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Users Manual for DAD 4.2 - The Software DAD

1. Variable of interest y Compulsory Size Variable S Optional Group Variable c Optional Group Number k Optional Poverty line Z Compulsory p p Compulsory Commands Compute to compute g p z To compute the standard deviation choose the option for computing with standard deviation 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 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 gt Poverty Gap Quantile 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows 89 Variable of interest y y Compulsory Size Variable g g Optional Group Variable c Optional Group Number k k Optional Poverty line Zi Z Compulsory p Pi Po Compulsory 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 seek an intersection over a particular range use Range Difference to compute the difference g z p 2
2. 126 Background to select the background colour of the legend quadrant Text font to select the font of the text legends 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 MCunve 1 Bi Cune 2 Line Form Cune 1 Curvest2 Name By default the names of the curves are curveftl curve 2 etc You can change these names in these fields DAD 4 2 Graph Properties sansserif 10 oi 127 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 Label insets to change the labels position Top Left Bottom Right indicated in pixels 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 tick markers You can also select the font of the tick labels DAD 4 2 Graph Properties IT 2 L 2 B 2 R 2 T 2 L 1 B 2 R 1 128 Other Range to select the minimum and maximum values for the range of the vertical axis To do this unselect the option Aut
3. 2wi i l Union sum of gaps The union sum of gaps using G dimensions or commodities is equal to n G k g g yw c Xi i l g l n k 2 i l P k z 27 Intersection sum of gaps The intersection sum of gaps using G dimensions or commodities is equal to Soi Se x5 Tit 2x5 Pis e e i l 56 Intersection product of gaps The intersection product of gaps using G dimensions or commodities is equal to Sefe ex TI ex PES QNS _ i l P Iz zig gs 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 gt Bidimensional FGT index 2 Choose the different vectors and parameter values as follows Commodity X Compulsory Commodity X Compulsory 57 Size variable S Optional Group Variable c Optional Group Number k Optional Poverty line 1 z Compulsory Poverty line 2 2 Compulsory alphal Qa Compulsory alpha2 Q5 Compulsory Results of this application are FGT index for commodity 1 corresponding to areas I II in the graphical illustration FGT index for commodity 2 corresponding to areas II III in the graphical illustration FGT index for the two commodities Union approach corresponding to areas IHIIHI in the graphical illustration
4. 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 5 136 Stat Transfer NBRINDID TSEX String Date Date Time Time 137
5. Print Cancel 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 Edit gt Templates The following window appears TEDAD 4 2 Chart Template 15 xl 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 133 Editing coordinates To edit coordinates of curves select Edit Edit Coordinates The following windows appears 16 500000 18 000000 19 500000 21 000000 22 500000 rmm You can change the decimal number by using the item Tools To close this window click on the button OK 134 Preparing DAD ASCII Files in daf Format 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 2 1 2 2 In the field ASCH File Writer select the Delimiter Spaces Select the option Write variable names in first row To do this only once
6. Case 2 Two distributions To compute the quantiles of two distributions l From the main menu choose the item Curves gt Quantile 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Variable of interest y y Compulsory Size Variable g s Optional Group Variable el E Optional Group Number k k Optional p Pi Po Compulsory Commands e Crossing to check if the two quantile curves 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 p3 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 88 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
7. FGT index for the two commodities Intersection approach corresponding to areas II in the graphical illustration Example Food and non food expenditures per day in F CFA Cameroon 1996 Food poverty line evaluated at 256 F CFA and non food poverty line evaluated at 117 F CFA Food and non food expenditure in F CFA Cameroon 1996 nditure pel a N a e e e Non food ex 50 c2 E TIUS WB Coordinates 58 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 number of distributions 3 Choose the different vectors and parameter values as follows Distribution 1 Distribution 2 Commodity Xi Xi Compulsory Commodity X2 X2 Compulsory Size variable sl S2 Optional Group Variable c c Optional Group Number k k Optional Poverty line 1 z Z Compulsory Poverty line 2 z z Compulsory alphal Q Qa Compulsory alpha2 7 Q 5 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 P k z a is as follows P k z a pc Op IMP 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 chan
8. The FGT poverty index for a population composed of K groups can be written as follows K P z a 2 o 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 k P k z To perform the decomposition of the FGT index l From the main menu choose the item Decomposition gt FGT 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 Optional Group Variable c Optional Poverty line Z Compulsory alpha a Compulsory Group numbers separated by k k 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 To perform the decomposition of the FGT index for two groups l From main menu choose the item Decomposition FGT Decomposition for two groups 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows 75 Variable of interest
9. ben daf ben daf D ok D 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 I line 17 F EIDAD 4 2 jas Edit Inequality Poverty Welfare Decomposition Redistribution Dominance Curves Distribution Graph Window Weight Without size z No Selection m 1 Option s mmm m Ps Standard Deviation without STD T gt i gt ee esas a F D E A Main menu B The name of the application and the name of the file used C Set of variables and parameters 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 appli
10. wem 3 3 o wemwes mme a o e smwmm wem Ee pos ome emm eme Fmmemwe m This example uses only one group variable INS LEV level of instruction of the household head categorized as l Primary 2 Secondary 3 Superior 4 Not available 5 None The output shows Code The exact code of the group Group The group number 1 2 3 OBS The number of observations in the group W S 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 119 Example 2 TEIDAD 4 2 HTML Result iewer inl xl File Edit Cross Table W S a 177258 009487 110309 799805 155290200577 11267399826 64246 700333 630328 899189 0 000000 Lz J 0 000000 0 000000 0 000000 0 000000 4974 400063 57321 999954 Probability P groupl group2 2 e ecoeee 0 000000 0 000000 0 000000 0 000000 0 004108 0 047335 Indicator Result 1 Result 2 Result 3 ll Save i Load 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 120 The editing saving and printing of results Editing of results Generally the windows of results ta
11. Preview Results Number of OBS 1613 Number of Vectors 3 Warning Data Preview Vector_ 1 Vector_ 2 Vector_ 3 Vector_ 4 Vector_ 5 Weight Expend Group gt 7 0 124729 0 2 0 5 0 200749 0 1 0 5 0 96102 0 1 0 6 0 267149 0 2 0 4 0 125015 0 1 0 3 0 271719 0 1 0 1 0 247010 0 1 0 4 0 224617 0 1 0 fa gt ok cance 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 on the button Advanced makes the following windows appear 55 Advanced Choices Decimal separator or dot orcomma Drop first spaces V Drop empty lines v Number of treated lines in ASCII file Number V Treat All Number of edited missing or not convertible values Number fi 00 Edit All 2 Agree 2 Cancel We do not by default nee
12. Series 2 S1 i S2 i Series 1 Series 2 S1 i S2 Series 1 Series 2 S1 i S2 i Series 1 Series 2 S1 S2 Series 1 Number S1 i Number Series 1 Number S1 i Number Series 1 Number S1 i Number Series 1 Number S1 i Number Exp Series 1 Exp S1 i Log Series 1 Log S1 i Series 1 Series 2 f SI i S2 i otherwise 0 Series 1 Number if S1 i S2 i otherwise 0 Series 1 gt Series 2 if S1 i gt S2 i otherwise 0 Series 1 gt Number tif S1 i S2 i otherwise 0 Series 1 lt Series 2 if S1 i S2 i otherwise 0 Series 1 lt Number E mE pk mE if SIG lt S2 i otherwise 0 Finally click on the button Execution to generate the new vector 14 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 S Input X 2 Enter the new number of observations Annuler 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 s
13. estimates choose the option for computing with standard deviation 108 Distribution 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 l 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 Mean Standard deviation Minimum Maximum Name of variable 2 Mean Standard deviation Minimum Maximum 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 1 Total As X 2 Mean 2 9 25i iwi 3 Ratio lt wi Yi To activate this application for one distribution follow these steps l From the main menu choose Distribution gt Statistics 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows 109 Variable of intere
14. DAD is conceived to run on operating systems Windows 95 98 NT Windows2000 and Windows XP A PC of 100MHz or more is also required The steps for installation of this software are as follows Insert the CD ROM that contains the DAD installation file and click on the icon 1 jinstall The following window appears xat xl amp Installer U n iversite Lava Sur le point d installer Distributive Analysis Updated in 2002 05 09 MIMAP PROJECT Copyright 6 2002 are DAD es Duclo ie softy yas d esI ed by eal V Araar Abdelkrim and programmed with JDK1 4 i i JExpress Installer 1997 2001 DeNova Inc Tous droits r serv s dans le monde entier June 2002 Annuler lt lt Pr c dent 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 gt Distributive Analysis gt DAD4 2 Databases in DAD4 2 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 35 DAD 4 2 la ole File Edit Inequality Poverty Welfare Decomposition Redistribution Do
15. Lx p Cx p Cx 1 p Lx p Transfer Ca p Lx p Cx Lx p 101 Comparing the progressivity of two taxes or transfers Let X be gross income TI and T2 be two taxes B and B2 be two transfers 1 TR Approach T1 is more TR progressive than T2 if C p Cq p 0 Vpe lol B1 is more TR progressive than B2if Cy p Cg p 0 Vpe lol 2 IR approach T1 is more IR progressive than T2 if Cy m p Cx m p gt 0 Ype lil B1 is more IR progressive than B2 if Cx D Cx p p gt 0 Vpe p To reach this application 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 Size variable S Optional Group Variable c Optional Group number k Optional rho p Compulsory p p Compulsory 102 Commands e The command S Gini to compute TR Approach IR Approach Tax IC p ICz p ICx r2 P IC 4 p Transfer IC p ICs p ICy 55 9 IC g P where IC p is the S Gini coefficient of concentration e The command Crossing to seek t
16. i l CDi k z s Y wiKG y yl E y ly z f z if s l n k gt Wi i l where K is a kernel function Dominance of order s is checked by setting a s 1 The C Dominance curve normalized by z which is denoted by CD is given by ED 1 Swtg y yi if s22 Z Y k isl Wi EE i l CD k z s Y wiKG y yl Ely y z if s 1 wi i l D The C Dominance curve normalized by the mean is defined as and the C al Dominance curve normalized both by z and the mean equals a Case 1 One distribution To compute the C Dominance curve for one distribution l From the main menu choose Curves gt C Dominance curve 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows 97 Variable of interest y Compulsory Component y Compulsory Size Variable SZ Optional Group Variable c Optional Group Number k Optional Order s S Compulsory Poverty line Z Compulsory 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 C Dominance curve 2 In the
17. parameter a 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 1 From the main menu choose the item Poverty gt FGT index 2 n the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows 48 Distribution 1 Distribution 2 Variable of interest y y Compulsory Size variable s s Optional Group Variable c c Optional Group number k k Optional Poverty lines Zi Z Compulsory alpha Q4 az Compulsory To compute the standard deviation of this index choose the option for computing with standard deviation To compute the normalised index choose this option in the window of inputs The Watts poverty index The Watts poverty index PW k z for the population subgroup k is defined as gt wi losty 2 PW k z n k 25 i l 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 gt Watts index 2 In the configuration of application choose for the number of distributions 3 Choose the different vectors and parameter values as follows 49 Variable of interest y Compulsory Size variable S Optional Group Variable c Option
18. 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 number of statistical 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 HFRS Units within SU 4 Complete Selection Random Selection Sample observations 21 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 r
19. Group Number k Optional Level of X or p Compulsory Smoothing parameter h Optional 117 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 The command Compute to compute ST x e The command 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 The command Range to specify the range of the horizontal axis Group information This application 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 1 118 iBl x TEDAD 4 2 HTML Result iewer Fie Edit Group Information Distribution Thu Apr 25 09 36 37 EDT 2002 0 03 sec Weight variable Without size Group variable INS LEV Group variable 2 No Selection Group Variable INS LEV C m 9 T I x o a a ow emsenm wmm 3 3 s ow
20. In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Distribution 1 Distribution 2 Variable of interest y y Compulsory Size variable g s Optional Group Variable c c Optional Group Number k k Optional epsilon j Compulsory Among the buttons you find the command Compute To compute the standard deviation of this index choose the option for computing with standard deviation 30 S Gini index Denoting the S Gini index of inequality for the group k by 1 5 P and the S Gini social welfare index by P we have k amp k dp PO p u k where n E P p E k p gt Vi Vin yi ub v P and Vi Ywi 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 Variable of interest y Compulsory Size variable S Optional Group Variable c Optional Group Number k Optional rho p Compulsory Two choices of commands appear among the buttons Compute to compute the S Gini index To compute the standard deviation of this index choose t
21. No selection 1 Without size Yi Size For the 10 households No selection 1 With size Yi Si For households living in town V1 Without size Yi Without Ci Size 4 For households living in town V1 With size Yi Si Ci For households living in town V2 Without size Yi Without Ci 2 Size For households living in town V2 with size Yi S Ci 2 1 This choice does not affect the results since no group variable has been selected 2 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 19 In this following table we present the basic notations used in the user manual of DAD Basic Notation in DAD Symbl e Idiaton O y the variable of interest Yi the value of the variable of interest for observation 1 sw the Sampling Weight SWi the Sampling Weight for observation 1 s the size variable Si the size of observation i for example the size of household i Wi SW Si c the group variable Ci the group of observation i k A group value an integer wis w if c k and w 0 otherwise Example The mean of group k u k is then estimated as n wey uk e i l 20 Taking into account sampling design in DAD Sampling
22. P Ga P C a when sign P 6 n a P 6 n a sign P n o P 6 n a 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 l From main menu choose the item Dominance Poverty Dominance 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Variable of interest y y Compulsory Size variable g s Optional Group Variable c c Optional Group Number k k Optional S S Compulsory 83 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 1 dominates distribution 2 in inequality at order s over the conditional range of proportions of the mean I T only if Pi Apy 0t gt Po Apt a v Ael where a s 1 These are normalis
23. 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 PAD pA pA x OT X gt lt K x x x Ox X Indicate that the variable is selected 26 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 e 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 TFT loj xi File Edit Inequality Poverty Welfare Decomposition Redistribution Dominance Curves Distribution Window B amp GA oes 2 romana daf 27 To show the SD information select from main men
24. These are the minimum of wH CD k z CD k z over an interval l z of poverty lines z It gives the maximum ratio of the MCPF for commodity 2 over that for commodity 1 up to which 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 Variable of interest y Compulsory Size variable S Optional Commodity 1 X1 Compulsory Commodity 2 X2 Compulsory Group Variable c Optional Group Number k Optional Poverty line Z Compulsory S S Compulsory gamma y Compulsory Commands e Critical z to compute the values of the poverty lines at which the CD curves CD k z and yCD k z cross To specify a range for a search of crossing points choose the command Range e Critical y to compute the critical gamma for tax dominance The range lz z 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 86 Curves A number of curves are useful to present a general descriptive view of the distribution of living standards M
25. When multiplied by 196 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 of Component Growth Variable of interest y Compulsory Component y Compulsory Size variable S Optional Group Variable c Optional Group Number k Optional Rho P Compulsory 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 45 The Gini Component Elasticity The Gini j component elasticity is given by al p oy 2 IC Oy l n Y p 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 y Compulsory Component y Compulsory Size variable S Optional Group Variable c Optional Group Number k Optional rho P Compulsory Among the buttons you will find Compute to compute the
26. Z23p gt Graph to draw the difference g z p g z p as a function of p 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 X why ly lt Q kp L k p n k 2 Wiyi i l where I y lt Q k p 1 if y 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 i L k p Remark The application for the Lorenz curve is similar in structure to the one for the generalised Lorenz curve Case 1 One distribution To compute the Lorenz curve for one distribution 90 From the main menu choose the item Curves Lorenz curve 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows Variable of interest y Compulsory Size Variable S Optional Group Variable C Optional Group Number k Optional rho p Compulsory p p Compulsory Commands Compute to compute L k p To compute the standard deviation choose the option for computing with standard deviation 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
27. 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 amp Adobe My Virtual Machines 4 country4 C Bookt opf Files My Webs 4 F1000 ea Ma musique Photo a romano Mes images phti la romanoi E Mes vid os recette 4 testo Messenger Service Received Files i burkina n Nom de Fichier Enregistrer 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 a data amp e data cross dad ta dad C Nouveau dossier data dad test dad araar dad docar dad Test2 dad j roma dad test3 dad romar1 dad romarin dad romarion dad Ouvrir Fchersautvoe Dannie MEN Nom de Fichier 11 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 d
28. axis choose the item Graph Management Change range of x from the main menu e Range to specify the range of the horizontal axis e 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 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 93 Ranking variable y y Compulsory Variable of interest T T Compulsory Size Variable g s Optional Group Variable c g Optional Group Number k k Optional rho Pi p Compulsory p Di Po Compulsory 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 in the concentration curves e Graph to draw the difference in the curves 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 IC k p IC k p e Covariance to com
29. click on the button Save to save these preferences SS E Transfer Variables Observations Options 1 Options 2 About r ASCII File Rea Delimiter Field Names Numeric Missing Value String Quote Character Maximum Number of Fields Maximum Line Width Maximum Lines to Examine Decimal Point Thousands Separator Century Changeover Year AutoSense Autos ense a oss janes far m L po ASCII File Writ Delimiter Spaces String Quote Character E Numeric Missing Value V Write variable names in first row Input Worksheet Data Range AutoSense gt Range Field Name Row aucseme xl Row Blank Rows StopReadng Restore Defaults Restore Saved Save Help 2 The usual next step is to select the item Transfer 2 1 2 2 First select the type of the input file SPSS EXCEL By using Browse indicate the location of the input file 135 Stat Transfer SPSS Data File C documents and settings araar abdelkrimNbureauNburkinaM Y ASCII Delimited HE C documents and settings araar abdelkrimsbureauSburkinas z 2 3 Select ASCH Delimited as the type of output file 2 4 By using Browse indicate the location of the output file and write name with extension daf For example the name is Data1 daf 2 5 Click on the Button Transfer to produce the new file
30. configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Variable of interest y y Compulsory Component y Compulsory Size Variable sz sz Optional Group Variable c c Optional Group Number k Es Optional Poverty line Zi 25 Compulsory Order s S1 S2 Compulsory 98 Commands Difference to compute the difference CD k z s CD k z s Graph to draw the difference CD k z s CD k z s as a function of z Range to specify the range of the horizontal axis 99 Redistribution This section regroups the following applications ls p 3 4 5 6 Estimating the progressivity of a tax or a transfer Comparing the progressivity of two taxes or two transfers Comparing the progressivity of a transfer and a tax Estimating horizontal inequity Estimating redistribution Estimating a coefficient of concentration Estimating the progressivity of a tax or a transfer Let 1 X be gross income T be a tax B be a transfer TR progressivity A tax T is TR progressive if Lx p Cr gt 0 Ype ji A transfer B is TR progressive if Cy p Lx p 0 Ype joi 2 IR progressivity A tax T is IR progressive if Cx p Ex p gt 0 vp e bil A transfer B is IR progressive if Cx amp D Lx p 0 vp e Joi To reach this application 1 2 3 4 From the main menu choose the item Redistr
31. 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 24 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 1 3 6 24 a 1 4 6 24 5 3 l 5 20 6 3 2 5 20 q 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
32. minimum bound and max is the maximum one A 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 the form y 1 2 3 1 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 i i 0 pooo i t k i i 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 Value X Bl without Correction Bil With 1 order correction 112 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 000225 EON oreet tentare poenitet Aaaa Ea tasse sepocpessere cai iso d CM D M IC M MIC LLL nr MERE EMEN 700065 eee UP a a a aS ce perse Dod ilL CE EUDE CC ECCE CE w
33. variable S Optional Group Variable c Optional Group Number k Optional 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 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 Distribution 2 Variable of interest y y Compulsory Size variable g s Optional Group Variable c c Optional Group Number k k Optional 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 38 The Logarithmic Variance Index Denote the Logarithmic Variance index of inequality for the group k by LV it can be expressed as follows n 2 n gt wi log y Imu Y wiy i l where Imu log n k k UW LW Z LV Case 1 One distribution If you wish to compute the Logarithmic Variance index of inequality for only one distribution follow these steps l From the main menu choose the following items Inequality gt Logarithmic Variance 2
34. y where k is the proportion of the population found in subgroup k u k is the mean income of group k I k is the inequality within group k I 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 80 Variable of interest y Compulsory Size Variable S Optional Group Variable c Optional theta 0 Compulsory Group numbers separated by k k Compulsory The following information appears in the output window l The entropy index for the whole population 2 The entropy index for between group inequality T 9 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 0 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 two periods We can decompose the difference in social w
35. y Compulsory Size Variable S Optional Group Variable c Optional Poverty line Z Compulsory alpha a Compulsory Numbers for the 2 subgroups separated by k k Compulsory In the output window you will find the following information 1 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 I z a P 2 z a 4 The percentage difference in the contribution of the two population subgroups POPA z a 2 P 2 z a P z a 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 We can decompose variation of the FGT Index between two periods tl and t2 into growth and redistribution effects as follows P P P u n P u n P u x P u n R Variation Cl C2 Variation Difference in poverty between t1 and t2 Cl Growth Impact C2 Contribution of redistribution effect R Residual P u xil the FGT index of the first period when we multiply all incomes yt of the first period by the ratio ut u P u zt the FGT index of the second period when we multiply all incomes yi of the second period by the ratio Th T 76 To perform the decomposition of the FGT index across growth and redistribution effects l From the main menu choose the item Decomposition
36. 2 L k5 0 1 Cov L k 0 2 L k 0 2 Cov L kj 51 L gt k 0 1 Cov L k D L5 k5 0 2 Cov L ky 1 L kD 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 dw Ty lt Asp C k p i l where I y lt Q k p 1 if y lt Q k p and 0 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 X wh Ty lt Q k p C k p Wi M ll 1 Remark The application for the concentration curve is similar in structure to the one for the generalised concentration curve 92 Case 1 One distribution To compute the concentration curve for one distribution l From the main menu choose the item Curves concentration curve 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows Variable of interest T Compulsory Ranking variable y Compulsory Size Variable S Optional Group Variable C Optional Group Number k Optional rho p Compulsory p p Compulsory Commands e Compute to compute the concentration curve C k p To compute the standard deviation choose the option for computing with standard deviation e Graph to draw the concentration curve To specify a range for the horizontal
37. 8 CQU DOIDOT eene ennt sie nennen enne nennen eene eene eene enne nennen eene e eene nennt EN roce M DOE o0 GN oy LaeVs ee ee te tt e dd RT Teed Ut GTN Tt eri ee tye Pe ud ge ee ee en See en ge 0 00000 1 1 1 t t 1 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 3850 900 950 1000 Value X IBI Without correction i With 1 order correction W With 2 order correction The joint density function The gaussian kernel estimator of the joint density function f x y is defined as l 2 1 1 x x Y y y f f x y SL ij i OS a a Bl Tag J wh i 1 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 113 Variable of interest x Compulsory Variable of interest y Compulsory Size variable S Optional Group Variable c Optional Group Number k Optional Parameter x Compulsory Parameter y Compulsory Smoothing parameter h Optional On the first execution bar you find e The command 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 From the main menu choose the item Distribution Distribution function 2 Choose the different ve
38. DAD DISTRIBUTIVE ANALYSIS ANALYSE DISTRIBUTIVE USER S MANUAL Universite Laval MIMAP PROJECT J J Ha i il Ae i PD AD Abdelkrim June 2002 Jean Yves Duclos jyves ecn ulaval ca Abdelkrim Araar aabd ecn ulaval ca Carl Fortin cfortin gel 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 10 11 12 Estimation of indices of Poverty Watts CHU FGT S Gini Sen normalised and un normalised 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 Decomposition of Poverty across population subgroups Inequality across population subgroups or by factor components e g by type of consumption expenditures or source of income Pro
39. Gini component elasticity To obtain the standard deviation of that estimate choose the option for computing with a standard deviation 46 Poverty indices DAD offers four possibilities for fixing the poverty line 1 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 distributed 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 m and 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 l and for the distributions 1 and 2 respectively b Proportion of quantile indicate the proportions m and mo and specify the desired quantiles by indicating the percentiles of populatio
40. Growth and redistribution 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Distribution Distribution t2 t1 Variable of interest y y Compulsory Size Variable g g Optional Group Variable e c Optional Index of group k k Optional Poverty lines Z Compulsory alpha a Compulsory 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 P P o K P k3z a P k z o P k 2 0 k a po k z a P k3z o o k Variation Variation Difference in poverty 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 1 From the main menu choose Decomposition gt Sectoral 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows 77 Distribution 1 Distribution 2 Variable of interest y y Compulsory Size Variable g g Optional Group Variable al c Optional Poverty lines Z Compulsory alpha a Compulsory Group numbe
41. 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 y Compulsory Size variable s Optional Group Variable c Optional Group Number k Optional 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 39 Distribution 1 Distribution 2 Variable of interest y y Compulsory Size variable g g Optional Group Variable c c Optional Group Number k k Optional 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 n 2 n Y wi logy Imu Y wi log y VL where Imu Ho Ywi Ywi i l i l Case 1 One dis
42. 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 25 EB 15 x Sampling Design Information Testa daf Sirata No Selection PSU No Selecion z LSU No Selection Sampling Weight No Selection z Correction Factor No Selection 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
43. 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 clearly 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 23 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 th
44. You can save and use graphs in many popular text processors including Word and Excell The available formats are Extension Description png Portable Network Graphic jpg JPEG File Interchange Format pdf Portable Document Format ps Postscript tif Tag Image File Format bmp Bitmat Image File To save a graph made in DAD select File gt Save and select the format by selecting the extension of the file i a Save xi Save in My Documents 1 E E3 F8 F Adobe My eBooks My Pictures TS My Computer File name ODE Files of type image file jpg Cancel 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 131 Printing graphs To print a graph select File gt Print The following windows appears HP LaserJet 5P 5MP PostScript aa Jv Collate Select the desired Printer To change orientation or margins select Page Setup When the following window appears select the desired orientation and margins 132 Size Letter Source Automatically Select x Orientation gt Margins C Portrait left Gn right Gn 35 Landscape h o h o C Reverse Portrait top in bottom in ho fho V3 C Reverse Landscape
45. al Group number k Optional Poverty line Z Compulsory Commands The command Compute to compute the Watts index To compute the standard deviation choose the option for computing with standard deviation 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 gt Watts index 2 n the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Distribution 1 Distribution 2 Variable of interest y y Compulsory Size variable g s Optional Group Variable c c Optional Group number k k Optional Poverty lines Zi Z Compulsory To compute the standard deviation choose the option for computing with standard deviation 50 The S Gini poverty index The S Gini poverty index P k z p for the population subgroup k is defined as P ks2ip 2 nee il MP i l 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 gt S Gini index 2 In the configuration of application choose 1 distribution 3 Choose the differe
46. 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 a is as follows IMTR 2 CD k z LCD k z pc 2 where z is the poverty line CD 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 given by ine X To compute the impact of the tax reform l From the main menu choose the item Poverty gt Impact of tax reform 2 Choose the different vectors and parameter values as follows Variable of interest y Compulsory Size variable S Optional Commodity 1 X1 Compulsory Commodity 2 X5 Compulsory Group Variable c Optional Group Number k Optional Poverty line Z Compulsory alpha a Compulsory 61 gamma Y Compulsory 1 s price change pc 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 e Critical y to compute the gamma at which the tax reform will have zero impact on poverty The value of this critical gamma equals CD k z OD k z e Graph z to draw
47. and 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 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 Variable of interest y y Compulsory Size variable g s Optional Group Variable c c Optional Group number k k Optional Poverty lines Z Z3 Compulsory rho Pi po Compulsory 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 a for the population subgroup k is as follows n S LG xD P k z a 4 k 2 5 i l where z is the poverty line for good g and t max t 0 The normalised index is defined by 55 P k z a P k z o z a Union headcount The union headcount based on G dimensions or commodities is equal to Soif Te lt P k z z 2 i l Intersection headcount The intersection headcount based on G dimensions or commodities is equal to n G k yw Lc gt x i l g l P k z z
48. andomly 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 individuals 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 Stratification Complete Selection 22 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 St
49. antile Ratio index with two distributions 36 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 Distribution 2 Variable of interest y y Compulsory Size variable g s Optional Group Variable c e Optional Group Number k k Optional Percentile for numerator Pi P Compulsory Percentile for p p Compulsory 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 n 2 k 2 E 03 Wiyi gt Wi cM i l 2 u n cv 37 Case 1 One distribution If you wish to compute the Coefficient of Variation index of inequality for only one distribution follow these steps l From the main menu choose the item Inequality gt 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 Variable of interest y Compulsory Size
50. any 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 quantiles 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 y 9ys SoSy Sy SS yn If PE FO FY then we define Q p Yiat The normalised quantile is defined as Q p Qp u l Case 1 One distribution To compute the quantiles of one distribution l From the main menu choose the item Curves gt Quantile 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows Variable of interest y Compulsory Size Variable S Optional Group Variable C Optional Group Number k Optional p p Compulsory Commands e Compute to compute the quantile at a point p To compute the standard deviation choose the option for computing with standard deviation 87 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
51. ard deviation choose the option for computing with standard deviation e The command 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 management gt Change range of x from the main menu e The command 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 gt i Ki K x Y f x where Xx K x exp 0 53 and A 69 1 hJ2n 111 and where the scalar K x is defined as K x w x P A x o 3 dE ue x 2 s 1 X max h x min 0 06 0 h 7 v x 2 M 1 f kaara 1 A OB min is the
52. atabase 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 25 Enregistrer Enregistrer dans a Mes documents f el Adobe O My webs Book1_opf_files Photo 24 Ma musique phti E mes images recette EE Mes vid os donado dad Messenger Service Received Files My Virtual Machines Nom de Fichier dadl Enregistrer Fichiers du type bap file dad Ande 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 12 Modifying 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 lox Change Column Name Vector s name Weight weight Vector 11 fvector 11 Expend Exena Vector 12 ecorsi2 Grup Group Vector 13 Vecorsi3 Vector 34 ve ctor 34 Vector 14 V
53. ation of application choose 2 distributions 3 Choose the different vectors and parameter values as follows 95 Variable of interest y y Compulsory Size Variable g s Optional Group Variable c c Optional Group Number k k Optional Poverty line Zi Z Compulsory rho pi p Compulsory p P p Compulsory 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 kipi z Go k5p5 z e Graph to draw the difference G k p z G k p z 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 p P z p e Covariance to compute the following covariance matrix CoG k 0 1 Z G gt k5 0 4z CowG k50 52 G5 k5 0 2722 CowG k 0 1 z G5 k3L4z CowG k 0 277 G5 k5 0 1 2 CowG k 02z G k5 0 2775 CowG k bz G4 k 0 52 CowG k bz G k 0 27222 CowG k Ez G k z 96 C Dominance Curve The j Commodity or Component dominance curve is defined as follows s 1 Y wiG y X yl if s22 k i wi E
54. cation 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 18 Example Suppose that you wish to compute the mean of a variable y with y denoting the e 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 siis the size of observation household i We can also assign to each of these observations a code Ci 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 Observation y c sw Si Variable of Group Sampling Size i interest Variable Weight variable Variable l 500 1 3 2 2 200 2 1 1 3 300 1 1 4 4 1000 1 2 5 5 700 2 3 5 6 450 1 1 7 7 300 1 1 3 8 200 2 3 3 9 300 2 2 4 10 400 1 1 8 The user then has six possibilities for computing the mean as shown in the following table The mean Variable of Size Group Index of Interest Variable Variable group P Eor the 10 households l Without
55. ck the following form TEDAD 4 2 HTML Result Viewer lol x 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 599 17753283 13583 42675781 599 17753283 144000 00000000 0 00000000 El Save 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 Parameter used indicates the value of the parameter used for this computation 121 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 e
56. ctors and parameter values as follows Variable of y Compulsory interest Size variable S Optional Group Variable c Optional Group Number k Optional Parameter y Compulsory On the first execution bar you find e The command Compute to compute the estimate of the distribution function To compute the 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 The command Range to specify the range of the horizontal axis 114 Plot Scatt XY This application plots a scatter graph of two variables To activate this application choose from the main menu the item Distribution gt 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 _ gt WiKi Yi BG Dwi K x O y x From this the derivate of y x with respect to x is given by Ob y x _ a x B x a x Ox BC BO Remark the instructions for non parametric derivative regression are similar t
57. d 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 are detected Missining or non convertible values Cancel 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 Data Import Wizard uo ASCII File In
58. e configuration of the application choose 1 distribution 3 After confirming the configuration the application appears Choose the different vectors and parameter values as follows Ranking variable y Compulsory Variable of interest T Compulsory Size variable S Optional Group Variable c Optional Group number k Optional rho p Compulsory 107 Commands e 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 e 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 concentration 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows choose the Variable of interest T T Compulsory Ranking variable y y Compulsory Size variable g s Optional Group variable c c Optional Group number k k Optional rho Pi p Compulsory Redistribution Coefficient of 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
59. e different vectors and parameter values as follows Distribution 1 Distribution 2 Variable of interest y y Compulsory Size variable g s Optional Group Variable a c Optional Group number k k Optional Poverty lines Zi Z5 Compulsory epsilon Bi B Compulsory 53 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 Hli a na Y w I y lt z H2 n k LW i i SW Gay q Le i i 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 1 From the main menu choose the item Poverty gt Sen index 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows Variable of interest y Compulsory Size variable S Optional Group Variable c Optional Group number k Optional Poverty line Z Compulsory rho p Compulsory 4 To compute the normalised index choose this option in the window of inputs 54 Commands The command Compute to compute the Sen index To compute the standard deviation choose the option for computing with standard deviation The comm
60. e 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 a is as follows a TEA OAA if 21 and FGTisnot normalised Hy INT 24a P k zi a zP k z o D if a21 and FGTis normalised Uk Eu if a 0 Hy 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 To compute that impact l From the main menu choose the item Poverty gt Inequality neutral Targeting 2 Choose the different vectors and parameter values as follows 63 Variable of interest y Compulsory Size variable Ww Optional Group Variable c Optional Group Number k Optional Poverty line Z Compulsory alpha a Compulsory 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 elas
61. e 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 If the variable FCP is not specified f h 0 for all observations When the variable specified 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 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 b N h The following table contains an example of vectors used to specify the type of SD shown i 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
62. ector 14 Vector 3 5 ve ctor 355 Vector 315 vector 5 Vector_ 6 ve ctor 3 6 Vector 6 Vector 16 Vector 37 ve ctor 37 Vector 317 vector 7 Vector x8 ve ctor 38 Vector 318 vector 8 Vector_ 9 ve ctor 38 Vector 3819 ector 9 vector 10 vector 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 13 Es Operation Series1 Series Series 1 Number fol Weight 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 Series 2 Operation B Result Denote vector 1 by S1 1 and vector 2 by S2 i The following table then presents the type of operations available and their results S Type of operation Results Series 1
63. ed stochastic dominance curves at order s or normalised FGT curves for a s 1 This application checks for the points at which there is 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 Au a for which Pi Apy a P2 Au a when sign P A m p 0 P A m p5 0 sign P A mp5 0 P A m p 0 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 84 Variable of interest y y Compulsory Size variable g g Optional Group Variable a c Optional Group Number k k Optional S S Compulsory 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 ov
64. ed 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 2 of DAD E E E FE PH A new specific format to saving and load data in DAD Provision of a new output window that adds significantly to the amount of information provided and results in a higher quality of output display A new window to edit the results that can then be saved in HTML format Estimation of new indices and curves and addition of new options for the estimation of indices and curves This version compiled with JDK 1 4 can run on Windows 95 98 2000 and Widows XP More effective data handling resulting in better memory use and increased capacity to deal with large data bases Optimized algorithms for processing data yielding a much increased speed of execution for several computations Installation and required equipment
65. elfare as measured by the EDE Atkinson index between two populations and 2 as follows 5 61 1j I2 u uo pi A I 2 711 I2 I2 c 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 gt Decomposition of Social Welfare 2 Choose the different vectors and parameter values as follows 81 Variable of interest y y Compulsory Size Variable g g Optional Group Variable g ee Optional Group number k k Optional epsilon e Compulsory To compute the standard deviation choose the option for computing with standard deviation 82 Dominance 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 dominates distribution 2 at order s over the conditional range z z if only if P Ga gt P G a Y Ge z 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 1s the values of C and P Ga for which
66. er 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 FGT 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 s over the conditional range lz z if only if CDi k gt yCD gt ki V Ge z 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 1 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 CDi k C and yCD 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 Q for which CD k 6 yCD gt k C when sign CDi k n yCD2 k m sign CD2 k n CDi k Gm for a small n The crossing points of can also be referred to as critical poverty lines 85 Critical values of y are also provided
67. ex To compute the Atkinson Gini social welfare index 1 From the main menu choose the following item Welfare S Gini index 2 In the configuration of the application choose 1 for the number of distributions 3 After confirming the configuration the application appears Choose the different vectors and values of parameters as follows Variable of interest y Compulsory Size variable S Optional Group Variable c Optional Group number k Optional epsilon Compulsory rho p Compulsory Press the command Compute to compute the 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 gt Atkinson Gini 2 In the configuration of application choose 2 for the number of distributions 70 3 Choose the different vectors and parameter values as follows Variable of interest y y Compulsory Size variable g s Optional Group Variable a c Optional Group number k k Optional rho Pi p Compulsory epsilon B5 Compulsory 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 Soc
68. f the standard errors of some distributive indices using asymptotic theory DAD and the BTS procedure Atkinson Index 0 5 0 09131119 W Strata Psu Lsu Size psu St err DAD St err BTS x 0 00403011 0 00404464 x x 0 00396117 0 00391402 x x 0 00479089 0 00473645 x x x 0 00414549 0 00412479 x x x x 0 00455368 0 00454454 FGT Q 1 z 3000 566 47774194 W Strata Psu Lsu Size psu St err DAD St err BTS x 30 15130207 30 31106186 x x 29 76615787 29 82831383 x x 34 90968660 34 49846649 x x x 31 21606735 31 36449814 x x x X 40 20904414 40 10400009 Lorenz p 0 5 0 26371264 W Strata Psu Lsu Size psu St err DAD St err BTS x 0 00618343 0 00617247 x x 0 00612036 0 00614563 X x 0 00695073 0 00697490 X x X 0 00632417 0 00636899 X x x X 0 00726710 0 00724934 Gini p 22 0 42403734 W Strata Psu Lsu Size psu St err DAD St err BTS x 0 00801557 0 00809321 x X 0 00786047 0 00781983 x x 0 00964692 0 00964823 x X X 0 00820847 0 00827642 x X x X 0 00949502 0 00946204 Notes W Sampling weight X Sampling design feature is used Inequality yi is the living standard of observation i We assume that the n observations have been ordered in increasing values of y such that Yi S Yin VizL n l The Atkinson index Denote the Atkinson inde
69. formation Delimiters Other information Space Semi colon Colon Tab r Other v Treat consecutive delimiters as one i dvanced Preview Results Number of OBS 1612 Number of Vectors 3 E Data Preview Weight Expend Group Vector_ 4 Vector_ 5 7 0 124729 0 2 0 Z 5 0 200749 0 1 0 5 0 96102 0 1 0 5 0 267149 0 2 0 4 0 125015 0 1 0 3 0 271719 0 1 0 1 0 247010 0 1 0 4 0 224617 0 1 0 6 0 146591 0 2 0 ji gt ok D cancer 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 clicking 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 10 Loading a DAD ASCII format file With DAD you can
70. ge and pc is the percentage price change for good l 59 2 a l ovf 2 x if a21 and Normalised 1 i l IMP 4 gt wi z y ys x if a21 and Not Normalised k i l 2 wiK y xi Elx y z f if 0 n i l where xi is expenditure on commodity 1 by individual i and f 2 max f 0 Note that if the FGT index is normalized IMP CD k z pe To compute the impact of the price change From the main menu choose the item Poverty Impact of price change 2 Choose the different vectors and parameter values as follows Variable of interest y Compulsory Size variable S Optional Commodity X Compulsory Group Variable C Optional Group Number k Optional Poverty line Z Compulsory alpha a Compulsory Price change in pe Compulsory Commands 60 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 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
71. ge 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 Boundary corrected non parametric regression and non parametric derivative regression For the boundary corrected non parametric regression the estimation is as follows WK OK x Yi 2 w Ki OK x O y x The boundary corrected non parametric derivate regression is obtained by differentiating the above with respect to x XN K500 K 00 y Ki GOK Q9 y ws Ki OK K OK 0 p r y x Y KI 0K x Y w KiG K 0 Note that 116 K x w x P A x and P A X X 2 s 1 1 v x 2M I jiko raya i A T Be I 0 0 0 K x Ww L P w EMS M x where Ox Ox 6M x _ MO OM x Li ae um M e 209 M x Conditional standard deviation A kernel estimator for the Conditional Standard Deviation of y at x can be defined as Nile ST x gt w KE ly y x wK x where K is a kernel function and y x is the expected value of y conditional on x To reach this application 1 From the main menu choose Distribution Conditional Standard Deviation 2 Choose the different vectors and parameter values as follows Exogenous Variable X X Compulsory Endogenous Variable Y y Compulsory Size variable s Optional Group Variable c Optional
72. gressivity and equity across different taxes and or tranfers and subsidies Poverty changes across growth and redistribution effects Checks for the robustness of distributive comparisons Estimation of stochastic dominance curves of the primal and dual types for poverty social welfare inequality and equity dominance Robustness of decompositions into population subgroups and factor components 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 Estimation of popular primal curves cumulative distribution functions poverty deficit curves poverty depth curves etc Estimation of differences in curves and indices Estimation of critical poverty lines for absolute and relative poverty comparisons Estimation of crossing points for dual curves 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 computations take into account the randomness of the sampling weights when such weights are provided by the user Allowance for sampling errors in the poverty lines specifi
73. he Generalised Entropy index of inequality for only one distribution l From the main menu choose the item Inequality Entropy 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 34 Variable of interest y Compulsory Size variable S Optional Group Variable c Optional Group Number k Optional theta 0 Compulsory Among the buttons you find the following choices Compute computes the Generalised Entropy index To compute the standard deviation of this index choose the option for computing with the standard deviation Graph to draw the value of index according to the parameter 9 To specify a range for the horizontal axis choose the item Graph Management 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 Entropy index 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Distribution 1 Distribution 2 Variable of interest y y Compulsory Size variable w w2 Optional Group Variable c c Optional Group Number k Optional theta 0 0 Compulsory Among the buttons you w
74. he configuration the application appears Choose the different vectors and parameter values as follows Variable of interest y Compulsory Size variable S Optional Group Variable c Optional Group Number k Optional epsilon E Compulsory rho p Compulsory 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 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows 33 Variable of interest y y Compulsory Size variable g g Optional Group Variable c Optional Group Number k k Optional rho Pi p Compulsory epsilon E 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 kis as follows xe if 0201 o 0 1 w i u k I k 0 Ew og E if 0 0 wf i yi i l k ty Bgl if 8 1 wk Hk ek i l Case 1 One distribution To compute t
75. he 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 TR Approach IR Approach TX Cro p Cri p Cx_11 P Cx 12 p Transfer C B1 p m Cp p Cx pi p Cx B2 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 curves as a function of p TR Approach IR Approach 2 Cr p Cr p Cx ri P Cx rs p Transfer Cai p Cg p Cx mi p Cxig2 D 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 amp p Ly p gt Ly p Cq p vp e J IR Approach The transfer B is more IR progressive than a tax T if Cx p Cy 4 p vp e bil 103 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 X Compulsory Variable of tax T Co
76. he option for computing with standard deviation 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 31 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 vectors and parameter values as follows Variable of interest y yl Compulsory Size variable g s Optional Group Variable c c Optional Group Number k kz Optional rho pi p 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 Atkinson Gini index Denoting the Atkinson Gini index of inequality for the group k by k p and the S Gini social welfare index by amp k p we have I k s p m uk a amp k p u k where poe OS po zlez20 and p21 V E k p Ed l and p2l and 32 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 t
77. ial Welfare index amp s is as follows IMpw 259 y Op 1 IMPW 47 si s2 i lt S3 pc if sl exp s2 s1 s3 s1 pc if gzl and Eu s2 9 wiy s3 9 wiy x if s sl w s2 w log yj s3 9 wxly if e 1 where Xi is expenditure on commodity by individual i y 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 71 Variable of interest y Compulsory Size variable S Optional Commodity X Compulsory Group Variable c Optional Group Number k Optional epsilon Compulsory Price change in pc 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 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 1 and 2 u
78. ibution gt Tax or transfer Specify if you wish to estimate the progressivity of a tax or of a transfer Choose the approach to be either TR or IR Choose the different vectors and parameter values as follows 100 Gross income X Compulsory Tax transfer T or B Compulsory Size variable S Optional Group Variable c Optional Group number k Optional rho p Compulsory p p Compulsory Commands e The command S Gini to compute TR Approach IR Approach us IC p Ly p Ix p ICy p Transfer Ix p ICR p Ix p ICx 5 p where IC p is the S Gini coefficient of concentration and I 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 TR Approach IR Approach Tax Lx p Cz p Cx 1 p Lx p Transfer Cs p Lx p Cx p 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 TR Approach IR Approach Tax
79. ication 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 X Compulsory Tax transfer or B Compulsory Size variable S Optional Group variable c Optional Group numberof interest k Optional rho p Compulsory p p Compulsory Commands e The command S Gini to compute Tax Transfer Ix _7 p ICy 7 p yap p ICy 5 p The command Difference to compute Tax Transfer Cx 1 p Lx 1 p Cy 3 p Ly ip P e The command Range to specify the range of the horizontal axis in the drawing of a graph 105 e The command Graph To draw the following curves as a function of p Tax Transfer Cx 1 p Lx 7p Cxip p Lx g p Redistribution A tax ora transfer 7 redistributes if Tax gt Ly 4q p Lx p 70 vp e oll Transfer Ly 4 p Lx p 0 vp e Jil To reach this application l From the main menu choose the item Redistribution gt 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 or B Compulsory Size variable S Optional Group variable c Optional Group number k Optional rho p C
80. ill find the command Compute To compute the standard deviation of this index choose the option for computing with standard deviation 35 The Quantile Ratio and the Interquantile Ratio Index Denote the Quantile Ratio for group k by QR k p p it can be expressed as follows Q k p R l p p QR k p p Q k p where Q k p denote the p quantile of group k The Interquantile Ratio IQR k p p is defined as k 14 k 2 IR p p As e 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 Variable of interest y Compulsory Size variable S Optional Group Variable c Optional Group Number k Optional Percentile for numerator P Compulsory Percentile for p 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 Qu
81. indicate the desired width and height of the graph in pixels inches or centimetres click 790 x on the button Set to confirm your selection fo fo Ei TRE oo o oo o E Draw Horizontal Line to draw a horizontal line at a giving height of the Y 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 LI a LI L E LI Draw 45 Lines to draw a 45 line Antia aliasing option One of the most important techniques in making graphics and text 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 125 Main Title By default the main 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 Poverty Second Title By default the second title is Chart You can dialog 18 change or delete the second title in the field Text You can Select also change its font and its colour To do this just click on the button select and indicate the desired font or colour
82. indow of inputs The Clark Hemming and Ulph CHU poverty index The poverty index P k z for the population subgroup k is defined as 1 1 awo z if e 1 and g20 UW P k z n Ywlny z exp EL if gel Ewi where z is the poverty line and y b H yi2 Z Otherwise Case 1 One distribution To compute the CHU index l From the main menu choose the item Poverty CHU index 2 In the configuration of application choose 1 for the number of distributions 52 3 Choose the different vectors and parameter values as follows Variable of interest y Compulsory Size variable S Optional Group Variable c Optional Group number k Optional Poverty line Z Compulsory epsilon Compulsory 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 Management 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 gt CHU index 2 In the configuration of application choose 2 distributions 3 Choose th
83. is given by Var 6 Var V MV with M the covariance matrix of the amp and V the gradient of 0 Rao C R 1973 Linear Statistical Inference and Its Application New York Wiley E 0a o 0a 00 OQ 0 can be estimated consistently using estimates 0a Oa The gradient elements t a of the true derivatives The covariance matrix is defined as 0a OQ Var a Cov a a Cov a a B Cov a a Var a Cov a a Cov a a Cov a a Var a The elements of the covariance matrix are again estimated consistently using the sample data replacing for instance Var amp by Var 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 then uses 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 fol
84. lowing steps the BTS approach for a sample drawn using Simple Random Sampling 1 Draw with replacement m 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 observations in stratum 1 and m2 observations in stratum 2 e Observations in every stratum were selected randomly with equal probabilities The first step will then consist in selecting randomly and with the same probability ml observations from stratum1 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 Sum of weights 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 8 800 80 10 The following tables present estimates o
85. m de fichier Enregistrer Favoris 1 Fichiers du type nm File Chtml bd Annuler 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 123 Graphs in DAD4 2 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 many properties of a graph For this select the item Tools Properties This can also be done by activating the Popup Menu Properties 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 124 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 background gif Width and Height to
86. minance Curves Distribution Window B ea vector 1 4 E D DAD 4 2 NOTICE Wok DAD 4 2 A Software for Distributive Analysis Analyse Distributive This programme is freely distributed and freely available Please acknowledge its use by quoting it as Jean Yves Duclos Abdelkrim Araar and Carl Fortin DAD A software for Distributive Analysis Analyse Distributive MIMAP programme International Development Research Centre Government of Canada and CREFA Universit Laval ox cance 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 7 In the main menu click on the command File and select the option New File A window asks the user to indicate the desired number of observations for the new file Entr e Q Enter the new number of observations M e mooo Annuler 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 71 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 P
87. mpulsory Variable of transfer B Compulsory Size variable S Optional Group variable C Optional Group number k Optional Rho p Compulsory p p Compulsory Commands e The command S Gini to compute TR Approach IR Approach 21x p 1Cr p ICs p ICy 4 p ICx p p where IC p is the coefficient of concentration e The command Crossing to seek the first point 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 Cs p Lx p Cx a p e The command Difference to compute TR Approach IR Approach Cz p Cs p 2Lx p Cx a p Cx 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 104 TR Approach Cr p Ca p 2Lx p IR Approach Cx P Cx 7 p Horizontal inequity A tax or a transfer T causes reranking and is therefore horizontally inequitable if Tax Cy 4 p Ly 4 p 0 for at least one value of p 0 I Transfer Cy p Ly 4 p 0 for at least one value of p e 0 1 To reach this appl
88. n Deviation index of inequality for the group k by RMD It can be expressed as follows X wy u 1 RMD il n k UW i l Case 1 One distribution If you wish to compute the relative mean deviation index of inequality for only one distribution follow these steps 41 l From the main menu choose the following items Inequality gt 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 y Compulsory Size variable S Optional Group Variable c Optional Group Number k Optional Among the buttons you will find 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 To compute the relative mean deviation of two distributions l From the main menu choose the item Inequality Relative Mean Deviation 2 n the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Variable of interest y y Compulsory Size variable g s Optional Group Variable al c Optional Group Number k k Optional Among the buttons you will find the command Compute To compute
89. n p and po c Estimated line indicate the estimates of the poverty lines z and zz and their standard deviations stdz and stdzp The FGT index The Foster Greer Thorbecke poverty index FGT P k z o for the population subgroup k is as follows 1 n P k z 0 4 9 wi z y k j wi i 1 47 where z is the poverty line and x max x 0 The normalised index is defined by P k z a P k z a z Case 1 One distribution To compute the FGT index l From the main menu choose the item Poverty gt FGT index 2 In the configuration of application choose 1 distribution 3 Choose the different vectors and parameter values as follows Variable of interest y Compulsory Size variable S Optional Group Variable c Optional Group number k Optional Poverty line Z Compulsory alpha a Compulsory 4 To compute the normalised index choose that option in the window of inputs Among the buttons you find e The command Compute to compute the FGT index To compute the standard deviation of this index choose the option for computing with standard deviation e 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 e The command Graph2 to draw the value of FGT asa function ofa range of
90. nder 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 E e is as follows IMWTR E s X E EO ee Op X Op 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 TN X TT commodity 1 is given by Y Pe 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 72 l From the main menu choose Welfare Impact of tax reform 2 Choose the different vectors and parameter values as follows Variable of interest y Compulsory Size variable S Optional Commodity 1 X1 Compulsory Commodity 2 X5 Compulsory Group Variable c Optional Group Number k Optional epsilon B Compulsory gamma y Compulsory 1 s price change pc 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 S
91. nt vectors and parameter values as follows Variable of interest y Compulsory Size variable S Optional Group Variable c Optional Group number k Optional Poverty line Z Compulsory rho p Compulsory 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 51 l From the main menu choose the item Poverty gt S Gini index 2 In the configuration of application choose 2 distributions 3 Choose the different vectors and parameter values as follows Distribution 1 Distribution 2 Variable of interest y y Compulsory Size variable g s Optional Group Variable c c Optional Group number k k Optional Poverty lines Zi Z Compulsory rho Pi p Compulsory The first execution bar contains the command Compute To compute the standard deviation choose the option for computing with standard deviation 4 To compute the normalised index choose this option in the w
92. o adjust range 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 v Auto adjust range Minimum range value c 0 Maximum range value 0 8044284156011178 Other Ticks Range Grid I Show grid lines Grid stroke Setstroke Gridpaint I setpaint 129 Curve 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 xi 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 X Select the desired thickness and click on the button OK to confirm your selection DAD 4 2 Graph Properties xi General Title Legend Axis Curve General Curves Settings Curved curves Curve stroke 4 8 Set stroke Cumepaint EE Set paint Thickness e o Set thickness Annuler Curve Paint To choose the colour of a giving curve click on the button Set Paint and choose the new colour 130 Saving graphs
93. o 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 y Compulsory Size variable s Optional Group Variable c Optional Group Number k Optional Level of X or p x Compulsory Smoothing parameter h Optional 115 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 The command Compute to compute dy 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 S Compute bandwith CVh method by Default vj min 0 max 1000 reject 5 e The command Graph to draw y x asa function of x To specify a ran
94. ocial Welfare Index The impact of growth in the j component on the Atkinson Social Welfare index amp s is as follows 1 0 amp s j si s2 s3 pc if se 1 OX exp s2 s1 s3 s1 pe if sx and l wi S2 5 wyi s3 gt wy a if gzl sl DW s2 w log y s3 wix l y if g 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 73 To compute the impact of that change l From the main menu choose the item Welfare Impact of Income component growth 2 Choose the different vectors and parameter values as follows Variable of interest y Compulsory Size variable S Optional Component X Compulsory Group Variable C Optional Group Number k Optional Epsilon Compulsory Component change pc Compulsory in 9o Commands e Compute to compute the impact of the Income component growth 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 parameter To specify that range and thus the range of the horizontal axis choose the command Range 74 The decomposition of inequality and poverty The decomposition of the FGT index
95. ompulsory p p Compulsory Commands e The command S Gini to compute Tax Transfer Ix p Ix 4 p Ix p Ix p e The command Crossing to seek the first point at which the curves L p and Ls p or Ly 3 p and L 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 106 Tax Transfer Ly 1 p Lx p LxB Lx 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 Tax Transfer Ly_7 p Lx p Ly 3 p Lx 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 coefficient of concentration of T for the group k is denoted as IC k p and defined as T 1 V 204 p Ivi where V Ywt Ur m J IC k p 1 One distribution To compute the coefficient of concentration for only one distribution l From the main menu choose the following item Redistribution gt Coefficient of concentration 2 In th
96. onal 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 distributions 3 Choose the different vectors and parameter values as follows Variable of interest y y Compulsory Size variable g s Optional Group Variable ci c Optional Group Number k k Optional percentile pi Di Compulsory percentile p p Compulsory percentile ps ps Compulsory percentile Py b 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 Gini Impact of Component Growth Let J components yJadd up to y that is J yi Dy j l The S Gini index of inequality can be expressed as follows u 4C p J I p Hy J 44 u The contribution of the j component to total inequality in y is NES eR where uy IC p is the coefficient of concentration of the j component and Hj 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 Oy ou of oy H y IC p Kp
97. one distribution 1 From the main menu choose the following item Welfare S Gini index 2 In the configuration of the application choose 1 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 y Compulsory Size variable S Optional Group Variable c Optional Group number k Optional rho p Compulsory 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 parameter p To specify such a range for the horizontal axis choose the item Graph Management gt 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 gt S Gini index 2 In the configuration of application choose 2 for the number of distributions 69 3 Choose the different vectors and parameter values as follows Variable of interest y y Compulsory Size variable g g Optional Group Variable el c Optional Group number k k Optional rho Pi p Compulsory To compute the standard deviation choose the option for computing with standard deviation The Atkinson Gini social welfare ind
98. oose Poverty gt Impact of Component Growth Variable of interest y Compulsory Income Component y Compulsory Size variable W Optional Group Variable c Optional Group Number k Optional Alpha g Compulsory Poverty line Z Compulsory 65 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 The Component Elasticity of Poverty The j component elasticity of poverty measured by the normalized FGT index is P kz o where CD is the normalized C dominance curve of the component j If you wish to CD k z a compute this elasticity choose Poverty Component Elasticity Variable of interest y Compulsory Income Component yl Compulsory Size variable S Optional Group Variable c Optional Group Number k Optional Alpha s Compulsory Poverty line Z Compulsory Among the buttons you will find e Compute to compute the statistics To obtain the standard deviation choose the option for computing with a standard deviation 66 67 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 Atkin
99. preadsheet 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 ASCH 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 15 nS Input O EEEEEESSN Look mue 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 16 Applications in DAD Introduction to applications Remember 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 Configuration of distributions lOl xl hen daf C 2 Distributions Independent distributions File for distribution 1 File for distribution 2
100. pute the following covariance matrix Cov C k 0 1 C5 k gt 30 1 Cov C k 0 1 C5 k4 0 2 Cov C k1 0 1 C3 k 5 1 Cov C k 0 2 C k 0 D Cov C k 0 2 C k 0 2 Cov C k 1 C k 30 1 Cov C k C5 k5 0 2 Cov C k D C k5 1 94 The Cumulative Poverty Gap CPG curve The CPG curve at p for a subgroup k and poverty line z is Y w z y Ky Qkp G k p z Y v i 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 y Compulsory Size Variable S Optional Group Variable c Optional Group Number k Optional Poverty line Z Compulsory p p 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 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 Case 2 Two distributions To reach the application for two distributions From the main menu choose the item Curves CPG curve 2 In the configur
101. rated by the das 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 The decomposition of the S Gini index of inequality Let J components yladd up to y that is L yi ay j We can decompose the S Gini index of inequality as follows I p Y Pc p u J j The contribution of the j th component to inequality in y Is IC p Hy where IC p is the coefficient of concentration of the rus component and us is the mean of that component To perform the decomposition of the S Gini index of inequality l From the main menu choose the item Welfare and inequality Decomposition S Gini decomposition 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows 79 Size Variable S Optional rho p Compulsory Vector s of interest Index1 index2 Compulsory The following results appear in the output window The S Gini index for y 2 The coefficients of concentration for every component of y 3 The ratio T u for every component of y 4 The contribution for every component The decomposition of the Generalised Entropy index of inequality The Generalised Entropy index of inequality can be decomposed as follows 0 K _ 6 Y c 28 I k 0 I 0 k l
102. ratification 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 supposing 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 1s 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
103. ress 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 l 2 EA 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 55 Ouvrir Rechercher dans a Mes documents f ei Adobe My Virtual Machines 4 country4 Book opf files My Webs 4 F1000 a Ma musique Photo a romano el Mes images phti a romano EE Mes vid os recette 4 testo mn Messenger Service Received Files la burkina n Nom de Fichier daf Ouvrir Fichiers du type DAD ASCII file daf Annuler Remark if 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 55 Data Import Wizard o ASCII File Information Delimiters Other information Semi colon V Treat consecutive delimiters as one Colon Tab Ir SP ia T irst row includes name of variables E Other Advanced
104. rs separated by k k Compulsory a7 To compute the standard deviation of this index choose the option for computing with standard deviation 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 CON pc the total estimated impact on poverty is as follows AP co P z a 2o k Pica pc If the population proportion of group s increases by absolute pc percent of the total population such that t et pc the total estimated impact on poverty is as follows K AP Pazo 2s Pica pc where P k z a is the FGT poverty index for subgroup k and Q k is the proportion of the population found in that subgroup To perform this estimation 1 From the main menu choose Decomposition gt Impact of Demographic Change 2 After confirming the configuration the application appears Choose the different vectors and parameter values as follows 78 Variable of interest y Compulsory Size Variable S Optional Group Variable c Optional Changed group t Compulsory Poverty line Z Compulsory Alpha a Compulsory Group numbers separated by k k Compulsory Remark moe The group numbers sepa
105. son index 2 In the configuration of the application choose 1 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 y Compulsory Size variable S Optional Group Variable c Optional Group number k Optional epsilon Compulsory 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 range of parameters g To specify such 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 with two distributions 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 68 Variable of interest y y Compulsory Size variable g g Optional Group Variable o c Optional Group number k k Optional epsilon i 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
106. 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 Variable of interest y y Compulsory Size Variable g s Optional Group Variable c E Optional Group Number k k Optional rho Pi p Compulsory p Pi Po Compulsory 91 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 L ky pi Li k5p 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 L k5 p e Covariance to compute the following covariance matrix Cov L k 0 1 L5 k5 0 1 Cov L k 0 D L5 k5 0 2 Cov L k 0 1 L5 k 1 Cov L k 30
107. st x Compulsory 1 Size Variable 1 s x Optional Variable of interest y Optional 2 Size Variable 2 s y Optional Group Variable C Optional Group Number k Optional To activate this application for one distribution follow these steps From the main menu choose the item Distribution Statistics 2 In the configuration of application choose 2 distribution 3 Choose the different vectors and parameter values as follows Variable of interest 1 x x Compulsory Size Variable 1 s x s x Optional Variable of interest 2 yl y Optional Size Variable 2 s y s y Optional Group Variable c ci Optional Group Number kl k Optional Density function The gaussian kernel estimator of a density function f x is defined as w K x X 2v X and K amp 1 X X Y w hJ2x f x exp 0 5 2 x and A x where h is a bandwidth which acts as a smoothing parameter 110 To reach this application l From the main menu choose the item Distribution gt Density function 2 Choose the different vectors and parameter values as follows Variable of interest y Compulsory Size variable S Optional Group Variable c Optional Group Number k Optional Parameter y Compulsory Smoothing parameter h Optional On the first execution bar you find e The command Compute to compute f x To compute the stand
108. the standard deviation of this index choose the option for computing with standard deviation 42 The Conditional Mean Ratio Denote the Conditional Mean for group k by u k p p where p and p specify the percentile p range of those we wish to include in the computation of the conditional mean These percentile values p are such that p p p j k p p i formally defined as odspyap u k p 3p 2 P2 P and is the average income of those whose rank in the population is between p and po The Conditional Mean Ratio for group k is then given by CMR ki k2 p1 p2 p3 p4 and is defined as U k Pi pi CMR k k p1 p2 p3 p4 WE pp 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 y Compulsory Size variable S Optional Group Variable c Optional Group Number k Optional Percentile P Compulsory Percentile p Compulsory Percentile ps Compulsory Percentile Py Compulsory 43 Among the buttons you will find the following command e Compute to compute the Conditi
109. 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 y 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 o is as follows aP k za 1 if a21 and Not Normalised LST P kza if 21 and Normalised Z f k z if 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 To compute that impact l From the main menu choose the item Poverty gt Lump sum Targeting 2 Choose the different vectors and parameter values as follows Variable of interest y Compulsory Size variable s Optional Group Variable c Optional 62 Group Number k Optional Poverty line Z Compulsory alpha a Compulsory Commands e Compute to compute the impact of the income 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 th
110. ticity GREL of poverty when growth comes exclusively from growth within a group k which is within that group inequality neutral is given by P k z a zP k z a 1 P z a if al GREL Zf k z F z if a 0 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 gt Growth Elasticity 2 Choose the different vectors and parameter values as follows Variable of interest y Compulsory 64 Size variable S Optional Group Variable c Optional Group Number k Optional Poverty line Z Compulsory alpha a Compulsory 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 The Impact of Component Growth The per capita dollar impact of growth in the j component on the normalized FGT index ofthe group is as follows OP k z a j a ay CD k z 0 ou ay where CD is the normalized C dominance curve of the component j If you wish to compute that impact ch
111. 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 gt 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 Variable of interest y Compulsory Size variable S Optional Group Variable c Optional Group Number k Optional 40 Among the buttons you will find the command e 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 Variable of interest y y Compulsory Size variable g s Optional Group Variable A c Optional Group Number k k Optional 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 Mea
112. u the item Edit gt Summarize Sample Design The following window appears TEDAD 4 2 Sampling Design HTML Result Viewer mi xl File Edi Sampling Design Information Code of PSU Strata l 1 2 Sirata 2 1 2 28 Computation of standard errors in DAD 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 approximation 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 9 4 4 with a asymptotically expressible as a 2 Yi jel where Ocan be expressed as a continuous function g of the o s m is the number of sample observations and yx 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 6 Var 0 Var LUE LUN NE NE a k a4 0a 0a O0 In matrix format the variance of
113. x of inequality for the group k by 1 amp 8 It can be expressed as follows ok Wi Yi I k KE 50s 8 5 8 where u k Z o ier il The Atkinson index of social welfare is as follows 1 l g 1 n wo ifzzl andgz20 k i l S k g yw In y 5 1 n k j 2 wi S i l Exp 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 gt 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 29 Variable of interest y Compulsory Size variable S Optional Group Variable c Optional Group Number k Optional epsilon Compulsory Among the buttons you find the following commands 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 s If you want to specify 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 index of two distributions l From the main menu choose the item Inequality Atkinson index 2
114. xecution 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 2 Current decimal number 8 Please enter new decimal number 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 buttons Result1 Result2 122 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 J amp A Adobe graph develop files Help Andr files E Label CD_files a Mes images Bureau Messenger Service Received Files LN My eBooks We My Webs Mes docume Nouveau dossier wj Paterns files us resu2 Poste de tra No

Users Manual for DAD 4.2 - The Software DAD

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