exogenous variables namexo suffix log indicates the results for log transformed entries e mod file redform GSA log fig shows bar chart of all sensitivity indices for each pa rameter this allows one to notice parameters that have a minor effect for any of the reduced form coefficients Detailed results of the analyses are shown in the subfolder mod file GSA redform stab where the detailed results of the estimation of the single functional relationships between parameters 0 and reduced form coefficient are stored in separate directories named as e lt namendo gt _vs_ lt namlagendo gt for the entries of the transition matrix e namendo vs namexo for entries of the matrix of the shocks Moreover analyses for log transformed entries are denoted with the following suffixes y denotes the generic reduced form coefficient e log y log y e minuslog y log y e logsquared y log y for symmetric fat tails e logskew y log y A for asymmetric fat tails The optimal type of transformation is automatically selected without the need of
128. eries Analysis by State Space Methods Second Revised Edition Oxford University Press Fair Ray and John Taylor 1983 Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectation Models Econometrica 51 1169 1185 Fern ndez Villaverde Jes s and Juan Rubio Ram rez 2004 Comparing Dynamic Equilib rium Economies to Data A Bayesian Approach Journal of Econometrics 123 153 187 Fern ndez Villaverde Jes s and Juan Rubio Ram rez 2005 Estimating Dynamic Equilib rium Economies Linear versus Nonlinear Likelihood Journal of Applied Econometrics 20 891 910 Fern ndez Villaverde Jestis 2010 The econometrics of DSGE models SERIEs 1 3 49 Geweke John 1992 Evaluating the accuracy of sampling based approaches to the calcu lation of posterior moments in J O Berger J M Bernardo A P Dawid and A F M Smith eds Proceedings of the Fourth Valencia International Meeting on Bayesian Statistics pp 169 194 Oxford University Press Geweke John 1999 Using simulation methods for Bayesian econometric models Inference development and communication Econometric Reviews 18 1 1 73 Chapter 10 Bibliography 151 e Ireland Peter 2004 A Method for Taking Models to the Data Journal of Economic Dynamics and Control 28 1205 26 e Iskrev Nikolay 2010 Local identification in DSGE models Journal of Monetary Eco nomics 57 2 189 202 e Judd Kenneth 1996 Approximat
129. ers are automatically created Options This command accepts the following options planner_discount EXPRESSION Declares the discount factor of the central planner Default 1 0 instruments VARIABLE_NAME Declares instrument variables for the computation of the steady state under optimal policy Requires a steady_state_model block or a _steadystate m file See below Steady state Dynare takes advantage of the fact that the Lagrange multipliers appear linearly in the equations of the steady state of the model under optimal policy Nevertheless it is in general very difficult to compute the steady state with simply a numerical guess in initval for the endogenous variables It greatly facilitates the computation if the user provides an analytical solution for the steady state in steady state model block orina _steadystate m file In this case it is necessary to provide a steady state solution CONDITIONAL on the value of the instruments in the optimal policy problem and declared with option instruments Note that choosing the instruments is partly a matter of interpretation and you can choose instruments that are handy from a mathematical point of view but different from the instruments you would refer to in the analysis of the paper A typical example is choosing inflation or nominal interest rate as an instrument ramsey policy VARIABLE NAME Command ramsey policy OPTIONS VARIABLE NAME Command D
130. es are unix or windows There is no default value Example node Name n1 ComputerName localhost CPUnbr 1 node Name n2 ComputerName dynserv cepremap org CPUnbr 5 UserName usern RemoteDirectory home usern Remote DynarePath home usern dynare matlab MatlabOctavePath matlab node Name n3 ComputerName dynserv dynare org Port 3333 CPUnbr 2 4 UserName usern RemoteDirectory home usern Remote DynarePath home usern dynare matlab MatlabOctavePath matlab Chapter 6 Time Series 110 6 Time Series Dynare provides a Matlab Octave class for handling time series data which is based on a class for handling dates Dynare also provides a new type for dates so that the basic user do not have to worry about class and methods for dates Below you will first find the class and methods used for creating and dealing with dates and then the class used for using time series 6 1 Dates 6 1 1 dates in a mod file Dynare understands dates in a mod file Users can declare annual quarterly monthly or weekly dates using the following syntax 1990Y 1990Q3 1990M11 1990W49 Behind the scene Dynare s preprocessor translates these expressions into instantiations of the Matlab Octave s class dates described below Basic operations can be performed on dates plus binary operator An integer scalar interpreted as a number of periods can be added to a date For instance if a 195001
131. es contained in the dseries provided to the data page 141 option If empty use all series provided to data page 141 option Default empty shade dates The date range showing the portion of the graph that should be shaded Default none shadeColor MATLAB_COLOR_NAME The color to use in the shaded portion of the graph Default green shadeOpacity DOUBLE The opacity of the shaded area must be in 0 1 Default 2 title STRING Title for the graph Default none xlabel STRING The x axis label Default none ylabel STRING The y axis label Default none xrange dates The boundary on the x axis to display in the graph Default all xTicks NUMERICAL_VECTOR Used only in conjunction with xTickLabels page 142 this option denotes the numerical position of the label along the x axis The positions begin at 1 Default set by Matlab Octave xTickLabels CELL_ARRAY_STRINGS The labels to be mapped to the ticks provided by xTicks page 142 Default the dates of the dseries yrange NUMERICAL_VECTOR The boundary on the y axis to display in the graph represented as a NUMERICAL_ VECTOR of size 2 with the first entry less than the second entry Default all showZeroline BOOLEAN Display a solid black line at y 0 Default false addTable data showHlines precision range seriesToUse title titleSize Method on Report vlineAfter vlineAfterEndOfPeriod show Vlines Adds a Table to a Section Options Chapter
132. es object as he would extract some elements from a vector in Matlab Octave Let a 1950Q1 1951Q1 be a dates object then a 1 1950Q1 returns 1 a end 1951Q1 returns 1 and a end 1 end selects the two last elements of a by instantiating the dates object 1950Q4 1951Q1 RemarkDynare substitutes any occurrence of dates in the mod file into an instantiation of the dates class regardless of the context For instance d 195001 will be translated as d dates 1950Q1 This automatic substitution can lead to a crash if a date is defined in a string Typically if the user wants to display a date disp Initial period is 1950Q1 Dynare will translate this as disp Initial period is dates 1950Q1 which will lead to crash because this expression is illegal in Matlab For this situation Dynare provides the escape parameter The following expression disp C Initial period is 1950Q1 will be translated as disp Initial period is 1950Q1 in the generated MATLAB script 6 1 2 dates class The dates class has three members freq an integer equal to 1 4 12 or 52 resp for annual quarterly monthly or weekly dates ndat an integer scalar the number of declared dates in the object time a ndat 2 array of integers the years are stored in the first column the subperiods 1 for annual dates 1 4 for quarterly dates 1 12 for monthly dates and 1 52 for weekly dates are stored in the second column
133. escription This command computes the first order approximation of the policy that maximizes the policy maker objective function submitted to the constraints provided by the equilibrium path of the economy The planner objective must be declared with the planner objective command Chapter 4 The Model file 78 See Section 4 6 Auxiliary variables page 21 for an explanation of how this operator is handled internally and how this affects the output Options This command accepts all options of stoch_simul plus planner discount EXPRESSION Declares the discount factor of the central planner Default 1 0 instruments VARIABLE NAME Declares instrument variables for the computation of the steady state under optimal policy Requires a steady state model block or a steadystate m file See below Note that only first order approximation is available i e order 1 must be specified Output This command generates all the output variables of stoch_simul In addition it stores the value of planner objective function under Ramsey policy in oo planner objective value Steady state Dynare takes advantage of the fact that the Lagrange multipliers appear linearly in the equations of the steady state of the model under optimal policy Nevertheless it is in general very difficult to compute the steady state with simply a numerical guess in initval for the endogenous variables It greatly facilitates the computation if th
134. essian matrix of the posterior kernel or likelihood Obviously this ap proximation has to be a square positive definite and sym metric matrix Default 1e 4 eye nx where nx is the number of parameters to be estimated 6 Available options are gt NumberOfMh Number of MCMC run sequentially Default 3 ncov mh Number of iterations used for updating the covariance ma trix of the jumping distribution Default 20000 nscale mh Maximum number of iterations used for adjusting the scale parameter of the jumping distribution 200000 nclimb Number of iterations in the last MCMC climbing mode Chapter 4 The Model file 10 58 InitialCovarianceMatrix Initial covariance matrix of the jumping distribution De fault is previous if option mode file is used prior otherwise gt AcceptanceRateTarget A real number between zero and one The scale pa rameter of the jumping distribution is adjusted so that the effective acceptance rate matches the value of option AcceptanceRateTarget Default 1 0 3 0 Available options are gt MaxIter Maximum number of iterations Default 5000 gt MaxFunEvals Maximum number of objective function evaluations No default MaxFunvEvalFactor Set MaxFunvEvals equal to MaxFunvEvalFactor times the number of estimated parameters Default 500 TolFun Tolerance parameter w r t the objective function Default 1e 4 To1X Tolerance parame
135. essor to omit line numbering information in the inter mediary mod file created after the macro processing step Useful in conjunction with savemacro when one wants that to reuse the intermediary mod file without having it cluttered by line numbering directives nolog Instructs Dynare to no create a logfile of this run in FILENAME 1og The default is to create the logfile nowarn Suppresses all warnings warn uninit Display a warning for each variable or parameter which is not initialized See Section 4 4 Parameter initialization page 18 or load params and steady state page 105 for initialization of parameters See Section 4 7 Initial and terminal con ditions page 22 or load_params_and_steady_state page 105 for initialization of endogenous and exogenous variables console Activate console mode In addition to the behavior of nodisplay Dynare will not use graphical waitbars for long computations nograph Activate the nograph option see nograph page 41 so that Dynare will not pro duce any graph nointeractive Instructs Dynare to not request user input Chapter 3 Running Dynare 8 M cygwin Tells Dynare that your MATLAB is configured for compiling MEX files with Cygwin see Section 2 1 Software requirements page 3 This option is only available under Windows and is used in conjunction with use d11 msvc Tells Dynare that your MATLAB is configured for compiling MEX files with Mi crosoft Visual C see
136. fficient and reliable way especially during estimation where the steady state has to be recomputed for every point in the parameter space Each line of this block consists of a variable either an endogenous a temporary variable or a parameter which is assigned an expression which can contain parameters exogenous at the steady state or any endogenous or temporary variable already declared above Each line therefore looks like VARIABLE NAME EXPRESSION Note that it is also possible to assign several variables at the same time if the main function in the right hand side is a MATLAB Octave function returning several arguments VARIABLE_NAME VARIABLE_NAME EXPRESSION Dynare will automatically generate a steady state file of the form FILENAME_steadystate2 m using the information provided in this block Steady state file for deterministic models steady_state_model block works also with deterministic models An initval block and when necessary an endval block is used to set the value of the exogenous variables Each initval or endval block must be followed by steady to execute the function created by steady_state_ model and set the initial respectively terminal steady state Example varmPceWRkd n 1 gy obs gp_obs y dA varexo e a e_m parameters alp bet gam mst rho psi del parameter calibration dynamic model declaration shock calibration Chapter 4 The Model file 35 Steady state model dA exp gam g
137. for which to compute IRFs Default all relative irf Requests the computation of normalized IRFs in percentage of the standard error of each shock irf plot threshold DOUBLE Threshold size for plotting IRFs All IRFs for a particular variable with a maximum absolute deviation from the steady state smaller than this value are not displayed Default 1e 10 nocorr Don t print the correlation matrix printing them is the default nofunctions Don t print the coefficients of the approximated solution printing them is the de fault nomoments Don t print moments of the endogenous variables printing them is the default nograph Do not create graphs which implies that they are not saved to the disk nor dis played If this option is not used graphs will be saved to disk to the format specified by graph format option except if graph format none and displayed to screen unless nodisplay option is used nodisplay Do not display the graphs but still save them to disk unless nograph is used graph format FORMAT graph format FORMAT FORMAT Specify the file format s for graphs saved to disk Possible values are eps the default pdf fig and none under Octave only eps and none are available If the file format is set equal to none the graphs are displayed but not saved to the disk noprint Don t print anything Useful for loops print Print results opposite of noprint order INTEGER Order of Taylor
138. foreign a L_foreign 1 a end echo MACRO_EXPRESSION Macro directive Asks the preprocessor to display some message on standard output The argument must evaluate to a string error MACRO_EXPRESSION Macro directive Asks the preprocessor to display some error message on standard output and to abort The argument must evaluate to a string 4 20 3 Typical usages 4 20 3 1 Modularization The include directive can be used to split mod files into several modular components Example setup modeldesc mod Contains variable declarations model equations and shocks declarations simul mod Includes modeldesc mod calibrates parameters and runs stochastic simulations estim mod Includes modeldesc mod declares priors on parameters and runs Bayesian estimation Dynare can be called on simul mod and estim mod but it makes no sense to run it on modeldesc mod The main advantage is that it is no longer needed to manually copy paste the whole model at the beginning or changes to the model during development 4 20 3 2 Indexed sums or products The following example shows how to construct a moving average define window 2 var x MA_x model MA x 1 0 2 window 1 for i in window window x i endfor Chapter 4 The Model file 102 end After macro processing this is equivalent to var x MA_x model MA x 1 5 x 2 x 1 x 0 x 1 x 2 end 4 20 3 3 Multi cou
139. formations Note that the INIT variable can be either a dates object or a string which could be used to instantiate the same dates object dseries DATA MATRIX INITIAL DATE LIST OF NAMES dseries LIST_OF_TEX_NAMES If the data is not read from a file it can be provided via a TxN matrix as the first argument to dseries constructor with T representing the number of observations on N variables The optional second argument INITIAL_DATE can be either a dates object representing the period of the first observation or a string which would be used to instantiate a dates object Its default value is dates 1Y The optional third argument LIST OF NAMES is a N by 1 cell of strings with one entry for each variable name The default name associated with column i of DATA_MATRIX is Variable i The final argument LIST OF TEX NAMES is a N by 1 cell of strings composed of the ATFX names associated with the variables The default ATEX name associated with column i of DATA MATRIX is VariableN i Examples Chapter 6 Time Series 121 Various ways to create a dseries object In a mod file doi do2 dseries 199903 dseries filename csv do3 dseries 1 2 3 199903 var123 var_ 123 In a Matlab Octave script dseries dates 199903 dseries filename csv dseries 1 2 3 dates 1999Q3 var1i23 var_ 123 gt gt gt gt gt gt doi do2 do3 On
140. g graphLineStyle graphLineWidth 1 5 Section 2 rep rep addSection rep rep addTable title Table 1 range dates 2012Y dates 2014Y shortNames US EU longNames United States Euro Area for i 1 length shortNames rep rep addSeries data dsa GDP_ shortNames i delta dsa GDP_ shortNames i dsca GDP_ shortNames i delta delta tex_rename Delta rep rep addSeries data delta tableShowMarkers true tableAlignRight true end hh Write amp Compile Report Chapter 7 Reporting 146 rep write rep compile Chapter 8 Examples 147 8 Examples Dynare comes with a database of example mod files which are designed to show a broad range of Dynare features and are taken from academic papers for most of them You should have these files in the examples subdirectory of your distribution Here is a short list of the examples included For a more complete description please refer to the comments inside the files themselves ramst mod An elementary real business cycle RBC model simulated in a deterministic setup examplei mod example2 mod Two examples of a small RBC model in a stochastic setup presented in Collard 2001 see the file guide pdf which comes with Dynare example3 mod A small RBC model in a stochastic setup presented in Collard 2001 The ste
141. g static variables appear first then purely backward variables then mixed variables and finally purely forward variables Inside each category variables are arranged according to the declaration order Chapter 4 The Model file 47 Variable oo dr order var maps DR order to declaration order and variable oo dr inv order var contains the inverse map In other words the k th variable in the DR order corresponds to the endogenous variable numbered oo dr order var k in declaration order Conversely k th declared variable is numbered oo dr inv order var k in DR order Finally the state variables of the model are the purely backward variables and the mixed variables They are ordered in DR order when they appear in decision rules elements There are M nspred M_ npred M nboth such variables Similarly one has M nsfwrd M nfwrd M nboth and M ndynamic M nfwrd M nboth M npred 4 13 3 First order approximation The approximation has the stylized form Ye yi Ayr Bu where y is the steady state value of y and y y y The coefficients of the decision rules are stored as follows e y is stored in oo dr ys The vector rows correspond to all endogenous in the declaration order e A is stored in oo dr ghx The matrix rows correspond to all endogenous in DR order The matrix columns correspond to state variables in DR order e B is stored oo dr ghu The matrix rows correspond to all endogeno
142. he previous version of the toolbox in order to work properly the GSA toolbox no longer requires that the Dynare estimation environment is set up Sensitivity analysis results are saved locally in mod file GSA where mod file mod is the name of the DYNARE model file 4 17 1 Sampling The following binary files are produced e mod file prior mat this file stores information about the analyses performed sampling from the prior ranges i e pprior 1 and ppost 0 e mod file mc mat this file stores information about the analyses performed sampling from multivariate normal i e pprior 0 and ppost 0 e mod file post mat this file stores information about analyses performed using the Metropolis posterior sample i e ppost 1 4 17 2 Stability Mapping Figure files produced are of the form mod file prior fig and store results for stability mapping from prior Monte Carlo samples e mod file prior stab SA fig plots of the Smirnov test analyses confronting the cdf of the sample fulfilling Blanchard Kahn conditions with the cdf of the rest of the sample e mod file prior stab indet SA fig plots of the Smirnov test analyses confronting the cdf of the sample producing indeterminacy with the cdf of the original prior sample e mod file prior stab unst SA fig plots of the Smirnov test analyses confronting the cdf of the sample producing unstable explosive roots behavior with the cdf of the original prior
143. he system works only with homogenous grids only Windows or only Unix machines The following routines are currently parallelized e the Metropolis Hastings algorithm e the Metropolis Hastings diagnostics e the posterior IRFs e the prior and posterior statistics e some plotting routines Note that creating the configuration file is not enough in order to trigger parallelization of the computations you also need to specify the parallel option to the dynare command For more details and for other options related to the parallelization engine see see Section 3 1 Dynare invocation page 6 You also need to verify that the following requirements are met by your cluster which is com posed of a master and of one or more slaves For a Windows grid e astandard Windows network SMB must be in place e PsTools must be installed in the path of the master Windows machine e the Windows user on the master machine has to be user of any other slave machine in the cluster and that user will be used for the remote computations For a UNIX grid e SSH must be installed on the master and on the slave machines e SSH keys must be installed so that the SSH connection from the master to the slaves can be done without passwords or using an SSH agent We now turn to the description of the configuration directives cluster Configuration block Description When working in parallel cluster is required to specify the group of computers that
144. iable 2 1Y 0 703 2Y 0 75415 3Y 0 54729 gt gt tsi tsi data 1 ans is a dseries object minus Variable 2 0 703 1Y 0 2Y 0 051148 3Y 0 15572 gt gt tsi data 1 ts1 ans is a dseries object minus 0 703 Variable_2 1Y 0 2Y 0 051148 3Y 0 15572 Chapter 6 Time Series 133 C mpower A B dseries C Overloads the mpower operator for dseries objects and computes element by element power is a dseries object with N variables and T observations If B is a real scalar then mpower A B returns a dseries object C with C data t n A data t n C If B isa dseries object with N variables and T observations then mpower A B returns a dseries object C with C data t n A data t n C data t n Example gt gt tsO dseries transpose 1 3 gt gt tsi ts0 2 tsi is a dseries object pover Variable 1 2 1Y l1 2Y 4 3Y 9 gt gt ts2 tsO tsO ts2 is a dseries object power Variable_1 Variable_1 1Y 1 2Y 4 BY 27 mrdivide A B dseries Overloads the mrdivide operator for dseries objects element by element division like the Matlab Octave operator If both A and B are dseries objects they do not need to be defined over the same time ranges If A and B are dseries objects with 74 and Tg observations and N4 and Ng variables then N4 must be equal to Ng or 1 and Ng must be equal to N4 or 1 If T4 Tg isequal A init B init returns 1 and Ny Np then th
145. ication Analysis Options identification INTEGER If equal to 1 performs identification anlysis forcing redform 0 and morris 1 If equal to 0 no identification analysis Default 0 morris INTEGER See morris page 83 morris nliv INTEGER See morris nliv page 83 Chapter 4 The Model file 86 morris_ntra INTEGER See morris ntra page 83 load ident files INTEGER Loads previously performed identification analysis Default O useautocorr INTEGER Use autocorrelation matrices in place of autocovariance matrices in moments for identification analysis Default O ar INTEGER Maximum number of lags for moments in identification analysis Default 1 lik_init INTEGER See lik init page 54 identification Command identification OPTIONS Command Description This command triggers identification analysis Options ar INTEGER Number of lags of computed autocorrelations theoretical moments Default 1 useautocorr INTEGER If equal to 1 compute derivatives of autocorrelation If equal to 0 compute deriva tives of autocovariances Default O load ident files INTEGER If equal to 1 allow Dynare to load previously computed analyzes Default O prior mc INTEGER Size of Monte Carlo sample Default 1 prior range INTEGER Triggers uniform sample within the range implied by the prior specifications when prior mc 1 Default 0 advanced INTEGER Shows a more detailed analysis
146. icense txt in Dynare distribution It is available for the Windows Mac and Linux platforms and is fully documented through a user guide and a reference manual Part of Dynare is programmed in C while the rest is written using the MATLAB pro gramming language The latter implies that commercially available MATLAB software is required in order to run Dynare However as an alternative to MATLAB Dynare is also able to run on top of GNU Octave basically a free clone of MATLAB this possibility is particularly interesting for students or institutions who cannot afford or do not want to pay for MATLAB and are willing to bear the concomitant performance loss The development of Dynare is mainly done at Cepremap by a core team of researchers who devote part of their time to software development Currently the development team of Dynare is composed of St phane Adjemian Universit du Maine Gains and Cepremap Houtan Bastani Cepremap Michel Juillard Banque de France Fr d ric Karam Universit du Maine Gains and Cepremap Junior Maih Norges Bank Ferhat Mihoubi Universit Paris Est Cr teil Epee and Cepremap George Perendia Johannes Pfeifer University of Mannheim Marco Ratto JRC and S bastien Villemot Cepremap Increasingly the developer base is expanding as tools developed by researchers outside of Cepremap are integrated into Dynare Financial support is provided by Cepremap Banque de France and DSGE net an internation
147. ies class dseries transpose 1 4 1950Q1 dseries object Variable 1 1 2 3 4 ts0 lag dseries object lag Variable_1 1 NaN 1 2 3 ts0 lag 2 dseries object lag Variable_1 2 NaN NaN 1 2 129 dseries dseries overloads the parenthesis so that ts lag p can be written more compactly as ts p For instance gt gt ts0 lag 1 ans is a dseries object 1950Q1 1950Q2 1950Q3 195004 or alternatively gt gt ts0 1 lag Variable 1 1 NaN C ND HG Chapter 6 Time Series 130 ans is a dseries object lag Variable_1 1 1950Q1 NaN 195002 1 195003 2 195004 3 B lead Al p dseries Returns leaded time series Default value of p the number of leads is 1 As for the lag method the dseries class overloads the parenthesis so that ts lead p is equivalent to ts p Example gt gt tsO dseries transpose 1 4 195001 gt gt tsi ts0 lead tsi is a dseries object lead Variable 1 1 195001 2 195002 3 195003 4 1950Q4 NaN gt gt ts2 tsO 2 ts2 is a dseries object lead Variable_1 2 1950Q1 3 195002 4 195003 NaN 1950Q4 NaN Remark The overloading of the parenthesis for dseries objects allows to easily create new dseries objects by copying pasting equations declared in the model block For instance if an Euler equation is defined in the model block model 1 C beta C 1 exp A 1 K alpha 1 1 delt
148. if the date A i preceeds the date B i Example gt gt A dates 1950Q1 1951Q2 gt gt B dates 195001 1950Q2 gt gt A lt B max A B C dates Overloads the Matlab Octave max function All input arguments must be dates objects The function returns a single element dates object containing the greatest date Example gt gt A dates 1950Q2 dates 195304 1876Q2 dates 1794Q3 gt gt max A ans dates 195304 gt min A B C dates Overloads the Matlab Octave min function All input arguments must be dates objects The function returns a single element dates object containing the smallest date Example gt gt A dates 1950Q2 dates 195304 1876Q2 dates 1794Q3 gt gt min A ans dates 1794Q3 minus A B dates Overloads the Matlab Octave minus operator If both input arguments are dates objects then number of periods between A and B is returned so that A C B If B is a vector of integers the minus operator shifts the dates object by B periods backward Example gt gt di dates 1950Q1 1950Q2 1960Q1 gt gt d2 dates 1950Q3 195004 1960Q1 gt gt ee d2 di ee 2 2 Chapter 6 Time Series 118 gt gt di ee ans dates 195003 1950Q4 1960Q1 C ne 4 B dates Overloads the Matlab Octave ne not equal operator dates
149. ifer Johannes 2013 A Guide to Specifying Observation Equations for the Estimation of DSGE Models e Rabanal Pau and Juan Rubio Ramirez 2003 Comparing New Keynesian Models of the Business Cycle A Bayesian Approach Federal Reserve of Atlanta Working Paper Series 2003 30 e Ratto Marco 2008 Analysing DSGE models with global sensitivity analysis Computa tional Economics 31 115 139 e Schorfheide Frank 2000 Loss Function based evaluation of DSGE models Journal of Applied Econometrics 15 6 645 670 e Schmitt Groh Stephanie and Martin Uribe 2004 Solving Dynamic General Equilibrium Models Using a Second Order Approximation to the Policy Function Journal of Economic Dynamics and Control 28 4 755 775 e Sims Christopher A Daniel F Waggoner and Tao Zha 2008 Methods for inference in large multiple equation Markov switching models Journal of Econometrics 146 255 274 e Smets Frank and Rafael Wouters 2003 An Estimated Dynamic Stochastic General Equilib rium Model of the Euro Area Journal of the European Economic Association 1 5 1123 1175 e Villemot S bastien 2011 Solving rational expectations models at first order what Dynare does Dynare Working Papers 2 CEPREMAP Command and Function Index Command and Function Index pup MC ET 112 120 RE thee E E E 137 DATA_MATRIXE 120 DATES a dm roc 112 DATES cd n eat 112 FILENAME ccr
150. ign Default 6 morris ntra INTEGER Number trajectories in Morris design Default 20 ppost INTEGER If equal to 1 use Metropolis posterior sample If equal to 0 do not use Metropolis posterior sample NB This overrides any other sampling option Default O neighborhood width DOUBLE When pprior 0 and ppost 0 allows for the sampling of param eters around the value specified in the mode file in the range xparami xparami x neighborhood width Default 0 Stability Mapping Options stab INTEGER If equal to 1 perform stability mapping If equal to 0 do not perform stability mapping Default 1 load stab INTEGER If equal to 1 load a previously created sample If equal to 0 generate a new sample Default 0 alpha2 stab DOUBLE Critical value for correlations p in filtered samples plot couples of parmaters with p gt alpha2_stab Default 0 3 ksstat DOUBLE Critical value for Smirnov statistics d plot parameters with d gt ksstat Default 0 1 pvalue ks DOUBLE The threshold pvalue for significant Kolmogorov Smirnov test i e plot parameters with pvalue lt pvalue ks Default 0 001 Chapter 4 The Model file 84 pvalue_corr DOUBLE The threshold pvalue for significant correlation in filtered samples i e plot bivariate samples when pvalue lt pvalue corr Default 0 001 Reduced Form Mapping Options redform INTEGER If equal to 1 prepare Monte Carlo sample of reduced form matrices If
151. ill be exactly the same This behaviour allows to easily identify the consequences of a change on the model the priors or the estimation options But one may also want to check that across multiple runs with different sequences of proposals the returned results are almost identical This should be true if the number of iterations ie the value of mh replic is important enough to ensure the convergence of the MCMC to its ergodic distribution In this case the default behaviour of the random number generators in not wanted and the user should set the seed according to the system clock before the estimation command using the following command set dynare seed clock so that the sequence of proposals will be different across different runs Algorithms The Monte Carlo Markov Chain MCMC diagnostics are generated by the estimation command if mh replic page 54 is larger than 2000 and if option nodiagnostic page 59 is not used If mh nblocks page 54 is equal to one the convergence diagnostics of Geweke 1992 1999 is Chapter 4 The Model file 53 computed It uses a chi square test to compare the means of the first and last draws specified by geweke interval page 63 after discarding the burnin of mh drop page 54 The test is computed using variance estimates under the assumption of no serial correlation as well as using tapering windows specified in taper_steps page 63 If mh nblocks page 54 is larger than 1 the converge
152. in DR order The matrix columns correspond to the Kronecker product of state variables in DR order followed by exogenous in declaration order Note that the Kronecker product is stored in a folded way i e symmetric elements are stored only once which implies that the matrix has n n 1 2 columns More precisely each column of this matrix corresponds to a pair i1 i2 where each index represents an element of z and is therefore between 1 and n Only non decreasing pairs are stored i e those for which 7 iz The columns are arranged in the lexicographical order of non decreasing pairs Also note that for those pairs where i Z since the element is stored only once but appears two times in the unfolded Gz matrix it must be multiplied by 2 when computing the decision rules e G is stored in oo dr g 3 The matrix rows correspond to all endogenous in DR order The matrix columns correspond to the third Kronecker power of state variables in DR order followed by exogenous in declaration order Note that the third Kronecker power is stored in a folded way i e symmetric elements are stored only once which implies that the matrix has n n 1 n 2 6 columns More precisely each column of this matrix corresponds to a tuple i1 i2 43 where each index represents an element of z and is therefore between 1 and n Only non decreasing tuples are stored i e those for which i ig lt 43 The columns are arranged in the lexic
153. ion Perturbation and Projection Methods in Economic Analysis in Handbook of Computational Economics ed by Hans Amman David Kendrick and John Rust North Holland Press 511 585 e Juillard Michel 1996 Dynare A program for the resolution and simulation of dynamic models with forward variables through the use of a relaxation algorithm CEPREMAP Cou verture Orange 9602 e Kim Jinill Sunghyun Kim Ernst Schaumburg and Christopher A Sims 2008 Calculat ing and using second order accurate solutions of discrete time dynamic equilibrium models Journal of Economic Dynamics and Control 32 11 3397 3414 e Koop Gary 2003 Bayesian Econometrics John Wiley amp Sons e Koopman S J and J Durbin 2003 Filtering and Smoothing of State Vector for Diffuse State Space Models Journal of Time Series Analysis 24 1 85 98 e Laffargue Jean Pierre 1990 R solution d un mod le macro conomique avec anticipations rationnelles Annales d conomie et Statistique 17 97 119 e Lubik Thomas and Frank Schorfheide 2007 Do Central Banks Respond to Exchange Rate Movements A Structural Investigation Journal of Monetary Economics 54 4 1069 1087 e Mancini Griffoli Tommaso 2007 Dynare User Guide An introduction to the solution and estimation of DSGE models e Pearlman Joseph David Currie and Paul Levine 1986 Rational expectations models with partial information Economic Modelling 3 2 90 105 e Pfe
154. ion for more information dynare version MATLAB Octave command Output the version of Dynare that is currently being used i e the one that is highest on the MATLAB Octave path write latex definitions MATLAB Octave command Writes the names IATEX names and long names of model variables to tables in a file named M fname latex definitions tex Chapter 5 The Configuration File 106 5 The Configuration File The configuration file is used to provide Dynare with information not related to the model and hence not placed in the model file At the moment it is only used when using Dynare to run parallel computations On Linux and Mac OS X the default location of the configuration file is HOME dynare while on Windows it is 4APPDATAA Ndynare ini typically C Documents and Settings USERNAME Application Data dynare ini under Windows XP or C Users USERNAME AppData dynare ini under Windows Vista 7 8 You can specify a non standard location using the conffile option of the dynare command see Section 3 1 Dynare invocation page 6 The parsing of the configuration file is case sensitive and it should take the following form with each option choice pair placed on a newline commandO optionO choiceO optioni choicel command1 optionO choiceO optioni choicel The configuration file follows a few conventions selfexplanatory conventions such as USERNAME have been excluded for concision COMPUTER NAME Indic
155. is listed all endogenous variables are printed dynasave FILENAME VARIABLE NAME Command This command saves the listed variables in a binary file named FILENAME If no VARI ABLE NAME are listed all endogenous variables are saved In MATLAB or Octave variables saved with the dynasave command can be retrieved by the command load mat FILENAME Chapter 4 The Model file 98 4 20 Macro processing language It is possible to use macro commands in the mod file for doing the following tasks including modular source files replicating blocks of equations through loops conditionally executing some code writing indexed sums or products inside equations The Dynare macro language provides a new set of macro commands which can be inserted inside mod files It features e file inclusion e loops for structure e conditional inclusion if then else structures e expression substitution Technically this macro language is totally independent of the basic Dynare language and is processed by a separate component of the Dynare pre processor The macro processor transforms a mod file with macros into a mod file without macros doing expansions inclusions and then feeds it to the Dynare parser The key point to understand is that the macro processor only does text substitution like the C preprocessor or the PHP language Note that it is possible to see the output of the macro processor by using the savemacro option of
156. is passed the same number of processors will be used but the range will be adjusted to begin at one ComputerName COMPUTER NAME The name or IP address of the node If you want to run locally use localhost case sensitive Port INTEGER The port number to connect to on the node The default is empty meaning that the connection will be made to the default SSH port 22 UserName USER NAME The username used to log into a remote system Required for remote runs on all platforms Password PASSWORD The password used to log into the remote system Required for remote runs origi nating from Windows RemoteDrive DRIVE NAME The drive to be used for remote computation Required for remote runs originating from Windows Chapter 5 The Configuration File 109 RemoteDirectory PATH The directory to be used for remote computation Required for remote runs on all platforms DynarePath PATH The path to the matlab subdirectory within the Dynare installation directory The default is the empty string MatlabOctavePath PATH AND FILE The path to the MATLAB or Octave executable The default value is matlab SingleCompThread BOOLEAN Whether or not to disable MATLAB s native multithreading The default value is true Option meaningless under Octave OperatingSystem OPERATING SYSTEM The operating system associated with a node Only necessary when creating a cluster with nodes from different operating systems Possible valu
157. it loops to select variables names GDP_1 GDP_2 GDP_3 GDP_4 GDP_5 GDP_6 GDP_7 GDP_8 GDP_9 GDP_10 GDP_11 GDP_12 HICP 1 HICP 2 HICP 3 HICP_4 HICP_5 HICP_6 HICP_7 HICP_8 HICP_9 HICP 10 HICP 11 HICP_12 ts0 dseries randn 4 24 dates 1973Q1 names ts0 GDP HICP _ 1 3 50 ans is a dseries object GDP_1 GDP_3 GDP_5 HICP_1 HICP_3 HICP_5 1973Q1 1 7906 1 6606 0 57716 0 60963 0 52335 0 26172 1973Q2 2 1624 3 0125 0 52563 0 70912 1 7158 1 7792 1973Q3 0 81928 1 5008 1 152 0 2798 0 88568 1 8927 197394 0 03705 0 35899 0 85838 1 4675 2 1666 0 62032 D horzcat A Bl dseries Overloads the horzcat Matlab Octave s method for dseries objects Returns a dseries object D containing the variables in dseries objects passed as inputs A B If the inputs are not defined on the same time ranges the method adds NaNs to the variables so that the variables are redefined on the smallest common time range Note that the names in the dseries objects passed as inputs must be different and these objects must have common frequency Example gt gt tsO dseries rand 5 2 1950Q1 nifnif noufnouf gt gt tsi dseries rand 7 1 1950Q3 nafnaf Chapter 6 Time Series 126 B gt gt
158. lck n where n is the number of estimated parameters array of doubles Current state of the MCMC Chapter 9 Dynare misc commands 149 InitialLogPost A Nblck 1 array of doubles Initial value of the posterior kernel LastLogPost A Nblck 1 array of doubles Current value of the posterior kernel InitialSeeds A 1 Nblck structure array Initial state of the random number genera tor LastSeeds A 1 Nblck structure array Current state of the random number gen erator AcceptanceRatio A 1 Nblck array of doubles Current acceptance ratios Chapter 10 Bibliography 150 10 Bibliography Abramowitz Milton and Irene A Stegun 1964 Handbook of Mathematical Functions Courier Dover Publications Adjemian St phane Matthieu Darracq Parri s and St phane Moyen 2008 Towards a monetary policy evaluation framework European Central Bank Working Paper 942 Aguiar Mark and Gopinath Gita 2004 Emerging Market Business Cycles The Cycle is the Trend NBER Working Paper 10734 Andreasen Martin M Jes s Fern ndez Villaverde and Juan Rubio Ram rez 2013 The Pruned State Space System for Non Linear DSGE Models Theory and Empirical Applica tions NBER Working Paper 18983 Backus David K Patrick J Kehoe and Finn E Kydland 1992 International Real Business Cycles Journal of Political Economy 100 4 745 775 Boucekkine Raouf 1995 An alternative methodology for solving nonlinear forward looking models
159. lement an arbitrary EXPRESSION is allowed instead of a simple constant but in that case you need to enclose the expression in parentheses The order of the covariances in the matriz is the same as the one used in the varexo declaration Example varexo u e Sigma e 0 81 phi 0 9 0 009 0 000081 This sets the variance of u to 0 81 the variance of e to 0 000081 and the correlation between e and u to phi 4 9 Other general declarations dsample INTEGER INTEGER Command Reduces the number of periods considered in subsequent output commands periods INTEGER Command Description This command is now deprecated but will still work for older model files It is not necessary when no simulation is performed and is replaced by an option periods in simul and stoch simul This command sets the number of periods in the simulation The periods are numbered from 1 to INTEGER In perfect foresight simulations it is assumed that all future events are perfectly known at the beginning of period 1 Example periods 100 4 10 Steady state There are two ways of computing the steady state i e the static equilibrium of a model The first way is to let Dynare compute the steady state using a nonlinear Newton type solver this should work for most models and is relatively simple to use The second way is to give more guidance to Dynare using your knowledge of the model by providing it with a steady state file 4 10 1 Fi
160. lently Y multiplybytwo X the object X is left unchanged and the object Y is a modified copy of X C append A B dates Appends dates object B or a string that can be interpreted as a date to the dates object A If B is a dates object it is assumed that it has no more than one element Example gt gt D dates 1950Q1 195002 gt gt d dates 1950037 gt gt E D append d gt gt F D append 1950Q3 isequal E F ans gt gt F F lt dates 1950Q1 1950Q2 1950Q3 gt C colon A B dates C colon A i B dates Overloads the Matlab Octave colon operator A and B are dates objects The optional increment i is a scalar integer default value is i 1 This method returns a dates object and can be used to create ranges of dates Example gt gt A dates 1950Q1 gt gt B dates 1951Q2 gt gt C A B C dates 1950Q1 1950Q2 195003 1950Q4 1951Q1 gt gt gt D A 2 B D dates 1950Q1 195003 1951Q1 gt B double A dates Overloads the Matlab Octave double function A is a dates object The method returns a floating point representation of a dates object the integer and fractional parts respectively corresponding to the year and the subperiod The fractional part is the subperiod number minus one divided by the frequency 1 4 12 or 52 Chapter 6 Time Series 114 Example gt gt a dates 1950Q1 dates 195004 gt gt
161. lue of periods option oo exo simul MATLAB Octave variable This variable stores the path of exogenous variables during a simulation computed by simul Stoch simul or extended path The variables are arranged in columns in order of declaration as in M endo names Periods are in rows Note that this convention regarding columns and rows is the opposite of the convention for oo endo simul 4 13 Stochastic solution and simulation In a stochastic context Dynare computes one or several simulations corresponding to a random draw of the shocks The main algorithm for solving stochastic models relies on a Taylor approximation up to third order of the expectation functions see Judd 1996 Collard and Juillard 2001a Collard and Juillard 2001b and Schmitt Groh and Uribe 2004 The details of the Dynare implementation of the first order solution are given in Villemot 2011 Such a solution is computed using the stoch simul command As an alternative it is possible to compute a simulation to a stochastic model using the extended path method presented by Fair and Taylor 1983 This method is especially useful when there are strong nonlinearities or binding constraints Such a solution is computed using the extended path command Chapter 4 The Model file 40 4 13 1 Computing the stochastic solution stoch simul VARIABLE NAME Command stoch simul OPTIONS VARIABLE NAME Command Description Stoch
162. lues for OPTION are default Uses the default solver for Sylvester equations gensylv based on On dra Kamenik s algorithm see the Dynare Website for more informa tion fixed point Uses a fixed point algorithm to solve the Sylvester equation gensylv_ fp This method is faster than the default one for large scale models Default value is default Sylvester fixed point tol DOUBLE It is the convergence criterion used in the fixed point Sylvester solver Its default value is 1e 12 dr OPTION Determines the method used to compute the decision rule Possible values for OPTION are default Uses the default method to compute the decision rule based on the generalized Schur decomposition see Villemot 2011 for more infor mation cycle reduction Uses the cycle reduction algorithm to solve the polynomial equation for retrieving the coefficients associated to the endogenous variables in the decision rule This method is faster than the default one for large scale models logarithmic reduction Uses the logarithmic reduction algorithm to solve the polynomial equa tion for retrieving the coefficients associated to the endogenous variables in the decision rule This method is in general slower than the cycle reduction Default value is default dr cycle reduction tol DOUBLE The convergence criterion used in the cycle reduction algorithm Its default value is le 7 dr_logarithmic_reduction_tol DOUBLE The convergence c
163. lues for the non linear solver The command resid can be used to compute the equation residuals for the given initial values Used in perfect foresight mode the types of forward looking models for which Dynare was de signed require both initial and terminal conditions Most often these initial and terminal conditions are static equilibria but not necessarily One typical application is to consider an economy at the equilibrium trigger a shock in first period and study the trajectory of return at the initial equilibrium To do that one needs initval and shocks see Section 4 8 Shocks on exogenous variables page 27 Another one is to study how an economy starting from arbitrary initial conditions converges toward equilibrium To do that one needs initval and endval For models with lags on more than one period the command histval permits to specify different historical initial values for periods before the beginning of the simulation initval Block initval OPTIONS Block Description Chapter 4 The Model file 23 The initval block serves two purposes declaring the initial and possibly terminal conditions in a simulation exercise and providing guess values for non linear solvers This block is terminated by end and contains lines of the form VARIABLE NAME EXPRESSION In a deterministic i e perfect foresight model First it provides the initial conditions for all the endogenous and exogenous variables at
164. lytic derivatives Iskrev 2010 jointly with the mapping of the acceptable region The identification analysis with derivatives can also be triggered by the commands identification This does not do the mapping of acceptable regions for the model and uses the standard random sampler of Dynare It completely offsets any use of the sensitivity analysis toolbox 4 17 7 Performing Sensitivity and Identification Analysis dynare sensitivity Command dynare_sensitivity OPTIONS Command Description This command triggers sensitivity analysis on a DSGE model Options Chapter 4 The Model file 83 Sampling Options nsam INTEGER Size of the Monte Carlo sample Default 2048 ilptau INTEGER If equal to 1 use LP quasi Monte Carlo If equal to 0 use LHS Monte Carlo Default 1 pprior INTEGER If equal to 1 sample from the prior distributions If equal to 0 sample from the multivariate normal N 0 X where 0 is the posterior mode and X H t H is the Hessian at the mode Default 1 prior range INTEGER If equal to 1 sample uniformly from prior ranges If equal to 0 sample from prior distributions Default 1 morris INTEGER If equal to 0 ANOVA mapping Type I error If equal to 1 Screening analysis Type II error If equal to 2 Analytic derivatives similar to Type II error only valid when identification 1 Default 1 when identification 1 0 otherwise morris nliv INTEGER Number of levels in Morris des
165. me exu vex S E EE ER 136 report On Report 2 14 cv ns xe E ER 140 I6Sld 0elivaguesqadevu b vara Eau edd due 27 Iplot 2 5 54r ee rera aeta eke es 9T S save params and steady state 104 SDVAE oai eregina ne Eg Dux idis EU ds 88 set _dynare seed ii cele ILI ikt sitoki 104 Set nameg iniLicvlnesu e ad Ede SS dames whee aes 137 setdiff oes oars PE use ato 115 shock_decomposition 67 SHOCKS Los tes ior RUNI Lobo items 28 SXgnol ligiu ts PMP 16 cha PEE 38 SIN ae Diesel rrr EET 16 SLA Di 11e armament Deere 138 SOL E E E E E ramasse pese 119 SOT rre 16 steady enisi ILES atest SERERE tenues 30 STEADY STATE gases aban cae eae Ae Reine a 15 steady state model selle 34 stoch Simul peneeenereyerane b gud E Eni 40 SVAL AEE E EEE REX aes E a NEUE bu Ede iore 88 svar_identification 89 T CAN D 16 Tex Tenam 4 s seeds eeuqu rq eeibes a Tin 138 trend var 5229 es ect sn uu e tton d 14 U WMA TUS E puede fie aed are heeded ae ead fie wai ore RE Ends eus 119 138 VTL OD M 119 UNIQUE gu RR sensed Gage adie aud sn eg 119 unit root VarS ienaat aAa ERRARE araa 68 UP MUS suisses roin ane i nai done 119 V DE DS eO Dara did eer E PH ud tee HE UE ONDE 10 VarexOllisnenepRbleIPcxenereeB5RET MeFe eR nee TR yarexo det olo yu ve REG niet nine Ti Michaele PC rp 49 Verbatim 252r dore died 104 Verbtcat LE e wad Samco bene wae Sa E 138
166. mmand will draw all the variables in ts on the same figure gt gt h plot ts If one wants to modify the properties of the plotted time series line style colours the set function can be used see Matlab s documentation gt gt set h 1 k linewidth 2 gt gt set h 2 r The follwing command will plot Variable_1 against exp Variable_1 gt gt plot ts Variable_1 ts Variable_1 exp Q ok Again the properties can also be modified using the returned plot handle and the set function gt gt h plot ts ts exp gt gt set h 1 ok gt gt set h 2 r C plus A B dseries Overloads the plus operator for dseries objects element by element addition If both A and B are dseries objects they do not need to be defined over the same time ranges If A and B are dseries objects with T4 and Tg observations and Ny and Np variables then N4 must be equal to Ng or 1 and Ng must be equal to Ny or 1 If T4 Tg isequal A init B init returns 1 and N4 Ng then the plus operator will compute for each couple t n with 1 t T4 and 1 n lt Ny C data t n A data t n B data t n If Ng is equal to 1 and Ny gt 1 the smaller dseries object B is broadcast across the larger dseries A so that they have compatible shapes the plus operator will add the variable defined in B to each variable in A If B is a double scalar then the method plus will add B t
167. mns oo_ conditional_variance_decomposition MATLAB Octave variable After a run of stoch_simul with the conditional variance decomposition option contains a three dimensional array with the result of the decomposition The first dimension corresponds to forecast horizons as declared with the option the second dimension corresponds to endogenous variables in the order of declaration the third dimension corresponds to exogenous variables in the order of declaration oo_ irfs MATLAB Octave variable After a run of stoch_simul with option irf different from zero contains the impulse responses with the following naming convention VARIABLE NAME SHOCK NAME For example oo irfs gnp ea contains the effect on gnp of a one standard deviation shock on ea The approximated solution of a model takes the form of a set of decision rules or transition equations expressing the current value of the endogenous variables of the model as function of the previous state of the model and shocks observed at the beginning of the period The decision rules are stored in the structure oo dr which is described below extended path Command extended path OPTIONS Command Description extended path solves a stochastic i e rational expectations model using the extended path method presented by Fair and Taylor 1983 Time series for the endogenous variables are generated by assuming that the agents believe that there will no more shocks
168. n a variable named jumping_ covariance must be square positive definite and have the same di mension as the number of estimated parameters Note that the covariance matrices are still scaled with mh_jscale page 55 Default value is hessian mode_check Tells Dynare to plot the posterior density for values around the computed mode for each estimated parameter in turn This is helpful to diagnose problems with the optimizer mode_check_neighbourhood_size DOUBLE Used in conjunction with option mode_check gives the width of the window around the posterior mode to be displayed on the diagnostic plots This width is expressed in percentage deviation The Inf value is allowed and will trigger a plot over the entire domain see also mode_check_symmetric_plots Default 0 5 mode_check_symmetric_plots INTEGER Used in conjunction with option mode_check if set to 1 tells Dynare to ensure that the check plots are symmetric around the posterior mode A value of 0 allows to have asymmetric plots which can be useful if the posterior mode is close to a domain boundary or in conjunction with mode_check_neighbourhood_size Inf when the domain in not the entire real line Default 1 mode_check_number_of_points INTEGER Number of points around the posterior mode where the posterior kernel is evaluated for each parameter Default is 20 Chapter 4 The Model file 57 prior_trunc DOUBLE Probability of extreme values of the prior density th
169. nal conditions are only necessary for forward variables If some variables endogenous or exogenous are not mentioned in the endval block the value assumed is that of the last initval block or steady command Note that if the endval block is immediately followed by steady command its semantics is changed The steady command will compute the steady state of the model for all the endogenous variables assuming that exogenous variables are kept constant to the value declared in the endval block and using the values declared for the endogenous as initial guess values for the non linear solver An endval block followed by steady is formally equivalent to an endval block with the same values for the exogenous and with the associated steady state values for the endogenous Options all_values_ required See all_values_required page 23 Example var c K varexo X initval c 1 25 k 12 steady The initial equilibrium is computed by steady for x 1 and the terminal one for x 2 Chapter 4 The Model file 25 Example var c K varexo x model C k aa x k 1 alph 1 delt k 1 c gam 1 bet 1 aa alph x 1 k alph 1 1 delt c 1 gam end initval c 1 2 endval c 2 k 20 x 1 1 end simul periods 200 In this example the problem is finding the optimal path for consumption and capital for the periods t 1 to T 200 given the path of the exogenous technology level x Se
170. name QUOTED_STRING Description This required command declares the endogenous variables in the model See Section 4 1 Conven tions page 10 for the syntax of VARIABLE NAME and MODEL EXPRESSION Optionally it is possible to give a IATEX name to the variable or if it is nonstationary provide information regarding its deflator Chapter 4 The Model file 11 var commands can appear several times in the file and Dynare will concatenate them Options If the model is nonstationary and is to be written as such in the model block Dynare will need the trend deflator for the appropriate endogenous variables in order to stationarize the model The trend deflator must be provided alongside the variables that follow this trend deflator MU DEL EXPRESSION The expression used to detrend an endogenous variable All trend variables endoge nous variables and parameters referenced in MODEL EXPRESSION must already have been declared by the trend var log trend var var and parameters com mands The deflator is assumed to be multiplicative for an additive deflator use log deflator log deflator MODEL EXPRESSION Same as deflator except that the deflator is assumed to be additive instead of multiplicative or to put it otherwise the declared variable is equal to the log of a variable with a multiplicative trend long name QUOTED STRING This is the long version of the variable name Its value is stored in M endo names long
171. nce diagnostics of Brooks and Gelman 1998 are used instead As described in section 3 of Brooks and Gelman 1998 the univariate convergence diagnostics are based on comparing pooled and within MCMC moments Dynare displays the second and third order moments and the length of the Highest Probability Density interval covering 80 of the posterior distribution Due to computational reasons the multivariate convergence diagnostic does not follow Brooks and Gelman 1998 strictly but rather applies their idea for univariate convergence diagnostics to the range of the posterior likelihood function instead of the individual parameters The posterior kernel is used to aggregate the parameters into a scalar statistic whose convergence is then checked using the Brooks and Gelman 1998 univariate convergence diagnostic Options datafile FILENAME The datafile a m file a mat file a csv file or a x1s x1sx file under Octave the io from Octave Forge is required for the csv xls and xlsx formats in addition for the x1s and xlsx formats the java package is required along with a Java Runtime Environment xls sheet NAME The name of the sheet with the data in an Excel file xls range RANGE The range with the data in an Excel file nobs INTEGER The number of observations to be used Default all observations in the file nobs INTEGER1 INTEGER2 Runs a recursive estimation and forecast for samples of size ranging of INTEGER1 t
172. nding the steady state with Dynare nonlinear solver steady Command steady OPTIONS Command Description Chapter 4 The Model file 31 This command computes the steady state of a model using a nonlinear Newton type solver and displays it When a steady state file is used steady displays the steady state and checks that it is a solution of the static model More precisely it computes the equilibrium value of the endogenous variables for the value of the exogenous variables specified in the previous initval or endval block steady uses an iterative procedure and takes as initial guess the value of the endogenous variables set in the previous initval or endval block For complicated models finding good numerical initial values for the endogenous variables is the trickiest part of finding the equilibrium of that model Often it is better to start with a smaller model and add new variables one by one Options maxit INTEGER Determines the maximum number of iterations used in the non linear solver The default value of maxit is 10 The maxit option is shared with the simul command So a change in maxit in a steady command will also be considered in the following simul commands solve algo INTEGER Determines the non linear solver to use Possible values for the option are 0 Use fsolve under MATLAB only available if you have the Optimiza tion Toolbox always available under Octave 1 Use Dynare s own nonlinear equation s
173. ng like 1 5 o 5r B I I Stationary component of y Filtered y ill y A yhti l fia M 1 i i 1 1 i e od hi bog Igi du P AN Vat lu la had uit 1 1 fi L 1 1 fi 1 1 1954Q4 1959Q4 1964Q4 1969Q4 1974Q4 1979Q4 1984Q4 1989Q4 1994Q4 1999Q4 hptrend A lambda dseries Extracts the trend component from a dseries A object using Hodrick Prescott 1997 filter and returns a dseries object B Default value for lambda the smoothing parameter is 1600 ExampleUsing the same generating data process as in the previous example tsi dseries stochastic trend deterministic trend 195001 Apply the HP filter ts2 tsO hptrend 4 Plot the filtered time series plot tsi data k Plot of the nonstationary components hold on plot ts2 data r Plot of the estimated trend hold off axis tight id get gca XTick set gca XTickLabel strings ts0 dates id Chapter 6 Time Series 128 The previous code should produce something like I I I Nonstationary component of y Estimated trend of y 20 1 L L 1 L 1 L L 1 1954Q4 1959Q4 1964Q4 1969Q4 1974Q4 1979Q4 1984Q4 1989Q4 1994Q4 1999Q4 C insert A B I dseries Inserts variables contained in dseries object B in dseries object A at positions specified by integer scalars in vector 1 returns augmented dseries object C Th
174. ntation Default portrait paper a4 letter Paper size Default a4 title STRING Report Title Default none Chapter 7 Reporting 141 addPage footnote orientation paper title titleFormat Method on Report Adds a Page to the Report Options footnote STRING A footnote to be included at the bottom of this page Default none orientation landscape portrait See orientation page 140 paper a4 letter See paper page 140 title STRING CELL ARRAY STRINGS With one entry a STRING the title of the page With more than one entry a CELL ARRAY STRINGS the title and subtitle s of the page Default none titleFormat STRING CELL ARRAY STRINGS A string representing the ATEX markup to use on the title page 141 The number of cell array entries must be equal to that of the title page 141 option Default none addSection cols height Method on Report Adds a Section to a Page Options cols INTEGER The number of columns in the section Default 1 height STRING A string to be used with the sectionheight ATEX command Default addGraph data figname figDirName graphSize showGrid showLegend Method on Report showLegendBox legendLocation legendOrientation legendFontSize series To Use shade shadeColor shadeOpacity title xlabel ylabel xrange x Ticks xTickLabels yrange showZeroline Adds a Graph to a Section Options data
175. ntrolled by the irf option Results are stored in oo PosteriorIRF dsge see below for a description of this variable dsge var DOUBLE Triggers the estimation of a DSGE VAR model where the weight of the DSGE prior of the VAR model is calibrated to the value passed see Del Negro and Schorfheide 2004 It represents ratio of dummy over actual observations To assure that the prior is proper the value must be bigger than k 4 n T where k is the number of estimated parameters n is the number of observables and T is the number of observations NB The previous method of declaring dsge prior weight as a parameter and then calibrating it is now deprecated and will be removed in a future release of Dynare dsge var Triggers the estimation of a DSGE VAR model where the weight of the DSGE prior of the VAR model will be estimated as in Adjemian et alii 2008 The prior on the weight of the DSGE prior dsge prior weight must be defined in the estimated params section NB The previous method of declaring dsge prior weight as a parameter and then placing it in estimated params is now deprecated and will be removed in a future release of Dynare dsge varlag INTEGER The number of lags used to estimate a DSGE VAR model Default 4 moments varendo Triggers the computation of the posterior distribution of the theo retical moments of the endogenous variables Results are stored in oo_ PosteriorTheoreticalMoments see oo Posteri
176. ntry models Here is a skeleton example for a multi country model define countries US EA AS Jp RC define nth co US for co in countries var Y_ co K_ co L_ co i_ co E_ f co parameters a_ co varexo endfor model for co in countries Y_ co K_ co a_ co L_ co 1 a_ co if co nth_co 1 i_ co 1 i_ nth_co E_ co 1 E_ co UIP relation else E_ co 1 endif endfor end 4 20 3 4 Endogeneizing parameters When doing the steady state calibration of the model it may be useful to consider a parameter as an endogenous and vice versa For example suppose production is defined by a CES function y aV Ee V 1 a V egi i e ED The labor share in GDP is defined as lab rat w py In the model o is a share parameter and 1ab rat is an endogenous variable It is clear that calibrating o is not straightforward but on the contrary we have real world data for lab rat and it is clear that these two variables are economically linked The solution is to use a method called variable flipping which consist in changing the way of computing the steady state During this computation will be made an endogenous variable and Chapter 4 The Model file 103 lab rat will be made a parameter An economically relevant value will be calibrated for lab rat and the solution algorithm will deduce the implied value for
177. o INTEGER2 Option forecast must also be specified The forecasts are stored in the RecursiveForecast field of the results structure see RecursiveForecast page 66 first obs INTEGER The number of the first observation to be used Default 1 prefilter INTEGER A value of 1 means that the estimation procedure will demean each data series by its empirical mean Default O i e no prefiltering presample INTEGER The number of observations to be skipped before evaluating the likelihood These first observations are used as a training sample Default O loglinear Computes a log linear approximation of the model instead of a linear approximation As always in the context of estimation the data must correspond to the definition of the variables used in the model see Pfeifer 2013 for more details on how to correctly specify observation equations linking model variables and the data If you specify the loglinear option Dynare will take the logarithm of both your model variables and of your data as it assumes the data to correspond to the original non logged model variables The displayed posterior results like impulse responses smoothed variables and moments will be for the logged variables not the original un logged ones Default computes a linear approximation Chapter 4 The Model file 54 plot priors INTEGER Control the plotting of priors 0 No prior plot 1 Prior density for each estimated parameter is plotted It is impo
178. o Ratto and S bastien Villemot 2011 Dynare Reference Manual Version 4 Dynare Working Papers 1 CEPREMAP Note that citing the Dynare Reference Manual in your research is a good way to help the Dynare project If you want to give a URL use the address of the Dynare website http www dynare org Chapter 2 Installation and configuration 3 2 Installation and configuration 2 1 Software requirements Packaged versions of Dynare are available for Windows XP Vista 7 8 Debian GNU Linux Ubuntu and Mac OS X Leopard Snow Leopard Dynare should work on other systems but some compila tion steps are necessary in that case In order to run Dynare you need one of the following e MATLAB version 7 3 R2006b or above e GNU Octave version 3 6 or above Packages of GNU Octave can be downloaded on the Dynare website The following optional extensions are also useful to benefit from extra features but are in no way required e If under MATLAB the optimization toolbox the statistics toolbox the control system toolbox e If under GNU Octave the following Octave Forge packages optim io java statistics control If you plan to use the use dll option of the model command you will need to install the necessary requirements for compiling MEX files on your machine If you are using MATLAB under Windows install a C compiler on your machine and configure it with MATLAB see instructions on the Dynare wiki Users of Octave under
179. o all the observations variables in A If B is a row vector of length N4 then the plus method will add B i to all the observations of variable i for 1 N4 If B is a column vector of length T4 then the plus method will add B to all the variables C pop A B dseries Removes variable B from dseries object A By default if the second argument is not provided the last variable is removed Example Chapter 6 Time Series 136 gt gt ts0 dseries ones 3 3 gt gt tsi tsO pop Variable 27 tsi is a dseries object Variable 1 Variable 3 1Y 1 1 2Y 1 1 S3Y 3 1 B qdiff A dseries B qgrowth A dseries Computes quarterly differences or growth rates Example gt gt tsO dseries transpose 1 4 195001 gt gt tsi tsO qdiff tsi is a dseries object qdiff Variable 1 195001 NaN 1950Q2 1 195003 1 195004 1 gt gt tsO dseries transpose 1 6 1950M1 gt gt tsi ts0 qdiff tsi is a dseries object qdiff Variable_1 1950M1 NaN 1950M2 NaN 1950M3 NaN 1950M4 3 1950M5 3 1950M6 3 B rename A oldname newname dseries Rename variable oldname to newname in dseries object A Returns a dseries object Example gt gt tsO gt gt tsi tsi is a dseries ones 2 2 tsO rename Variable_1 Stinkly dseries object Stinkly Variable_2 1Y 14 2Y 1 1 1 Chapter 6 Time Series 137 save A basename format
180. observed series plots in red the cdf of the log posterior corresponding to the best 1096 RMSEs in green the cdf of the rest of the sample and in blue the cdf of the full sample this allows one to see idiosyncratic behavior Chapter 4 The Model file 82 e lt mod_file gt _rmse_prior_lnprior fig for each observed series plots in red the cdf of the log prior corresponding to the best 10 RMSEs in green the cdf of the rest of the sample and in blue the cdf of the full sample this allows one to see idiosyncratic behavior e mod file rmse prior lik SA fig when lik only 1 this shows the Smirnov tests for the filtering of the best 1096 log likelihood values e mod file rmse prior post SA fig when lik only 1 this shows the Smirnov test for the filtering of the best 1096 log posterior values 4 17 5 Screening Analysis Screening analysis does not require any additional options with respect to those listed in Sampling Options page 83 The toolbox performs all the analyses required and displays results The results of the screening analysis with Morris sampling design are stored in the subfolder mod file GSA SCREEN The data file mod file prior stores all the information of the anal ysis Morris sample reduced form coefficients etc Screening analysis merely concerns reduced form coefficients Similar synthetic bar charts as for the reduced form analysis with Monte Carlo samples are saved e mod file redfo
181. od file should be chosen in such a way that the generated m files described above do not conflict with m files provided by MATLAB Octave or by Dynare Not respecting this rule could cause crashes or unexpected behaviour In particular it means that the mod file cannot be given the name of a MAT LAB Octave or Dynare command Under Octave it also means that the mod file cannot be named test mod Options noclearall By default dynare will issue a clear all command to MATLAB or Octave thereby deleting all workspace variables this options instructs dynare not to clear the workspace debug Instructs the preprocessor to write some debugging information about the scanning and parsing of the mod file notmpterms Instructs the preprocessor to omit temporary terms in the static and dynamic files this generally decreases performance but is used for debugging purposes since it makes the static and dynamic files more readable savemacro FILENAME Instructs dynare to save the intermediary file which is obtained after macro processing see Section 4 20 Macro processing language page 98 the saved output will go in the file specified or if no file is specified in FILENAME macroexp mod onlymacro Instructs the preprocessor to only perform the macro processing step and stop just after Mainly useful for debugging purposes or for using the macro processor independently of the rest of Dynare toolbox nolinemacro Instructs the macro preproc
182. od is evaluated with a particle filter based on a second order approximation of the model see Fernandez Villaverde and Rubio Ramirez 2005 Default is 1 ie the likelihood of the linearized model is evaluated using a standard Kalman filter irf INTEGER See irf page 41 Only used if bayesian_irf page 59 is passed irf shocks VARIABLE NAME VARIABLE NAME See irf shocks page 41 Only used if bayesian irf page 59 is passed Cannot be used with dsge var page 59 irf plot threshold DOUBLE See irf plot threshold page 41 Only used if bayesian_irf page 59 is passed Chapter 4 The Model file 62 aim_solver See aim solver page 42 sylvester OPTION See sylvester page 43 sylvester_fixed_point_tol DOUBLE See sylvester fixed point tol page 43 lyapunov OPTION Determines the algorithm used to solve the Lyapunov equation to initialized the variance covariance matrix of the Kalman filter using the steady state value of state variables Possible values for OPTION are default Uses the default solver for Lyapunov equations based on Bartels Stewart algorithm fixed point Uses a fixed point algorithm to solve the Lyapunov equation This method is faster than the default one for large scale models but it could require a large amount of iterations doubling Uses a doubling algorithm to solve the Lyapunov equation disclyap fast This method is faster than the two previous one fo
183. oduct of the vector of state variables in DR order e Dis stored in oo dr ghuu The matrix rows correspond to all endogenous in DR order The matrix columns correspond to the Kronecker product of exogenous variables in declaration order e F is stored in oo dr ghxu The matrix rows correspond to all endogenous in DR order The matrix columns correspond to the Kronecker product of the vector of state variables in DR order by the vector of exogenous variables in declaration order Chapter 4 The Model file 48 4 13 5 Third order approximation The approximation has the form Ye y Go Giz Go z Ga z4 Q 4 Q where y is the steady state value of y and z is a vector consisting of the deviation from the steady state of the state variables in DR order at date t 1 followed by the exogenous variables at date t in declaration order The vector z is therefore of size n M_ nspred M_ exo_nbr The coefficients of the decision rules are stored as follows e y is stored in oo dr ys The vector rows correspond to all endogenous in the declaration order e Gp is stored in oo dr g 0 The vector rows correspond to all endogenous in DR order e Gi is stored in oo dr g 1 The matrix rows correspond to all endogenous in DR order The matrix columns correspond to state variables in DR order followed by exogenous in declaration order e G is stored in oo dr g 2 The matrix rows correspond to all endogenous
184. ographical order of non decreasing tuples Also note that for tuples that have three distinct indices i e i Z i2 and i iz and iy iz since these elements are stored only once but appears six times in the unfolded G3 matrix they must be multiplied by 6 when computing the decision rules Similarly for those tuples that have two equal indices i e of the form a a b or a b a or b a a since these elements are stored only once but appears three times in the unfolded G4 matrix they must be multiplied by 3 when computing the decision rules 4 14 Estimation Provided that you have observations on some endogenous variables it is possible to use Dynare to estimate some or all parameters Both maximum likelihood as in Ireland 2004 and Bayesian techniques as in Rabanal and Rubio Ramirez 2003 Schorfheide 2000 or Smets and Wouters 2003 are available Using Bayesian methods it is possible to estimate DSGE models VAR models or a combination of the two techniques called DSGE VAR Note that in order to avoid stochastic singularity you must have at least as many shocks or measurement errors in your model as you have observed variables The estimation using a first order approximation can benefit from the block decomposition of the model see block page 19 Chapter 4 The Model file 49 varobs VARIABLE NAME Command Description This command lists the name of observed endogenous variables for the estimation pro
185. olver a Newton like algorithm with line search 2 Splits the model into recursive blocks and solves each block in turn using the same solver as value 1 3 Use Chris Sims solver 4 Same as value 2 except that it does not try to adapt the search direction when the Jacobian is nearly singular 5 Newton algorithm with a sparse Gaussian elimination SPE requires bytecode option see Section 4 5 Model declaration page 18 6 Newton algorithm with a sparse LU solver at each iteration requires bytecode and or block option see Section 4 5 Model declaration page 18 7 Newton algorithm with a Generalized Minimal Residual GMRES solver at each iteration requires bytecode and or block option see Section 4 5 Model declaration page 18 not available under Octave 8 Newton algorithm with a Stabilized Bi Conjugate Gradient BICGSTAB solver at each iteration requires bytecode and or block option see Section 4 5 Model declaration page 18 Default value is 2 homotopy_mode INTEGER Use a homotopy or divide and conquer technique to solve for the steady state If you use this option you must specify a homotopy_setup block This option can take three possible values 1 In this mode all the parameters are changed simultaneously and the distance between the boundaries for each parameter is divided in as Chapter 4 The Model file 32 many intervals as there are steps as defined by homotopy_steps op tion the problem is s
186. olves as many times as there are steps 2 Same as mode 1 except that only one parameter is changed at a time the problem is solved as many times as steps times number of parame ters 3 Dynare tries first the most extreme values If it fails to compute the steady state the interval between initial and desired values is divided by two for all parameters Every time that it is impossible to find a steady state the previous interval is divided by two When it succeeds to find a steady state the previous interval is multiplied by two In that last case homotopy_steps contains the maximum number of computations attempted before giving up homotopy_steps INTEGER Defines the number of steps when performing a homotopy See homotopy_mode option for more details homotopy_force_continue INTEGER This option controls what happens when homotopy fails 0 steady fails with an error message 1 steady keeps the values of the last homotopy step that was successful and continues BE CAREFUL parameters and or exogenous variables are NOT at the value expected by the user Default is O nocheck Don t check the steady state values when they are provided explicitly either by a steady state file or a steady state model block This is useful for models with unit roots as in this case the steady state is not unique or doesn t exist markowitz DOUBLE Value of the Markowitz criterion used to select the pivot Only used when solve_ algo 5 Def
187. oot where there is an infinity of steady states An equation tagged dynamic would give the law of motion of the nonstationary variable like a random walk To pin down one specific steady state an equation tagged static would affect a constant value to the nonstationary variable Example This is a trivial example with two endogenous variables The second equation takes a different form in the static model var c K varexo X Chapter 4 The Model file 36 model C k aa x k 1 alph 1 delt k 1 dynamic c gam 1 bet 1 aa alph x 1 k alph 1 1 delt c 1 gam static k delt bet x aa alph 1 alph 1 end 4 11 Getting information about the model check Command check solve algo INTEGER Command Description Computes the eigenvalues of the model linearized around the values specified by the last initval endval or steady statement Generally the eigenvalues are only meaningful if the linearization is done around a steady state of the model It is a device for local analysis in the neighborhood of this steady state necessary condition for the uniqueness of a stable equilibrium in the neighborhood of the steady state is that there are as many eigenvalues larger than one in modulus as there are forward looking variables in the system An additional rank condition requires that the square submatrix of the right Schur vectors corresponding to the forward looking variables
188. orTheoreticalMoments page 65 The number of lags in the autocorrelation function is controlled by the ar option conditional_variance_decomposition INTEGER See below conditional_variance_decomposition INTEGER1 INTEGER2 See below conditional_variance_decomposition INTEGER1 INTEGER2 Computes the posterior distribution of the conditional variance de composition for the specified period s The periods must be strictly positive Conditional variances are given by var yiz t For period 1 the conditional variance decomposition provides the decomposition Chapter 4 The Model file 60 of the effects of shocks upon impact The results are stored in oo PosteriorTheoreticalMoments dsge ConditionalVarianceDecomposition but currently there is no displayed output Note that this option requires the option moments varendo to be specified filtered vars Triggers the computation of the posterior distribution of filtered endogenous variables one step ahead forecasts i e Eua Results are stored in oo FilteredVariables see below for a description of this variable smoother Triggers the computation of the posterior distribution of smoothed endogenous variables and shocks ie the expected value of variables and shocks given the information available in all observations up to the final date Erw Results are stored in oo_ SmoothedVariables oo_ SmoothedShocks and oo S8moothedMeasurementErrors Also triggers the computation
189. ote that there is no boolean type false is represented by integer zero and true is any non null integer The following operators can be used on integers e arithmetic operators e comparison operators gt lt gt e logical operators amp amp e integer ranges using the following syntax INTEGER1 INTEGER2 for example 1 4 is equivalent to integer array 1 2 3 4 The following operators can be used on strings e comparison operators e concatenation of two strings Ch apter 4 The Model file 99 extraction of substrings if s is a string then s 3 is a string containing only the third character of s and s 4 6 contains the characters from 4th to 6th The following operators can be used on arrays dereferencing if v is an array then v 2 is its 2nd element concatenation of two arrays difference returns the first operand from which the elements of the second operand have been removed extraction of sub arrays e g v 4 6 testing membership of an array in operator for example b in a b c returns 1 getting the length of an array length operator for example length a b c returns 3 and hence 1 length a b c is equivalent to integer array 1 2 3 Macro expressions can be used at two places inside macro directives directly in the body of the mod file between an at sign and curly braces like expr the macro processor will subs
190. outine isdate can be used to test if a string is interpretable as a date If more than one argument is provided they should all be dates represented as strings the resulting dates object contains as many elements as arguments to the constructor dates DATES dates dates DATES DATES dates Returns a copy of the dates object DATES passed as input arguments If more than one argument is provided they should all be dates objects The number of elements in the instantiated dates object is equal to the sum of the elements in the dates passed as arguments to the constructor dates FREQ YEAR SUBPERIOD dates where FREQ is a single character Y A Q M W or integer 1 4 12 or 52 specifying the frequency YEAR and SUBPERIOD are n 1 vectors of integers Returns a dates object with n elements If FREQ is equal to Y A or 1 the third argument is not needed because SUBPERIOD is necessarily a vector of ones in this case Examples Chapter 6 Time Series 113 doi dates 1950Q1 do2 dates 1950Q2 1950Q3 do3 dates doi do2 do4 dates Q 1950 1 A list of the available methods by alphabetical order is given below Note that the Matlab Octave classes do not allow in place modifications when a method is applied to an object a new object is instantiated For instance to apply the method multiplybytwo to an object X we write Y X multiplybytwo or equiva
191. p plan fplan y u surprise 2013Q4 2014Q4 1 1 1 1 2 1 1 k fplan flip plan fplan r e perfect_foresight 2013Q4 2014Q4 2 1 9 1 9 1 9 dset forecast det cond forecast fplan smoothed plot dset_forecast y u plot dset_forecast r e Chapter 4 The Model file 75 4 16 Optimal policy Dynare has tools to compute optimal policies for various types of objectives You can either solve for optimal policy under commitment with ramsey policy for optimal policy under discretion with discretionary policy or for optimal simple rule with osr osr VARIABLE NAME Command osr OPTIONS VARIABLE NAME Command Description This command computes optimal simple policy rules for linear quadratic problems of the form min E yW yi such that Ai Eye Ayi Asyi i Ce 0 where e E denotes the unconditional expectations operator e are parameters to be optimized They must be elements of the matrices A1 A A3 i e be specified as parameters in the params command and be entered in the model block e y are the endogenous variables specified in the var command whose co variance enters the loss function e e are the exogenous stochastic shocks specified in the var exo command e W is the weighting matrix The linear quadratic problem consists of choosing a subset of model parameters to minimize the weighted co variance of a specified sub
192. perator e endogenous variables with leads or lags greater or equal than two will have been removed replaced by new auxiliary variables and equations e for a stochastic model exogenous variables with leads or lags will also have been replaced by new auxiliary variables and equations Compiling the TEX file requires the following IATEX packages geometry fullpage breqn write latex static model Command Description This command creates a ATEX file containing the static model If your mod file is FILENAME mod then Dynare will create a file called FILENAME static tex containing the list of all the equations of the steady state model If ATEX names were given for variables and parameters see Section 4 2 Variable declarations page 10 then those will be used otherwise the plain text names will be used Note that the model written in the TEX file will differ from the model declared by the user in the some dimensions see write latex dynamic model page 21 for details Also note that this command will not output the contents of the optional steady state model block see steady_state_model page 34 it will rather output a static version i e without leads and lags of the dynamic model declared in the model block Compiling the TEX file requires the following IXTEX packages geometry fullpage breqn 4 6 Auxiliary variables The model which is solved internally by Dynare is not exactly the model declared by the use
193. pk end estimated_params bet normal pdf 1 0 05 end estimated params init Block estimated_params_init OPTIONS Block This block declares numerical initial values for the optimizer when these ones are different from the prior mean It should be specified after the estimated_params block as otherwise the specified starting values are overwritten by the latter Each line has the following syntax stderr VARIABLE NAME corr VARIABLE NAME 1 VARIABLE NAME 2 PARAMETER NAMEN gt INITIAL VALUE Options use calibration For not specifically initialized parameters use the deep parameters and the elements of the covariance matrix specified in the shocks block from calibration as starting Chapter 4 The Model file 52 values for estimation For components of the shocks block that were not explicitly specified during calibration or which violate the prior the prior mean is used See estimated params page 49 for the meaning and syntax of the various components estimated params bounds Block This block declares lower and upper bounds for parameters in maximum likelihood estimation Each line has the following syntax stderr VARIABLE NAME corr VARIABLE NAME 1 VARIABLE NAME 2 PARAMETER NAMEN LOWER BOUND UPPER BOUND See estimated params page 49 for the meaning and syntax of the various components estimation VARIABLE NAME Command estimation OPTIONS VARIABLE NAME J Command
194. put file tag page 93 simulation file tag FILENAME See simulation file tag page 94 horizon INTEGER The forecast horizon Default 12 filtered probabilities Uses filtered probabilities at the end of the sample as initial conditions for regime probabilities Only one of filtered probabilities regime and regimes may be passed Default off error band percentiles DOUBLE1 The percentiles to compute Default 0 16 0 50 0 84 If median is passed the default is 0 5 shock draws INTEGER The number of regime paths to draw Default 10 000 Shocks per parameter INTEGER The number of regime paths to draw under parameter uncertainty Default 10 thinning factor INTEGER Only 1 thinning factor of the draws in posterior draws file are used Default 1 free parameters NUMERICAL VECTOR A vector of free parameters to initialize theta of the model Default use estimated parameters parameter uncertainty Calculate IRFs under parameter uncertainty Requires that ms simulation has been run Default off regime INTEGER Given the data and model parameters what is the ergodic probability of being in the specified regime Only one of filtered probabilities regime and regimes may be passed Default off Chapter 4 The Model file 96 regimes Describes the evolution of regimes Only one of filtered probabilities regime and regimes may be passed Default off median A shortcut to setting error band percentiles 0
195. quare brackets e EXPRESSION indicates a mathematical expression valid outside the model description see Section 4 3 Expressions page 14 e MODEL EXPRESSION indicates a mathematical expression valid in the model description see Section 4 3 Expressions page 14 and Section 4 5 Model declaration page 18 e MACRO EXPRESSION designates an expression of the macro processor see Section 4 20 1 Macro expressions page 98 e VARIABLE NAME indicates a variable name starting with an alphabetical character and can t contain or accentuated characters e PARAMETER NAME indicates a parameter name starting with an alphabetical character and can t contain or accentuated characters e LATEX NAME indicates a valid INTEX expression in math mode not including the dollar signs e FUNCTION NAME indicates a valid MATLAB function name e FILENAME indicates a filename valid in the underlying operating system it is necessary to put it between quotes when specifying the extension or if the filename contains a non alphanumeric character 4 2 Variable declarations Declarations of variables and parameters are made with the following commands var VARIABLE NAME S LATEX NAMES long_name QUOTED_STRING Command var deflator MODEL_EXPRESSION VARIABLE NAME LATEX_NAMES Command ong name QUOTED STRING var log deflator M DEL EXPRESSION VARIABLE NAME LATEX NAMES Command 1ong_
196. r In some cases Dynare will introduce auxiliary endogenous variables along with corresponding auxiliary equations which will appear in the final output The main transformation concerns leads and lags Dynare will perform a transformation of the model so that there is only one lead and one lag on endogenous variables and in the case of a stochastic model no leads lags on exogenous variables Chapter 4 The Model file 22 This transformation is achieved by the creation of auxiliary variables and corresponding equa tions For example if x 2 exists in the model Dynare will create one auxiliary variable AUX_ ENDO LEAD x 1 and replace x 42 by AUX ENDO LEAD 1 A similar transformation is done for lags greater than 2 on endogenous auxiliary variables will have a name beginning with AUX ENDO LAG and for exogenous with leads and lags auxiliary variables will have a name beginning with AUX_EXO_LEAD or AUX_EXO_LAG respectively Another transformation is done for the EXPECTATION operator For each occurrence of this oper ator Dynare creates an auxiliary variable defined by a new equation and replaces the expectation operator by a reference to the new auxiliary variable For example the expression EXPECTATION 1 x 1 is replaced by AUX EXPECT LAG 1 1 and the new auxiliary variable is declared as AUX EXPECT LAG 1 x 2 Auxiliary variables are also introduced by the preprocessor for the ramsey policy command In
197. r Octave prompt with the filename of the mod given as argument In practice the handling of the model file is done in two steps in the first one the model and the processing instructions written by the user in a model file are interpreted and the proper MATLAB or GNU Octave instructions are generated in the second step the program actually runs the computations Both steps are triggered automatically by the dynare command dynare FILENAME mod OPTIONS MATLAB Octave command Description This command launches Dynare and executes the instructions included in FILENAME mod This user supplied file contains the model and the processing instructions as described in Chapter 4 The Model file page 10 dynare begins by launching the preprocessor on the mod file By default unless use d11 option has been given to model the preprocessor creates three intermediary files FILENAME m Contains variable declarations and computing tasks FILENAME dynamic m Contains the dynamic model equations Note that Dynare might introduce auxil iary equations and variables see Section 4 6 Auxiliary variables page 21 Outputs are the residuals of the dynamic model equations in the order the equations were declared and the Jacobian of the dynamic model equations For higher order ap proximations also the Hessian and the third order derivatives are provided When computing the Jacobian of the dynamic model the order of the endogenous vari
198. r an estimation with Metropolis fields are of the form o0o_ FilteredVariables MOMENT_NAME VARIABLE NAME oo FilteredVariablesKStepAhead MATLAB Octave variable Variable set by the estimation command if it is used with the filter step ahead option The k steps are stored along the rows while the columns indicate the respective variables The third dimension of the array provides the observation for which the forecast has been made For example if filter step ahead 1 2 4 and nobs 200 the element 3 5 204 stores the four period ahead filtered value of variable 5 computed at time t 200 for time t 204 The periods at the beginning and end of the sample for which no forecasts can be made e g entries 1 5 1 and 1 5 204 in the example are set to zero oo FilteredVariablesKStepAheadVariances MATLAB Octave variable Variable set by the estimation command if it is used with the filter step ahead option oo Filtered Variables X step ahead MATLAB Octave variable Variable set by the estimation command if it is used with the filter step ahead option in the context of Bayesian estimation Fields are of the form oo Filtered Variables X step ahead VARIABLE NAME The nth entry stores the k step ahead filtered variable computed at time n for time n k oo PosteriorIRF dsge MATLAB Octave variable Variable set by the estimation command if it is used with the bayesian_irf option Fields are of the form oo PosteriorIRF dsge MO
199. r large scale models square root solver Uses a square root solver for Lyapunov equations dlyapchol This method is fast for large scale models available under MATLAB if the control system toolbox is installed available under Octave if the control package from Octave Forge is installed Default value is default lyapunov fixed point tol DOUBLE This is the convergence criterion used in the fixed point Lyapunov solver Its default value is 1e 10 lyapunov doubling tol DOUBLE This is the convergence criterion used in the doubling algorithm to solve the Lya punov equation Its default value is 1e 16 analytic derivation Triggers estimation with analytic gradient The final hessian is also computed ana lytically Only works for stationary models without missing observations ar INTEGER See ar page 40 Only useful in conjunction with option moments varendo endogenous prior Use endogenous priors as in Christiano Trabandt and Walentin 2011 use univariate filters if singularity is detected INTEGER Decide whether Dynare should automatically switch to univariate filter if a singular ity is encountered in the likelihood computation this is the behaviour if the option is equal to 1 Alternatively if the option is equal to 0 Dynare will not automati cally change the filter but rather use a penalty value for the likelihood when such a singularity is encountered Default 1 qz zero threshold DOUBLE See aqz
200. r mode posterior mean posterior median Specify the parameter set to use for the forecasting No default value mandatory option controlled varexo VARIABLE NAME Specify the exogenous variables to use as control variables No default value manda tory option periods INTEGER Number of periods of the forecast Default 40 periods cannot be less than the number of constrained periods Chapter 4 The Model file 72 replic INTEGER Number of simulations Default 5000 conf_sig DOUBLE Level of significance for confidence interval Default 0 80 Output The results are not stored in the oo_ structure but in a separate structure forecasts saved to the harddisk into a file called conditional forecasts mat forecasts cond MATLAB Octave variable Variable set by the conditional forecast command It stores the conditional forecasts Fields are periods 1 by 1 vectors storing the steady state time 0 and the subsequent periods forecasts periods Fields are of the form forecasts cond FORECAST MOMENT VARIABLE NAME where FORECAST MOMENT is one of the following Mean Mean of the conditional forecast distribution ci Confidence interval of the conditional forecast distribution The size corresponds to conf sig forecasts uncond MATLAB Octave variable Variable set by the conditional forecast command It stores the unconditional forecasts Fields are of the form forecasts uncond F ORECAST MOMENT VARIABLE NAME foreca
201. r of 0 0348 Example 2 stoch simul irf 60 y k Performs the simulation of a model and displays impulse response functions on 60 periods for variables y and k oo_ mean MATLAB Octave variable After arun of stoch_simul contains the mean of the endogenous variables Contains theoretical mean if the periods option is not present and empirical mean otherwise The variables are arranged in declaration order oo_ var MATLAB Octave variable After a run of stoch_simul contains the variance covariance of the endogenous variables Con tains theoretical variance if the periods option is not present or an approximation thereof for order 2 and empirical variance otherwise The variables are arranged in declaration order oo autocorr MATLAB Octave variable After a run of stoch_simul contains a cell array of the autocorrelation matrices of the endoge nous variables The element number of the matrix in the cell array corresponds to the order of autocorrelation The option ar specifies the number of autocorrelation matrices available Contains theoretical autocorrelations if the periods option is not present or an approxima tion thereof for order 2 and empirical autocorrelations otherwise The field is only created if stationary variables are present The element oo autocorr i k 1 is equal to the correlation between y and y where y resp y is the k th resp l th endogenous variable in the declaration order Note that if
202. re respectively denoted by MODEL EXPRESSION and EXPRESSION Unlike MATLAB or Octave expressions Dynare expressions are necessarily scalar ones they cannot contain matrices or evaluate to matrices Expressions can be constructed using integers INTEGER floating point numbers DOUBLE parameter names PARAMETER NAME variable names VARIABLE NAME operators and functions The following special constants are also accepted in some contexts inf Constant Represents infinity nan Constant Not a number represents an undefined or unrepresentable value l Note that arbitrary MATLAB or Octave expressions can be put in a mod file but those expressions have to be on separate lines generally at the end of the file for post processing purposes They are not interpreted by Dynare and are simply passed on unmodified to MATLAB or Octave Those constructions are not addresses in this section Chapter 4 The Model file 15 4 3 1 Parameters and variables Parameters and variables can be introduced in expressions by simply typing their names The semantics of parameters and variables is quite different whether they are used inside or outside the model block 4 3 1 1 Inside the model Parameters used inside the model refer to the value given through parameter initialization see Section 4 4 Parameter initialization page 18 or homotopy setup when doing a simulation or are the estimated variables when doing an estimation V
203. red using the predetermined variables command Thus when plotting computing or simulating variables Dynare will follow the convention to use variables that are decided in the current period For example when generating impulse response functions for capital Dynare will plot k which is the capital stock decided upon by investment today and which will be used in tomorrow s production function This is the reason that capital is shown to be moving on impact because it is k and not the predetermined k 1 that is displayed It is important to remember that this also affects simulated time series and output from smoother routines for predetermined variables Compared to non predetermined variables they might otherwise appear to be falsely shifted to the future by one period Example The following two program snippets are strictly equivalent Using default Dynare timing convention var y k i model y k 1 alpha k i 1 delta k 1 end Using the alternative timing convention var y k i predetermined variables k model y k alpha k 1 i 1 delta k end Chapter 4 The Model file 14 trend var growth factor MODEL_EXPRESSION VARIABLE NAME Command SLATEX_NAMES Description This optional command declares the trend variables in the model See Section 4 1 Conventions page 10 for the syntax of MODEL_EXPRESSION and VARIABLE_NAME Optionally it is possible to give a IATEX name to the variable
204. rfuncname nargs 2 first deriv provided second deriv provided external function name yetotherfuncname nargs 3 first deriv provided funcname deriv 4 3 4 A few words of warning in stochastic context The use of the following functions and operators is strongly discouraged in a stochastic context max min abs sign gt lt gt The reason is that the local approximation used by stoch simul or estimation will by nature ignore the non linearities introduced by these functions if the steady state is away from the kink And if the steady state is exactly at the kink then the approximation will be bogus because the derivative of these functions at the kink is bogus as explained in the respective documentations of these functions and operators Note that extended path is not affected by this problem because it does not rely on a local approximation of the model 4 4 Parameter initialization When using Dynare for computing simulations it is necessary to calibrate the parameters of the model This is done through parameter initialization The syntax is the following PARAMETER NAME EXPRESSION Here is an example of calibration parameters alpha bet beta 0 99 alpha 0 36 A 1 alpha beta Internally the parameter values are stored in M_ params M_ params MATLAB Octave variable Contains the values of model parameters The parameters are in the order that was used in the parameters command
205. riables Those that appear only at current and past period in the model but not at future period i e at t and t 1 but not t 1 The number of such variables is equal to M npred Purely forward variables Those that appear only at current and future period in the model but not at past period i e at t and t 1 but not t 1 The number of such variables is stored in M nfwrd Mixed variables Those that appear at current past and future period in the model i e at t t 1 and t 1 The number of such variables is stored in M nboth Static variables Those that appear only at current not past and future period in the model i e only at t not at t 1 or t 1 The number of such variables is stored in M nstatic Note that all endogenous variables fall into one of these four categories since after the creation of auxiliary variables see Section 4 6 Auxiliary variables page 21 all endogenous have at most one lead and one lag We therefore have the following identity M npred M both M nfwrd M nstatic M endo nbr Internally Dynare uses two orderings of the endogenous variables the order of declaration which is reflected in M endo names and an order based on the four types described above which we will call the DR order DR stands for decision rules Most of the time the declaration order is used but for elements of the decision rules the DR order is used The DR order is the followin
206. riables VARIABLE NAME After an estimation with Metropolis fields are of the form oo UpdatedVariables MOMENT NAME VARIABLE NAME oo PosteriorTheoreticalMoments MATLAB Octave variable Variable set by the estimation command if it is used with the moments varendo option Fields are of the form oo PosteriorTheoreticalMoments dsge THEORETICAL MOMENT ESTIMATED OBJECT MOMENT g NAME VARIABLE NAME where THEORETICAL MOMENT is one of the following covariance Variance covariance of endogenous variables correlation Auto and cross correlation of endogenous variables Fields are vectors with corre lations from 1 up to order options ar VarianceDecomposition Decomposition of variance unconditional variance i e at horizon infinity ConditionalVarianceDecomposition Only if the conditional variance decomposition option has been specified oo posterior density MATLAB Octave variable Variable set by the estimation command if it is used with mh_replic gt 0 or load mh file option Fields are of the form oo_ posterior_density PARAMETER_NAME oo_ posterior_hpdinf MATLAB Octave variable Variable set by the estimation command if it is used with mh_replic gt 0 or load_mh_file option Fields are of the form oo_ posterior_hpdinf ESTIMATED_OBJECT VARIABLE_NAME oo_ posterior_hpdsup MATLAB Octave variable Variable set by the estimation command if it is used with mh_replic gt 0 or load_mh_file option Fields are of the fo
207. ries Dynare offers a user friendly and intuitive way of describing these models It is able to perform simulations of the model given a calibration of the model parameters and is also able to estimate these parameters given a dataset In practice the user will write a text file containing the list of model variables the dynamic equations linking these variables together the computing tasks to be performed and the desired graphical or numerical outputs A large panel of applied mathematics and computer science techniques are internally employed by Dynare multivariate nonlinear solving and optimization matrix factorizations local functional approximation Kalman filters and smoothers MCMC techniques for Bayesian estimation graph algorithms optimal control Various public bodies central banks ministries of economy and finance international organi sations and some private financial institutions use Dynare for performing policy analysis exercises and as a support tool for forecasting exercises In the academic world Dynare is used for research and teaching purposes in postgraduate macroeconomics courses Dynare is a free software which means that it can be downloaded free of charge that its source code is freely available and that it can be used for both non profit and for profit purposes Most of the source files are covered by the GNU General Public Licence GPL version 3 or later there are some exceptions to this see the file L
208. riorIRF dsge 64 oo PosteriorTheoreticalMoments 65 oo_ RecursiveForecast 66 oo_ shock_decomposition 68 oo SmoothedMeasurementErrors 64 o0_ SmoothedShocks 64 o0_ SmoothedVariables 65 00 Steady state sass ss REIR UR RETE Res 32 oo UpdatedVariables 65 OO VAT 5 soc theres ir eee de hres baste cie ous 44 oo_ variance_decomposition 45 OPTIONS 25 88 06 sun aus Ra hex rede Pe P eque onde 8 S Sigma Q ioxasa diet he yu e ee PU Ep E ER Eis 29
209. riterion used in the logarithmic reduction algorithm Its default value is le 12 dr_logarithmic_reduction_maxiter INTEGER The maximum number of iterations used in the logarithmic reduction algorithm Its default value is 100 loglinear See loglinear page 53 Note that ALL variables are log transformed by using the Jacobian transformation not only selected ones Thus you have to make sure that your variables have strictly positive steady states stoch_simul will display the Chapter 4 The Model file 44 moments decision rules and impulse responses for the log linearized variables The decision rules saved in oo dr and the simulated variables will also be the ones for the log linear variables Output This command sets oo dr oo mean oo var and oo autocorr which are described below If option periods is present sets oo endo simul see oo_ endo_simul page 39 and also saves the simulated variables in MATLAB Octave vectors of the global workspace with the same name as the endogenous variables If options irf is different from zero sets oo irfs see below and also saves the IRFs in MATLAB Octave vectors of the global workspace this latter way of accessing the IRFs is deprecated and will disappear in a future version Example 1 shocks var stderr 0 0348 end stoch simul Performs the simulation of the 2nd order approximation of a model with a single stochastic shock e with a standard erro
210. rity of the covariance matrix of the prediction errors during the Kalman filter minimum allowed reciprocal of the matrix condition number Default value is 1e 10 filter covariance Saves the series of one step ahead error of forecast covariance matrices filter step ahead INTEGER1 INTEGER2 See below filter step ahead INTEGER1 INTEGER2 Triggers the computation k step ahead filtered values Stores results in oo FilteredVariablesKStepAhead and 00 FilteredVariablesKStepAheadVariances Chapter 4 The Model file 61 filter_decomposition Triggers the computation of the shock decomposition of the above k step ahead filtered values diffuse_filter Uses the diffuse Kalman filter as described in Durbin and Koopman 2012 and Koopman and Durbin 2003 to estimate models with non stationary observed variables When diffuse filter is used the lik init option of estimation has no effect When there are nonstationary exogenous variables in a model there is no unique deterministic steady state For instance if productivity is a pure random walk Qt Qt 1 t any value of a of a is a deterministic steady state for productivity Consequently the model admits an infinity of steady states In this situation the user must help Dynare in selecting one steady state except if zero is a trivial model s steady state which happens when the linear option is used in the model declaration The user can either provide the ste
211. rm endo name vs lags fig shows bar charts of the elementary effect tests for the ten most important parameters driving the reduced form coefficients of the selected endogenous variables namendo versus lagged endogenous variables namlagendo e mod file redform endo name vs shocks fig shows bar charts of the elementary effect tests for the ten most important parameters driving the reduced form coefficients of the selected endogenous variables namendo versus exogenous variables namexo e mod file redform screen fig shows bar chart of all elementary effect tests for each parameter this allows one to identify parameters that have a minor effect for any of the reduced form coefficients 4 17 6 Identification Analysis Setting the option identification 1 an identification analysis based on theoretical moments is performed Sensitivity plots are provided that allow to infer which parameters are most likely to be less identifiable Prerequisite for properly running all the identification routines is the keyword identification in the Dynare model file This keyword triggers the computation of analytic derivatives of the model with respect to estimated parameters and shocks This is required for option morris 2 which implements Iskrev 2010 identification analysis For example the placing identification dynare sensitivity identification 1 morris 2 in the Dynare model file trigger identification analysis using ana
212. rm oo_ posterior_hpdsup ESTIMATED_OBJECT VARIABLE_NAME 4 When the shocks are correlated it is the decomposition of orthogonalized shocks via Cholesky decomposition according to the order of declaration of shocks see Section 4 2 Variable declarations page 10 Chapter 4 The Model file 66 00 posterior mean MATLAB Octave variable Variable set by the estimation command if it is used with mh_replic gt 0 or load mh file option Fields are of the form oo_ posterior_mean ESTIMATED_OBJECT VARIABLE_NAME 00 posterior mode MATLAB Octave variable Variable set by the estimation command if it is used with mh_replic gt 0 or load mh file option Fields are of the form o0_ posterior_mode ESTIMATED_OBJECT VARIABLE_NAME 00 posterior std MATLAB Octave variable Variable set by the estimation command if it is used with mh_replic gt 0 or load mh file option Fields are of the form 0o posterior std ESTIMATED OBJECT VARIABLE NAME Here are some examples of generated variables 00 posterior mode parameters alp 00 posterior mean shocks std ex 00 posterior hpdsup measurement errors corr gdp conso oo RecursiveForecast MATLAB Octave variable Variable set by the forecast option of the estimation command when used with the nobs INTEGER1 INTEGER2 option see nobs page 53 Fields are of the form oo RecursiveForecast F RECAST OBJECT VARIABLE NAME where FORECAST OBJECT is one of the following
213. rtant to check that the actual shape of prior densities matches what you have in mind Ill chosen values for the prior standard density can result in absurd prior densities Default value is 1 nograph See nograph page 41 nodisplay See nodisplay page 41 graph format FORMAT graph format FORMAT FORMAT See graph format page 41 lik init INTEGER Type of initialization of Kalman filter 1 For stationary models the initial matrix of variance of the error of forecast is set equal to the unconditional variance of the state variables 2 For nonstationary models a wide prior is used with an initial matrix of variance of the error of forecast diagonal with 10 on the diagonal 3 For nonstationary models use a diffuse filter use rather the diffuse filter option 4 The filter is initialized with the fixed point of the Riccati equation Default value is 1 For advanced use only lik algo INTEGER For internal use and testing only conf sig DOUBLE Confidence interval used for classical forecasting after estimation See See conf sig page 69 mh conf sig DOUBLE Confidence HPD interval used for the computation of prior and posterior statistics like parameter distributions prior posterior moments conditional variance decom position impulse response functions Bayesian forecasting Default 0 9 mh replic INTEGER Number of replications for Metropolis Hastings algorithm For the time being mh_ replic should
214. rwrite the value of compiler contained in the report object Hence passing the value here is useful for using different IXTEX compilers or just for passing the value at the last minute Example The following code creates a one page report The first part of the page contains two graphs displayed across two columns and one row The bottom of the page displays a centered table 44 Create dseries dsq dseries quarterly csv dsa dseries annual csv dsca dseries annual control csv hh Report rep report Page 1 rep rep addPage title My Page Title titleFormat large bfseries Section 1 rep rep addSection cols 2 rep rep addGraph title Graph 1 1 showLegend true xrange dates 2007q1 dates 2013q4 shade dates 2012q2 dates 2013q4 rep rep addSeries data dsq SERIES1 color b graphLineWidth 1 rep rep addSeries data dsq SERIES2 color g graphLineStyle graphLineWidth 1 5 rep rep addGraph title Graph 1 2 showLegend true xrange dates 2007q1 dates 2013q4 shade dates 2012q2 dates 2013q4 rep rep addSeries data dsq SERIES3 color b graphLineWidth 1 rep rep addSeries data dsq SERIES4 color
215. rzcat operator All the input arguments must be dates objects The returned argument is a dates object gathering all the dates given in the input arguments repetitions are not removed Example gt gt A dates 1950Q1 gt gt B dates 1950Q2 gt gt C A B gt gt C C dates 195001 1950Q2 gt intersect A B dates Overloads the Matlab Octave intersect function All the input arguments must be dates objects The returned argument is a dates object gathering all the common dates given in the input arguments If A and B are disjoint dates objects the function returns an empty dates object Returned dates in dates object C are sorted by increasing order Example Vv Vv gt l dates 19500Q1 dates 1951Q4 gt gt B dates 1951Q1 dates 1951Q4 gt gt C intersect A B C dates 1951Q1 195102 1951Q3 1951Q4 gt setdiff A B dates Overloads the Matlab Octave setdiff function All the input arguments must be dates objects The returned argument is a dates object all dates present in but not in B If A and B are disjoint dates objects the function returns A Returned dates in dates object C are sorted by increasing order Example gt gt A dates 1950Q1 dates 1969Q4 gt gt B dates 1960Q1 dates 1969Q4 gt gt C dates 1970Q1 dates 1979Q4 gt gt di setdiff d1 d2 gt gt d2 setdiff d1 d3
216. s the file must contain a column of the same name supported under Octave if the io and java packages from Octave Forge are installed along with a Java Runtime Environment Warning The extension must be omitted in the command argument Dynare will automatically figure out the extension and select the appropriate file type 4 8 Shocks on exogenous variables In a deterministic context when one wants to study the transition of one equilibrium position to another it is equivalent to analyze the consequences of a permanent shock and this in done in Dynare through the proper use of initval and endval Another typical experiment is to study the effects of a temporary shock after which the system goes back to the original equilibrium if the model is stable A temporary shock is a temporary change of value of one or several exogenous variables in the model Temporary shocks are specified with the command shocks In a stochastic framework the exogenous variables take random values in each period In Dynare these random values follow a normal distribution with zero mean but it belongs to the user to specify the variability of these shocks The non zero elements of the matrix of variance covariance of the shocks can be entered with the shocks command Or the entire matrix can be directly entered with Sigma e this use is however deprecated If the variance of an exogenous variable is set to zero this variable will appear in the report
217. s also suggest another way of looking at the use of steady after initval and endval Instead of saying that the implicit unspecified conditions before and after the simulation range have to fit the initial terminal conditions of the endogenous variables in those blocks steady specifies that those conditions at t lt 0 and t gt 201 are equal to being at the steady state given the exogenous variables in the initval and endval blocks and sets the endogenous variables at t 0 and t 201 to the corresponding steady state equilibrium values The fact that c at t 0 and k at t 201 specified in initval and endval are taken as given has an important implication for plotting the simulated vector for the endogenous variables this vector will also contain the initial and terminal conditions and thus is 202 periods long in the example When you specify arbitrary values for the initial and terminal conditions for forward and backward looking variables respectively these values can be very far away from the endogenously determined values at t 1 and t 200 While the values at t 0 and t 201 are Chapter 4 The Model file 26 unrelated to the dynamics for 0 t 201 they may result in strange looking large jumps In the example above consumption will display a large jump from t 0 to t 1 and capital will jump from t 200 to t 201 histval Block Description In a deterministic perfect foresight context In models with lags on more than one period the histval
218. s the same options including restricting the endogenous variables by listing them after the command as stoch simul see Section 4 13 1 Computing the stochastic solution page 40 plus maxit INTEGER Determines the maximum number of iterations used in the non linear solver Default 1000 tolf DOUBLE Convergence criterion for termination based on the function value Iteration will cease when it proves impossible to improve the function value by more than tolf Default 1e 7 Chapter 4 The Model file 76 The value of the objective is stored in the variable oo osr objective function which is described below After running osr the parameters entering the simple rule will be set to their optimal value so that subsequent runs of stoch simul will be conducted at these values osr params PARAMETER NAME Command This command declares parameters to be optimized by osr optim_weights Block This block specifies quadratic objectives for optimal policy problems More precisely this block specifies the nonzero elements of the weight matrix W used in the quadratic form of the objective function in osr An element of the diagonal of the weight matrix is given by a line of the form VARIABLE NAME EXPRESSION An off the diagonal element of the weight matrix is given by a line of the form VARIABLE NAME VARIABLE NAME EXPRESSION Example var y inflation r varexo y inf parameters delta sigma alpha kappa gammarr gammaxO gammac
219. s variable indicated between quotes in the second argument The shock type has to be specified in the third argument between quotes surprise in case of an unexpected shock or perfect foresight for a perfectly anticipated shock The fourth argument indicates the period of the shock using a dates class see dates class members page 111 The last argument is the shock path indicated as a Matlab vector of double This function return the handle of the updated forecast scenario Chapter 4 The Model file 74 The forecast scenario can also contain a constrained path on an endogenous variable The values of the related exogenous variable compatible with the constrained path are in this case computed In other words a conditional forecast is performed This kind of shock is described with the function flip plan HANDLE flip plan HANDLE VARIABLE NAME MATLAB Octave command VARIABLE NAME SHOCK TYPE DATES MATLAB VECTOR OF DOUBLE DOUBLE EXPRESSION DOUBLE EXPRESSION Adds to the forecast scenario a constrained path on the endogenous variable specified between quotes in the second argument The associated exogenous variable provided in the third argu ment between quotes is considered as an endogenous variable and its values compatible with the constrained path on the endogenous variable will be computed The nature of the expectation on the constrained path has to be specified in the fourth argument between quotes s
220. sample e mod file prior stable corr fig plots of bivariate projections of the sample fulfilling Blanchard Kahn conditions Chapter 4 The Model file 80 e mod file prior indeterm corr fig plots of bivariate projections of the sample pro ducing indeterminacy e mod file prior unstable corr fig plots of bivariate projections of the sample pro ducing instability e mod file prior unacceptable corr fig plots of bivariate projections of the sample producing unacceptable solutions i e either instability or indeterminacy or the solution could not be found e g the steady state solution could not be found by the solver Similar conventions apply for mod file mc fig files obtained when samples from multi variate normal are used 4 17 3 Reduced Form Mapping The mapping of the reduced form solution forces the use of samples from prior ranges or prior distributions i e pprior 1 and ppost 0 It uses 250 samples to optimize smoothing parameters and 1000 samples to compute the fit The rest of the sample is used for out of sample validation One can also load a previously estimated mapping with a new Monte Carlo sample to look at the forecast for the new Monte Carlo sample The following synthetic figures are produced e mod file redform endo name vs lags fig shows bar charts of the sensitivity in dices for the ten most important parameters driving the reduced form coefficients of the selected
221. set of endogenous variables subject to a linear law of motion implied by the first order conditions of the model A few things are worth mentioning First y denotes the selected endogenous variables deviations from their steady state i e in case they are not already mean 0 the variables entering the loss function are automatically demeaned so that the centered second moments are minimized Second osr only solves linear quadratic problems of the type resulting from combining the specified quadratic loss function with a first order approximation to the model s equilibrium conditions The reason is that the first order state space representation is used to compute the unconditional co variances Hence osr will automatically select order 1 Third because the objective involves minimizing a weighted sum of unconditional second moments those second moments must be finite In particular unit roots in y are not allowed The subset of the model parameters over which the optimal simple rule is to be optimized y must be listed with osr_params The weighting matrix W used for the quadratic objective function is specified in the optim_ weights block By attaching weights to endogenous variables the subset of endogenous variables entering the objective function y is implicitly specified The linear quadratic problem is solved using the numerical optimizer csminwel of Chris Sims Options The osr command will subsequently run stoch simul and accept
222. st 1 dA A temporary variable m mst Three other temporary variables khst 1 gst bet 1 del alp gst alp bet 1 alp 1 xist khst gst alp 1 gst 1 del khst mst 1 nust psi mst 2 1 alp 1 psi bet gst alp khst alp n xist nust xist P xist nust k khst n 1 psi mst n 1 psi 1 n c mst P d 1 mst 1 y k alp n 1 alp gst alp R mst bet You can use MATLAB functions which return several arguments W e my_function 1 n gp_obs m dA gy_obs dA end steady 4 10 3 Replace some equations during steady state computations When there is no steady state file Dynare computes the steady state by solving the static model i e the model from the mod file from which leads and lags have been removed In some specific cases one may want to have more control over the way this static model is created Dynare therefore offers the possibility to explicitly give the form of equations that should be in the static model More precisely if an equation is prepended by a static tag then it will appear in the static model used for steady state computation but that equation will not be used for other computations For every equation tagged in this way you must tag another equation with dynamic that equation will not be used for steady state computation but will be used for other computations This functionality can be useful on models with a unit r
223. sts instruments MATLAB Octave variable Variable set by the conditional forecast command Stores the names of the exogenous instruments forecasts controlled variables MATLAB Octave variable Variable set by the conditional forecast command Stores the position of the constrained endogenous variables in declaration order forecasts graphs MATLAB Octave variable Variable set by the conditional forecast command Stores the information for generating the conditional forecast plots Example var y amp varexo e u estimation conditional forecast paths var y periods 1 3 4 5 values 2 5 var a periods 1 5 values 3 Chapter 4 The Model file 73 end conditional forecast parameter set calibration controlled varexo e u replic plot conditional forecast periods 10 a y conditional forecast paths Block Describes the path of constrained endogenous before calling conditional forecast The syntax is similar to deterministic shocks in shocks see conditional forecast for an example The syntax of the block is the same than the deterministic shocks in the shocks blocks see Section 4 8 Shocks on exogenous variables page 27 plot conditional forecast VARIABLE NAME Command plot conditional forecast periods INTEGER VARIABLE NAME Command Description Plots the conditional plain lines and unconditional dashed lines forecasts To be used after conditional forecast
224. symbol is assigned in initval or endval Output Depending on the computing tasks requested in the mod file executing the dynare command will leave variables containing results in the workspace available for further processing More details are given under the relevant computing tasks The M_ oo and options structures are saved in a file called FILENAME results mat If they exist estim params bayestopt dataset and estimation info are saved in the same file Example dynare ramst dynare ramst mod savemacro The output of Dynare is left into three main variables in the MATLAB Octave workspace MATLAB Octave variable Structure containing various information about the model options MATLAB Octave variable Structure contains the values of the various options used by Dynare during the computation Chapter 3 Running Dynare 9 00 MATLAB Octave variable Structure containing the various results of the computations 3 2 Dynare hooks It is possible to call pre and post Dynare preprocessor hooks written as MATLAB scripts The script MODFILENAME hooks priorprocessing m is executed before the call to Dynare s prepro cessor and can be used to programmatically transform the mod file that will be read by the preprocessor The script MODFILENAME hooks postprocessing m is executed just after the call to Dynare s preprocessor and can be used to programmatically transform the files generated by Dynare s preprocessor before
225. t it in a file called octaverc in your home directory under Windows this will generally be c NDocuments and Settings USERNAME while under Mac OS X it is Users USERNAME This file is run by Octave at every startup 2 3 3 Some words of warning You should be very careful about the content of your MATLAB or Octave path You can display its content by simply typing path in the command window The path should normally contain system directories of MATLAB or Octave and some sub directories of your Dynare installation You have to manually add the matlab subdirectory and Dynare will automatically add a few other subdirectories at runtime depending on your configu ration You must verify that there is no directory coming from another version of Dynare than the one you are planning to use You have to be aware that adding other directories to your path can potentially create problems if any of your M files have the same name as a Dynare file Your file would then override the Dynare file making Dynare unusable Chapter 3 Running Dynare 6 3 Running Dynare In order to give instructions to Dynare the user has to write a model file whose filename extension must be mod This file contains the description of the model and the computing tasks required by the user Its contents is described in Chapter 4 The Model file page 10 3 1 Dynare invocation Once the model file is written Dynare is invoked using the dynare command at the MATLAB o
226. tages INTEGER The small and large perturbation are repeated until improvement has stopped This specifics the maximum number of stages allowed Default 20 random function convergence criterion DOUBLE The convergence criterion for the objective function when number of large perturbations is positive Default 0 1 random parameter convergence criterion DOUBLE The convergence criterion for parameter values when number of large perturbations is positive Default 0 1 Chapter 4 The Model file 93 Example ms estimation datafile data initial year 1959 final year 2005 nlags 4 max repeated optimization runs 1 max number of stages 0 ms estimation file tag second run datafile data initial year 1959 final year 2005 nlags 4 max repeated optimization runs 1 max number of stages 0 ms estimation file tag second run output file tag third run no create init max repeated optimization runs 5 number of large perturbations 10 ms simulation Command ms simulation OPTIONS Command Description Simulates a Markov switching SBVAR model Options file_tag FILENAME The portion of the filename associated with the ms estimation run Default lt mod_ file output file tag FILENAME The portion of the output filename that will be assigned to this run Default file tag mh replic INTEGER The number of draws to save Default 10 000 drop INTEGER The number of burn in draws Default
227. ter w r t the instruments Default 1e 4 InitialSimplexSize Initial size of the simplex expressed as percentage deviation from the provided initial guess in each direction Default 05 Available options are gt MaxIter Maximum number of iterations MaxFunEvals Maximum number of objective function evaluations De fault Inf TolFun Tolerance parameter w r t the objective function Default 1e 7 To1X Tolerance parameter w r t the instruments Default 1e 7 Available options are gt MaxIter Maximum number of iterations Default 5000 gt MaxFunvEvals Maximum number of objective function evaluations No default TolFun Tolerance parameter w r t the objective function Default 1e 4 To1X Tolerance parameter w r t the instruments Default 1e 4 Chapter 4 The Model file 59 gt EndTemperature Terminal condition w r t the temperature When the tem perature reaches EndTemperature the temperature is set to zero and the algorithm falls back into a standard simplex algorithm Default 1 Example 1 To change the defaults of csminwel mode_compute 4 estimation mode compute 4 optim NumgradAlgorithm 3 TolFun 1e j B o3 nodiagnostic Does not compute the convergence diagnostics for Metropolis Hastings Default diagnostics are computed and displayed bayesian irf Triggers the computation of the posterior distribution of IRFs The length of the IRFs are co
228. the value given in the corresponding parameter initialization see Section 4 4 Parameter initialization page 18 for an endogenous or exogenous variable it refers to the value given in the most recent initval or endval block 4 3 2 Operators The following operators are allowed in both MODEL EXPRESSION and EXPRESSION e binary arithmetic operators x e unary arithmetic operators e binary comparison operators which evaluate to either O or 1 lt gt lt gt Note that these operators are differentiable everywhere except on a line of the 2 dimensional real plane However for facilitating convergence of Newton type methods Dynare assumes that at the points of non differentiability the partial derivatives of these operators with respect to both arguments is equal to 0 since this is the value of the partial derivatives everywhere else The following special operators are accepted in MODEL EXPRESSION but not in EXPRES SION STEADY STATE MUDEL EXPRESSION Operator This operator is used to take the value of the enclosed expression at the steady state A typical usage is in the Taylor rule where you may want to use the value of GDP at steady state to compute the output gap EXPECTATION INTEGER M DEL EXPRESSION Operator This operator is used to take the expectation of some expression using a different information set than the information available at current period For example EXPECTATION
229. then b 195102 and b a 5 are identical plus unary operator Increments a date by one period 1950Q1 is identical to 195002 1950Q1 is iden tical to 1951Q1 minus binary operator Has two functions difference and subtraction If the second argument is a date calculates the difference between the first date and the second date e g 1951Q2 195001 is equal to 5 If the second argument is an integer X subtracts X periods from the date e g 1951Q2 2 is equal to 19504 minus unary operator Subtracts one period to a date 1950Q1 is identical to 194904 The unary minus operator is the reciprocal of the unary plus operator 1950Q1 is identical to 1950Q1 colon operator Can be used to create a range of dates For instance r 1950Q1 1951Q1 creates a dates object with five elements 1950Q1 1950Q2 1950Q3 195004 and 1951Q1 By default the increment between each element is one period This default can be changed using for instance the following instruction 195001 2 1951Q1 which will instantiate a dates object with three elements 1950Q1 1950Q3 and 1951Q1 horzcat operator Concatenates dates objects without removing repetitions For instance 1950Q1 195002 is a a dates object with two elements 1950Q1 and 1950Q2 vertcat operator 1 Same as horzcat operator eq operator equal Tests if two dates objects are equal 1950Q1 1950Q2 returns 1 1950Q1 1950Q2 returns O If the compared objects ha
230. theoretical moments have been requested oo autocorr ij is the same than oo_ gamma_y i 1 Chapter 4 The Model file 45 oo gamma y MATLAB Octave variable After a run of stoch_simul if theoretical moments have been requested i e if the periods option is not present this variable contains a cell array with the following values where ar is the value of the option of the same name oo_ gamma 1 Variance co variance matrix oo_ gamma i 1 for i 1 ar Autocorrelation function see oo_ autocorr page 44 for more details Beware this is the autocorrelation function not the autocovariance function oo_ gamma nar 2 Unconditional variance decomposition see oo_ variance decomposition page 45 oo_ gamma nar 3 If a second order approximation has been requested contains the vector of the mean correction terms In case of order 2 the theoretical second moments are a second order accurate approximation of the true second moments see conditional_variance_decomposition oo_ variance_decomposition MATLAB Octave variable After a run of stoch_simul when requesting theoretical moments periods 0 contains a matrix with the result of the unconditional variance decomposition i e at horizon infinity The first dimension corresponds to the endogenous variables in the order of declaration and the second dimension corresponds to exogenous variables in the order of declaration Numbers are in percent and sum up to 100 across colu
231. tial conditions and future information varexo det commands can appear several times in the file and Dynare will concatenate them Options long name QUOTED STRING Like long_name page 11 but value stored in M exo det names long Example varexo m gov varexo det tau parameters PARAMETER NAME LATEX NAMES Command ong name QUOTED STRING Description This command declares parameters used in the model in variable initialization or in shocks declarations See Section 4 1 Conventions page 10 for the syntax of PARAMETER NAME Optionally it is possible to give a IATEX name to the parameter The parameters must subsequently be assigned values see Section 4 4 Parameter initialization page 18 parameters commands can appear several times in the file and Dynare will concatenate them Options long name QUOTED STRING Like long_name page 11 but value stored in M param names long Example parameters alpha bet change type var varexo varexo_det parameters VARIABLE NAME Command PARAMETER_NAME Description Changes the types of the specified variables parameters to another type endogenous exogenous exogenous deterministic or parameter It is important to understand that this command has a global effect on the mod file the type change is effective after but also before the change type command This command is typically used when flipping some variables for steady
232. titute the expression with its value In the following MACRO EXPRESSION designates an expression constructed as explained above 4 20 2 Macro directives include FILENAME Macro directive This directive simply includes the content of another file at the place where it is inserted It is exactly equivalent to a copy paste of the content of the included file Note that it is possible to nest includes i e to include a file from an included file Example include modelcomponent mod define MACRO VARIABLE MACRO EXPRESSION Macro directive Defines macro variable Example 1 define x 5 Integer define y US String define v 1 2 4 Integer array define w US EA String array define z 3 v 2 Equals 5 Qidefine t US in w Equals 1 true Example 2 define x B C define i 2 model A x il end is strictly equivalent to Chapter 4 The Model file 100 model A C end if MACRO EXPRESSION Macro directive ifdef MACRO VARIABLE Macro directive ifndef MACRO VARIABLE Macro directive Qitelse Macro directive endif Macro directive Conditional inclusion of some part of the mod file The lines between if ifdef or ifndef and the next else or G endif is executed only if the condition evaluates to a non null integer The else branch is optional and if present is only evaluated if the condition evaluates
233. to 0 Example Choose between two alternative monetary policy rules using a macro variable Qitdefine linear mon pol 0 or 1 model if linear mon pol i w i 1 1 w i ss w2 pie piestar Qitelse i i 1 w i ss 1 w pie piestar w2 Qitendif end Example Choose between two alternative monetary policy rules using a macro variable As linear mon pol was not previously defined in this example the second equation will be chosen model ifdef linear mon pol i w i 1 1 w i ss w2 pie piestar Qitelse i i 1 w i ss 1 w pie piestar w2 Qitendif end Choose between two alternative monetary policy rules using a macro variable As linear mon pol was not previously defined in this example the first equation will be chosen model ifndef linear mon pol i w i 1 1 w i ss w2 pie piestar Qitelse i i 1 w i ss 1 w pie piestar w2 Qitendif end Qitfor MACRO VARIABLE in MACRO EXPRESSION Macro directive endfor Macro directive Loop construction for replicating portions of the mod file Note that this construct can enclose variable parameters declaration computational tasks but not a model declaration Chapter 4 The Model file 101 Example model for country in home foreign GDP_ country A K Ofcountryl a L_ country 1 a endfor end is equivalent to model GDP_home A K home a L home 1 a GDP_foreign A K
234. tribution of the respective shocks Column M exo nbr 1 stores the contribution of the initial conditions while column M exo nbr 2 stores the smoothed value of the respective endogenous variable The third dimension stores the time periods unit root vars VARIABLE NAME Command This command is deprecated Use estimation option diffuse filter instead for estimating a model with non stationary observed variables or steady option nocheck to prevent steady to check the steady state returned by your steady state file Dynare also has the ability to estimate Bayesian VARs bvar density Command Computes the marginal density of an estimated BVAR model using Minnesota priors See bvar a la sims pdf which comes with Dynare distribution for more information on this command Dynare can also run the smoother on a calibrated model calib smoother VARIABLE NAME Command calib smoother OPTIONS VARIABLE NAME Command Description This command computes the smoothed variables and possible the filtered variables on a calibrated model datafile must be provided and the observable variables declared with varobs The smoother is based on a first order approximation of the model By default the command computes the smoothed variables and shocks and stores the results in oo SmoothedVariables and oo SmoothedShocks It also fills oo UpdatedVariables Options datafile FILENAME See datafile page 53
235. ts2 is a dseries object Chapter 6 Time Series 139 nifnif noufnouf 1950Q1 0 82558 0 31852 1950Q2 0 78996 0 53406 1950Q3 0 089951 0 13629 1950Q4 0 11171 0 67865 B ydiff 4 dseries B ygrowth A dseries Computes yearly differences or growth rates Chapter 7 Reporting 140 7 Reporting Dynare provides a simple interface for creating IXTEX reports comprised of IATEX tables and TikZ graphs You can use the report as created through Dynare or pick out the pieces you want for inclusion in your own paper Reports are created and modified by calling methods on class objects The objects are hierarchical with the following order from highest to lowest Report Page Section Graph Table Vspace Series For simplicity of syntax we abstract away from these classes allowing you to operate directly on a Report object while maintaining the names of these classes in the Report Class methods you will use The report is created sequentially command by command hence the order of the commands matters When an object of a certain hierarchy is inserted all methods will function on that object until an object of equal or greater hierarchy is added Hence once you add a Page to the report every time you add a Section object it will be added to this Page until another Page is added to the report via addPage page 141 This will become more clear with the example at the end of the section Options to the methods
236. tting x 1 1 in the endval block without a shocks block implies that technology jumps to this new level in t 1 and stays there forever Because the law of motion for capital is backward looking we also need an initial condition for k at time 0 specified in the initval block Similarly because the Euler equation is forward looking we need a terminal condition for c at t 201 which is specified in the endval block Specifying c in the initval block and k in the endval block has no impact on the results due to the optimization problem in the first period being to choose c k at t 1 given predetermined capital stock k inherited from t 0 as well as the current and future values for technology the value for c at time t 0 plays no role The same applies to the choice of c k at time t 200 which does not depend on k at t 201 As the Euler equation shows that choice only depends on current capital as well as future consumption c and technology x but not on future capital k The intuitive reason is that those variables are the consequence of optimization problems taking place in at periods t 0 and t 201 respectively which are not considered Thus when specifying those values in the initval and endval blocks Dynare takes them as given and basically assumes that there were realizations of exogenous variables and states basically initial terminal conditions at the unspecified time periods t 0 and t gt 201 that make those choices equilibrium values Thi
237. unctions used in an EXPRESSION external function OPTIONS Command Description This command declares the external functions used in the model block It is required for every unique function used in the model block external function commands can appear several times in the file and must come before the model block Options name NAME The name of the function which must also be the name of the M MEX file imple menting it This option is mandatory nargs INTEGER The number of arguments of the function If this option is not provided Dynare assumes nargs 1 first deriv provided NAME If NAME is provided this tells Dynare that the Jacobian is provided as the only output of the M MEX file given as the option argument If NAME is not provided this tells Dynare that the M MEX file specified by the argument passed to name returns the Jacobian as its second output argument second deriv provided NAME If NAME is provided this tells Dynare that the Hessian is provided as the only output of the M MEX file given as the option argument If NAME is not provided this tells Dynare that the M MEX file specified by the argument passed to name returns the Hessian as its third output argument NB This option can only be used if the first deriv provided option is used in the same external function command Example Chapter 4 The Model file 18 external function name funcname external_function name othe
238. urprise in case of an unexpected path or perfect foresight for a perfectly anticipated path The fifth argument indicates the period where the path of the endogenous variable is constrained using a dates class see dates class members page 111 The last argument contains the constrained path as a Matlab vector of double This function return the handle of the updated forecast scenario Once the forecast scenario if fully described the forecast is computed with the command det_ cond forecast DSERIES det cond forecast HANDLE DSERIES MATLAB Octave command DATES Computes the forecast or the conditional forecast using an extended path method for the given forecast scenario first argument The past values of the endogenous and exogenous variables provided with a dseries class see dseries class members page 120 can be indicated in the second argument By default the past values of the variables are equal to their steady state values The initial date of the forecast can be provided in the third argument By default the forecast will start at the first date indicated in the init plan command This function returns a dset containing the historical and forecast values for the endogenous and exogenous variables Example conditional forecast using extended path method with perfect foresight on r path var y r varexo e u smoothed dseries smoothed variables csv fplan init_plan 201304 202904 fplan fli
239. us in DR order The matrix columns correspond to exogenous variables in declaration order Of course the shown form of the approximation is only stylized because it neglects the required different ordering in y and y The precise form of the approximation that shows the way Dynare deals with differences between declaration and DR order is ye oo_ dr order_var y oo_ dr order_var A y_1 00_ dr order_var k2 y oo dr order var k2 B u where k2 selects the state variables y and y are in declaration order and the coefficient matrices are in DR order Effectively all variables on the right hand side are brought into DR order for computations and then assigned to y in declaration order 4 13 4 Second order approximation The approximation has the form ge y 0 5A Ay Bu 0 50 y 1 yp 0 5D u amp uj Ely ui where y is the steady state value of y y y y and A is the shift effect of the variance of future shocks For the reordering required due to differences in declaration and DR order see the first order approximation The coefficients of the decision rules are stored in the variables described for first order approx imation plus the following variables e A is stored in oo dr ghs2 The vector rows correspond to all endogenous in DR order e C is stored in oo dr ghxx The matrix rows correspond to all endogenous in DR order The matrix columns correspond to the Kronecker pr
240. ust approximate by an horizon of simulation far enough in the future Another exercise for which Dynare is well suited is to study the transition path to a new equilibrium following a permanent shock For deterministic simulations the numerical problem consists of solving a nonlinar system of simultaneous equations in n endogenous variables in T periods Dynare offers several algorithms for solving this prob lem which can be chosen via the stack solve algo option By default stack solve algo 0 Dynare uses a Newton type method to solve the simultaneous equation system Because the result ing Jacobian is in the order of n by T and hence will be very large for long simulations with many variables Dynare makes use of the sparse matrix capacities of MATLAB Octave A slower but potentially less memory consuming alternative stack solve algo 6 is based on a Newton type algorithm first proposed by Laffargue 1990 and Boucekkine 1995 which uses relaxation tech niques Thereby the algorithm avoids ever storing the full Jacobian The details of the algorithm can be found in Juillard 1996 The third type of algorithms makes use of block decomposition techniques divide and conquer methods that exploit the structure of the model The principle is to identify recursive and simultaneous blocks in the model structure and use this information to aid the solution process These solution algorithms can provide a significant speed up on large models simul
241. ve both n 1 elements the eq operator returns a column vector n by 1 of zeros and ones Chapter 6 Time Series 111 ne operator not equal Tests if two dates objects are not equal 1950Q1 1950Q2 returns O while 1950Q1 1950Q2 returns 1 If the compared objects both have n 1 elements the ne operator returns an n by 1 column vector of zeros and ones It operator less than Tests if a dates object preceeds another dates object For instance 1950Q1 lt 1950Q3 returns 1 If the compared objects have both n 1 elements the 1t operator returns a column vector n by 1 of zeros and ones gt operator greater than gt Tests if a dates object follows another dates object For instance 1950Q1 gt 1950Q3 returns O If the compared objects have both n 1 elements the gt operator returns a column vector n by 1 of zeros and ones le operator less or equal lt Tests if a dates object preceeds another dates object or is equal to this object For instance 1950Q1 lt 1950Q3 returns 1 If the compared objects have both n gt 1 elements the le operator returns a column vector n by 1 of zeros and ones ge operator greater or equal gt Tests if a dates object follows another dates object or is equal to this object For instance 1950Q1 gt 1950Q3 returns 0 If the compared objects have both n gt 1 elements the ge operator returns a column vector n by 1 of zeros and ones One can select an element or some elements in a dat
242. with the color denoted by tableNegColor page 144 For those greater than tableMarkerLimit mark the cell with the color denoted by tablePosColor page 144 Default 1e 4 tableNegColor LATEX COLOR The color to use when marking Table data that is less than zero Default red tablePosColor LATEX COLOR The color to use when marking Table data that is greater than zero Default blue tableSubSectionHeader STRING header for a subsection of the table No data will be associated with it It is equivalent to adding an empty series with a name Default zerotol DOUBLE The zero tolerance Anything smaller than zerotol and larger than zerotol will be set to zero before being graphed Default 1e 6 addVspace hline number Method on Report Adds a Vspace vertical space to a Section Options hline INTEGER The number of horizontal lines to be inserted Default 0 number INTEGER The number of new lines to be inserted Default 1 write Method on Report Writes the IXTEX representation of this Report saving it to the file specified by filename page 140 compile compiler Method on Report Compiles the report written by write page 144 into a pdf file If the report has not already been written determined by the existence of the file specified by filename page 140 write page 144 is called optionshead Chapter 7 Reporting 145 compiler FILENAME Like compiler page 140 except will not ove
243. x taper rne x Relative numerical efficiency RNE when using an x taper pooled mean Mean of the parameter when pooling the beginning and end parts of the chain spec ified in geweke_interval page 63 and weighting them with their relative precision It is a vector containing the results under the iid assumption followed by the ones using the taper steps page 63 see taper_steps page 63 pooled nse NSE of the parameter when pooling the beginning and end parts of the chain and weighting them with their relative precision See pooled mean prob chi2 test p value of a chi squared test for equality of means in the beginning and the end of the MCMC chain See pooled mean A value above 0 05 indicates that the null hypothesis of equal means and thus convergence cannot be rejected at the 5 percent level Differing values along the taper steps page 63 signal the presence of significant autocorrelation in draws In this case the estimates using a higher tapering are usually more reliable model comparison FILENAME DOUBLE Command model comparison marginal density laplace modifiedharmonicmean Command FILENAME DOUBLE Description This command computes odds ratios and estimate a posterior density over a collection of models see e g Koop 2003 Ch 1 The priors over models can be specified as the DOUBLE values otherwise a uniform prior over all models is assumed In contrast to frequentist econometrics th
244. zero threshold page 36 Chapter 4 The Model file 63 taper steps INTEGER1 INTEGER2 Percent tapering used for the spectral window in the Geweke 1992 1999 conver gence diagnostics requires mh nblocks page 54 1 The tapering is used to take the serial correlation of the posterior draws into account Default 4 8 15 geweke interval DOUBLE DOUBLE Percentage of MCMC draws at the beginning and end of the MCMC chain taken to compute the Geweke 1992 1999 convergence diagnostics requires mh nblocks page 54 1 after discarding the first mh drop page 54 percent of draws as a burnin Default 0 2 0 5 Note If no mh jscale parameter is used in estimated params the procedure uses mh jscale for all parameters If mh jscale option isn t set the procedure uses 0 2 for all parameters Output After running estimation the parameters M_ params and the variance matrix M_ Sigma_e of the shocks are set to the mode for maximum likelihood estimation or posterior mode computation without Metropolis iterations After estimation with Metropolis iterations option mh_replic gt 0 or option load mh file set the parameters M params and the variance matrix M_ Sigma_e of the shocks are set to the posterior mean Depending on the options estimation stores results in various fields of the oo structure described below In the following variables we will adopt the following shortcuts for specific field names

Dynare: Reference Manual Version 4

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