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The User Manual of DAD 4.3 (complete pdf file

1. Tick Label Insets to change the Tick label position Top Left Bottom Right indicated in pixels Other Tick to show or not to show the tick labels or the Iv k labels tick markers You can also select the font of the tick labels saneseritt0 M Other Range to select the minimum and maximum values for the range of the vertical axis To do this unselect the option Auto adjust range M 0 8044284156011178 Other Grid To plot the horizontal grid lines select the option Show grid lines You can also select the stroke and the colour of these grid lines Other Ticks Range Grid I show grid lines K Set stroke Gridpaint E Set paint For every curve a combination of the three flowing options can be chosen Curve Stroke To choose the stroke of a giving curve click on the button Set stroke The following widows appear Stroke Selection Select the desired stroke and click on the button OK to confirm your selection Curve Thickness To choose the thickness of a giving curve click on the button Set Thickness The following widows appear Thickness Selection Select the desired thickness and click on the button OK to confirm your selection Curve Paint To choose the colour of a giving curve click on the buttonSet Paint and choose the new colour Saving graphs With the version 4 3 of DAD we can save and load the DAD Graph Format d
2. Sampling weight UX Sampling design feature is used Standard deviation confidence intervals and hypothesis testing Starting with version 4 3 of DAD one can for some of the applications compute confidence intervals and perform statistical tests by using standard or pivotal bootstrap approaches To see how activate the following dialogue box from the application frame by clicking on the button S D STD After choosing the desired options click on the button Confirm to confirm your choice Options A Sampling Design option One can choose between two categories of sampling design 1 A broad and general one activated through The full sampling design 2 A simple one activated through Simple random sampling For more information concerning this see the section Taking into account sampling design in DAD B Approaches to estimating the sampling variability of DAD s estimates DAD generally supports two approaches 1 The asymptotic approach for many of the applications 2 The bootstrap approach for some of the applications C Bootstrap options We can choose tetween two types of bootstrap options and the number of bootstrap replications 1 standard 2 and pivotal D Confidence Level Here we can choose the 1 Confidence level by default 95 of our confidence intervals 2 and whether the confidence intervals should be Two Sided or be Lower Bounded or Upper Bounded E
3. 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Po Distribution 1 Distribution 2 Po Variable of interest Compulsory Among the buttons you will find the command Compute To compute the standard deviation of this index choose the option for computing with standard deviation The Generalised Entropy index of inequality The Generalised Entropy Index of inequality for the group k is as follows yw 4 iff 040 6 1 w i u k I k 0 4 E P violet f 0 0 k f w yi i l k ty Mii jog Yi if 1 Ewi TUD HW i l Case 1 One distribution To compute the Generalised Entropy index of inequality for only one distribution l From the main menu choose the item Inequality gt Entropy index 2 In the configuration of the application choose distribution 3 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Variable of interest Compulsory Size variable Group Variable Group Number theta Compulsory Among the buttons you find the following choices e Compute computes the Generalised Entropy index To compute the standard deviation of this index choose the option for computing with the standard deviation e Graph to draw the value of index according to the parameter To specify a range for the horizontal axis c
4. e Intersection product of gaps The intersection product of gaps using G dimensions or commodities is equal to G Y wt x5 fje gt xf i l i l PUG2 Fr OO 12 Graphical illustration for two commodities Commodity 2 Zi Commodity 1 Case 1 One distribution To compute the bi dimensional FGT indices for two goods l From the main menu choose the item Poverty Bidimensional FGT index 2 Choose the different vectors and parameter values as follows i Results of this application are e FGT index for commodity 1 corresponding to areas I II in the graphical illustration 13 e FGT index for commodity 2 corresponding to areas II III in the graphical illustration e FGT index for the two commodities Union approach corresponding to areas I II IID in the graphical illustration e FGT index for the two commodities Intersection approach corresponding to areas ID in the graphical illustration Example Food and non food expenditures per day in F CFA Cameroon 1996 Food poverty line evaluated at 256 FCFA and non food poverty line evaluated at 117 F CFA Food and non food expenditure in F CFA Cameroon 1996 S 3 amp 100 i i Case 2 Two distributions To compute the FGT indices for two goods and for two distribution l From the main menu choose the item Poverty gt Two Dimensions FGT index 2 Inthe configuration of application choose 2 for the n
5. E oh tPaszo Je rare If the population proportion of group s increases by absolute pc percent of the total population such that 0 t gt t pc the total estimated impact on poverty is as follows AP Pezo 2o P k z i pe where P k z q is the FGT poverty index for subgroup k and k is the proportion of the population found in that subgroup To perform this estimation l From the main menu choose Decomposition Impact of Demographic Change 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Variable of interest OoOo y O Compulsory Size Variable lt i SOptional Group Variable Te Optional Changed group oOo to Compulsory Poverty line z Compubory Apa Compusory Group numbers separated by koke Compulsory Remark The group numbers separated by the dash should be integer values For example we may have two subgroups coded by the integers I and 2 In this case we would write in the field Group Numbers the values 1 2 before proceeding to the decomposition 23 The social welfare indices DAD can compute the following types of social welfare indices The Atkinson social welfare index Case 1 One distribution To compute the Atkinson index of social welfare for one distribution l From the main menu choose the following item Welfare Atkinson index 2 In the configuration of the application c
6. Edit Templates The following window appears EDAD 4 2 Chart Template R Size 600 X 280 Size 600 X 380 Size 560 X 760 Select Select e Template 1 can be inserted within a third of a page of a Word document e Template 2 can be inserted within half a page of a Word document e Template 3 can be inserted within a page of a Word document with landscape orientation Editing coordinates To edit coordinates of curves select Edit Edit Coordinates The following window appears You can change the decimal number by using the item Tools To close this window click on the button OK Preparing DAD ASCII Files in daf F ormat with Stat Transfer A useful tool to produce DAD Ascii Format DAF files is Stat Transfer http www stattransfer com The following steps explain how one can prepare DAF files from any other format 1 After opening Stat Transfer select from the main menu the item Option 2 1 1 In the field ASCH File Writer select the Delimiter Spaces 1 2 Select the option Write variable names in first row To do this only once click on the button Save to save these preferences Stat Transfer 2 The usual next step is to select the item Transfer 2 1 First select the type of the input file SPSS EXCEL 2 2 By using Browse indicate the location of the input file Stat Transfer C documents
7. 3 Choose the different vectors and parameter values as follows Po Distribution 1 Distribution 2 P Variable of interest Compulsory To compute the standard deviation choose the option for computing with standard deviation The S Gini poverty index The S Gini poverty index p k z p for the population subgroup k is defined as P k z p z y aaa vi i l fev and V ywk h i where z is the poverty line and X max x 0 Case 1 One distribution To compute the S Gini index l From the main menu choose the item Poverty S Gini index 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory Size variable Group Variable Group number Poverty line Tho 4 To compute the normalised index choose this option in the window of inputs Commands e The command Compute to compute the S Gini index To compute the standard deviation choose the option for computing with standard deviation e The command Graph to draw the value of the index according to a range of poverty lines z To specify such a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Case 2 Two distributions To compute the S Gini index with two distributions l From the main menu choose the item Poverty S Gini index 2 In the configuration of application choose 2
8. G k 0 15z CowG k 1 z G kK 0 2z CowG k 31z G k Lz C Dominance Curve The Commodity or Component dominance curve is defined as follows s 1 yw z y y if s22 k i l CDi k 2 8 4 i Y wK y y Ely ly z f z _____ if s 1 dw i l where K is a kernel function Dominance of order s is che cked by setting a s 1 The C Dominance curve normalized by z which is denoted by CD is given by wt vi if s22 jaa Seal i Y w K z yi yi Ely ly Joea ___ if s l bw i 1 The C Dominance curve normalized by the mean is defined as j and the C a Dominance curve normalized both by z and the mean equals Case 1 One distribution To compute the C Dominance curve for one distribution l From the main menu choose Curves C Dominance curve 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows ee Variable of interest Among the buttons you will find e Compute to compute the C Dominance curve at z and for a given alpha To obtain the standard deviation choose the option for computing with a standard deviation e Graph to draw the value of the C Dominance curve over a range of z Case 2 Two distributions To reach the application for two distributions 1 From the main menu choose Curves gt C Dominance curve 2 In the c
9. To perform the decomposition of the FGT index for two groups l From main menu choose the item Decomposition FGT Decompostion for two groups 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows _ O me Variable of interest fy Compulsory Size Variable __ Optional Group Variable ec Optional a ae Ses Cae alpha o Compulsory Numbers for the 2 subgroups separated by Compulsory In the output window you will find the following information l The FGT index for the whole population 2 The FGT index for each of the two subgroups 3 The difference in the indices of the two groups P 1 z a P 2 z a 4 The percentage difference in the contribution of the two population subgroups OPU z amp O 2 P 2 z a4 P z 0 To compute the standard deviations for these statistics choose the option computing with standard deviation The decomposition of the FGT index across growth and redistribution effects According to Datt amp Ravallion 1992 approach we can decompose variation of the FGT Index between two periods tl and t2 into growth and redistribution effects as follows P P Pu n P a Pte P e R ref 1 Variation cl C2 P P Peun 2 P u 1 2y14 Pqi x _ Pua yLER ref Variation cl C2 Variation Difference in poverty between t1 and t2 C1 Growth Impact C2 Contribution of
10. Change range of x from the main menu To compute the standard deviation choose the option for computing with standard deviation Case 2 Two distributions To reach the application for two distributions l From the main menu choose the item Curves Relative Deprivation curve 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Variable of interest y BS Commands e Difference to compute the difference p1 p2 R edistribution This section regroups the following applications l Estimating the progressivity of a tax or a transfer 2 Comparing the progressivity of two taxes or two transfers 3 Comparing the progressivity of a transfer and a tax 4 Estimating horizontal inequity 5 Estimating redistribution 6 Estimating a coefficient of concentration Estimating the progressivity of a tax or a transfer Let X be gross income T bea tax B bea transfer 1 TR progressivity A tax T is TR progressive if Lx p Cr p gt 0 Ype Joul A transfer B is TR progressive if Cg p Lx p gt 0 Vpe Jo 2 IR progressivity A tax T is IR progressive if Cx 7 p Lx p gt 0 Ype lol A transfer B is IR progressive if Cx s P Lx p gt 0 Vpe Jof To reach this application 1 From the main menu choose the item Redistribution Tax or transfer 2 Specify if you wish to estimate the progressivity of a tax or of a t
11. Commands e Compute to compute the impact of the price change To compute the standard deviation of this estimated impact choose the option for computing with standard deviation e Graph to draw the value of the impact as a function of a range for the parameter To specify that range and thus the range of the horizontal axis choose the command Range Impact of a tax reform on the Atkinson Social Welfare Index This tax reform consists of a variation in the prices of two commodities and 2 under the constraint that it leaves unchanged total government revenue The effect of this constraint is given by an efficiency parameter gamma y which is the ratio of the marginal cost of public funds MCPF from a tax on 2 over the MCPF from a tax on 1 The impact of this tax reform denoted IMWTR on the Atkinson Social Welfare index Ele is as follows 0 e _ Xy 0 8 p X P2 IMWTR where pc is the percentage price change of commodity 1 and X is the total expenditure on the good g Under the government revenue constraint the percentage price change of X commodity 1 is given by 1 pc The computation can be made solely within a group of 2 individuals This is done by specifying the group number k and the group variable c To compute the impact of the tax reform l From the main menu choose Welfare Impact of tax reform 2 Choose the different vectors and parameter values as foll
12. From the main menu choose the item Inequality Coefficient of Variation 2 In the configuration of the application choose 1 distribution 3 After confirming the configuration the application appears Choose the different vectors and values of parameters as follows este params e Variable of interest Compulsory Group Variable Group Number E Among the buttons you will find the following command e Compute to compute the Variation Logarithms index If you also want the standard deviation of this index choose the option for computing with a standard deviation 10 Case 2 Two distributions To compute the Coefficient of Variation of two distributions l From the main menu choose the item Inequality Coefficient of Variation 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Distribution 1 Distribution2 Variable of interest Compulsory Group Number Among the buttons you will find the command Compute To compute the standard deviation of this index choose the option for computing with standard deviation The Logarithmic Variance Index Denote the Logarithmic Variance index of inequa lity for the group k by LV it can be expressed as follows n 2 n wi log y Imu Dwi LV _____ ___ where Imu log Lwi Lwi i i l Case 1 One distribution If you wish to compute the Log
13. Generalised Entropy index of inequality can be decomposed as follows 0 K k _ 1 0 id 1 0 16 k 1 Hy where o k is the proportion of the population found in subgroup k u k is the mean income of group k I k 6 is the inequality within group Kk 1 0 is population inequality if each individual in subgroup k is given the mean income of subgroup k u k To perform the decomposition of the entropy index l From the main menu choose the item Welfare and inequality Decomposition Entropy decomposition 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Variable of interest y Compulsory Size Variable s Group Variable e theta sees Compulsory O numbers separated by Compulsory The following information appears in the output window 1 The entropy index for the whole population 2 The entropy index for between group inequality 3 The entropy index within every subgroup I k 0 4 The ratio u k u Normalised mean for every subgroup 5 The absolute contribution to total inequality of inequality within every subgroup that is u k 1 6 k 1 k 8 6 The relative contribution to total inequality of inequality within every subgroup To compute the standard deviations for these statistics choose the option computing with standard deviation Decomposition of variation of social welfare index between
14. a reversal of the above dominance conditions for inequality orderings Said differently it provides the crossing points of the FGT curves that is the values of and P Aw 0 for which Pi Afi 0 P2 Au 2 0 When sign Pi A nu 0 P 1 sign P A M br30 P A 1 for a small n These crossing points at can also be referred to as critical relative poverty lines when the poverty lines are a proportion of the mean and when the indices are normalised by the poverty line To check for those crossing points l From main menu choose the item Dominance gt Inequality Dominance 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Variable of interest OoOo yp Compulsory Optional y y Group Number Compuso os E Group Variable Pt Commands e Compute to provide the critical relative poverty lines and the crossing points of the sample normalised dominance curves When the option with STD is specified the standard deviation on the estimates of the critical relative poverty lines and on the estimates of the crossing points of the normalised FGT curves are also given e Range to specify the range of A over which to check the presence of critical values With this command you can also specify the incremental step of search for these crossing points e Graph to draw the normalised F
15. clear to edit your database GetOBS and SetOBS commands To obtain the number of observations of your active file choose the command GetOBS If you would like to set a new number of observations choose the command SetOBS The following window appears 2 Enter the new number of observations After this enter the new number of observations and click on the button OK The first SetOBS observations will now be used for the computations Changing the names of spreadsheet To change the name of the spreadsheet from the main menu select the item Edit Change current sheet name and indicate the new name Dimension of the spreadsheet The length of the spreadsheet varies according to the following gt By default the length of the spreadsheet is 160 000 observations This is done when a new file is created gt If you download an ASCII file the length of spreadsheet corresponds to the number of observations read from this file gt In all cases you can specify explicitly a desired length for the spreadsheet by indicating the new length after choosing the command Edit and the item Enter the new length of the spreadsheet E Input O ox Annus The new length of the spreadsheet cannot be below the number of observations OBS The number of columns fixes the width of the spreadsheet By default the number of columns is 16 Applications in D AD Introduction to applications Remember
16. computing with standard deviation 4 To compute the normalised index choose this option in the window of inputs The Bounded Income and Overload Indices e Gap index The Gap index GI k z1 z2 a for the population subgroup k is as follows E wE z2 y FIZI lt y lt z2 GI k z1 z2 0 E If the index is relative to the group of those with zl lt y lt z2 we have Ew z2 y PII lt y lt 22 GI k z1 z2 0 E w I ZzI lt y lt z2 i l e Surplus index The Surplus index SI k z1 z2 a for the population subgroup k is as follows E wh y z Mz Sy 72 SI k3z 1 22 o1 ________ Lwi i l If the index is relative to the group zl lt y lt z2 we have wi y ZI I Zz1 lt y lt z2 SI k321 22 0 1 will lt y lt z2 i l e Overload index The Over Load Index OLI k z amp for the population subgroup k is as follows OLI a GI k1 z1 0 z2 z a SI k2 z3 z z4 Where k1 is the poor group and k2 the non poor group of population l From the main menu choose the item Poverty Bounded income index 2 Choose the different vectors and parameter values as follows a re sf Optional Group Variable Z Variable of interest Size variable s Group number Lower bound 1 Compulsory Upper bound Compulsory Z Poverty line Compulsory for OLI alpha Compulsory Among the buttons you find e The command Compute to co
17. du type After this select the file type DAD file dad select the file and click on the Button Open Remark DAD files contain two sheets such as Filel and File2 with every sheet containing one database It is possible that one of the two sheets be empty Saving a file You can save an active file in DAD s file format daf or dad The procedure is simple Begin with the command File and select the item Save The next window asks for the name and the directory where you would like to save the file Da Enregistrer X Enregistrer dans T Mes documents r l el Adobe My Webs Q Book1_opf files Photo eh Ma musique pht1 2 mes images recette E Mes vid os donado dad Messenger Service Received Files My virtual Machines Nom de fichier aad Enregistrer Fichiers du type baD file dad v PEN E After specifying your choice for the name and directory click on Save to save the active file Close a file To close the active file click on File and then select Close Exit the software To exit the software click on File and then select Exit The next window appears for the specification of the type of operation that you wish to apply E Operation of x Operation Series1 Series Series1 Veight w Series 2 B Number fi o Result Execution Choose the type of operation you need to carry out by clicking on the
18. has values lt 1 it is directly interpreted as a stratum sampling rate f h n_h N_h where n_h number of PSUs sampled from the strata to which h belongs and N_h total number of PSUs in the population belonging to stratum h e When the variable specified has values greater than or equal to n_h it is interpreted as representing N_h f h is then set to n_h N_h The following table contains an example of vectors used to specify the type of SD shown in Figure 2 Table 2 Example of SD OBS Strata PSU LSU SW 1 1 1 1 6 2 1 1 2 6 3 1 2 1 6 4 1 2 2 6 5 3 1 1 5 6 3 1 2 5 7 3 2 1 5 8 3 2 2 5 9 2 1 1 3 10 2 2 1 3 SUM 3 6 10 50 Omitting SW will systematically bias both the estimators of the values of indices and points on curves as well as the estimation of the sampling variance of those estimators Consider for instance the estimation of total population income from the data shown in table 2 4 households appear in strata 1 but the population number of households in that strata is six times as large that is 24 and this is captured by the SW variable Total population income for strata 1 would therefore be estimated to be six times that of total sample income for strata 1 Table 3 Example of SD OBS Strata LSU SW Nh 1 1 1 6 24 2 1 2 6 24 3 l 3 6 24 4 1 4 6 24 5
19. intersection over a particular range use Range e Difference to compute the difference L k 3p L k gt p5 e Graph to draw the difference L k p L k p as a function of p e Range to specify the range for the search of a crossing between the two curves This also specifies the range of the horizontal axis e S Gini to compute the difference I k p I k p e Covariance to compute the following covariance matrix Cov L k 0 1 L k 0 1 Cov L k 0 1 L k 0 2 Cov L k 0 1 L k sD Cov L k 0 2 L k 0 1I Cov L k 0 2 L4 k 0 2 Cov L k sl L k 0 1 Cov L k 1 L k 0 2 Cov L i k D L k 1 Concentration curve and generalised concentration curve The concentration curve for the variable T ordered in terms of y at p and for a population subgroup k is E WET I lt QQ p Cr k p E n wT i l where I y lt Q ksp 1 if y lt SQ k p and O otherwise Q k p is the p quantile of y for the subgroup k The generalised concentration curve at p for a population subgroup p is E WET lt Qk p a k L wi i l Remark The application for the concentration curve is similar in structure to the one for the generalised concentration curve Case 1 One distribution To compute the concentration curve for one distribution 1 From the main menu choose the item Curves gt concentration curve 2 In the configuration of application cho
20. lol B1 is more TR progressive than B2 if C p C p gt 0 Vpe oi 2 IR approach T1 is more IR progressive than T2 if Cyx m p Cx r p gt 0 Ype lol B1 is more IR progressive than B2 if Cy p p Cx4p2 p gt 0 Vpe pal To reach this application l From the main menu choose the item Redistribution Transfer Tax vs Transfer Tax 2 In front of the indicators Tax Transfer 1 and 2 specify the two vectors of taxes or transfers 3 Choose the approach to be either TR or IR 4 Choose the different vectors and parameter values as follows Gross income x Compulsory Tax transfer 1 Tl or BI Compulsory Tax transfer 2 T2 or B2 Compulsory a ce i Group Variable Group number Option tho P Compulsory p Compulsory Size variable Commands e The command S Gini to compute ee TR Approach IR Approach ICu P IC 9 ICx r2 P IC yn P ICs2 P ICp P ICx n9 P ICxspi P where C p is the S Gini coefficient of concentration e The command Crossing to seek the first intersection of the two concentration curves DAD indicates the co ordinates of that first intersection and their standard deviation if the option of computing with standard deviation is chosen e The command Difference to compute Se TR Approach IR Approach Cro P Cn Cyn Cyr Cu P Cral EA e The command Range to specify a range of p for the search of the first intersection between
21. menu choose Distribution gt Statistics 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory Size Variable 1 s x 1 2 i ty Size Variable 2 s y Group Variable Group Number To activate this application for one distribution follow these steps l From the main menu choose the item Distribution gt Statistics 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Variable of interest Density function The gaussian kernel estimator of a density function f x is defined as X X x w K tao ATKO and K x exp 0 54 x and 1 T 1 h27 hw where h is a bandwidth which acts as a smoothing parameter To reach this application l From the main menu choose the item Distribution Density function 2 Choose the different vectors and parameter values as follows Variable of interest Compulsory Size variable Group Variable Group Number Parameter Smoothing parameter On the first execution bar you find e The command Compute to compute f x To compute the standard deviation choose the option for computing with standard deviation e Thecommand Graph to draw the value of the function as a function of x To specify a range for the horizontal axis choose the item Graph mana
22. seek an intersection over a particular range use Range Difference to compute the difference in the concentration curves Graph to draw the difference in the curves as a function of p Range to specify the range for the search of a crossing between the two curves This also specifies the range of the horizontal axis S Gini to compute the difference IC k 0 IC k p Covariance to compute the following covariance matrix Cov C k 0 1 C k 3 0 1 Cov C k 0 1 C k 30 2 Cov C k 0 1 C k 31 Cov C k 0 2 C k 0 1 Cov C k 0 2 C k 0 2 Cov C k 1 C k 530 D Cov C k 1 C k 0 2 lt Cov C k 31 C k 531 The Cumulative Poverty Gap CPG curve The CPG curve at p for a subgroup k and poverty line z is E wiz y My Qkk p n k yw i l Case 1 One distribution To compute the CPG curve for one distribution l From the main menu choose the item Curves CPG curve 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory Size Variable Optional Optional Optional Compulsory Pp Compulsory Commands e Compute to compute G k p z To compute the standard deviation choose the option for computing with standard deviation e Graph to draw the curve as a function according of p To specify a range for the hor
23. sign P 6 n amp P E n sign P n P 6 n for a small n The crossing points of can also be referred to as critical poverty lines To check for the crossing points of the dominance curves of two distributions From main menu choose the item Dominance Poverty Dominance After confirming the configuration the application appears Choose the different vectors and parameter values as follows Variable of interest Compulsory i a g 2 Cc Cc k k Compulsory Commands e Compute to provide the critical poverty lines and the crossing points of the sample dominance curves When the option with STD is specified the standard deviation on the estimates of the critical poverty lines and on the estimates of the crossing points of the FGT curves are also given e Range to specify the range of poverty lines over which to check for the presence of critical poverty lines With this command you can also specify the incremental step of search for these crossing points e Graph to draw the FGT curves for the two distributions Inequality dominance Distribution dominates distribution 2 in inequality at order g over the conditional range of proportions of the mean h Ae only if Pi ApLy 0 gt P2 A 0 Y Ae li 1 where a s l These are normalised stochastic dominance curves at order s or normalised FGT curves for s 1 This application checks for the points at which there is
24. standard deviation choose the option for computing with standard deviation e The command Graph to draw the distribution function F x along values of x To specify a range for the horizontal axis choose the item Graph management gt Change range of x from the main menu e Thecommand Range to specify the range of the horizontal axis Plot _ Scatt_xXY e This application plots a scatter graph of two variables To activate this application choose from the main menu the item Distribution Plot_Scatt_XY When the window of this application appears choose the two X and Y variables and click on the button Graph You can also use the command Range to specify the range of the horizontal axis X Non parametric regression and non parametric derivative regression The Gaussian kernel regression of y on x is as follows a x _ L wK yi Bo wK C ylx From this the derivate of y x with respect to x is given by AP y1 x _ a x Baa Ox Boxy Bo Remark the instructions for non parametric derivative regression are similar to those for non parametric regression To reach this application l From the main menu choose the item Distribution Non parametric regression 2 Choose the different vectors and parameter values as follows Exogenous Variable X x Compulsory Endogenous Variable Y Compulsory Group Variable Group Number Level of X or p Compulsory Smoot
25. the two curves The command also allows to specify the range of the horizontal axis in the drawing of a graph e The command Graph To draw the following curves as a function of p TR Approach IR Approach Cra p Cri p Cy 1 P Cx 7H Cu Car Ca P Cua Comparing the progressivity of a transfer and of a tax Let X be gross income T beatax B atransfer TR Approach The transfer B is more TR progressive than a tax T if C p Lx p gt Lx p Cr p Ype f IR Approach The transfer B is more IR progressive than a tax T if Craig p gt Cxr p Vpe pf To reach this application l From the main menu choose the item Redistribution Transfer vs Tax 2 Choose the approach to be either TR or IR 3 Choose the different vectors and parameter values as follows Gross income Variable of tax Variable of transfer Size variable Group variable Group number Compulsory Compulsory Compulsory Optional Optional Optional Compulsory Compulsory Gross income X Compulsory Variable of tax p Compulsory Variable of transfer _ p Compulsory Size variable s Optional Group variable e f Optional Group number k Optional Rho o p y Compulsory pooo oo p Compulsory _ Commands e The command S Gini to compute 21 p IC p IC P ICy_7 p ICy 2 Pp where IC p is the coefficient od concentration e The command Crossing to seek the first po
26. title is the name of application You can change the main title in the field Text You can also change its font and its colour To do this just click on the button select and indicate the desired font or colour FGT P overty Second Title By default the second title is Chart You dialog 18 can change or delete the second title in the field Text You Select can also change its font and its colour To do this just click on the button select and indicate the desired font or colour Background to select the background colour of the legend quadrant Text font to select the font of the text legends EE 2 s Text font to select the colour of the text legends Legend Marker to select Marker legends By default the markers have square form but you can select the line form with this option Square Form Line Form Name By default the names of the curves are curve 1 curve 2 etc You can change these names in these fields Remark The options for the horizontal axis are similar to those for the vertical axis Name By default the name of the vertical axis is Value Y You can change this name with this field Font to select the font of the name of the vertical axis Paint to select the colour of the name of the vertical axis EA Beer ee Label insets to change the labels position op Left Bottom Right indicated in pixels l Saek Boe
27. 110309 799805 155290 200577 11267399826 64246 700333 630328899189 0 000000 e 0 000000 0 000000 0 000000 0 000000 0 000000 4974400063 57321 999954 Probability P group1 group2 0 000000 0 000000 0 000000 0 000000 0 000000 0 004108 0 047335 Ea Ea The Cross Table table shows the sum of the products of Sampling Weight times Size for those observations belonging to the two groups simultaneously The second table Probability shows the estimated proportion of the population who belong to both of the groups 12 The editing saving and printing of results Editing of results Generally the windows of results tack the following form TEDAD 4 2 HTML Result iewer File Edit FGT Poverty Tue May 21 14 20 33 EDT 2002 0 581 sec Without size No Selection 1 NO 1 0 13583 42675781 699 17753283 13583 42675781 99 17753283 144000 00000000 000000000 fd Save E Load The window contains the name of the application and the results of the execution We can divide these results displayed in the last figure in three blocks 1 General information this first block is composed of Indicates the time at which the results were computed Indicates the computation time 2 The block of inputs composed by File name indicates the name of the file that is used OBS _ indicates the number of observations indicates the value of the parameter used for this compu
28. 3 1 5 20 6 3 2 5 20 7 3 3 5 20 8 3 4 5 20 9 2 1 3 6 10 2 2 3 6 SUM 3 10 50 The FPC factor accounts for the reduction in sampling variance that occurs when a sample is drawn without replacement from a finite population as compared to sampling with replacement According to table 3 the four LSU s of strata 1 were selected without replacement from a population of 24 LSU s These fuor LSU s are then necessarily distinct by design If sampling had been done with replacement then multiple observations of the same population LSU s could have been generated Because sampling without replacement guarantees that sample observations represent different sampling units it therefore generates greater sampling information and leads to smaller sampling variances than with sampling with replacement For strata 1 of Table 3 data from four distinct LSU s or PSU s out of 24 are necessarily generated after sampling The fh factor for that strata is then 4 24 0 1666 Important Remark We can initialise and use the FPC correction just when the SD is based on one stage of random selection of LSU s In this case PSU s and LSU s are equivalent To initialize the SD after loading the database select from the main menu the item Edit gt Set Sample Design The following window then appears ce ziaz Sampling Design Information Testa daf Sirata No Selection PSU No Selection LSU No Selection Sampling W
29. Case 2 Two distributions To reach the application for two distributions l From the main menu choose the item Curves Poverty Gap Quantile 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows y Optional Z Variable of interest Size Variable Compulsory p Computory Group Number Commands Ooo m e Crossing to search the first intersection of the curves If the two curves intersect DAD indicates the co ordinates of the first intersection and their standard deviation if the option of computing with standard deviation is chosen To seek an intersection over a particular range use Range e Difference to compute the difference 21 Z13P1 82 Z23P2 e Graph to draw the difference z p g z p as a function of p e Range to specify the range for the search for a crossing between the two curves This also specifies the range of the horizontal axis Lorenz curve and generalised Lorenz curve The Lorenz curve at p for a population subgroup k is given by Lwi yiI lt Qksp L k p ______ _ L wi yi isl where I y lt Q k p 1 if yi lt Q k p and 0 otherwise Q k p is the p quantile of the subgroup k The generalised Lorenz curve at p for a population subgroup k is GL k p u L k p Remark The application for the Lorenz curve is similar in structure to the one for the generalised Lorenz
30. DAD DISTRIBUTIVE ANALYSIS ANALYSE DISTRIBUTIVE USER S MANUAL a JA 43 Jean Yves Duclos Araar Abdelkrim and Carl Fortin 2004 The software DAD was designed by Jean Yves Duclos and raar Abdelkrim and programmed with JAwA by 4raar Abdelkrim and Carl Fortin fg LAVAL January 2004 Jean Yves Duclos jyves ecn ulaval ca Abdelkrim Araar aabd ecn ulaval ca Carl Fortin cfortin ecn ulaval ca Universit Laval Introduction DAD was designed to facilitate the analysis and the comparisons of social welfare inequality poverty and equity across distributions of living standards Its features include the estimation of a large number of indices and curves that are useful for distributive comparisons as well as the provision of asymptotic standard errors to enable statistical inference The features also include basic descriptive statistics and provide simple non parametric estimations of density functions and regressions The main facilities of DAD are the l Estimation of indices of Poverty Watts CHU FGT SGini Sen normalised and unnormalised or absolute and relative poverty indices with absolute and relative poverty lines Social Welfare Atkinson S Gini Atkinson Gini Inequality S Gini Atkison Entropy Atkinson Gini and others Redistribution progressivity vertical equity reranking and horizontal inequity 2 Decomposition of Poverty across population subgroups 3 In
31. GT curves for the two distributions along values of the parameter Indirect tax dominance Taxing commodity 2 is better than taxing commodity 1 at order of dominance gs over the conditional range lz7 z if only if CD k 6 gt yCD 2 k 6 Y Ce lz z These are CD curves of order s If this condition holds then an increase in the price of good 2 with the benefit of a decrease in the price of good 1 will decrease poverty for poverty lines between Z and Z and for poverty indices of order s The ratio of the marginal cost of public funds MCPF from a tax on 2 over the MCPF from a tax on is also used to determine whether increasing the tax on 2 for the benefit of decreasing the tax on good 1 can be deemed to be socially efficient This application computes differences between CD 1 k C and yCD gt k C It also checks for the points at which there is a reversal of the dominance conditions Said differently it provides the crossing points of the CD curves that is the values of and CD k 6 for which CD k C yCD2 k when sign CD 1 k n YCD2 k n sign CD k CDi k n for a small n The crossing points of can also be referred to as critical poverty lines Critical values of y are also provided These are the minimum of atl CD k z CD k z over an interval z of poverty lines z It gives the maximum ratio of the MCPF for commodity 2 over that for commodity 1 up to whi
32. Hypothesis testing We can carry out hypothesis testing by checking the box Do test and by inserting the appropriate values for the hypothesis test procedure 1 Asymptotic approach Using the law of large mmbers and the central limit theorem it is possible to show that most of DAD s estimators fi say of some distributive value u are consistent and asymptotically normally distributed with a sampling variance given by s z s is almost always unknown but we can generally estimate it consistently by and this is typically provided by DAD Then asymptotically we can write that fi N u 8 3 which also implies that EE _N 1 Sp Hypothesis testing and statistical decisions The decision to reject or not some null hypothesis depends on the significance level a of the test Let m be the value that takes in a particular sample the estimate of u The rejection rule can be described as follows Case a a symmetric test Reject H u u in favor of H u u if and only if uo lt M S Zia OF Ho gt M Zy This is because we have that P Ho iZan OF E gt y iZan za f Note that this is equivalent to Zo lt Z 2 OF Z gt Z 4 Where Z M Mo p Case b testing an upper bound null hypothesis Reject H u lt u in favour of H u gt py ifand only if po lt m Z a whichis equivalent to z gt z _ Case c testing a lower bound null hypothesis test Reject H u2u in favour of H u lt p if and only
33. P Lx P e The command Range to specify the range of the horizontal axis in the drawing of a graph e The command Graph To draw the following curves as a function of p Cx r p Lx r p Cx B P L xin p Redistribution A tax or a transfer T redistributes if Tax Lx r p Lx p gt 0 vpe f Transfer Lyg p Lx p gt 0 Vpe lol To reach this application l From the main menu choose the item Redistribution Redistribution 2 Specify if you are using a tax or a transfer 3 Choose the different vectors and parameter values as follows Basic variable x Compulsory Interest variable T o B Compulsory Size variable Group variable Group number Optional rho Compulsory Compulsory Commands e The command S Gini to compute LO L P Ixa P e The command Crossing to seek the first point at which the curves L p and Lx p Lx gB p and Ly p cross DAD indicates the co ordinates of that first crossing and their standard deviation if the option of computing with standard deviation is chosen e The command Difference with this command to compute Ly_r p Lx p Lxip p Lyx p The command Range to specify a range of p for the search of the first intersection between the two curves The command also allows to specify the range of the horizontal axis in the drawing of a graph The command Graph to draw the following curves as a function of p Ly_r p Lx p Ly
34. alues p are such that p lt p lt p u k p p 18 formally defined as P2 Qc p dp Lk p p P2 7P and is the average income of those whose rank in the population is between p and pp The Conditional Mean Ratio for group k is then given by CMR k ko p1 p2 p3 p4 and is defined as 15 Wk Pipo CMR k k pl p2 p3 p4 U k p33P4 Case 1 One distribution If you wish to compute the Conditional Mean Ratio index of inequality for only one distribution follow these steps l From the main menu choose Inequality Conditional Mean Ratio index 2 In the configuration of the application choose 1 distribution 3 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Variable of interest Compulsory Size variable Optional Group Variable Optional Group Number Optional Percentile Compulsory Percentile Compulsory Percentile Compulsory Percentile 7 Compulsory Among the buttons you will find the following command e Compute to compute the Conditional Mean Ratio If you also want the standard deviation of this index choose the option for computing with a standard deviation Case 2 Two distributions To compute the Conditional Mean Ratio with two distributions l From the main menu choose the item Inequality Conditional Mean Ratio index 2 In the configuration of application choose 2 for the number of distributi
35. and settings arser abdelkrim buresu burkina ti ASCII Delimited E C documents and settingssaraar abdelkrim bureau burkinas S 2 3 Select ASCI Delimited as the type of output file 24 By using Browse indicate the location of the output file and write name with extension daf For example the name is Datal daf 2 5 Click on the Button Transfer to produce the new file If you wish to save only some selected vectors in the DAF file after step 2 2 select the item Variables and select those vectors you wish to save in the new DAF file After this continue to steps 2 3 to 2 5 Stat Transfer f Date e Date lime C Time
36. are detected p Missining or non convertible values In the panel Choose one option there are three options to treat missing or not convertible values In our example we would just indicate that the first row includes the names of variables Hence we click on the button cancel and we indicate this 5 Data Import Wizard ASCII File Information Delimiters 4 Other information V Space J Semi colon V Treat consecutive delimiters as one Colon Tab F Comma Other aa ii Advanced Preview Results Number of OBS 1612 Number of Vectors 3 Compact Data Preview Weight Expend Yector_ 4 Yector_ 5 124729 0 200749 0 96102 0 267149 0 125015 0 271719 0 247010 0 224617 0 146591 0 After selecting the option First row includes names of variables the button Compact replaces the button Warning This button indicates that all values in the three columns are acceptable to DAD At this stage you can click on the button ENTER to finalize the loading of the data Remark after loading the ASCII file we can save this file with the DAD ASCII format daf Loading a second ASCII database As already mentioned for many applications in DAD we can use simultaneously two databases To activate a second database the user should load another file To activate a second database follow these steps 1 Activate the second file by cli
37. arithmic Variance index of inequality for only one distribution follow these steps l From the main menu choose the following items Inequality Logarithmic Variance 2 In the configuration of the application choose 1 distribution 3 After confirming the configuration the application appears Choose the different vectors and values of parameters as follows 11 Variable of interest Compulsory 3 Group Variable i Group Number Among the buttons you find the following command e Compute to compute the Logarithmic Variance index If you also want the standard deviation of this index choose the option for computing with a standard deviation Case 2 Two distributions To compute the Logarithmic Variance index of two distributions l From the main menu choose the item Inequality Logarithmic Variance 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Distribution 1 Distribution2 Variable of interest Compulsory 1 2 Group Nomer Among the buttons you find the command Compute To compute the standard deviation of this index choose the option for computing with standard deviation The Variance of Logarithms Denote the Variance of Logarithms index of inequality for group k by VL It can be expressed as follows 12 2 wi log y Imu yw logy VL a a where Imu Case 1 One dis
38. arly wasteful to adopt multi stage sampling it would be sufficient to draw one household from each cluster in order to know the distribution of income within that cluster It would be more informative to draw randomly other clusters Sampling Design in DAD By default when a data file is loaded in DAD the type of SD assigned to the data is the SRS presented in Figure 1 Once the data are loaded the exact SD structure can nevertheless be easily specified Up to 5 vectors can help specify that structure Table 1 Description of vectors used in DAD to specify the SD Strata Specifies the name of the variable integer type that contains stratum identifiers PSU Specifies the name of the variable integer type that contains identifiers for the Primary Sampling Units LSU Specifies the name of the variable integer type that contains identifiers for the Last Sampling Units SW Specifies the name of the variable for the Sampling Weights Sampling weights are the inverse of the sampling rate Roughly speaking they equal the number of observations in the underlying population that are represented by each sample observation FPC Specifies the name of the variable for the Finite Population Correction factor With FPC DAD derives an indicator f for each observation h which is then used to compute SD corrected sampling errors e Ifthe variable FCP is not specified f_h 0 for all observations e When the variable specified
39. ative mean deviation index of inequality for only one distribution follow these steps l From the main menu choose the following items Inequality Relative Mean Deviation 2 In the configuration of the application choose 1 distribution 3 After confirming the configuration the application appears Choose the different vectors and values of parameters as follows Variable of interest Compulsory Group Variable Group Number Among the buttons you will find 14 e Compute to compute the relative mean deviation If you also want the standard deviation of this index choose the option for computing with a standard deviation Case 2 Two distributions i To compute the relative mean deviation of two distributions 2 From the main menu choose the item Inequality Relative Mean Deviation 3 In the configuration of application choose 2 distributions 4 Choose the different vectors and parameter values as follows Ss Distribution 1 Distribution2 Variable of interest Ooy S op eann 1 E Group Nabe Among the buttons you will find the command Compute To compute the standard deviation of this index choose the option for computing with standard deviation The Conditional Mean Ratio Denote the Conditional Mean for group k by k p p Where pi and p specify the percentile p range of those we wish to include in the computation of the conditional mean These percentile v
40. buttons Result1 Result2 Saving and printing results DAD easily saves results in the HTML format This allows the edition of these results with browsers like Explorer or Netscape To save the results from the window of results choose the command File gt Save html format The following window appears Enregistrer dans Mes documents 7 BoB Adobe graph develop _files Help Andr _files Label CD_files Mes images Messenger Service Received Files Law My eBooks bs My Webs Mes docume Nouveau dossier wE Paterns_files aa resu2 Nom de fichier Enregistrer Fichiers du type Hrm File html v Annuler Poste de tra After making your choice of name and directory click on the button Save to save the results To print these results choose from the main window the command File gt Print The printing window appears just choose the name of your printer and confirm by clicking on the button OK Graphs in DAD 4 3 Drawing graphs Most applications in DAD offer the possibility of plotting graphs to illustrate the results of those applications For example the FGT poverty index application can plot a curve of this index against the Y axis according to alternative levels of the poverty line shown on the X axis as in the following figure Figure 01 The FGT Curve alpha 0 Benin 1995 Changing graph properties We can change man
41. ch taxing commodity 2 can be deemed socially efficient To use these functions l From the main menu choose the item Dominance gt Indirect tax dominance 2 Choose the different vectors and parameter values as follows a ae Variable of interest Compulsory Size variable Commodity 1 Compulsory Commodity 2 X2 Compulsory Group Variable Group Number Poverty Tine gamma Commands e Critical z to compute the values of the poverty lines at which the CD curves CDi k z and yCD gt k z cross To specify a range for a search of crossing points choose the command Range e Critical to compute the critical gamma for tax dominance The range lz 2 is specified under Range e Difference to compute the difference CD k z yCD gt k z e Graph to draw the value of CDi k z and yCD gt k z as a function of a range of poverty lines z To specify that range choose the command Range e Step the value of the incremental steps with which the critical z is searched Curves A number of curves are useful to present a general descriptive view of the distribution of living standards Many of these curves can also serve to check the robustness of distributive orderings in terms of poverty inequality social welfare and equity Quantiles and normalised quantiles Remark The application for computing normalised quantiles is similar in structure to the one for computing quan
42. cking on the button File2 2 The procedures to follow after this are identical to those presented for loading the first ASCII file Remark The active file in the software DAD is the selected file Loading a DAD ASCII format file With DAD you can also save and load files in DAD s specific format and with the extension daf To open a daf file click on the command File and select the command Open The following window appears asking for some information concerning the data file Enregistrer dans ja Mes documents x Adobe Q My Virtual Machines 3 country4 Book1_opf_files My Webs 3 F1000 Photo i7 romano Q pht1 i romanot Q recette i testo Messenger Service Received Files 1 burkina Nom de fichier Enregistrer Fichiers dutype a af Preyer After this select the file type DAD file daf select the file and click on the Button Open Loading a DAD file With DAD you can also save and load files in DAD s specific format and with the extension dad To open a dad file click on the command File and select the command Open The following window appears asking for some information concerning the data file Rechercher dans am data x amp cH data cross dad ta dad Q Nouveau dossier 2 data dad test dad araar dad docar dad Test2 dad i roma dad test3 dad j romar1 dad romarin dad romarion dad Nom de fichier Fichiers
43. ctor_ 10 ecto r_ 10 Vector_ 20 vector 20 OK CANCEL You can insert the new name of a vector and click on the button OK to confirm the change Generating new vectors You may need to generate a new vector in the active database The following steps describe the necessary procedures for this l In the main menu choose the command Edit and select the item Edition of columns The next window appears for the specification of the type of operation that you wish to apply E Operation of x Operation Series1 Series Series1 Veight w Series 2 B Number fi o Result Execution Choose the type of operation you need to carry out by clicking on the icon A Select the vectors to be used to generate the new vector by clicking on the icons B and C If a number is used to generate the new vector write its value after Number By default this number is set to 10 Select the vector of results by clicking on the icon D Denote vector 1 by S1 i and vector 2 by S2 i The following table then presents the type of operations available and their results 1 if S1 i S2 i otherwise 0 1 if S1 i S2 i otherwise 0 1 if S1 i gt S2 i otherwise 0 1 if S1 i lt S2 i otherwise 0 6 Finally click on the button Execution to generate the new vector Copy paste and clear commands You can select some cells with your mouse and use the commands copy paste and
44. curve Case 1 One distribution To compute the Lorenz curve for one distribution l From the main menu choose the item Curves gt Lorenz curve 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory Size Variable Group Variable Optional Group Number Optional tho Commands e Compute to compute L k p To compute the standard deviation choose the option for computing with standard deviation e Graph to draw the Lorenz curve To specify a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Range to specify the range of the horizontal axis To compute the standard deviation choose the option for computing with standard deviation Case 2 Two distributions To compute the Lorenz curve with two distributions l From the main menu choose the item Curves Lorenz curve 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows y ee ee Variable of interest Size Variable Optional Number 7 Commands e Crossing to search the first intersection of the curves If the two curves intersect DAD indicates the co ordinates of the first intersection and their standard deviation if the option of computing with standard deviation is chosen To seek an
45. d deviation Case 2 Two distributions To compute the Share Ratio with two distributions l From the main menu choose the item Inequality Share Ratio index 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows Ss Distribution 1 Distribution2 Variable of interest Compulsory Among the buttons you will find the command Compute To compute the standard deviation of this index choose the option for computing with standard deviation 18 Income Component Proportional Growth e Change per 100 Option Let J components yjadd upto y that is J yi y j l The S Gini index of inequality can be expressed as follows 1p P Ac p J y u The contribution of the j component to total inequality in y is IC p where y IC p is the coefficient of concentration of the j component and M is the mean of that component The impact on the S Gini index of growth in y coming exclusively from growth in the j component is al p dy u oy IC I py When multiplied by 1 this says for instance by how much in absolute not in percentage terms the Gini index will change if total income increases by 1 when that growth is entirely due to growth from the j component If you wish to compute this statistics choose from the main menu the following items Inequality Impact
46. distributions 3 Choose the different vectors and parameter values as follows Po Distribution 1 Distribution 2 P Variable of interest ae a oe S The first execution bar contains the command Compaie gt To compute the standard deviation choose the option for computing with standard deviation 4 To compute the normalised index choose this option in the window of inputs The Clark Hemming and Ulph CHU poverty index The poverty index P k z e for the population subgroup k is defined as a 1 1 Lwi gp z ____ if s 1 and 20 Lwi P k z 4 i Ewhiny Z exp f e 1 Lwi i l y if y lt z where z is the poverty line and y i z otherwise Case 1 One distribution To compute the CHU index l From the main menu choose the item Poverty gt CHU index 2 In the configuration of application choose 1 for the number of distributions 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory Optional Group Variable Optional 4 To compute the normalised index choose this option in the window of inputs Commands e The command Compute to compute the CHU index To compute the standard deviation choose the option for computing with standard deviation e The command Graph to draw the value of the index according to a range of poverty lines z To specify such a range for the horizontal axis choose the item Graph Managemen
47. draw the value of the impact as a function of a range of poverty lines z To specify that range and thus the range of the horizontal axis choose the command Range Impact of a tax reform on the FGT indices This tax reform consists of a variation in the prices of two commodities 1 and 2 under the constraint that it leaves unchanged total government revenue The effect of this constraint is given by an efficiency parameter gamma y which is the ratio of the marginal cost of public funds MCPF from a tax on 2 over the MCPF from a tax on 1 The impact of this tax reform denoted IMTR on the FGT poverty index P k z amp is as follows X IMTR CD k z YS CD k z pe 2 where z is the poverty line CD1 k z and CD k z are the consumption dominance curves of commodities 1 and 2 and pc is the percentage price change of commodity 1 Under the government revenue constraint the percentage price change of commodity 1 is iven b pe on ee To compute the impact of the tax reform l From the main menu choose the item Poverty Impact of tax reform 2 Choose the different vectors and parameter values as follows 17 ae ae apa Compulsory _ 1 s price change Commands e Compute to compute the impact of the tax reform To compute the standard deviation of this estimated impact choose the option for computing with standard deviation e Critical to compute the gamma at wh
48. duals or agents found within that LSU These individuals or agents are not selected information on all on them appears in the sample They therefore do not represent the LSUs in statistical terminology Figure 2 Sampling Design with two levels of random selection Sub Units Random Selection E Stratification U Complete Selection Impact of SD on the sampling error of DAD s estimators a Impact of stratification Generally speaking a variable of interest such as household income tends to be less variable within strata than across the entire population This is because households within the same stratum typically share to a greater extent than in the entire population some socio economic characteristics such as geographical locations climatic conditions and demographic characteristics and that these characteristics are determinants of the living standards of these households Stratification ensures that a certain number of observations are selected from each of a certain number of strata Hence it helps generate sample information from a diversity of socio economic areas Because information from a broader spectrum of the population leads on average to more precise estimates stratification generally decreases the sampling variance of estimators For instance suppose at the extreme that household income is the same for all households in a stratum and this for all strata In this case supposi
49. e Income component growth To compute the standard deviation of this estimated impact choose the option for computing with standard deviation Graph to draw the value of the impact as a function of a range for parameter To specify that range and thus the range of the horizontal axis choose the command Range The decomposition of inequality and poverty The decomposition of the FGT index The FGT poverty index for a population composed of K groups can be written as follows P z a 5 f k P k z a k 1 where P k z a is the FGT poverty index for subgroup k and k is the proportion of the population in this subgroup The contribution of group k to the poverty index for the whole population equals o k P k z Q To perform the decomposition of the FGT index l From the main menu choose the item Decomposition FGT Decomposition 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Variable of interest Compulsory Size Variable Group Variable es falpha iY Compulsory Group numbers separated by i ee Compulsory Remark The group numbers separated by the dash should be integer values For example we may have two subgroups coded by the integers 1 and 2 In this case we would write in the field Group Numbers the values 1 2 before proceeding to the decomposition The decomposition of the FGT index for two groups
50. e form y 1 2 3 i 1 999 1000 because it is drawn from a uniform distribution The density at any income between 0 and 1000 is the same and equals 1 1000 The following figure shows the impact of the above correction on the density estimation Density Fonction with and without correction 0 0000 i t t 0 50 100 150 200 250 300 350 400 450 SOO 550 600 650 700 750 800 850 900 950 1000 Value X E without Correction W With 1 order correction This shows that a correction of order 1 corrects well the boundary problem of estimating the density close to 0 and 1000 Example 2 Suppose that an observed vector of interest y takes the form y 1 2 2 3 3 3 1000 1000 The total number of observations sums to N 1000 1 1000 2 50500 The population density equals f x x 500 The following figure shows the impact of a correction of order 1 and 2 on the density estimation Density Fonction without and with correction 0 00225 OpODOT eee reece tet tc ec eecec ec ee ce ee ee ee cence cece ce ceteeeeeeneenaneneensaenneneneeneasecenenenesesasanataneeesenenanessed OOLRS a O lee allele ae lec Sinccsdctecacecnssecsdecsncnenscdues 5 AAEE AA 7 A ee ras a a PTT E SOT SSSOLOSOcOSEEESESESISESISESESESESESES ESS SESESESESES DOES ESSE ODORS E ore nenenenenecenenesenenenenesesesesecasesesesesesesnsnsesasnsnsnsnsnensnenenseed ODOOSOT a cence ec eeeeeeeeeneeeeneneeeeeeneesen
51. e20 Lwi i 1 k e 4 1 a k Exp Lwi bh y gt e 1 pwt i 1 Case 1 One distribution If you wish to compute the Atkinson index of inequality for only one distribution follow these steps l From the main menu choose Inequality Atkinson index 2 In the configuration of the application choose 1 distribution 3 After confirming the configuration the application appears Choose the different vectors and values of parameters as follows Variable of interest Compulsory Size variable Optional Group Number epsilon Optional Compulsory Group Variable Optional Among the buttons you find the following commands e Compute to compute the Atkinson index If you also want the standard deviation of this index choose the option for computing with a standard deviation Graph to draw the value of the index according to the parameter g If you want to specify a range for the horizontal axis choose the item Graph Management gt Change range of x from the main menu Case 2 Two distributions To compute the Atkinson index of two distributions l From the main menu choose the item Inequality Atkinson index 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Distribution 1 Distribution2 Variable of interest Compulsory Group Number Among the buttons you find the command Compute T
52. ecify such a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Case 2 Two distributions To compute the Sen index with two distributions l From the main menu choose the item Poverty Sen index 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows 10 Distribution 1 Distribution2 Variable of interest Compulsory Group number Optional 4 To compute the normalised index choose this option in the window of inputs The Bi dimensional FGT index The Foster Greer Thorbecke poverty index for a good g P k z amp for the population subgroup k is as follows n k 78 g wie x P k z 5 a Lwi i l where Z is the poverty line for good g and t max t 0 The normalised index is defined by P k z 5 P k z a z Union headcount The union headcount based on G dimensions or commodities is equal to yw 1 T i lt x i l P k z z 11 e Intersection headcount The intersection headcount based on G dimensions or commodities is equal to 5 x eo I z gt x P k z z mie e Union sum of gaps The union sum of gaps using G dimensions or commodities is equal to e Intersection sum of gaps The intersection sum of gaps using G dimensions or commodities is equal to
53. ector V be defined as V tystys ta such that Where and i are respectively the average of the bootstrap Mi and the standard deviation of the estimator estimated from the bootstrap sample with estimate i The rejection rule is then a RejectH w in favour of Hu u iif uy lt m gt a2 Or Uo gt f S itin b RejectH u lt y in favour of H u gt u iif u lt m t a c RejectH 2p in favour of H u lt py iif u gt m pt The following table summarizes the confidence ntervals and pvalues according to the pivotal bootstrap approach Case Confidenceinterval p Value Type a o M 8ptian MSate 2 min E lt to XIE t B Two sided i l i l B b u S ut Yt gt t B Lower bounded confidence interval i l B c gt us ti LI lt t B Upper bounded confidence interval i l nequality yi is the living standard of observation 1 We assume that the n observations have been ordered in increasing values of y such that Yi Sip Vi L n1 The variable ci indicates the group to which observation i belongs The sampling weights are defined as w if c k O if c k where k represents the index of a population subgroup e W The Atkinson index Denote the Atkinson index of inequality for the group k by 1 amp 8 It can be expressed as follows E k Ewy mg EO Shere py i l The Atkinson index of social welfare is as follows 1l Ywity if e 1 and
54. eight No Selection J Correction Factor No Selection 7 Auto compute the FPC ok canceL This allows DAD to take into account a wide variety of possible SD This is made by selecting or not selecting vectors for any of the five choices offered above In the case of SRS within a number of strata there would be an indicator of a strata vector without any indication of a vector of PSU s The following table presents some of these combinations SD is SRS without sampling weights X SD is stratified with SW X X X No stratification but multi stage sampling and SW X Random one stage sampling of LSU s with LSU specific selection probabilities This can occur for instance if once an individual is selected all individuals in his household are also automatically selected Implicitly then it is the household that is selected as a LSU X X Stratification with only the first sampling stage specified by the user Stratification with one stage sampling and sampling weights wrongly omitted X Stratification with one stage sampling and sampling weights wrongly omitted Stratification with multi stage sampling and sampling weights wrongly omitted X Stratification with multi stage sampling and sampling weights provided X X Stratification with multi stage sampling and sampling weights provided The finite population correction factor is also provided this supposes that sampling for the statistical inferences X Indicate that t
55. elasticity GREL of poverty when growth comes exclusively from growth within a group k which is within that group inequality neutral is given by o Pik z0 zP k za 1 f asl P z GREL zf k z FG 20 where z is the poverty line k is the population subgroup in which growth takes place f z is the density function at level of income z and F z is the headcount To compute that growth elasticity l From the main menu choose the item Poverty Growth Elastic ity 2 Choose the different vectors and parameter values as follows Variable of interest Compulsory Size variable Group Variable Group Number Poverty line alpha Commands e Compute to compute the growth elasticity To compute the standard deviation of its estimate choose the option for computing with standard deviation e Graph to draw the value of the impact as a function of a range of poverty lines z To specify that range and thus the range of the horizontal axis choose the command Range Income Component Proportional Growth e Change per 100 of component C Assume that total income Y is the sum of C income components with Y YA Ye and c 1 where c is a factor that multiplies income component y and that can be subject to growth The derivative of the normalized FGT index with respect to A is given by OP k z 0 dh CD k z a Ac lhce l C Where C dominance curve of component c e Change per of co
56. enesensesesesenesnsnsssscenenenensesesesensnensneeseseeed O alla aaa aa a a t t t t t 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 Value X W without correction MP With 1 order correction W With 2 order correction 0 00000 The joint density function The gaussian kernel estimator of the joint density function f Y is defined as 2 2 A 1 z 1 1 x Xx y y f x y _ w exp L a Pa a a i To reach this application l From the main menu choose the item Distribution Joint density function 2 Choose the different vectors and parameter values as follows Variable of interest Compulsory Variable of interest Compulsory a p I lt a lt ps On the first execution bar you find e Thecommand Compute to compute the estimate of the joint density function To compute the standard deviation choose the option for computing with standard deviation The distribution function To reach this application l From the main menu choose the item Distribution gt Distribution function 2 Choose the different vectors and parameter values as follows Variable of interest Compulsory Group Variable Group Number Parameter Compulsory lt On the first execution bar you find e The command Compute to compute the estimate of the distribution function To compute the
57. equality across population subgroups or by factor components e g by type of consumption expenditures or source of income 4 Progressivity and equity across different taxes and or tranfers and subsidies 5 Poverty changes across growth and redistribution effects 6 Checks for the robustness of distributive comparisons 7 Estimation of stochastic dominance curves of the primal and dual types for poverty social welfare inequality and equity dominance 8 Robustness of decompositions into population subgroups and factor components 9 Estimation of popular dual curves ordinary and generalised Lorenz curves Cumulative Poverty Gap curves quantile curves normalised quantile curves poverty gap curves ordinary and generalised concentration curves 10 Estimation of popular primal curves cumulative distribution functions poverty deficit curves poverty depth curves etc 11 Estimation of differences in curves and indices 12 Estimation of critical poverty lines for absolute and relative poverty comparisons 13 Estimation of crossing points for dual curves 14 Provision of asymptotic standard deviations on all estimates of indices points on curves critical poverty lines crossing points etc allowing for dependence or independence in the samples being compared These standard deviations are currently computed under the assumption of identically and independently distributed sample observations but the co
58. gement gt Change range of x from the main menu e Thecommand Range to specify the range of the horizontal axis To compute the standard deviation choose the option for computing with standard deviation Corrected boundary Kernel estimators A problem occurs with kernel estimation when a variable of interest is bounded It may be for instance that consumption is bounded between two bounds a minimum and a maximum and that we wish to estimate its density close to these two bounds If the true value of the density at these two bounds is positive usual kernel estimation of the density close to these two bounds will be biased A similar problem occurs with non parametric regressions One way to alleviate these problems is to use a smooth corrected Kernel estimator following a paper by Peter Bearse Jose Canals and Paul Rilstone A boundary corrected Kernel density estimator can then be written as A WiK x K AKOKO f v i l where X X exp 0 54 x and A x 1 K aes and where the scalar K x is defined as K x w x PAX x 471 Po iN p seas oH w x M 1 KaVPAPAY AR 1 Aa p 1 a 0 0 0 min is the minimum bound and max is the maximum one h is the usual bandwidth This correction removes bias to order h DAD offers four options without correction and with correction of order 1 2 and 3 Example 1 Suppose that an observed vector of interest y takes th
59. gf You can also save and use graphs in many others popular text processors including Word and Excell The available formats are Portable Network Graphic JPEG File Interchange Format Portable Document Format Tag Image File Format Bitmat Image File To save a graph made in DAD select File Save and select the format by selecting the extension of the file jo My Documents x ce E Ey Adobe My eBooks My Pictures Desktop My Documents Cance Abort file chooser dialog Saving coordinates of curves To save the graph coordinates in ASCII format select File Save coordinates The generated ASCII file takes the following format Curvel Curve2 X1 Y1 X2 Y2 etc Printing graphs To print a graph select File Print The following windows appears HP LaserJet SP SMP PostScript v Select the desired Printer To change orientation or margins select Page Setup When the following window appears select the desired orientation and margins Media Size Letter Source Automatically Select x Orientation Margins A Portrait left in right in Landscape h o ho W Reverse Portrait top in bottom in ho Wo V C Reverse Landscape Templates You can select one of DAD s several graphical templates to change the properties of a graph These templates only use black and white colours To select a template select
60. ginal contribution when it is added randomly to anyone of the various subsets of components that one can choose from the set of all components When a component is missing from that set we assume that the observation values of that component are everywhere replaced by its average The following results appear in the output window To perform that decomposition of the S Gini index of inequality l From the main menu choose the item Welfare and inequality gt Decomposition S Gini decomposition 2 Select the desired decomposition approach 3 After confirming the configuration the application appears Choose the different vectors and parameter values as follows pe pme OE Size Variable Rho SSS ip _ Compulsory Vector s of interest Index 1 index2 Compulsory The decomposition of the S Gini index by population groups Let there be G population subgroups We wish to determine the contribution of every one of those subgroups to total population inequality Natural approach We rewrite the S Gini index as c 2 U T I L L T I g l u where the population share of group g P the contribution of inter group inequality to total inequality Hs the average revenue of those in group g u average revenue of total population I S Gini of group g The Shapley approach This decomposition has two steps The first one is to decompose total inequality into inter group and intra group contribution
61. he Atkinson Gini index To compute the standard deviation choose the option for computing with standard deviation Case 2 Two distributions To compute the Atkinson Gin social welfare with two distributions l From the main menu choose the item Welfare Atkinson Gini 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory a a E E EE To compute the standard deviation choose the option for computing with standard deviation Impact of a price change on the Atkinson Social Welfare Index The impact of a good 1 s marginal price change denoted IMPW on the Atkinson Social Welfare index Ele is as follows IMPW BO P 1 IMpw 1 s1 s2 s3 pe if e l exp s2 s1 s3 s1 pc if e l and E s2 wiy s3 wiy x if e l s w s2 w log y s3 w x y if e 1 where Xi is expenditure on commodity by individual i yi is the variable of interest living standard and pc is the percentage price change for good 1 To compute the impact of the price change l From the main menu choose Welfare Impact of price change 2 Choose the different vectors and parameter values as follows ee o Variable of interest Compulsory The computation can be made solely within a group of individuals This is done by specifying the group number k and the group variable c
62. he variable is selected X KO O K K x x gt lt K K x x Note that when DAD finds the values of the strata psu lsu variables to be the same across observations it supposes that these observations comefrom just one LSU If the option Auto compute FPC is activated DAD generates implicitly the FPC vector Remarks After initialization of the SD information the dataset is automatically ordered by when specified strata PSU s and LSU s There should be more than one PSU within each stratum e g 1 before initialization of the SD To show the SD information select from main menu the item Edit gt Summarize Sample Design The following window appears TEDAD 4 2 Sampling Design HTML Result Yiewer Sampling Design Information cove smara rsu isu ons remem Pcaw a fo f e e s fomwof o z ee o e l ee ee _ s s kee ee Code of PSU Strata l 1 2 Strata 2 1 2 Computation of standard errors in D AD This section shows how the standard errors of DAD s estimators of distributive indices and curves are computed The methodology is based on the asymptotic sampling distribution of such indices and curves All of DAD s estimators are asymptotically normally distributed around their true population value As will be discussed below we expect this methodology to provide a good approximat
63. hing parameter Remark 1 The option Level vs Percentile allows the estimation of the expected value of y either at a level of x or at a p quantile for x Remark 2 The option Normalised vs Not normalized by the mean or by x allows the estimation of the expected value of y normalized or not by x or by the overall mean of y You will find e Thecommand Compute to compute y x To compute its standard deviation choose the option for computing with standard deviation e The command Compute h to compute an optimal bandwidth according to the cross validation method of H rdle 1990 p 159 160 When you click on this command the following window appears giving you the option of choosing the min max bands and the percentage of observations to be rejected on each side of the range of x E Compute bandwith CVh method by Default v min 0 max 1000 reject 5 e Thecommand Graph to draw ylx as a function of x To specify a range for the horizontal axis choose the item Graph management Change range of x from the main menu e The command Range to specify the range of the horizontal axis g pecily g Boundary corrected non parametric regression and non parametric derivative regression For the boundary corrected non parametric regression the estimation is as follows YK OOK x y P yw KOK 9 The boundary corrected non parametric deri
64. hoose for the number of distributions 3 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Variable of interest Compulsory Compulsory Oy Group Variable ce re Commands e The command Compute to compute the Atkinson index To compute the standard deviation choose the option for computing with standard deviation e The command Graph to draw the value of the index according to a ange of parameters To specify such a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Case 2 Two distributions To compute the Atkinson with two distributions l From the main menu choose the item Welfare Atkinson index 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory To compute the standard deviation choose the option for computing with standard deviation The S Gini social welfare index Casel One distribution To compute the S Gini index of social welfare for one distribution l From the main menu choose the following item Welfare S Gini index 2 In the configuration of the application choose for the number of distributions 3 After confirming the configuration the application appears Choose the different vectors and parameter values as follow
65. hoose the item Graph Ma nagement Change range of x from the main menu Case 2 Two distributions To calculate the Generalised Entropy index for two distributions l From the main menu choose the item Inequality gt Entropy index 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Ss Distribution 1 Distribution2 Variable of interest Ooy ft oe 2 Group Number Optional ae 3 eg Among the buttons you will find the command Compute To compute the standard deviation of this index choose the option for computing with standard deviation The Quantile Ratio and the Interquantile Ratio Index Denote the Quantile Ratio for group k by QR kp p it can be expressed as follows Q k p QR k p p j k Q k p2 where Q k p denote the p quantile of group k The Interquantile Ratio IQR k p p is defined as k p Qk p IOR p p p a P2 Remark The instructions for the Interquantile Ratio are similar to those for the Quantile Ratio Case 1 One distribution If you wish to compute the Quantile Ratio for only one distribution follow these steps l From the main menu choose Inequality Quantile Ratio index 2 In the configuration of the application choose 1 distribution 3 After confirming your choice the application appears Choose the different vectors and values of parameters as follows Var
66. iable of interest Compulsory Size variable Optional Group Variable Optional Group Number Optional Percentile for numerator Compulsory Percentile for Compulsory denominator Among the buttons you will find the following command e Compute to compute the Quantile ration If you also want the standard deviation on the estimator of that index choose the option for computing with a standard deviation Case 2 Two distributions To compute the Quantile Ratio index with two distributions l From the main menu choose the item Inequality Quantile Ratio index 2 In the configuration of application choose 2 as the number of distributions 3 Choose the different vectors and parameter values as follows Distribution 1 Distribution2 Variable of interest Compulsory Oo k k Group Number k Optional Percentile for numerator Compulsory 1 a Oma r aii P2 P2 denominator Among the buttons you will find the command Compute To compute the standard deviation of the estimator of that index choose the option for computing with standard deviation The Coefficient of Variation Index Denote the Coefficient of Variation index of inequality for the group k by CV It can be expressed as follows 1 kk a 2 Lwy Yow TH _ i l izl 2 u CV Case 1 One distribution If you wish to compute the Coefficient of Variation index of inequality for only one distribution follow these steps l
67. ich the tax reform will have zero impact on poverty The value of this critical gamma equals CD w k z CD k z e Graph z to draw the value of the impact of the tax reform as a function of a range of poverty lines z To specify that range and the horizontal axis choose the command Range e Graph to draw the value of the impact as a function of a range of MCPF ratios y To specify that range and the horizontal axis choose the command Range Lump sum Targeting The per capita dollar impact of a marginal addition of a constant amount of income to everyone within a group k called Lump Sum Targeting LST on the FGT poverty index P k z is as follows QP k z a 1 if 21 and Not Normalised LST Be z a 1 if O21 and Normalised Z f k z f a 0 where z is the poverty line k is the population subgroup for which we wish to assess the impact of the income change and f k z is the density function of the group k at level of income Z 18 To compute that impact l From the main menu choose the item Poverty Lump sum Targeting 2 Choose the different vectors and parameter values as follows Commands Variable of interest Compulsory Size variable Optional Group Variable Optional Group Number Optional Poverty line Compulsory alpha Compulsory e Compute to compute the impact of the income change To compute the standard deviation of this estimated impact ch
68. icon A Select the vectors to be used to generate the new vector by clicking on the icons B and C If a number is used to generate the new vector write its value after Number By default this number is set to 10 Select the vector of results by clicking on the icon D Denote vector 1 by S1 i and vector 2 by S2 i The following table then presents the type of operations available and their results 1 if S1 i S2 i otherwise 0 1 if S1 i S2 i otherwise 0 1 if S1 i gt S2 i otherwise 0 1 if S1 i lt S2 i otherwise 0 6 Finally click on the button Execution to generate the new vector Copy paste and clear commands You can select some cells with your mouse and use the commands copy paste and clear to edit your database GetOBS and SetOBS commands To obtain the number of observations of your active file choose the command GetOBS If you would like to set a new number of observations choose the command SetOBS The following window appears 2 Enter the new number of observations After this enter the new number of observations and click on the button OK The first SetOBS observations will now be used for the computations Changing the names of spreadsheet To change the name of the spreadsheet from the main menu select the item Edit Change current sheet name and indicate the new name Dimension of the spreadsheet The length of the spreadsheet varies accordi
69. if My gt M pZ gt Z lt Z The following table summarizes the confidence intervals and p values corresponding to each of the three cases of the above hypothesis tests Case Confidenceinterval p Value Type a m g ran Papl 2 1 F 1z 1 Two sided b M A too 1 F z Lower bounded confidence interval c co m d Za F z Upper bounded confidence interval 2 Standard bootstrap approach Let the vector V regroup the ordered sample values of the estimator u computed from B simulated or bootstrap samples each drawn from the same initial sample In the bootstrap approach the vector V is the main tool to capture the distribution of the estimator u The number of replications B should be chosen so that a B 1 is an integer andB 2 1 a a Let u be the amp quintile of the vector V Once the significance level of the test is chosen the rejection rule becomes a RejectHy M VSH M M iif Mo gt Mio OF Ho lt Mars b RejectH MSW vsH u lt p iif su gt u c RejectH w2u vsH u gt p tif lt w The following table summarizes the confidence intervals and p values according to the standard bootstrap approach Case Confidenceinterval p Value Type K B x B x a Makian 2min Iu lt Ho NDD Ku gt H B Two sided i l i l B b u gt I u gt B Lower bounded confidence interval Me c uw I u lt u B Upper bounded confidence interval 3 Pivotal bootstrap approach Let the v
70. iguration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory Press Compute to compute the concentration coefficients and their difference for each of the two variables of interest To compute the standard deviation of those estimates choose the option for computing with standard deviation D istribution Descriptive statistics This application provides basic descriptive statistics on variables in the database the mean the standard deviation and the minimum and the maximum values of each of the vectors To reach this application From the main menu choose Distribution Statistics 2 Choose the data bases if you have activated two databases 3 Choose the weight variable if the observations must be weighted 4 Choose the group variable and the group number if you would like to compute the statistics for a specific group The results are as follows Name of variable 1 Standard deviation Name of variable 2 Standard deviation Statistics This application computes basic descriptive statistics for a given variable of interest as well as the ratio of two such variables The application also computes the effect of the sampling design on the sampling error of these basic statistics l Total w X ero ie Wi Ya To activate this application for one distribution follow these steps l From the main
71. in D AD 4 3 A database used in DAD is a set of vectors of data Each vector represents a specific variable By default the length of each vector determines the number of observations for that variable Each database contains a set of vectors whose number of observations must be the same Constructing a database with DAD After opening DAD the following window appears iw o D B a vector 1 1 dex vecton 1 Vector_ 2 Vector_ 3 Vector_ 4 Vectof 5 Vector_ 6 7 vector 8 Yector_ 9 I z c D DAD 4 2 NOTICE Woe B DAD 4 2 A Software for Distributive Analysis Analyse Distributive E This programme is freely distributed and freely available Please acknowledge its use by quoting it as Jean Yves Duclos Abdelkrim Araar and Cari Fortin DAD A software for Distributive Analysis Analyse Distributive MIMAP programme International Development Research Centre Government of Canada and CREFA Universit Laval Box WB cancr Fil 1 File2 No Name A Main menu B Toolbar C The selected cell D Value of the selected cell E Name of column F Index of observation G The selected file To construct a new database with DAD follow these steps l Ts In the main menu click on the command File and select the option New File A window asks the use
72. int at which the progressivity ranking of the tax and transfer is reversed DAD indicates the co ordinates of that first reversal and their standard deviation if the option of computing with standard deviation is chosen These co ordinates are TR Approach IR Approach Cg p Lx p Cx B p e The command Difference to compute TR Approach IR Approach Cr P Cg p 2Lx p Cx B P Cx r p e The command Range to specify a range of p for the search of the first reversal of the progressivity ranking The command also allows to specify the range of the horizontal axis in the drawing of a graph e The command Graph to draw the following curves as a function of p TR Approach IR Approach Cr p Cp p 2Lx p Cx B P Cx rP Horizontal inequity A tax or a transfer T causes reranking and is therefore horizontally inequitable if Tax gt Cx r p Lx r p gt 0 for at kast one value of pe Jof Transfer Cy 7 p Lx 7 p gt 0 for at least one value of pe lol To reach this application l From the main menu choose the item Redistribution Horizontal inequity 2 Specify if you are using a tax or a transfer 3 Choose the different vectors and parameter values as follows Gross income Tax transfer Size variable s Group variable c Group numberof interest k Commands e The command S Gini to compute Ixr ICy rp Ler O ICs P e The command Difference to compute ax Cx r Lxr Cx B
73. ion estimates the cross group composition of a population The group details are provided by the user through either or both of two Group variables To reach this application l From the main menu choose Distribution Group Information 2 Choose the first group variable 3 Choose the size variable if the observations must be weighted by size 4 Choose the second group variable if you would like cross group or cross tabulation information to be provided across two groups Example 1 10 TEDAD 4 2 HTML Result Viewer File Edt Group Information Distribution Thu Apr 25 09 36 37 EDT 2002 0 03 sec p Weight variable Without size Group variable INS_LEV Group variable 2 No Selection Group Variable INS_LEV C e f a f o O s S o O s w am o o o e omm n O o o omw oo E E S E EE This example uses only one group variable INS LEV level of instruction of the household head categorized as 1 Primary 2 Secondary 3 Superior 4 Notavailable 5 None The output shows The exact code of the group The group number 1 2 3 The number of observations in the group The sum of the products of Sampling Weight times Size P Group The estimated proportion of population found in that group The use of two group variablesshows the following information 11 Example 2 TEDAD 4 2 HTML Result Viewer 10 x File Edit Cross Table W S a 177250 099487
74. ion to the true sampling distribution of DAD s estimators for relative large samples Estimators of the distributive indices Estimators of distributive indices such as poverty and inequality indices take the following general form 6 g t k with o asymptotically expressible as O Ykj j l where Ocan be expressed as a continuous function g of the s m is the number of sample observations and y is usually some transform of the living standard of individual or household j We use Rao s 1973 linearization approach to derive the standard error of these distributive indices This approach says that the sampling variance 6 equals the variance of a linear approximation of 0 08 00 Gh Q a 270 00 va Var a Guza dQ A In matrix format the variance of 9 is given by Var Var V MV with M the covariance matrix of the amp and V the gradient of 00 0a 00 0a 00 00x Rao C R 1973 Linear Statistical Inference and Its Application New York Wiley 08 00 The gradient elements Se can be estimated consistently using estimates dQ JO 06 a e l O lof the true derivatives The covariance matrix is defined as o Oa Var O Cov a Q Cov Q QA vo Cov Q a Var Q CovQ Qx Cov Qk Q Co Qk Var Q The elements of the covariance matrix are again estimated consistently using the sample data replacing for instance Var a
75. izontal axis choose the item Graph Management gt Change range of x from the main menu e To compute the standard deviation choose the option for computing with standard deviation Case 2 Two distributions To reach the application for two distributions l From the main menu choose the item Curves CPG curve 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory Size Variable Optional Group Variable ca Commands e Crossing to search the first intersection of the curves If the two curves intersect DAD indicates the co ordinates of the first intersection and their standard deviation if the option of computing with standard deviation is chosen To seek an intersection over a particular range use Range e Difference to compute the difference G k p z G k3 p5 z e Graph to draw the difference G k p z G k p z 2 as a function of p e Range to specify the range for the search for a crossing between the two curves This also specifies the range of the horizontal axis e S Gini to compute the difference P Z 3P P gt z 3p e Covariance to compute the following covariance matrix Cow G k 0 1 z G k 30 1 z CowG k 30 1 z G k 0 2 z CowG k 0 1 z G k 1z CouG k 0 2 2 G k 0 1 z Cov G k 0 2 z G k 0 2 z Con G k 1z
76. mp by War amp It is at the level of the estimation of these covariance elements that the full sampling design structure is taken into account Finite sample properties of asymptotic results It may be instructive to compare the results of the above asymptotic approach to those of a numerical simulation approach like the bootstrap The bootstrap BTS is a method for estimating the sampling distribution of an estimator which proceeds by re sampling repetitively one s data For each simulated sample one recalculates the value of this estimator and thenuses that BTS distribution to carry out statistical inference In finite samples neither the asymptotic nor the BTS sampling distribution is necessarily superior to the other In infinite samples they are usually equivalent Bootstrap and simple random sampling The following steps the BTS approach for a sample drawn using Simple Random Sampling l Draw with replacementm observations from the initial sample 2 Compute the distributive estimator from this new generated sample 3 Repeat the first two steps N times 4 Compute the variance or the BTS distributions using these N generated estimators Bootstrap and complex sampling design The steps here are similar to those above with Simple Random Sampling Only the first step differs to take into account the precise way in which the original sample was drawn Suppose for example that e The data were drawn from two strata with m1 obse
77. mponent 21 h The per capita dollar impact of growth in the j component on the normalized FGT index of the k group is as follows OP k z a j Z s Y pe u ay where CD is the normalized C dominance curve of the component j e Elasticity with respect to component The component elasticity of poverty measured by the normalized FGT index is OD k z 0 P k z 0 Ary amp where CD is the normalized C dominance curve of the component j If you wish to compute this elasticity choose Poverty Component Elasticity If you wish to compute that impact choose Poverty gt Income Component Proportional Growth and select one of the tree options Variable of interest Compulsory Income Component Compulsory Size variable Optional Group Variable Optional Group Number Optional Alpha Compulsory Poverty line Compulsory Among the buttons you will find e Compute to compute the statistics If you also want its standard error choose the option for computing with a standard deviation 22 The impact of demographic changes This application computes the impact of a change by a given percentage in the proportion of a group t That change is accompanied by an exactly offsetting change in the proportion of the other groups If the population proportion of group t increases by pc percent such that o t gt O pe the total estimated impact on poverty is as follows AP orezo
78. mputations take into account the randomness of the sampling weights when such weights are provided by the user 15 Allowance for sampling errors in the poverty lines specified to compute absolute and relative poverty indices DAD s environment is user friendly and uses menus to select the variables and options needed for all applications The software can load simultaneously two data bases can carry out applications with only one data base or two and can allow for dependence or independence of data bases and vectors of living standards in computing standard errors on differences in indices and curves The databases can be built with the software or can be loaded from a hard disk or a floppy or CD ROM driver The databases can be edited new observations can be added and new vectors of data can be generated using arithmetical or logical operators Features of version 4 3 of DAD Standard deviations confidence intervals and hypothesis e DAD4 3 can now compute confidence intervals and perform statistical tests using standard or pivotal bootstrap approaches for some of the distributive indices programmed in DAD This can serve as alternatives to the long available asymptotic standard deviations in DAD Graph options e The possibility of saving graphs in the DAD Graph Format dgf that one can load and update e The possibility of deleting a selected curves New applications Bounded Income and Overload Indices These indice
79. mpute the selected index To compute the standard deviation of this index choose the option fa computing with standard deviation e The command Graph to draw the value of the overload index as a function of a range of poverty lines z To specify the range for the horizontal axis choose the item Graph Management Change range of x from the main menu The Watts poverty index The Watts poverty index PW k z for the population subgroup k is defined as wt logy 2 PW k z _______ yw i where z is the poverty line and x max x 0 Case 1 One distribution To compute the Watts index l From the main menu choose the item Poverty Watts index 2 In the configuration of application choose 1 for the number of distributions 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory Commands e The command Compute to compute the Watts index To compute the standard deviation choose the option for computing with standard deviation e The command Graph to draw the value of index according to a range of poverty lines z To specify such a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Case 2 Two distributions To compute the Watts index with two distributions l From the main menu choose the item Poverty Watts index 2 In the configuration of application choose 2 distributions
80. n the button Advanced makes the following windows appear Advanced Choices Decimal separator or dot orcomma Drop first spaces V Drop empty lines MV Number of treated lines in ASCII file Number V Treat All Number of edited missing or not convertible values Number fioo Edit All 2 Agree 2 Cancel We do not by default need to specify what the separator of decimals is but if we indicate that it is a dot then we may specify that the separator between the variables can be a comma Remark If the delimiter of columns is a comma the delimiter of decimals cannot also be a comma By selecting the option Drop first spaces we do not take into account spaces which precede the values of the first column We can also indicate the number of lines in the ASCII file to be treated as well as the number of missing or not convertible values to be edited The panel Preview results shows the number of observations and the number of columns in the ASCII file The panel Data Preview displays instantaneously the data as their reading changes according to selected options This a useful tool for reliable loading of ASCII data files Note in the panel Preview Results the message Button Warning If we click on the button the following window appears Drop observations when missing or not convertible values are detected Drop columns when missing or not convertible values
81. ng also that the population size of each stratum is known it is sufficient to draw one household from each stratum to know exactly the distribution of income in the population b Impact of clustering or multi stage sampling Multi stage sampling implies observations end up in a sample only subsequently to a process of multiple selection Groups of observations are first randomly selected within a population which may be stratified this is followed by further sampling within the selected groups which may be followed by yet another process of random selection within the subgroups selected in the previous stage The first selection stage takes place at the level of PSU s and generates what are often called clusters Generally variables of interest such as living standards vary less within a cluster than between clusters Hence multi stage selection reduces the diversity of information generated by sampling The impact of clustering sample observations is therefore to tend to decrease the precision of populations estimators and thus to increase their sampling variance Ceteris paribus the lower the variability of a variable of interest within clusters the larger the loss of information that there is in sampling further within the same clusters To see this suppose for instance an extreme case in which household income happens to be the same for all households in a cluster and this for all clusters In such cases it is cle
82. ng to the following gt By default the length of the spreadsheet is 160 000 observations This is done when a new file is created gt If you download an ASCII file the length of spreadsheet corresponds to the number of observations read from this file gt In all cases you can specify explicitly a desired length for the spreadsheet by indicating the new length after choosing the command Edit and the item Enter the new length of the spreadsheet E Input O ox Annus The new length of the spreadsheet cannot be below the number of observations OBS The number of columns fixes the width of the spreadsheet By default the number of columns is 16 M odifying the database DAD offers the possibility to modify the dimension of a database and also to generate a new vector of data using logical or arithmetic operators Changing the names of vectors To change the names of vectors click on the button Edit and then select the item Change column name The following windows appears eked columaname o Change Column Name Yector s name Weight Weight vector 11 Vector 11 Expend Expend vector 12 vector 2 Group Group vector 13 vector 3 Vector_ 4 e ctor_ 4 Vector_ 14 vector 4 Vector_ 5 e ctor_ 5 Vector_ 15 vector 15 Vector_ 6 e ctor_ 6 Vector_ 16 vector 6 Vector_ 7 e ctor_ 7 vector 17 rector 7 Vector_ 8 ecto r 8 vector 18 vector 8 Vector_ 9 e ctor_ 9 Vector_ 19 vector 9 Ve
83. o compute the standard deviation of this index choose the option for computing with standard deviation S Gini index Denoting the S Gini index of inequality for the group k by K P and the S Gini social welfare index by amp k p we have wk k p I k p k p ak where i VP SV ag Sk p iyi i l V P and Vi Ew Case 1 One distribution To compute the S Gini index of inequality for only one distribution l From the main menu choose the item Inequality S Gini index 2 In the configuration of the application choose 1 distribution 3 After confirming the configuration the application appears Choose the different vectors and values of parameters as follows Compulsory Group Variable i EES A Variable of interest Group Number Two choices of commands appear among the buttons e Compute to compute the S Gini index To compute the standard deviation of this index choose the option for computing with standard deviation e Graph to draw the value of the index according to the parameter p To specify such a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Case 2 Two distributions To reach the S Gini application with two distributions l From the main menu choose the item Inequality S Gini index 2 In the configuration of application choose 2 distributions 3 Choose the different vecto
84. of Component Growth Variable of interest Compulsory Component Compulsory Size variable Group Variable Group Number o 19 Among the buttons you will find e Compute to compute the impact on the S Gini index of growth in y coming exclusively from growth in the j component If you also want its standard deviation choose the option for computing with a standard deviation e Elasticity with respect to component option The Gini j component elasticity is given by dl p dy KP _ IC N 2 al ony u Ip dy This give the elasticity of the Gini index with respect to total income when the change in total income is entirely due to growth from the j component To compute this elasticity choose from the main menu the following items Inequality Gini Component Elasticity Variable of interest Compulsor Compulsory Optional Optional Optional rho Compulsory Among the buttons you will find e Compute to compute the Gini component elasticity To obtain the standard deviation of that estimate choose the option for computing with a standard deviation 20 Poverty indices DAD offers four possibilities for fixing the poverty line l A deterministic poverty line set by the user 2 A poverty line equal to a proportion of the mean 3 A poverty line equal to a proportion m of a quantile Q p 4 An estimated poverty line that is asymptotically normally distribu
85. olds Without Without size i Size For the 10 households With size S 1 For households living in town V1 Without Without size i Size For households living in town V1 With size i S For households living in town V2 Without Without size i Size This choice does not affect the results since no group variable has been selected Consult the Sampling design section to know how can we initialise the sampling weight Finally to compute the standard deviation on the estimate of the mean you just need to select the option of computing with STD Basic N otation in DAD In this following table we present the basic notations used in the user manual of DAD i W if ci k and 0 otherwise ae sw sw os a pi ra Torsone oT e a ok Example The mean of group k u k is then estimated as Taking into account sampling design in DAD Sampling Design and DAD With version 4 2 and higher of DAD the Sampling Design SD of the database can be specified in order to calculate the correct asymptotic sampling distribution of the various indices and statistics provided by DAD Data from sample surveys usually display four important characteristics l they come with sampling weights SW also called inverse probability weights 2 they are stratified 3 they are clustered 4 sample observations provide aggregate information such as household expenditures on a numberof stati
86. onfiguration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory Compulsory Compulsory Commands e Difference to compute the difference CD k z s CD k z s e Graph to draw the difference CD k z s CD k z s as a function of z e Range to specify the range of the horizontal axis The Relative Deprivation curve Let the relative deprivation of an individual with income Q p when comparing himself to another individual with income Q q be given by 0 if gt s a p QP 2 Qa Q q Qp otherwise The expected relative deprivation of an individual at rank p is then 6 p 1 d p 5 q p dq 0 Case 1 One distribution To compute the relative deprivation curve for one distribution l From the main menu choose the item Curves gt Relative Deprivation curve 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows Compulsor Optional Variable of interest ly Size Variable Group Variable Optional OOO P O Group Number po Commands Optional Compulsory Compute to compute 5 p To compute the standard deviation choose the option for computing with standard deviation Graph to draw the curve as a function according of p To specify a range for the horizontal axis choose the item Graph Management
87. ons 3 Choose the different vectors and parameter values as follows Distribution 1 Distribution2 _ 16 Among the buttons you will find the command Compute To compute the standard deviation of this index choose the option for computing with standard deviation The Share Ratio Denote the Share Ratio for population domain k by SR k pl p2 p3 p4 where p1 and p2are lower and upper percentiles that delimitate a first group and p3 and p4 are lower and upper percentiles that delimitate a second group The Share Ratio is the ratio of the income share of the first group over the income share of the second group L p2 L p1 SR k p1 p2 p3 p4 L p4 L p3 Case 1 One distribution If you wish to compute the Share Ratio for only one distribution follow these steps l From the main menu choose Inequality Share Ratio index 2 In the configuration of the application choose 1 distribution 3 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Compulsory Optional Optional Variable of interest Size variable Group Variable Le Group Number Optional py Percentile Compulsory Percentile Compulsory 17 3 Among the buttons you will find the following command Compute to compute the Share Ratio If you also want the standard deviation of this index choose the option for computing with a standar
88. oose the option for computing with standard deviation e Graph to draw the value of the impact as a function of a range of poverty lines z To specify that range and thus the range of the horizontal axis choose the command Range Inequality neutral Targeting The per capita dollar impact of a proportional marginal variation of income for the group k called Inequality Neutral Targeting on the FGT poverty index P k z is as follows INT 4 gee eet if o 21 and FGT isnot normalised U g SANE BOSD F gai md TOTS iodi U _ a k z if a 0 Ly where z is the poverty line k is the population subgroup for which we wish to assess the impact of the income change and f k z is the density function of the group k at level of income zZ 19 To compute that impact l From the main menu choose the item Poverty Inequality neutral Targeting 2 Choose the different vectors and parameter values as follows Variable of interest Compulsory Size variable Group Variable Group Number Poverty line alpha Commands e Compute to compute the impact To compute the standard deviation of this estimated impact choose the option for computing with standard deviation e Graph to draw the value of the impact as a function of a range of poverty lines z To specify that range and thus the range of the horizontal axis choose the command Range Growth Elasticity The overall growth
89. ose 1 distribution 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory Ranking variable Compulsory Size Variable Optional Group Variable Optional Group Number Optional ho Compulsory Compulsory Commands Compute to compute the concentration curve C k p To compute the standard deviation choose the option for computing with standard deviation Graph to draw the concentration curve To specify a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Range to specify the range of the horizontal axis To compute the standard deviation choose the option for computing with standard deviation Case 2 Two distributions To compute the concentration curve of two distributions l From the main menu choose the item Curves Concentration curve 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Ranking variable Variable of interest Size Variable y Compulsory T2 Compulsory s Optional Optional o Group Number Compulsory Compulsory y Pee E s Group Variable Ooo po Commands Crossing to search the first intersection of the curves If the two curves intersect DAD indicates the co ordinates of the first intersection and their standard deviation if the option of computing with standard deviation is chosen To
90. ows Variable of interest y Compulsory Size variable Optional Commodity 1 Compulsory Commodity 2 Compulsory Group Variable Optional Group Number OoOo kpo Optional epsilon Compulsory gamma Compulsor y 1 s price change pe Compulsory Commands e Compute to compute the impact of the tax reform To compute the standard deviation of this estimated impact choose the option for computing with standard deviation Impact of Income component growth on the Atkinson Social Welfare Index The impact of growth in the j component on the Atkinson Social Welfare index Ele is as follows 1 0 ECE T sl ea s2 s3 pe f e 1 xj exp s2 s1 s3 s1 pe if e l and x s2 wyi s3 wiy x if e 1 s f w s2 w log y s3 w x y if e 1 where x is the value of component j for individual i and pc is the percentage change in that j income component This tells us therefore by how much social welfare will change if a growth of pc is observed in a component j of total income To compute the impact of that change e From the main menu choose the item Welfare Impact of Income component growth e Choose the different vectors and parameter values as follows Variable of interest Compulsory Size variable Optional Component Compulsory Group Variable Optional Group Number Optional Epsilon Compulsory Component change Compulsory in Commands Compute to compute the impact of th
91. r to indicate the desired number of observations for the new file Entr e Enter the new number of observations Enter the number of observations of the new file and click on the button OK To begin editing the new vectors follow these steps Click on the cell vector 1 index 1 The contour of this cell changes to yellow Write the new value of the cell As a general rule with DAD the decimal part should be separated by a dot Press Enter Write the value of the next cell and repeat the procedure until all of values of vector 1 are registered To edit another vector select the first cell of this vector and repeat steps 3 up to 6 If you want to modify the value of any one cell follow these steps 1 2 3 Select the cell subject to be modified by clicking on it Write the new value of the cell Press Enter Loading an ASCII data base To load an ASCII data file click on the command File select the command Open The following window appears asking for some information concerning the data file Swi Ew Rechercher dans fm Mes documents Adobe Q My Virtual Machines i country4 Bookt_opf_files My webs i F1000 24 Ma musique Photo i romano A Mes images 2 phti la romanol FJ mes vid os Q recette i testo Messenger Service Received Files 1 burkina a Nom de fichier aaf Fichiers du type pap ASCII file dat Annuler Remark if
92. ransfer 3 Choose the approach to be either TR or IR 4 Choose the different vectors and parameter values as follows it armees Tax transfer Group number y Option tho Compulsory pp Compulsory Commands e The command S Gini to compute PTR Approach IRApproah IC p Ix p Ix p ICx_1 Ix p IC p 1x p ICx n 0 where C p is the S Gini coefficient of concentration and p is the S Gini index of inequality e The command Crossing to seek the first intersection of the concentration and Lorenz curves DAD indicates the co ordinates of that first intersection and their standard deviation if the option of computing with standard deviation is chosen e The command Difference to compute Pp O TR Approach IR Approach Lx p Cr p Cxr p Lx p Ce P Lx p Cxe p Lx p e The command Range to specify a range of p for the search of the first intersection between the two curves The command also allows to specify the range of the horizontal axis in the drawing of a graph e The command Graph to draw the following differences as a function of p YR Approach IR Approach Tax Lx p Cr p Cx r p Lx p Transfer Ca p Lx p Cx P Lx Comparing the progressivity of two taxes or transfers Let X be gross income T and T2 be two taxes B and B2 be two transfers 1 TR Approach T1 is more TR progressive than T2 if C p Cy p gt 0 Vpe
93. redistribution effect R Residual Ref Indicates the period of reference P i qt the FGT index of the first period when we multiply all incomes y of the first period by the ratio Ta u P u nt the FGT index of the second period when we multiply all incomes a of the second period by the ratio rT Iut According Kakwani 1997 approach we can decompose variation of the FGT Index between two periods tl and t2 into growth and redistribution effects as follows P P C C Variation 1 Ci 1pu a Puah pa m2 Pa n y C5 t pu r2 pat nth pqut x2 paut 2 nt To perform the decomposition of the FGT index across growth and redistribution effects l From the main menu choose the item Decomposition Growth and redistribution 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Distribution Distribution t2 tl Variable of interest Compulsory eg a fapha ia Complzory To compute the standard deviation of this index choose the option for computing with standard deviation The sectoral decomposition of differences in FGT indices We can decompose differences in FGT into sub group differences in poverty and population proportions as follows K P2 P l L 1 k P2 k z0 Pykix 0 at ia k 1 Variation K Piczo 0 01 wo K Paz P ssc 49 6 00 Variation Difference in pover
94. rs and parameter values as follows Distribution 1 Distribution2 Variable of interest Compulsory Group Number amiss Among the buttons you will find the command Compute To compute the standard deviation of this index choose the option for computing with standard deviation The Atkinson Gini index Denoting the Atkinson Gini index of inequality for the group k by k e p and the S Gini social welfare index by amp k e p we have u k amp k p I k p wk where d n P P E ajor yo gt e le gt 0 and p21 i l VDP TAE n gt P V gt P bo C ta my gt e 1 and p2l i l Vp and Case 1 One distribution To compute this index of inequality for only one distribution l From the main menu choose the item Inequality Atkinson Gini index 2 In the configuration of the application choose 1 distribution 3 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Variable of interest Compulsory Size variable Group Variable Group Number epson rho Among the buttons you will find the command Compute which computes the Atkinson Gini index To compute the standard deviation of this index choose the option for computing with standard deviation Case 2 Two distributions To reach the Atkinson Gini application with two distributions l From the main menu choose the item Inequality Atkinson Gini
95. rvations in stratum 1 and m2 observations in stratum 2 e Observations in every stratum were selected randomly with equal probabilities e The first step will then consist in selecting randomly and with the same probability m1 observations from stratum and independently m2 observations from stratum2 Aggregating these two sub samples will yield the new generated sample Repeating this N times will generate the BTS sampling distribution Illustrations The following table presents the sampling design information of a hypothetical sample of 800 observations Sampling Design Information 800 6200 0 2 strata in the Sampling Design CODE STRATA PSU LSU OBS P strata FPC f_h 1 1 30 300 300 0 193548 0 0 2 2 50 500 500 0 806452 0 0 Total 2 80 800 800 The following tables present estimates of the standard errors of some distributive indices using asymptotic theory DAD and the BTS procedure Cy p e J e e see e D S s Sara o a a Zx x 0 100790 0 002755 J x x x 00014549 0 004 12479 x0 00855568 0 005 ox 30 15 30207 O oas Pp x xX fT 29 76615787 2982831383 xO X34 90968660 34 49846649 Cx x 35121606735 31 36449814 Cx xf x i 40 209044 14 40 10400009 Smaa p Pea po dsa Sieps j Ster DAD f o Ser BIS _ iss ss pH ff 6 00695075 ft 0 00607490 Ei Eni rt Gini p 2 042403734 Lsu 0 00801557 0 00809321 0 00786047 0 00781983 0 00820847 0 00827642 o 0 00964692 0 00964823 0 00949502 0 00946204
96. s pen perce Variable of interest Compulsory Size variable Group Variable a Compulsory Group number rho Commands e Thecommand Compute to compute the SGini index To compute the standard deviation choose the option for computing with standard deviation e The command Graph to draw the value of the index according to a range of parameter p To specify such a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Case 2 Two distribution To compute the S Gini with two distributions l From the main menu choose the item Welfare S Gini index 2 In the configuration of application choose 2 for the number of distributions 3 Choose the different vectors and parameter values as follows Variable of interest 2 Compulsory Size variable y Group Variable X s2 Optional Compulsory To compute the standard deviation choose the option for computing with gandard deviation The Atkinson Gini social welfare index To compute the Atkinson Gini social welfare index l From the main menu choose the following item Welfare S Gini index 2 In the configuration of the application choose for the number of distributions 3 After confirming the configuration the application appears Choose the different vectors and values of parameters as follows ee he ee Variable of interest Compulsory Press the command Compute to compute t
97. s The second step is to espress the total intra group contribution as a sum of contributions of each of the groups In the first step we suppose that the two Shapley factors are inter group and intra group inequality The rules followed to compute inequality in the presence of one or two factors are to eliminate intra group inequality and to calculate inter group inequality we use a vector of incomes where each observation has the average income of its group e to eliminate inter group inequality and to calculate intra group inegality we use a vector of incomes where each observation has its income multiplied by the ratio u u The second step consists in decomposing total intra group inequality as a sum of group inequality To do this we proceed systematically simply by replacing the revenues of those in a group by the average income of that group such as to eliminate the intra group contribution of a given group To perform the decomposition of the S Gini index by groups l From the main menu choose the item Welfare and inequality Decomposition S Gini decomposition by groups 2 Select the desired decomposition approach 3 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Size Variable Optional Compulsory S P Group numbers separated by Compulsory The decomposition of the Generalised Entropy index of inequality The
98. s shed light on distributions of living standards using the size and the incomes of different economic groups such as e The poor Those vulnerable to poverty e The middle class e The richness The Share Ratio The decomposition of the S Gini index by sources Natural or Shapley approach The decomposition of the S Gini index by population groups Natural or Shapley approach The Relative Deprivation Curve Installation and required equipment DAD is conceived to run on operating systems Windows 95 98 NT Windows2000 and Windows XP A PC of 300MHz or more is also required The steps for installation of this software are as follows l Insert the CD ROM that contains the DAD installation file and click on the icon jinstall The following window appears amp Installer s Sur le point d installer Laval University Distributive Analysis Updated in 2003 06 23 MIMAP PROJECT Copyright 2003 The software DAD4 3 was designed by Jean Yves Duclos and Araar Abdelkrim and programmed http iwww mimap ecn_ulaval ca JExpress Installer 1997 2001 DeNova Inc June 2003 Tous droits r serv s dans le monde entier Annuler Precedent Click on the button continue and specify the installation directory At the end of the procedure of installation you can run this software like any other program by clicking on the button Start and selecting the item Program Distributive Analysis gt DAD4 3 D atabases
99. stical units such as individuals Figure 1 shows a graphical SD representation for the case of Simple Random Sampling SRS in which it is supposed that sample observations are directly and randomly selected from a base of sampling units SUs e g the list of all households within in a country Figure 1 Simple Random Sampling JSS Units within SU 4 Random Selection Sample observations Complete Selection SRS is rarely used to generate household surveys Hence most SD encountered in practice will not look like that in Figure 1 Most SD will look instead like that of Figure 2 A country is first divided into geographical or administrative zones and areas called strata Each zone or area thus represents a strata in Figure 2 The first random selection takes place within the Primary Sampling Units denoted as PSU s of each stratum Within each stratum a number of PSU s are randomly selected This random selection of PSU s provides clusters of information PSU s are often provinces departments villages etc Within each PSU there may then be other levels of random selection For instance within each province a number of villages may be randomly selected and within every selected village a number of households may be randomly selected The final sample observations constitute the Last Sampling Units LSU s Each sample observation may then provide aggregate information such as household expenditures on all indivi
100. t Change range of x from the main menu Case 2 Two distributions To compute the CHU index with two distributions l From the main menu choose the item Poverty CHU index 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows O O D Distribution2 __ Variable of interest eral Group number The first execution bar contains the command Compute To compute the standard deviation choose the option for computing with standard deviation The Sen Index The Sen index of poverty PS k z p for the population subgroup k is defined as PS H I pa yw I lt z H i 1 n Lwi i i Lwi le yi G is the Gini index of inequality among the poor and where z is the poverty line and X max x 0 Case 1 One distribution To compute the Sen index l From the main menu choose the item Poverty Sen index 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows pee eames ee Variable of interest Compulsory 4 To compute the normalised index choose this option in the window of inputs Commands e The command Compute to compute the Sen index To compute the standard deviation choose the option for computing with standard deviation e The command Graph to draw the value of the index according to a range of poverty lines z To sp
101. tation see also the illustrations for the computation of inequality indices Indicates the name of the variable used to compute the index of inequality indicates the size of variable Indicates the vector that contains group indices in this application the choice of such a vector is optional Indicates the selected group number by default its value equals one Indicates to the user the names and the values of the parameters The parameter names typically refer to the definition of indices and curves Indicates the options selected for this execution 3 The third and last block contains the results of the execution Index value Indicates the value of the index or point estimated The value within parentheses indicates the standard deviation for this estimate One can select a number of decimal values for the printing of results To do this choose the command Edit gt Change Decimal Number The following window appears Choose the desired number of decimals and confirm the choice by clicking on the button OK Q Current decimal number 8 Please enter new decimal number Sa a Annuler When another execution is performed a new window appears with the information concerning this new execution One can return to and edit the information on the previous executions by activating the window of the previous results For this click on the button representing the result look on the bottom of the window for the
102. ted with a standard deviation specified by the user For the first possibility just indicate the value of the deterministic poverty line in front of the indication Poverty line For the three other possibilities proceed as follows e Click on the button Compute line e Choose one of the three following options a Proportion of mean the proportion should be indicated b Proportion of quantile indicate the proportion mand the quantile Q p by specifying the desired percentile p of the population c Estimated line indicate the estimate of the poverty line z and its standard deviation stdz To compute the poverty line in the case of two distributions e Click on the button Computate line e Choose one of these three following options a Proportion of mean indicate the proportions and b for the distributions I and 2 respectively b Proportion of quantile indicate the proportions m and m and specify the desired quantiles by indicating the percentiles of population p and po c Estimated line indicate the estimates of the poverty lines z and z and their standard deviations stdz and stdzp The FGT index The Foster Greer Thorbecke poverty index FGT P k z for the population subgroup k is as follows 1 n Yiwi y k i l 1 P k z where z is the poverty line and x max x 0 The normalised index is defined by P k z ot P k z 00 z Case 1 One distribution To compute
103. ters to be chosen as gt Choice of variable of interest gt Choice of size variable gt Choice of group variable gt Choice of group number D Option to compute with or without standard deviation E Parameters to be specified F Set of Commands for this application You can to specify a weighting vector in order to weight your observations Also options shown in C allow you to compute an estimate for one specific group or sub sample or sub vector The following example illustrates those different options Example Suppose that you wish to compute the mean of a variable y with y denoting the i observation household of a person j We call the vector to be used the Variable of Interest The following table displays the observations of y for a sample of ten households The vector of sw Sampling Weight variable is the sampling weight to be applied to these observations and si is the size of observation household i We can also assign to each of these observations a code i that indicates the subgroup of the population to which the i observation belongs For example code 1 may indicate that households live in town V1 and code 2 that they live in town V2 Variable of Group Sampling Size interest Variable Weight Variable variable The user then has six possibilities for computing the mean as shown in the following table The mean Variable of Size Group Interest Variable Variable For the 10 househ
104. that DAD can activate one or two databases Once a database is activated the user can then call different applications of DAD Before you reach those applications however you must indicate how many databases are to be used in the application and which ones This is done through the following window TE Configuration of distributions IOl x benin daf le 2 Distributions Independent distributions File For distribution 1 File For distribution 2 benin daf benin daf ok cance Each database represents one distribution Generally you should indicate the following information 1 The number of distributions 2 The name of the file representing the first distribution 3 The name of the file representing the second distribution 4 When two distributions are to be used you should indicate if the two distributions represent dependent or independent samples for the accurate computation of standard errors that use information on the joint distribution Confirm your choice by clicking on the button OK Once the choice is confirmed you can reach the desired application Remark If the number of distributions is one the activated file is automatically the file specified on the 1 line TEDAD 4 3 Weight FIN without size z No Selection E 1 mo pE STD j A Main menu B The name of the application and the name of the file used C Set of variables and parame
105. the FGT index l From the main menu choose the item Poverty FGT index 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows i Variable of interest alpha Compulsory 4 To compute the normalised index choose that option in the window of inputs Among the buttons you find The command Compute to compute the FGT index To compute the standard deviation of this index choose the option for computing with standard deviation The command Graph1 to draw the value of the index as a function of a range of poverty lines z To specify the range for the horizontal axis choose the item Graph Management Change range of x from the main menu 1 The command Graph2 to draw the value of FGT a as a function of a range of parameter q To specify such a range for the horizontal axis choose the item Graph Management Change range of x from the main menu Case 2 Two distributions To compute the FGT index with two distributions l From the main menu choose the item Poverty FGT index 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Distribution 1 Distribution 2 ae Variable of interest dc eee a C E A Poverty lines Zi Zo Compulsory alpha OL a Compulsory To compute the standard deviation of this index choose the option for
106. tiles The p quantile at a percentile p of a continuous population is given by Q p F p where P F Y is the cumulative distribution function at y For a discrete distribution let the n observations of living standards be ordered such that Yi SY2 S L Yi S Yia SS Ya TF P FV Fi then we define Q p yi41 The normalised quantile is defined as QP Q p H Case 1 One distribution To compute the quantiles of one distribution l From the main menu choose the item Curves Quantile 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory od Commands e Compute to compute the quantile at a point p To compute the standard deviation choose the option for computing with standard deviation e Graph to draw the value of the curve according to the parameter p To specify a range for the horizontal axis for the p values choose the item Graph Management Change range of x from the main menu Case 2 Two distributions To compute the quantiles of two distributions l From the main menu choose the item Curves Quantile 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory Size Variable a Optional Group Variable ee Commands e Crossing to check if the two quantile c
107. tribution If you wish to compute the Variance of Logarithms index of inequality for only one distribution follow these steps l From the main menu choose the item Inequality Variance of Logarithms 2 In the configuration of the application choose 1 distribution 3 After confirming the configuration the application appears Choose the different vectors and values of parameters as follows ee imes e Size variable s Optional Among the buttons you will find the command Compute to compute the Variance of Logarithms If you also want the standard deviation of this index choose the option for computing with a standard deviation Case 2 Two distributions To compute the Variance of Logarithms of two distributions l From the main menu choose the item Inequality Variance of Logarithms 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows ssa aad e eae 13 Distribution 1 Distribution2 Variable of interest Ooy S op o Compulsory 1 2 y Among the buttons you will find the command Compute To compute the standard deviation of this index choose the option for computing with standard deviation The Relative Mean Deviation Index Denote the Relative Mean Deviation index of inequality for the group k by RMD It can be expressed as follows Case 1 One distribution If you wish to compute the rel
108. two periods We can decompose the difference in social welfare as measured by the EDE Atkinson index between two populations and 2 as follows G2 ly 1p My 2 by A Ty 2 Hy 1p Ip Cl C2 C3 where C1 Impact of change in inequality C2 Impact of change in mean C3 Interaction impact To perform this decomposition l From the main menu choose Decomposition Decomposition of Social Welfare 2 Choose the different vectors and parameter values as follows Compulsory Optional Variable of interest Po y y y fan Compulsory To compute the standard deviation choose the option for computing with standard deviation D ominance This section looks at the primal dominance conditions for ordering poverty and inequality across two distributions of living standards Corresponding dual dominance conditions are considered in the section on Curves Poverty dominance Distribution 1 dominates distribution 2 at order s over the conditional range z z if only if P C a gt P Ga y Celz z for a s 1 This involves comparing stochastic dominance curves at order s or FGT curves with a s 1 This application checks for the points at which there is a reversal of the dominance conditions Said differently it provides the crossing points of the dominance curves that is the values of and P a for which P t a P C a when
109. ty between 1 and 2 Cl Intra sectoral or intra group impacts C2 Impact of changes in subgroup proportions C3 Interaction effect To perform this decomposition l From the main menu choose Decomposition Sectoral 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows D T Distribution __ Variable of interest Compulsory Z Poverty lines pe __ Compaisory alpha ef Compalsory Group numbers separated by Compulsory To compute the standard deviation of this index choose the option for computing with standard deviation The decomposition of the S Gini index by sources or components Let J components y Jadd up to y that is A natural approach One natural approach to decomposing the S Gini index of inequality is as follows p pac p j l where JC p is the coefficient of concentration of the j component and u is the J J mean of that component The contribution of the jt component to inequality in y is then Bj LIC p Hy The following results appear in the output window l The S Gini index for y 2 The coefficients of concentration for every component of y 3 The ratio H u for every component of y 4 The contribution for every component The Shapley approach One supposes with the Shapley approach that the contribution of component j to total inequality is the expected value of its mar
110. umber of distributions 3 Choose the different vectors and parameter values as follows 14 Po Distribution 1 Distribution 2 Po PTX Compulsory Commodity x e Compulsory Poverty ine z z Compalsory Impact of a price change on the FGT index The impact of a good 1 s marginal price change denoted IMP on the FGT poverty index Pk z is as follows P k z a o T p CD k z pe where z is the poverty line k is the population subgroup for which we wish to assess the impact of the price change and pc is the percentage price change for good 1 15 i a l a Ae x if 21 and Normalised mE 2 Ywil z y ox if 21 and Not Normalised 1 k i W i l i l yi wikK y x Elx ly z f z ______ if a 0 k W i l where Xi is expenditure on commodity by individual i and f max f 0 Note that if the FGT index is normalized IMP CD k z pe To compute the impact of the price change l From the main menu choose the item Poverty Impact of price change 2 Choose the different vectors and parameter values as follows ae a Variable of interest Compulsory Compulsory i Group Variable o oke a O i 16 Commands e Compute to compute the impact of the price change To compute the standard deviation of this estimated impact choose the option for computing with standard deviation e Graph to
111. urves intersect If the two curves intersect DAD indicates the co ordinates of the first intersection and their standard deviation if the option of computing with standard deviation is chosen To seek an intersection over a particular range of P use Range to specify this range e Difference to compute the difference Q p Q p gt e Graph to draw the difference Q p Q p along values of the parameter p e Range to specify the range for the search for a crossing of the two curves also specifies the range of the horizontal axis Poverty Gap Curve The poverty gap quantile at a percentile p is g p Z z Q p Case 1 One distribution To compute the poverty gap quantile for one distribution l From the main menu choose the item Curves Poverty gap quantile 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows Variable of interest Compulsory Size Variable Optional Optional Optional Compulsory pS Compulsory Commands e Compute to compute g p z To compute the standard deviation choose the option for computing with standard deviation e Graph to draw the value of g p z as a function of p To specify a range for the horizontal axis choose the item Graph Management Change range of x from the main menu e To compute the standard deviation choose the option for computing with standard deviation
112. vate regression is obtained by differentiating the above with respect to x EKOKO yi tK OK y Vw K EYK K OK 0 y x es YEW K OOK x E w KIOK y Note that x rv eee uo K x y x P A x and ray pi s 1 VOMI f KOPOVPAVAA I A ATBR B ATMB sq 0 00 ro Oy P w PEL M x where W Mka B mo X Conditional standard deviation A kernel estimator for the Conditional Standard Deviation of y at x can be defined as Vw K amp xy y i stw Y w K x x where K is a kernel function and y x is the expected value of y conditional on x To reach this application l From the main menu choose Distribution Conditional Standard Deviation 2 Choose the different vectors and parameter values as follows Exogenous Variable X C go o o Compulsory Endogenous Variable Y r Compulsory Size variable ee Group Variable Optional Group Number k Omo Tadc S Compulsory Remark 1 The option Level vs Percentile allows the estimation of the conditional standard deviation of y either at a level of x or at a p quantile for x You will find e Thecommand Compute to compute ST x e Thecommand Graph to draw ST x as a function of x To specify a range for the horizontal axis choose the item Graph management Change range of x from the main menu e Thecommand Range to specify the range of the horizontal axis Group information This applicat
113. xip p Lyx p The coefficient of concentration Let a sample contain n joint observations y T on a variable y and a variable T Let observations be ordered in increasing values of y in such a way that y lt y The S Gini ccefficient of concentration of T for the group k is denoted as JC k p and defined as E ef l v P IC kip 1 Hr n where V wi hzi One distribution To compute the coefficient of concentration for only one distribution l From the main menu choose the following item Redistribution Coefficient of concentration 2 In the configuration of the application choose 1 distribution 3 After confirming the configuration the application appears Choose the different vectors and parameter values as follows pan ameer OE Ranking variable Compulsory Group Variable Variable of interest Compulsory tho _ Compulsory Commands The command Compute to compute the coefficient of concentration To compute the standard deviation of this index choose the option for computing with standard deviation The command Graph to draw the value of the coefficient as a function of the parameter p To specify a range for the horizontal axis choose the item Graph management Change range of x from the main menu Two distributions To reach this application l From the main menu choose the item Redistribution Coefficient of concentration 2 In the conf
114. y properties of a graph For this select the item Tools Properties This can also be done by activating the Popup Menu To activate the Popup Menu click on the right button of the mouse when you are within the quadrant of graph The items shows how to change graph properties in DAD The Popup Menu Background paint to select the background colour of the graph We can also select the option Gradient for the background colour Background paint to browse and select a picture GIF or PNG to be the background graph Width and Height to indicate the desired width and height of the graph in pixels inches or centimetres click on the button Set to confirm your selection Draw Horizontal Line to draw a horizontal line at a giving height of the axis Indicate that height and click the option Draw Vertical Line to draw a vertical line at a giving value of the X axis Indicate that value and click the option Draw 45 Lines to draw a 45 line Antiaaliasing option One of the most important techniques in making graphics and tex easy to read and pleasing to the eye on screen is anti aliasing Anti aliasing gets around the low 72dpi resolution of the computer monitor and makes objects appear smooth Activate X Y grid If this option is selected a grid is plotted in the graph Draw Border If this option is selected a border is plotted around the graph Main Title By default the main
115. your ASCII file s extension is not txt dat or prn choose in the option Type of File then indicate the file name After choosing the desired ASCII file and clicking on OK the following window appears Data Import Wizard P o amp ASCII File Information Delimiters 4 Other information aCe J Semi colon V Treat consecutive delimiters as one Colon M Tab First row includes name of variables comma Other Advanced Preview Results Number of OBS 1613 Number of vectors 3 Warning Data Preview Vector_ 1 Vector_ 2 Vector_ 3 Vector_ 4 Vector_ 5 Expend 124729 0 200749 0 936102 0 267149 0 125015 0 271719 0 247010 0 224617 0 These windows contain many options that facilitate the loading of an ASCII file By default the delimiter the character that separates variables is a space but you can specify other delimiters You can also specify the delimiter with the option Other In the Panel Other Information you can indicate the following information l By default the option Treat consecutive delimiters as one is selected Choosing this option makes it such that several succeeding delimiters are treated as one 2 By default the option First row includes names of variables is not selected In this example the ASCII file s first row includes the names of variables we thus select the option 3 Clicking o

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