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USER MANUAL DASP version 2.0 DASP

1. After clicking SUBMIT the following graph is plotted interactively with Gnu Plot 4 2 Bi dimensional poverty dominance Difference Lower bounded 0 5 r Upper bounded 0 4 0 3 N 0 2 0 1 P SS O27 Y S M S LBP S p Eke RSS 0 37 SSK 06 BS lt g 0 78 0 9 0 880 860 i 0 990 960 940 92 Dimension 2 Q 2 119 To make a simple test of multidimensional dominance one should check if the lower bounded confidence interval surface is always above zero for all combinations of relevant poverty lines or conversely o For this click on the panel Confidence interval and select the option lower bounded o Click again on the button Submit After clicking SUBMIT the following graph is plotted interactively with Gnu Plot 4 2 Bi dimensional poverty dominance Lower bounded 0 05 7 0 05 T 0 15 Dimensioni 2 3 X 50 98 1 t x 88 09 0 920 940 96 owe 0 82 0 84 0 86 0 78 Dimension 2 120 23 13 Testing for pro poorness of growth in Mexico The three sub samples used in these exercises are sub samples of 2000 observations drawn randomly from the three ENIGH Mexican household surveys for 1992 1998 and 2004 Each of these three sub samples contains the following variables strata The stratum psu The primary sampling unit weight Sampling weight inc Income hhsz Household size 1 Using the files
2. The two variables of interest dimensions should be selected specific population subgroup can be selected surfaces showing the joint density function are plotted interactively with the GnuPlot tool coordinates can be listed c coordinates can be saved in Stata or GnuPlot ASCII format Interested users are encouraged to consider the exercises that appear in Section 23 11 18 6 DASP and joint distribution functions The module sjdistrub can be used to draw joint distribution surfaces The joint distribution function F x y is defined as wi I x lt X I y lt y F x y With this module The two variables of interest dimensions should be selected specific population subgroups can be selected surfaces showing the joint distribution function are plotted interactively with the GnuPlot tool coordinates can be listed 52 coordinates can be saved in Stata or GnuPlot ASCII format Interested users are encouraged to consider the exercises that appear in Section 23 11 19 DASP and pro poor growth 19 1 DASP and pro poor indices The module ipropoor estimates simultaneously the three following pro poor indices 1 The Chen and Ravallion pro poor index 2003 _ Wi z Wo z F z Index where Wp z is the Watts index for distribution D 1 2 and A z is the headcount for index for the first distribution both with poverty lines z 2 The Kakwani and Pernia pro poor index 2000
3. ccssscccccessescssssssscesteorseescotestacetessesontersesscsescesoess 90 Figure 34 Differences between FGT Curves ests snciceceteyedinaneivcasitonna aes een 91 Figure 35 Drawing FGT curves with confidence interval cc ceeeseeceeeeceeeceeeeneeeeeeeeeeeeaees 92 Figure 36 FGT curves with confidence interval cceeccescesecseeeneeeseeeeeeeceaeceeceeeaeeeeeeeeeaees 93 Figure 37 Drawing the difference between FGT curves with confidence interval 94 Figure 38 Difference between FGT curves with confidence interval 0 94 Figure 39 Difference between FGT curves with confidence interval a 1 eee 95 Figure 40 Testing for poverty dominance eee eseeseeeeceseceseceecseeeseeeeeeaeceaeceeecaeeesereneeeeeaees 96 Figure 41 Decomposing FGT indices by SroupS eeceeeceseceseeseeeseeeeeeeceseceecaeeeseeeeeeeeaees 97 Figure 42 Lorenz and concentration CUIVES eee 100 Fig re43 Lorenz CUIVES cic rie nooo i a oo ooo o ob Dno ob ins 101 Figure 44 Drawing concentration CUIVES eee eeeceescecseeceseeeseeeeceecseeceaeeteeesaeecsaecaeeeseeeeaee es 102 Figure 45 Lorenz and concentration CUIVES eee 103 Pigure 6 Drawing Lorenz CEV69 ueso onie saka dada vzd ei erai dalo Boby 104 Figure 47 LOrPOnZCUFVSS 33 o fice sadou dod ao ada ate are abla a ae oda ooo o tease hades 104 Figure 48 Estimating Gini and concentration indices eee 106 Figure 49 Estimating concentration i
4. Conditions can be specified such as to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 27 14 3 The Foster and Wolfson 1992 polarization index ipolfw The Foster and Wolfson 1992 polarization index can be expressed as FW 2 2 0 5 Lorenz p 0 5 Gini median The user can select more than one variable of interest simultaneously For example one can estimate polarization by using simultaneously per capita consumption and per capita income A group variable can be used to estimate polarization at the level of a categorical group If a group variable is selected only the first variable of interest is then used Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed Main reference FOSTER J AND M WOLFSON 1992 Polarization and the Decline of the Middle Class Canada and the U S mimeo Vanderbilt University 14 4 Difference between Foster and Wolfson 1992 polarization indices dipolfw This module estimates differences between the FW indices of two distributions For ea
5. After clicking on SUBMIT we should see Poverty Index FGT Index Paraneter alpha 0 00 Est inate STO LE UE P Line Distr ibut ioni 0 510344 0 011601 1 4435 0 53314 41099 00 Distribution 0 5197 0 1195 0 471236 0 540753 41099 00 Difference 0 000153 0 023400 0 045427 0 045121 a Q 4 78 Poverty Index oo FGT Index Faraneter alpha 0 00 Est inate Sm LE UB F Line Distribution 1 0 16673 0 016297 0 17533 0 196608 41099 00 Distribution 0 103604 0 013419 0 07709 0 1159 41099 00 Difference 0 060889 0 021111 0 019513 0 102265 One can see that the change in poverty was significant only for urban residents Q 5 Restrict the estimation to male headed urban residents as follows o Set the number of Condition s to 2 o Set sex in the field next to Condition 2 and type 1 in the next field Figure 23 FGT differences across years by gender and zone E DASP Difference Between FGT Indices gt difgt command In xl Main Confidence Interval Results Distribution 1 Distribution 2 DatainFile CADATANDKIS8 dta Browse Data in Fie v C ADATASbkf94 dta Browse Variable of interest eepe ssi lt sSS Variable of interest Size variable ze t C OC Size variable ze lt t i i SC S Poverty line Poverty line Absolute 41099 Absolute 41099 C Relative EER of the Mean gt Relative 503 ofthe Mean gt
6. Range of percentiles p Size variable size 7 Group variable zone Minimum Maximum rs Figure 47 Lorenz curves 4 Graph Graph Lorenz Curves 104 23 9 Estimating Gini and concentration curves By how much do taxes and transfers affect inequality in Canada Using the can6 dta file 1 Estimate the Gini indices for gross income X and net income N 2 Estimate the concentration indices for variables T and N when the ranking variable is gross income X By how much has inequality changed in Burkina Faso between 1994 and 1998 Using the bkf94I dta file 3 Estimate the difference in Burkina Faso s Gini index between 1998 and 1994 a with variable of interest expegz for 1998 and expeg for 1994 b with size variable set to size 0 1 Steps Type use C data can6 dta clear To open the relevant dialog box type db igini Choose variables and parameters as in 105 Figure 48 Estimating Gini and concentration indices E DASP Gini amp Concentration Indices gt igini command After clicking SUBMIT the following results are obtained Variable Est inate ST LB IB i GHI X VE Lee 0476599 0 540313 2 GINIH 0 332355 0 012753 0 7318 0 357591 Q 2 Steps Choose variables and parameters as in 106 Figure 49 Estimating concentration indices ES DASP Gini amp Concentration Indices gt igini command Variable Est inate 10 1 OH
7. bu xfa Afo A In the Weights panel set SAMPLING WEIGHT VARIABLE as follows 68 Figure 17 Setting sampling weights S svyset Survey data settings Click on OK and save the data file To check if the sampling design has been well set type the command svydes The following will be displayed Survey Describing stage 1 sanpling units pueight weight WE linearized Strata 1 strata SU 1 peu FPE d lt zero gt H bz per Unit Stratun Whits Hibs Hin Hear Hay i 2 He 19 a ad 2 73 1 19 8 a 3 M 183 19 7 0 Fal 4 183 19 19 9 al 5 i ih B 19 5 a 4 TA i 19 0 fal 7 a 1937 19 a 2l 7 as i 19 8 fal 69 23 Examples and exercises 23 1 Estimation of FGT poverty indices How poor was Burkina Faso in 1994 1 Open the bkf94 dta file and label variables and values using the information of Section 22 1 1 Type the describe command and then label list to list labels 2 Use the information of Section 22 1 1 to set the sampling design and then save the file 3 Estimate the headcount index using variables of interest expcc and expeg a You should set SIZE to household size in order to estimate poverty over the population of individuals b Use the so called 1994 official poverty line of 41099 Francs CFA per year 4 Estimate the headcount index using the same procedure as above except that the poverty line is now set to 60 of the median 5 Using the official poverty
8. 0 4446 ST 0 0166 0 0 0 0464 75 leweli49 plinel41049 LE UE 0 4004 1 462 0 2089 0 354 0 4028 0 4863 F Line 41099 00 41099 00 41099 00 23 2 Estimating differences between FGT indices Has poverty Burkina Faso decreased between 1994 and 1998 1 Open the dialog box for the difference between FGT indices 2 Estimate the difference between headcount indices when a Distribution 1 is year 1998 and distribution 2 is year 1994 b The variable of interest is exppc for 1994 and exppcz for 1998 c You should set size to household size in order to estimate poverty over the population of individuals d Use 41099 Francs CFA per year as the poverty line for both distributions 3 Estimate the difference between headcount indices when a Distribution 1 is rural residents in year 1998 and distribution 2 is rural residents in year 1994 The variable of interest is exppc for 1994 and exppcz for 1998 c You should set size to household size in order to estimate poverty over the population of individuals d Use 41099 Francs CFA per year as the poverty line for both distributions 4 Redo the last exercise for urban residents Redo the last exercise only for members of male headed households 6 Test if the estimated difference in the last exercise is significantly different from zero Thus test H AP z 41099 a 0 0 against H AP z 41099 a 0 40 Set the significance level to 5 and assume that the test statistics f
9. Steps Type use C data bkf941 dta clear To open the relevant dialog box type db cfgts Choose variables and parameters as in Figure 35 Drawing FGT curves with confidence interval EE DASP FGT Curve with Confidence Interval gt cfgts command After clicking SUBMIT the following appears 92 Figure 36 FGT curves with confidence interval FGT curve alpha 0 Burkina Faso T T T T l 0 20000 40000 60000 80000 100000 Poverty line z Confidence interval 95 Estimate 0 2 Steps To open the relevant dialog box type db cfgtsd2 Choose variables and parameters as in 93 Figure 37 Drawing the difference between FGT curves with confidence interval EE DASP Curve of difference between FGT Indices gt cfgts2d command lt ci xi g v CADATASDKES4I dta Figure 38 Difference between FGT curves with confidence interval a 0 Difference between FGT curves 10 alpha 0 T T T T 0 20000 40000 60000 80000 100000 Poverty line z Confidence interval 95 Estimated difference 94 Figure 39 Difference between FGT curves with confidence interval a 1 Difference between FGT curves a alpha 1 T T T T 1 0 20000 40000 60000 80000 100000 Poverty line z Confidence interval 95 Estimated difference 23 6 Testing poverty d
10. T 0 595359 1 12253 2 COHC H 1 VH 0 3 Steps To open the relevant dialog box type db digini Choose variables and parameters as in 107 Figure 50 Estimating differences in Gini and concentration indices E DASP Difference Between Gini Concentration Indices gt digini command DatainFile C DATA bKf9SI dta After clicking SUBMIT the following information is obtained digini expegz expeg filell datahbkfO8I dtal hzizellzizel file2 Cs datavbkfS4 dta hzize sizel Est inate ST LE UE Dist ribut ion_1 GINT 0 44603 0 012016 0 419941 0 400755 Distr ibut ion Z GINTI 0 505 0 008613 0 435116 0 46694 Difference 0 005492 0 015444 0 035762 0 024778 108 23 10 Using basic distributive tools What does the distribution of gross and net incomes look like in Canada Using the can6 dta file 1 Draw the density for gross income X and net income N The range for the x axis should be 0 60 000 2 Draw the quantile curves for gross income X and net income N The range of percentiles should be 0 0 8 3 Draw the expected tax benefit according to gross income X The range for the x axis should be 0 60 000 Use a local linear estimation approach 4 Estimate marginal rates for taxes and benefits according to gross income X The range for the x axis should be 0 60 000 Use a local linear estimation approach 0 1 Steps Type use C data c
11. 0 5 Set the group variable to sex 13 F Line 27046 71 Figure 20 FGT indices differentiated by gender E DASP FGT and EDE FGT Index gt ifgt command Main Confidence Interval Results exppc of interest Size variable size v Group variable sex F Survey settings 15 x M Index options s Index FGT Ines o Type Nomad Bf Parameter s Parameter alpha fo M Poverty line Absolute jno C Relative EEE of the Median v F group variable is used poverty line is relative to The population gD Cancel Submit Clicking on SUBMIT the following should appear ifgt exppc alphal0 hsizelsize horouplsesx plinel 41099 Poverty Indes FGT Index Household size size Sanpling weight weight Group variable sox Faraneter alpha 0 00 Group Est inate S10 LE l Hale 0 421 0 06633 0 419404 Fonale 0 261350 DK 0 22411 PULATION 0 444565 0 016124 0 412873 Q 6 0 476256 F Line 41099 00 41099 00 41099 00 Using the panel CONFIDENCE INTERVAL set the confidence level to 99 and set the number of decimals to 4 in the RESULTS panel 74 ifat exppc alphalO hsizelsize horouplsex decid Foverty Index Household size Sanpling weight z Group variable Faraneter alpha Group 1 Hale z Fonale POPULATION FGT Index size ue ight ZAM 0 00 Est inate 0 422 0 2619
12. Z w z w CPC a z x wi i l Transient poverty equals TPC a z TP a z CPC a z Duclos Araar and Giles 2006 approach Let yt be the income of individual i in period t and u be average income over the T periods for individual i Let a z be the egually distributed eguivalent EDE poverty gap such that I a z TP a z Transient poverty is then defined as N w 9 a z TPC a z x wi i l T Va where 0 a z v 1 z and B y a Zz 2 a vb r 1 t and chronic poverty is given by CPC a z I a z TPC a z Note that the number of periods available for this type of exercise is generally small Because of this a bias correction is typically useful using either an analytical asymptotic or bootstrap approach To open the dialog box for module dtcpov type db dtcpov in the command window 37 Figure 10 Decomposition of poverty into transient and chronic components JS DASP Decomposition of the total poverty into transient and chronic poverty gt dtcpov command oj x Main Results pecon35 pecon97 pecon99 pecon 1 v Approach Jalan and Ravalion 1998 of interest Decomposition approach Censored incomes M Parameters Parameter alpha 2 Size variable hs v Poverty line 2 fi W Bias correction Approach Analytic im Survey settings Cancel Submit The user can select
13. eeeeeeeeeeeeeeeeeeeeeeen e 67 22 3 Appendix C setting the sampling d si n 3x00 ewan se peas d lka oak 68 23 Examples and eXerciseS renei ia ia ra a Re 70 23 1 Estimation of FGT poverty indices s seseeseeeeseeseesesseseesesseseesstseesesseseestssrseesseseesesse 70 23 2 Estimating differences between FGT indices eee 76 23 3 Estimating multidimensional poverty indices eee 80 23 4 Estimating FGT Curves s acs sea eal eee ea eA eee aig aed iaa 83 23 5 Estimating FGT curves and differences between FGT curves with confidence interyalS aeaiee a a e R oo oto od at A oo oko oto sats o do ooo oh oo oa 91 23 6 Testing poverty dominance and estimating critical values 95 23 7 Decomposing PG M66 Soja sea nak s eee eal aon eee ees 96 23 8 Estimating Lorenz and concentration CUIVES esceseescesseeeeeeeeeesecesetaeeeseeereeeeeaees 99 23 9 Estimating Gini and concentration Curves eee 105 23 10 Using basic distributive TO0IS sires costes ete cites ast sea Sit 109 23 11 Plotting the joint density and joint distribution function ee 115 23 12 Testing the bi dimensional poverty dominance eee 118 23 13 Testing for pro poorness of growth in Mexico 121 23 14 Benefit incidence analysis of public spending on education in Peru 1994 127 List of Figures Figure 1 Ouput Of net describe dasp ssc cas eiccts cnc iss nese ta detains ats eases ianens ass ghavasldedescnesNiseais
14. 68 Figure 17 Setting sampling weights 120k ce aad St vata Sa et aac Pala tht lanes o E 69 Figure 18 Estimating FGT indices zbyde side nedo dano skoda aci seo tae ea eee 72 Figure 19 Estimating FGT indices with relative poverty liNeS eee 173 Figure 20 FGT indices differentiated by gender us sen secci acta sacsesgendiisds taarsatbedoncsabaddesiacdneaem 74 Figure 21 Estimating differences between FGT indices eee 77 Figure 22 Estimating differences in FGT indices eee ee eeeeeeeee een 78 Figure 23 FGT differences across years by gender and Z0Ne eee 79 Figure 24 Estimating multidimensional poverty indices A 81 Figure 25 Estimating multidimensional poverty indices B 82 Fig re26 Drawing BGT COL VGS 6 ci s3 skis it d ez oi ad oka balit al A a Soos dob ooo 84 Figure27 Editing FGT CUTVOS kokot saacin vi eea ae dB tac danas 66s ei sea ed dos pa B ba 84 Fig re 28 Graph of MGW CUrVeS n pean has ode dny eae eas T tees oo oo 85 Fig re ZOLPGT Curves Dy ZO Mei jse sad tav kaz ncoacd neva p t sud dana eae witean kast au malas dea iiS 86 Figure 30 Graph of FGT curves Dy ZOMG v 5i4scce cisevsesdsvececcasouvscssecuzenstasus ccsavacesteacissstandecadasevetvas 87 Figure 341s Differences Of FG I Curves ov 2a rssk sta ey audio ee tenia es 88 Fig re3 2 listing COOLCIN ALCS z stadia tohaty kaz oad a dd gars einean Bisbee eas hea eave 89 Figure 33 Differences between FGT CUrves
15. DASP Pro poor indices gt difgt command In xj Main Confidence Interval Results Distribution 1 Distribution 2 Data in file CADATA Mexico mex_ 8_2ml d Browse Data in file C DATA Mexico mex_04_2mi d Browse Variable of interest finc Variable of interest finc Size variable hhsz Size variable hhsz I Condition s fi z T Condition s fi v Parameters and options Parameter alpha fi Poverty line 600 Type Normalised is Cancel Submit After clicking SUBMIT the following results appear Poverty line 00 00 Faraneter alpha 1 00 Prucpuur ind ives Esl ingle STO LB UB Grouth ratelg 0 59 0 125517 133631 DAM Chen amp Ravallion 2003 index 0 212235 1 009337 1 265970 ZE Kakuani amp Pernia 2000 index 13m 0 107 Lie 1 552 PEGE index 0 771879 0 137331 oe 1 1 PEGR g 110 ILS LEE 0 286257 23 14 Benefit incidence analysis of public spending on education in Peru 1994 1 Using the peredu94I dta file estimate participation and coverage rates of two types of public spending on education when The standard of living is exppc The number of household members that benefit from education is fr prim for the primary sector and fr_sec for the secondary one The number of eligible household members is el prim for the primary sector and el_sec for the secondary one Social groups are quintiles 127 Answer Type db bian in the windows c
16. Figure 7 Poverty and the targeting by population groups Pele Main Results Graphical Results Y Axis Axis Title Caption Legend Overall Variable of interest Options and parameters Jexppe Ea Parameter alpha jo Normalised by the cost Normalised i Size variable size zi Targeting type Lump sum constant amount Y Group variable zone he Poverty line z fi 00000 Minimum Maximum C Range of pov line fo fi 0000 Cancel Submit Reference DUCLOS J Y AND A ARAAR 2006 Poverty and Equity Measurement Policy and Estimation with DAD Berlin and Ottawa Springer and IDRC sec 12 1 11 2 Poverty and targeting by income components Proportional change per 100 of component J Assume that total income Y is the sum of J income components with Y gt A Vj and where c is a factor j l that multiplies income component y and that can be subject to growth The derivative of the normalized FGT index with respect to 4 is given by OP z a O J hj Lj LJ CD z a 17 where CD is the Consumption dominance curve of component j Change per of component The per capita dollar impact of growth in the j th component on the normalized FGT index of the k group is as follows OP z a OF 5 au CD z a dy where CD is the normalized consumption dominance curve of the component j Constant change per component Simply we assume that the change
17. R z a P za R z a FR z 4 1w a 3 The Kakwani Khandker and Son pro poor index 2003 Index R za P za Index 7 P z a P 2 uy 14h a where the average growth is g Lb 44 44 and where a second index is given by Index _2 Index l g One variable of interest should be selected for each distribution Conditions can be specified to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed A level for the parameter can be chosen for each of the two distributions 19 2 DASP and pro poor curves 53 Pro poor curves can be drawn using either the primal or the dual approach The former uses income levels The latter is based on percentiles 19 2 1 Primal pro poor curves The change in the distribution from state 1 to state 2 is s order absolutely pro poor with standard cons if A z s P z cons a s 1 P z a s 1 lt 0 vze 02 The change in the distribution from state 1 to state 2 is s order relatively pro poor if A z s netu s l A z a s o ze 0 2 M The module cpropoorp can be used to draw these primal pro poor curves and their associated confidence interval by taking into account sampling design The module can draw pro poor curves an
18. Sector 2 Quintile 1 317 084 280 540 Quintile 317 104 280 540 Quintile 3 312 184 200 540 Quintile 4 317 084 280 540 Quintile 5 32 04 280 540 All 317 084 280 540 Groups Sector Sector Quintile 1 0 135 0 065 Quintile 2 0 141 0 081 Quintile 3 0 137 0 084 Quintile 4 0 123 0 087 Quintile 5 0 087 0 065 All 0 624 1 3 131
19. Variable s of interest Index options s ji Index FGT Index z Type Normalised sd m Parameter s Size variable Parameter alpha fo Group variable M Poverty line Absolute 10000 C Relative 504 of the Mean s IF group variable is used poverty line is relative to Survey settings The population z PE ces d m For the second type of applications two distributions are needed For each of these two distributions the user can specify the currently loaded data file the one in memory or one saved on disk Figure 6 Estimating FGT poverty with two distributions E DASP Difference in FGT Indices gt difgt command Main Confidence Interval Results Distribution 1 Distribution 2 Data in Memory jd Data in File I CADATANDKFS4 dta Browse Variable of interest Variable of interest Size variable Size variable Poverty line Poverty line Absolute 10000 Absolute 10000 C Relative 503 of the Mean z C Relative 504 of the Mean s T Conditions fi s T Conditions fi z Parameters and Options Parameter alpha jo Type Normalised m aos Cancel Submit 12 Notes 1 DASP considers two distributions to be statistically dependent for statistical inference purposes if the same data set is used the same loaded dat
20. as in 80 Figure 24 Estimating multidimensional poverty indices A E DASP Multidimensional poverty indices gt imdpov command fer d N eae fos After clicking SUBMIT the following results appear indpoy exppc pliterate hsizelsize index 1 alpha O a4 1 pldt400 a 1l pl2to 9 H D Poverty index Chakravarty et al 1998 Household size size Est inate opulat ion 0 418 Q 2 Steps Choose variables and parameters as in 81 Figure 25 Estimating multidimensional poverty indices B EE DASP Multidimensional poverty indices gt imdpov command 3 bidimensional index 3 e d fo piese A fos After clicking SUBMIT the following results appear indpoy exppe pliterate hsizelsize index 7 alphali betafl1 gannald plit400 pleto 9 H D Poverty index Bourguignon and Chakravarty 2003 Household size size Est inate Populat ion 0 098 82 23 4 Estimating FGT curves How sensitive to the choice of a poverty line is the rural urban difference in poverty 1 Open bkf94I dta 2 Open the FGT curves dialog box 3 Draw FGT curves for variables of interest exppc and expeq with a parameter a 0 b poverty line between 0 and 100 000 Franc CFA c size variable set to size d subtitle of the figure set to Burkina 1994 4 Draw FGT curves for urban and rural residents with a variable of interest set to exp
21. command window 46 Figure 14 Consumption dominance curves E DASP Consumption Dominance Curves gt cdomc command iol x Main Results Graphical Results Y Axis X Axis Title Caption Legend Overall n Dominance order s gt 1 fi Normalised by the cost Notnomalised S m of interest M Options and parameters Size variable Poverty line 2 froood Component variables v Minimum Maximum C Range of pov line fo fi 0000 Cancel Submit 16 9 Differences consumption dominance curves with confidence interval cdomc2d The cdomc2d module draws differences between consumption dominance curves and their associated confidence intervals by taking sampling design into account The module can draw differences between consumption dominance curves and associated two sided lower bounded or upper bounded confidence intervals list or save the coordinates of the differences and their confidence intervals save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs 17 Dominance 17 1 Poverty dominance dompov Distribution 1 dominates distribution 2 at order s over the range z z if only if R a lt P Ga V Ge z z fora s l This
22. concerns the group with component level greater than zero Thus this is similar to targeting by the nonexclusive population groups The module itargetc allows to Estimate the impact of marginal change in income component on poverty Select the option normalised or non normalised by the average of component Select the design of change constant lump sum or proportional to income to keep inequality unchanged Draw curves of impact according for a range of poverty lines Draw the confidence interval of impact curves or the lower or upper bound of confidence interval Etc Reference DUCLOS J Y AND A ARAAR 2006 Poverty and Equity Measurement Policy and Estimation with DAD Berlin and Ottawa Springer and IDRC sec 12 12 Marginal poverty impacts and poverty elasticities 12 1 FGT elasticity s with respect to the average income growth efgtgr The overall growth elasticity GREL of poverty when growth comes exclusively from growth within a group k namely within that group inequality neutral is given by 18 _ Zf k z P F z GREL 4 _ _ P k z a P k z a 1 P z a if azl where z is the poverty line k is the population subgroup in which growth takes place f k z is the density function at level of income z of group k and F z is the headcount Araar Abdelkrim and Jean Yves Duclos 2007 Poverty and ineguality components a micro framework Working Paper 07 35 CIRPEE Departmen
23. confidence interval Figure 63 Testing the pro poor growth dual approach A 123 E DASP Pro poor curves dual renra erer mek rie nan Te Ce eaae OOOO gt cpropoord command Data in fle C Documents and Settings 4raa aE Data in file C Documents and Settingst raa O After clicking SUBMIT the following graph appears Absolute propoor curves Order s 1 Dif Q_2 p Q_1 p mu_2 mu_1 I T T T T 0 184 368 552 736 92 Percentiles p Difference Lower bound of 95 confidence interval Null horizontal line Q 2 Steps 124 To open the relevant dialog box type db cpropoord Choose variables and parameters as in with the lower bounded option for the confidence interval Figure 64 Testing the pro poor growth dual approach B E DASP Pro poor curves dual approach gt cpropoord command as Data in file C Documents and Settingst raa o After clicking SUBMIT the following graph appears 125 Absolute propoor curves Order s 2 Dif GL_2 p GL_1 p GL_2 p T T 0 184 368 552 736 92 Percentiles p Difference Lower bound of 95 confidence interval Null horizontal line Q 4 Steps To open the relevant dialog box type db ipropoor Choose variables and parameters as 126 E
24. i l i 0 Zw to if 0 0 wi 1 i i l SE gl 2 if 0 1 gt w 1 u i l The user can select more than one variable of interest simultaneously For example one can estimate inequality simultaneously for per capita consumption and for per capita income A group variable can be used to estimate inequality at the level of a categorical group Ifa group variable is selected only the first variable of interest is then used Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 13 4 Difference between generalized entropy indices diengtropy This module estimates differences between the generalized entropy indices of two distributions For each of the two distributions One variable of interest should be selected Conditions can be specified to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 24 13 5 Atkinson index iatkinson Denote the Atkinson index of inequality for the group k by I k e It can be expressed as follows n ns Wi yj I e Bree where u wi i l The Atkinson
25. income as a measure of individual living standards Household observations are weighted by household size and sampling weights to assess poverty over all individuals The six main income components are source_1 Employment income source_2 Agricultural income source_3 Fish processing income source_4 Non farm business income source_5 Remittances received source_6 All other income The Stata data file is saved after initializing its sampling design with the command svyset e To open the dialog box for module dfgts type db dfgts in the command window 31 Figure 1 Decomposition of the FGT index by income components E Decomposition of the FGT index by income components using the Shapley value gt dfgts command In x Main Results Variable s of interest Parameters sourcet sources 0 YS Parameter alpha o Poverty line z o Size variable hhsize g Weight variable Jweightes ti i s SOCS i Cancel Submit Indicate the varlist of the six income sources Indicate that the poverty line is set to 15 000 N Set the variable HOUSEHOLD SIZE Set the variable HOUSEHOLD WEIGHT Click on the button SUBMIT The following results appear digts sourcel source pline 15000 heizefhhsize hueightl ueighteal Deconposition of the FGT index by incone conponents using the Shapley valued Execution tine 5 03 second s Paraneter alpha 0 00 Poverty line 15000 00 FGT index 0 5849
26. index of social welfare is as follows ahs l e 1 a l e k y AW ife l ande20 Wi i l i l E 1 n Exp W In y gt e 1 Wi i l i l The user can select more than one variable of interest simultaneously For example one can estimate inequality simultaneously for per capita consumption and for per capita income A group variable can be used to estimate inequality at the level of a categorical group Ifa group variable is selected only the first variable of interest is then used Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 13 6 Difference between Atkinson indices diatkinson This module estimates differences between the Atkinson indices of two distributions For each of the two distributions One variable of interest should be selected Conditions can be specified to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 25 13 7 Quantile share ratio indices of inequality inineq The quantile ratio is estimated as QP OR p p gt OR p1 p2 ps where Q p denot
27. involves comparing stochastic dominance curves at order s or FGT curves with g s 1 This application estimates the points at which there is a reversal of the ranking of the curves Said 47 differently it provides the crossing points of the dominance curves that is the values of C and sign P 1 a P 7 a sign P 1n a P 7 a for a small 77 The crossing points C can also be referred to as critical poverty lines The dompov module can be used to check for poverty dominance and to compute critical values This module is mostly based on Araar 2006 Araar Abdelkrim 2006 Poverty Inequality and Stochastic Dominance Theory and Practice Illustration with Burkina Faso Surveys Working Paper 06 34 CIRPEE Department of Economics Universit Laval Interested users are encouraged to consider the exercises that appear in Section 23 6 17 2 Inequality dominance domineg Distribution 1 inequality dominates distribution 2 at the second order if and only if L p lt L p Y pe e l The module domineg can be used to check for such ineguality dominance It is based mainly on Araar 2006 Araar Abdelkrim 2006 Poverty Ineguality and Stochastic Dominance Theory and Practice Illustration with Burkina Faso Surveys Working Paper 06 34 CIRPEE Department of Economics Universit Laval Intersections between curves can be estimated with this module It can also used to check f
28. mex 92 2ml dta and mex 98 2ml dta test for first order relative pro poorness of growth when e The primal approach is used e The range of poverty lines is 0 3000 2 Repeat with the dual approach 3 By using the files mex 98 2ml dta and mex 04 2ml dta test for absolute second order pro poorness with the dual approach 4 Using mex 98 2ml dta and mex 04 2ml dta estimate the pro poor indices of module ipropoor e Parameter alpha set to 1 e Poverty line equal to 600 Answer 0 1 Steps To open the relevant dialog box type db cpropoorp 121 Choose variables and parameters as in select the upper bounded option for the confidence interval Figure 62 Testing the pro poor growth primal approach ES DASP Pro poor curves primal approach gt cpropoorp command Data in file C Documents and Settingst raa Data in file ov C Documents and Settingst raa After clicking SUBMIT the following graph appears 122 Relative propoor curve o a Order s 1 Dif P_2 m2 m1 z a s 1 P 1 z a s 1 AAN A re ad Na Dl al te 2a J LO o LO T T T T T 1 0 600 1200 1800 2400 3000 Poverty line z Difference Upper bound of 95 confidence interval Null horizontal line Q 2 Steps To open the relevant dialog box type db cpropoord Choose variables and parameters as in with the lower bounded option for the
29. on secondary sector sec_sec_exp Total public expenditures on university sector uni_pub_exp Estimate the average benefits per quintile and generate the benefit variables Answer 129 Set variables and options as follows Figure 66 Benefit Incidence Analysis unit cost approach E DASP Benefit incidence analysis gt bian command Main Resuts Label the public service Education Variable s of interest Options Standard living Jexppe hd Approach Unit cost benefit bed Number of sectors 2 hd Labels Frequency Eligible HH members Area indicator Regional pub expenditures Sector 1 Primary fra prim v eLprim s v pri pub exp v Sector 2 Secondary fra sec el sec sec pub exp Cancel Submit E DASP Benefit incidence analysis gt bian command Main Results M Result options Number of Decimals 34 Social groups Quintiles 7 Group variable s Displayed results IV Share and rate of participation IV Average benefits IV Proportion of benefits Cancel Submit After clicking on Submit the following appears 130 Average Bonet its by Quintile Groups Cat the level of eligible nenbers Groups Sector Sector Quintile 1 24 002 128 548 Quintile 2 257 883 179 816 Quintile 3 250 306 166 119 Quintile 4 225 527 192 4 Quintile 5 157 82 143 27 All 227 061 166 15 Groups Sector
30. public primary school npubsec Number of household members in public secondary school npubuniv Number of household members in public post secondary school 22 1 5 Peru LSMS survey 1994 A sample of 3623 household observations PERU_A_I dta List of variables hhid Household Id exppc Total expenditures per capita constant June 1994 soles per year size Household size literate Number of literate household members pliterate literate size 22 1 6 The 1995 Colombia DHS survey columbial dta This sample is a part of the Data from the Demographic and Health Surveys Colombia 1995 witch contains the following information for children aged 0 59 months List of variables hid Household id haz height for age waz weight for age whz weight for height sprob survival probability wght sampling weight Asset asset index 22 1 7 The 1996 Dominican Republic DHS survey Dominican republic19961 dta This sample is a part of the Data from the Demographic and Health Surveys Republic Dominican 1996 witch contains the following information for children aged 0 59 months 66 List of variables hid Household id haz height for age waz weight for age whz weight for height sprob survival probability wght sampling weight Asset asset index 22 2 Appendix B labelling variables and values The following do file can be used to set labels for the variables in bkf94 dta For more details on the use of label command type help label in
31. stata con support updates stata9 ado The tuo folluing sub packages nust be installed to run DASP PACKAGES you could net descr ibe dasp pl Distributive Analysis Stata Package PART I dasp_p2 Distributive Analysis Stata Package PART II d Type the syntax net install dasp_p1 pkg force replace net install dasp_p2 pkg force replace net install dasp_p3 pkg force replace 3 2 Adding the DASP submenu to Stata s main menu With Stata 9 sub menus can be added to the menu item User Here 2 DASP submenu ics User Window Help Data b Graphics E statistics tu s d Inequality gt Polarization gt Copyr ight 1984 2008 paver gt StataCorp Y 4905 Lakenay Drive ordi gt College Station Texas 77845 USA o m 800 STATA PC http uuu stata con Poverty and targeting policies f979 696 4600 statalstata con Poverty elasticities gt 979 696 4601 fax Decomposition b FGT Decomposition by groups Dominance b FGT Decomposition by income sources Curves gt FGT Growth and redistribution Distributive tools b FGT Decomposition into transient and chronic components Benefit analysis gt Generalised entropy Decomposition by groups Disaggregating data Gini Decomposition by groups Gini Decomposition by income sources gt DER Decomposition by population groups DER Decomposition by income sources To add the DASP sub menus the file profile do which is provided with the DASP p
32. to make its interval between 0 and 1 when the parameter a 1 BPR Fa p B bo u afatn afr jel k l 29 15 DASP and decompositions 15 1 FGT Poverty decomposition by population subgroups dfgtg The dgfgt module decomposes the FGT poverty index by population subgroups This decomposition takes the form A Ga A P z a Z s P z a g g l where G is the number of population subgroups The results show The estimated FGT index of subgroup g Plz a The estimated population share of subgroup De The estimated absolute contribution of subgroup g to total poverty d g P z a g The estimated relative contribution of subgroup g to total poverty Hg Plz a g PG a An asymptotic standard error is provided for each of these statistics To open the dialog box for module dfgtg type db dfgtg in the command window Figure 8 Decomposition of the FGT index by groups E DASP Decomposiotion of the FGT Index by Groups gt dfgtg command S xi Main Results Variable of interest ji v i Type Not Normalised v Size variable v Group variable n M Index oplion s M Parameters Parameter alpha jo Poverty line 2 fi 0000 Survey settings 2 R Cancel Submit Note that the user can save results in Excel format Interested users are encouraged to consider the exercises that appear in Section 23 7 30 FGT Poverty decomposition b
33. users are encouraged to consider the exercises that appear in Section 23 2 14 10 3 DASP and multidimensional poverty indices imdpov The general form of an additive multidimensional poverty index is gt P X Z P X Z gt i l where p X Z is individual Is poverty function with vector of attributes X Pans iz and vector of poverty lines Z Zis ZJ determining s contribution to total poverty P X Z 1 Chakravarty et al 1998 index J a ZX PAD a u j l IOM 2 Extended Watts index J z P X Z a In jal min z X 3 Multiplicative extended FGT index PEN m Ze j l j A 4 Tsui 2002 index b J z j PD i ja Min X 5 Intersection headcount index J p X Z an j l 6 Union headcount index J p X Z 1 z lt x j l 15 7 Bourguignon and Chakravarty bi dimensional 2003 index Wr P X Z C BPC y 4 Z7 Xil Z2 7X2 o and C ee Z1 Z2 i imdpov estimates the above multidimensional poverty indices as well as their standard errors where The user can select among the seven multidimensional poverty indices The number of dimensions can be selected 1 to 6 If applicable the user can choose parameter values relevant to a chosen index A group variable can be used to estimate the selected index at the level of a categorical group Standard errors and confidence intervals with a confidence level of 95 are p
34. when incomes of the complement group are preplaced by u k I denotes the Gini index Araar Abdelkrim and Jean Yves Duclos 2007 Poverty and inequality components a_micro framework Working Paper 07 35 CIRPEE Department of Economics Universit Laval 19 Kakwani N 1993 Poverty and economic growth with application to C te D Ivoire Review of Income and Wealth 39 2 121 139 To estimate FGT elasticity s with respect average income growth the group or the whole population The user can select more than one variable of interest simultaneously For example one can estimate poverty by using simultaneously per capita consumption and per capita income A group variable can be used to estimate poverty at the level of a categorical group If a group variable is selected only the first variable of interest is then used Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 12 3 FGT elasticities with respect to within between group components of inequality efgtg This module estimates the marginal FGT impact and FGT elasticity with respect to within between group components of inequality A group variable must be provided This module is mostly based on Araar and Duclos 2007 Araar Abdelkrim and Jean Yves Duclos 2007
35. 000 spread equally across all percentiles F 0 001 0 002 0 999 1 To avoid the value F 1 for the last generated observation we can simply replace F by F 0 5 NOBS gt For NOBS 2800 B_NOBS 1000 and T_NOBS 1000 with the bottom and top groups being the first and last deciles a F 0 0001 0 0002 0 0999 0 1000 in 0001 1000 b F 0 1010 0 1020 0 8990 0 9000 in 1001 1800 c F 0 9001 0 9002 0 9999 1 0000 in 1801 2800 Adjustments can also be made to avoid the case of F 1 1 The weight vector can easily be generated S12 Generating an initial distribution of incomes The user must indicate the form of distribution of the desegregated data Normal and log normal distributions Assume that x follows a lognormal distribution with mean y and variance o the Lorenz curve is defined as follows upo Bene dene o a oO oO We assume that u 1 and we estimate the variance using the procedure suggested by Shorrrocks and Wan 2008 a value for the standard deviation of log incomes o is obtained by averaging the m 1 estimates of o 0 p 0 L p k 1 m 1 where m is the number of classes and is the standard normal distribution function Aitchison and Brown 1957 Kolenikov and Shorrocks 2005 Appendix Generalized Quadratic Lorenz Curve It is assumed that L I L a p L bL p 1 c p L We can regress L I L on p L L p 1 and p L without an intercept dropping the
36. 10 Household size hheize Sanpling weight uveightea Sources Incore Absolute Relat ive Share Contribution Contribution z sourced z source z sourced z sourced z sourced z ource 32 sourcel f 0 022837 0 022328 d source D M 0 04 0 15221 source3 0 001848 0 00193 0 001988 4 sourced 0 0559 0 05661 0 054 5 sourceS 0 001297 0 001494 0 001597 sourceb 0 003113 0 003378 0 003506 level 6 sourcel sourced source3 d sourced 5 source5 source JN 15 2 F GT Poverty decomposition by income components using the Shapley value dfgts The dfgts module decomposes the total alleviation of FGT poverty into a sum of the contributions generated by separate income components Total alleviation is maximal when all individuals have an income greater than or egual to the poverty line A negative sign on a decomposition term indicates that an income component reduces poverty Assume that there exist K income sources and that s denotes income source k The FGT index is defined as n a a K an 7 P say 2 r A wi i l where w is the weight assigned to individual 7 and n is sample size The dfgts Stata module estimates The share in total income of each income source k The absolute contribution of each source k to the value of P 1 The relative contribution of each source k to the value of P 1 Note that the df
37. 525 0 144 0 14358 0 011808 0 014896 0 002459 Farners food 0 16204 OG 0 1101 0 008843 0 016403 0 005823 Inactive 0 144916 0 075956 OH 0 014994 0 004839 0 001332 0 006520 POPULATION 0 139197 1 000 0 13919 0 006553 0 000000 0 006553 0 000000 Q 2 Using the RESULTS panel change the number of decimals and unselect the option DISPLAY STANDARD ERRORS After clicking SUBMIT the following information is obtained dfgtg exppc hgrouplgsel hzizelzizel alphalil plinel 41099 detd 0 typelnorl decid FGT Index Deconposition by Groups Group FGT Index Populat ion Absolute Relat ive Share Contribution Contribution uage earning public sector uage sarning private sector Artisan or trading Others activities Farners crop Farners food Inactive Z R5888 M2 DG Mi NH n np m1 130 POPULATION mm M mou m 98 23 8 Estimating Lorenz and concentration curves How much do taxes and transfers affect inequality in Canada By using the can6 dta file 1 Draw the Lorenz curves for gross income X and net income N How can you see the redistribution of income 2 Draw Lorenz curves for gross income X and concentration curves for each of the three transfers B1 B2 and B3 and the tax T What can you say about the progressivity of these elements of the tax and transfer system What is the extent of inequality among Burkina Faso rural and urban households in 1994 By using the b
38. C Line gap T Inside plot region T Inside plot region T Span width of graph T Span width of graph T Box T Box Fill color Defaut z Fill calor Default z Line color Defaut 7 Line color Defaut z Margin z Margin z I Ignore text size ji Ignore tert size After clicking SUBMIT the following graph appears 84 Figure 28 Graph of FGT curves 5 Graph Graph lnx FGT Curves alpha 0 Burkina 1994 FGT z alpha 0 80000 100000 85 Q 4 Choose variables and parameters as in the following window Figure 29 FGT curves by zone EE DASP FGT Curves gt cfgt command Fe AH After clicking SUBMIT the following graph appears 86 Figure 30 Graph of FGT curves by zone 5 Graph Graph 2 5 x FGT Curves alpha 0 Burkina 1994 6 8 FGT z alpha 0 4 0 20000 s0000 100000 87 Choose the option DIFFERENCE and select WITH THE FIRST CURVE Indicate that the group variable is zone Select the Results panel and choose the option LIST in the COORDINATES quadrant In the GRAPH quadrant select the directory in which to save the graph in gph format and to export the graph in wmf format Figure 31 Differences of FGT curves EE DASP FGT Curves gt cfgt command 88 Figure 32 Listing coordinates E DASP FGT Curves gt cfgt command C Stata_graphs graph1
39. Figure 13 Lorenz and concentration curves E DASP Lorenz amp Concentration Curves gt clorenz command 101 x Main Results Y Axis X Ais Title Caption Legend Overall Variable s of interest Type of curve s T Type Mormalised by default T Ranking Variable v T Difference No v Size variable v T Range of percentiles p Group variable S Minimum Maximum o 0 fi 0 20 Cancel Submit Interested users are encouraged to consider the exercises that appear in Section 23 8 16 5 Lorenz concentration curves with confidence intervals clorenzs The clorenzs module draws a Lorenz concentration curve and its confidence interval by taking sampling design into account The module can 44 draw a Lorenz concentration curve and two sided lower bounded or upper bounded confidence intervals condition the estimation on a population subgroup draw Lorenz concentration curves and generalized Lorenz concentration curves list or save the coordinates of the curves and their confidence interval save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs 16 6 Differences between Lorenz concentration curves with confidence interval clorenzs2d T
40. Jv Conditions 2 x IV Conditions 2 x Condition 1 fzone fee ooo Condition 1 fzone 2 O AND Condition 2 fsex O AND Condition 2 fsex O Parameters and Options Parameter alpha fo Type Normalised x Cancel Submit After clicking on SUBMIT the following should be displayed Poverty Index FGT Index Faraneter alpha 0 00 Est inate ST LE WE F Line Distribution 1 0 17734 0 017701 0 137590 0 207179 41099 00 Distribut ion_2 0 10699 0 01306 0 070533 0 13345 41099 00 Difference 0 066388 0 022534 0 022222 0 110553 Q 6 79 We have that Lower Bound 0 0222 Upper Bound 0 1105 The null hypothesis is rejected since the lower bound of the 95 confidence interval is above zero 23 3 Estimating multidimensional poverty indices How much is bi dimensional poverty total expenditures and literacy in Peru in 1994 Using the peru94Ldta file 1 Estimate the Chakravarty et al 1998 index with parameter alpha 1 and Var of interest Pov line aj Dimension 1 exppc 400 1 Dimension 2 pliterate 0 90 1 2 Estimate the Bourguignon and Chakravarty 2003 index with parameters alpha beta gamma 1 and Var of interest Pov line Dimension 1 exppc 400 Dimension 2 literate 0 90 Q 1 Steps Type use C data peru94I dta clear To open the relevant dialog box type db imdpov Choose variables and parameters
41. PEE Department of Economics Universit Laval To open the dialog box of this module type the command db efgtc 21 EE DASP FGT Poverty elasticities with respect to income sources inequalities gt efgtc command sourcel sourceB After clicking on SUBMIT the following should be displayed efgtc sourcel source6 tot income hsize hhsize alpha 0 pline 14897 prc l Poverty and Inequality Indices Marginal Impacts Elasticities of poverty with respect to the within between inequality in income components 0 385605 0 537610 n k 0 211784 0 311798 0 171358 0 180533 In case one is interested in changing some income component only among those individuals that are effectively active in some economic sectors schemes nk T and A in the paper mentioned above the user should select the approach Truncated income component 22 13 DASP and inequality indices 13 1 Gini and concentration indices igini The Gini index is estimated as EEA u where 2 2 k V V n y a Yi and V Da Wy and Y2Y22 Yn 2Yn i l v h i The concentration index for the variable T when the ranking variable is Y is estimated as ICr 1 Sr HT where Ly is the average of variable T MP2 l amp gt Al WP n l n and where V gt wp and Yi5V5 gt Yn 1 gt Yn h i The user can select more than one variable of interest simultaneously For example one can estim
42. Poverty and inequality components a_micro framework Working Paper 07 35 CIRPEE Department of Economics Universit Laval To open the dialog box of this module type the command db efgtg E DASP FGT Poverty elasticities with respect to population group inequalities gt efgtg command i Sj je xj Main Results Parameters Variable of interest income v s Parameter alpha fo Size variable hhsize Poverty line 2 h 4997 Group variable zone Fercentage of change 10d Survey settings Cancel Submit After clicking on SUBMIT the following should be displayed 20 efgtg income hgroup zone hsize hhsize alpha 0 pline 14897 prc l dec 3 Poverty and Inequality Indices anaices Estimate Marginal Impact Elasticities By Groups Population Marginal Marginal Elasticity Share Impact on Ineq Impact on Pov South south South east o g South west North central North east North west E ele 12 4 FGT elasticities with respect to within between income components of inequality efgtc This module estimates the marginal FGT impact and FGT elasticity with respect to within between income components of inequality A list of income components must be provided This module is mostly based on Araar and Duclos 2007 Araar Abdelkrim and Jean Yves Duclos 2007 Poverty and inequality components a_micro framework Working Paper 07 35 CIR
43. TINSON eiere ereraa aiai a beda dada 25 13 6 Difference between Atkinson indices diatkinson ssssesessssssessssssessesssssresseeseese 25 13 7 Ouantile share ratio indices of inequality inineg sssessseessesssssesssessrsseesseesees 26 13 8 Difference between Ouantile Share indices dinineg ee 26 14 DASP and polarization indices sx lt sassccosegescvs das sevecodeceneccuapuseadeaang daavcvistadevasevapeaeiedeenzetsa 26 14 1 The DER index poli 34s zasade ian tao wie esi a a aA 26 14 2 Difference between DER polarization indices dipolar ee 27 14 3 The Foster and Wolfson 1992 polarization index ipolfW 28 14 4 Difference between Foster and Wolfson 1992 polarization indices dipolfw 28 14 5 The Generalised Esteban Gardin and Ray 1999 polarisation index ipoger 28 15 DASP and CECOMPOSICIONS zv su ches s ti eo cda S nudn des du cana r ta edeng Abs dade ca tadend cava feaeca beans cand 30 15 1 FGT Poverty decomposition by population subgroups dfgtg ce eeeeeeeeees 30 FGT Poverty decomposition by income components using the Shapley value dfgts 31 15 2 F GT Poverty decomposition by income components using the Shapley value dfgts 33 15 3 Decomposition of the variation in FGT indices into growth and redistribution COMMOMCTIES CEST SE ss 12055 adresa dana achat o deodbatn ab bota hooodn 35 15 4 Decomposition of FGT poverty by transient
44. USER MANUAL DASP version 2 0 DASP Distributive Analysis Stata Package By Abdelkrim Araar Jean Yves Duclos Universit Laval PEP CIRPEE and World Bank June 2009 Table of contents Table Of cont ntS is iania iea oK RT OaE AEE NOAR EE KERETE REA REAT ETA Te 2 Listof FIgUTE Senan a a aaa aaa aa aaaea ia aiis 5 t introduction oia e a E E Goa iro beg E oo E ono ooo ciate 7 Z DASP and Stata NCTSIONG iiir iseis sors innies nas ri KAK REES K R a VESKER ia os s 3 Installing and updating the DASP package ccesccesecesesseeeseeseeeseceaecueecseeeseeeeeeaeenaeenaeeaee 8 ork installing DASR m0 dtl Ose nnen a oo obr ooo ace 8 3 2 Adding the DASP submenu to Stata s main menu ooo eee een 9 A DASP and data fil s nisinsin seisin siirroissa s R Essare Tisa RAES anA Taat 9 5 Main variables for distributive analysis 0 cececccecsceceseceeeceeeeeeseecaeceeeeeeeenseecsaeenteeneees 10 6 How can DASP commands be invoked cs ycssicuscgsicesaicsaceusssseteses s n ease tances sis dodan a ee iecaeeess 10 7 How can help be accessed for a given DASP Module eee 11 oe Applhcations and filesin DASP riec tiai a a O E as SAR TEE Caia iiae 11 9 Basic Notation onari ne a a ad wp Sterns Bs Ss Sa e aiaa dead Sadu ode os a Sean es 13 10 DASP and poverty indices lt 5 in ciecssccstiahseiedeskevnddpssanceass stengeydpate oar Skoda oki henna oaRM antes 13 10 1 FGT and EDE FGT poverty indices ifgU e eee 13 10 2 Dif
45. a or data with the same path and filename for the two distributions 2 Ifthe option DATA IN FILE is chosen the keyboard must be used to type the name of the required variables 9 Basic Notation The following table presents the basic notation used in DASP s user manual Symbol Indication y variable of interest i observation number Ji value of the variable of interest for observation i hw sampling weight hw sampling weight for observation i hs size variable hsi size of observation i for example the size of household i Wi hwi hs hg group variable hgi group of observation i wi swik sw if hg k and 0 otherwise n sample size For example the mean of y is estimated by DASP as 1 10 DASP and poverty indices 10 1 FGT and EDE FGT poverty indices ifgt The non normalised Foster Greer Thorbecke or FGT index is estimated as n i Zw z n P za j F n ZW i where z is the poverty line and x max x 0 The usual normalised FGT index is estimated as Plz a Plc a z 13 The EDE FGT index is estimated as l a for a gt 0 EDE P z a Pe a There exist three ways of fixing the poverty line 1 Setting a deterministic poverty line 2 Setting the poverty line to a proportion of the mean 3 Setting the poverty line to a proportion of a quantile Q p The user can choose the value of parameter a The user can select more than one variable of interest si
46. ackage must be copied into the PERSONAL directory If the file profile do already exists add the contents of the DASP provided profile do file into that existing file and save it To check if the file profile do already exists type the command findfile profile do 4 DASP and data files DASP makes it possible to use simultaneously more than one data file The user should however initialize each data file before using it with DASP This initialization is done by 1 Labeling variables and values for categorical variables 2 Initializing the sampling design with the command svyset 3 Saving the initialized data file Users are recommended to consult appendices A B and C 5 Main variables for distributive analysis VARIABLE OF INTEREST This is the variable that usually captures living standards It can represent for instance income per capita expenditures per adult equivalent calorie intake normalized height for age scores for children or household wealth SIZE VARIABLE This refers to the ethical or physical size of the observation For the computation of many statistics we will indeed wish to take into account how many relevant individuals or statistical units are found in a given observation GROUP VARIABLE This should be used in combination with GROUP NUMBER It is often useful to focus one s analysis on some population subgroup We might for example wish to estimate poverty within a country s rural a
47. ade Density Kernel Estimate Statistics and probability Letters 16 397 405 e Silverman B W 1986 Density for Statistics and Data Analysis London Chapman and Hall p 30 18 4 Non parametric regression curves cnpe Non parametric regression is useful to show the link between two variables without specifying beforehand a functional form It can also be used to estimate the local derivative of the first variable with respect to the second without having to specify the functional form linking them Regressions with the cnpe module can be performed with one of the following two approaches 18 4 1 Nadaraya Watson approach A Gaussian kernel regression of y on x is given by DW K X Y E y x y x wK D From this the derivative of y x with respect to x is given by 2 x 2 Lelu The local linear approach is based on a local OLS estimation of the following functional form 18 4 2 Local linear approach K y MOK A DKA x X or alternatively of K x y aK 0 BK y x x v Estimates are then given by 51 7 dy _ E y x e 2 B Interested users are encouraged to consider the exercises that appear in Section 23 10 18 5 DASP and joint density functions The module sjdensity can be used to draw a joint density surface The Gaussian kernel estimator of the joint density function f x y is defined as 2 2 A n X X LV ene ee e 2nh hy 5 wi X y i l With this module
48. ally recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs Consumption dominance curves cdomc Consumption dominance curves are useful tools for studying the impact of indirect tax fiscal reforms on poverty The j th Commodity or Component dominance C Dominance for short curve is defined as follows lt s 2 j x w Z Yj yi if s22 CD z 5 wi K z yi yf E yly z no if s 1 n i l where K is a kernel function and y is the si commodity Dominance of order s is checked by setting a s 1 The cdomc module draws such curves easily The module can draw more than one CD curve simultaneously whenever more than one component is selected draw the CD curves with confidence intervals estimate the impact of change in price of a given component on FGT index CD curve for a specified poverty line draw the normalized CD curves by the average of the component list or save the coordinates of the curves save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs To open the dialog box of the module cdomc type the command db cdomc in the
49. an6 dta clear To open the relevant dialog box type db cdensity Choose variables and parameters as in Figure 51 Drawing densities J DASP Density Curves gt cdensity command In x Main Resuts Axis X Ais Title Caption Legend Overall r Variable s of interest M Parameters xN v Minimum Maximum Range fo 60000 Size variable JV Override optimal bandwidth Group variable Bandwidth of 1 0 20 Cancel Submit 109 After clicking SUBMIT the following appears Figure 52 Density curves Density Curves 00002 00003 00004 00005 00001 0 Q 2 Steps To open the relevant dialog box type db c_quantile Choose variables and parameters as in 110 Figure 53 Drawing quantile curves E DASP Quantile amp Normalised Curves gt c_quantile command After clicking SUBMIT the following appears Figure 54 Quantile curves Quantile Curves T 111 Q 3 Steps To open the relevant dialog box type db cnpe Choose variables and parameters as in Figure 55 Drawing non parametric regression curves E DASP Non parametric regression gt cnpe command Local linear approach B After clicking SUBMIT the following appears 112 Figure 56 Non parametric regression curves Q 4 Steps Non parametric regress
50. and chronic poverty components ALEDOV a zac aa hezka baloo neces dans aden aa Sao ods T dua diucseauthcan 3 ara is baz 8 36 15 5 Inequality decomposition by income sources diginis ee 38 15 6 Gini index decomposition by population subgroups diginig cece eeeeeees 40 15 7 Generalized entropy indices of inequality decomposition by population SUBS ROU IS GSE PODYB so atu zadu ten a genre Sao db B Jehuda neo 40 15 8 Polarization decomposition of the DER index by population groups dpolag 40 15 9 Polarization decomposition of the DER index by income sources dpolas 41 16 DASP and CUPVES ps csccdiscedsayesuesa kuk tona gkod k sko coctissatecavasteiasa KAS SCA EKAA EET a TEE Ena Esana 42 16 1 EGT CURVES CPL casi tices baze o dd secant caueie sateen tues bob E oo ho o N 42 16 2 FGT CURVE with confidence interval C StS eee eee 43 16 3 Difference between FGT CURVES with confidence interval cfgts2d 43 16 4 Lorenz and concentration CURVES clorenz een 43 16 5 Lorenz concentration curves with confidence intervals clorenzs 44 16 6 Differences between Lorenz concentration curves with confidence interval LOIS A Isaak oko eo oa o oo ooo o o ooo a oo Roo 45 16 7 Poverty curves CDOVERCY mis orrara anans aa dd aE ERT OO da a O anaes 45 16 8 Consumption dominance curves cdomc essssessesessssesseserssressessessressess
51. ariables for each sector Possibility of computing statistics according to groups of observations o Generation of statistics according to social demographic groups such as quartiles quintiles or deciles o Generally public expenditures on a given service can vary from one geographical or administrative area to another When the information about public expenditures is available at the level of areas this information can be used with the bian module to estimate unit cost more accurately Example 1 Observationi HH Eligible HH Frequency Area indicator Total level of size members regional public expenditures 1 7 3 2 1 14000 2 4 2 2 1 14000 3 5 5 3 1 14000 4 6 3 2 2 12000 5 4 2 1 2 12000 In this example the first observation contains information on household 1 e This household contains 7 individuals e Three individuals in this household are eligible to the public service e Only 2 among the 3 eligible individuals benefit from the public service e This household lives in area 1 In this area the government spends a total of 14000 to provide the public service for the 7 users of this area 2 2 3 The unit cost in area 1 equals 14000 7 2000 The unit cost in area 2 equals 12000 3 4000 By default the area indicator is set to 1 for all households When this default is used the variable Regional public expenditures the fifth column that appears in the dialog box should be set to total public expenditures at the national leve
52. ate inequality for instance by using simultaneously per capita consumption and per capita income To estimate a concentration index the user must select a ranking variable A group variable can be used to estimate inequality at the level of a categorical group Ifa group variable is selected only the first variable of interest is then used Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed Interested users are encouraged to consider the exercises that appear in Section 23 9 13 2 Difference between Gini concentration indices digini This module estimates differences between the Gini concentration indices of two distributions For each of the two distributions a One variable of interest should be selected To estimate a concentration index a ranking variable must be selected Conditions can be specified to focus on specific population subgroups 23 Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 13 3 Generalised entropy index ientropy The generalized entropy index is estimated as 1 P yvi Z 1 if 60 1 6 1 w i
53. cap b parameter a 0 c poverty line between 0 and 100 000 Franc CFA d size variable set to size 5 Draw the difference between these two curves and a save the graph in gph format to be plotted in Stata and in wmf format to be inserted in a Word document b List the coordinates of the graph 6 Redo the last graph witha 1 Answers Q 1 Open the file with use C data bkf941 dta clear 0 2 Open the dialog box by typing db difgt 0 3 Choose variables and parameters as follows 83 Figure 26 Drawing FGT curves B DASP FGT Curves gt cfgt command Main Resuts Y Axis XAxis Title Caption Legend Overall Variable s of interest Type of curvefs exppc expeq T Type Normalised z I Difference No v Size variable size Group variable Parameters Parameter alpha fo Minimum Maximum Poverty line z jo fi 00000 Cancel Submit To change the subtitle select the Title panel and write the subtitle Figure 27 Editing FGT curves E DASP FGT Curves gt cfgt command Main Results Y Axis X Axis Title Caption Legend Overall Title Subtitle Po Oaa So Size Defaut Justify beat x Size Defaut Justify Defaut x Color Defaut x Alignment beat Color Defaut Alignment EEC Position Defaut Margin o Position Defaut CZ Margin H Orientation Defaut z Line gap l Orientation EE
54. ch of the two distributions One variable of interest should be selected Conditions can be specified such as to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 14 5 The Generalised Esteban Gardin and Ray 1999 polarisation index ipoger The proposed measurement of polarisation by Esteban and Ray 1994 is defined as follows P f a X gt pi plej be jal k l 28 where u and p denote respectively the average income and the population share of group j The parameter a 11 6 reflelcs sensitivity of the society to polarisation The first step for the estimation reguires to define the exhaustive and mutually exclusive groups p This will involve some degree of error However as this grouping will generate some loss of information depending on the degree of income dispersion in each of the groups con sidered Taking into account this idea the measure of generalised polarisation proposed by Esteban et al 1999 is obtained after correcting the P a index applied to the simplified representation of the original distribution with a measure of the grouping error Nonetheless when dealing with personal or spatial income distributions there are no unanimous criteria for establishin
55. d their two sided lower bounded or upper bounded confidence intervals listor save the coordinates of the differences between the curves as well as those of the confidence intervals save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs Interested users are encouraged to consider the exercises that appear in Section 23 13 19 2 2 Dual pro poor curves Let Q p quantile at percentile p GL p Generalised Lorenz curve at percentile p U average living standards The change in the distribution from state 1 to state 2 is first order absolutely pro poor with standard cons 0 if A z s Q p O p gt 0V p e 0 p F z or equivalently if O p Q p ee Q p l gt 0 v pel 0 p F z The change in the distribution from state 1 to state 2 is first order relatively pro poor if 54 _Q p 4 Pr BY AG Fy gg oP SLOP F z The change in the distribution from state 1 to state 2 is second order absolutely pro poor if A z 8 GL p GL p gt 0 V p e 0 p F z or equivalently if _ GLy p GL p eo gt 0Vpe 0 p F z The change in the distribution from state 1 to state 2 is first order relatively pro poor if _GL p u se fo ass AD OY PE LOP F z The mo
56. dule cpropoord can be used to draw these dual pro poor curves and their associated confidence interval by taking into account sampling design The module can draw pro poor curves and their two sided lower bounded or upper bounded confidence intervals listor save the coordinates of the differences between the curves as well as those of the confidence intervals save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs Interested users are encouraged to consider the exercises that appear in Section 23 13 20 DASP and Benefit Incidence Analysis 20 1 Benefit incidence analysis The main objective of using a benefit incidence approach is to analyse the distribution of benefits from the use of public services according to the distribution of living standards Two main sources of information are used The first informs on the access of household members to public services This information can be found in the usual household surveys The second deals with the amount of total public expenditures on each public service This information is usually available at the national level and sometimes in a more disaggregated format such as at the regional level The benefit incidence approach combines the use of these two sources of infor
57. e available to change the appearance of the graphs Interested users are encouraged to consider the exercises that appear in Section 23 5 Lorenz and concentration CURVES clorenz Lorenz and concentration curves are useful distributive tools that can inter alia be used to Pech gt show the level of inequality test for inequality dominance between two distributions test for welfare dominance between two distributions test for progressivity The clorenz module draws Lorenz and concentration curves simultaneously The module can 43 draw more than one Lorenz or concentration curve simultaneously whenever more than one variable of interest is selected draw more than one generalized or absolute Lorenz or concentration curve simultaneously whenever more than one variable of interest is selected draw more than one deficit share curve draw Lorenz and concentration curves for different population subgroups whenever a group variable is selected draw differences between Lorenz and concentration curves list or save the coordinates of the curves save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs To open the dialog box of the module clorenz type the command db clorenz in the command window
58. ed in Section 22 3 or simply by typing svyset psu pweight weight strata strata vce linearized Typing svydes we obtain Survey Describing stage 1 sanpling units pueight weight WE linearized Strata 1 strata SU 1 psu FPC 1 dzerot Hibs per Unit Stratun hits Hibs Hin Haan Hay F B B 0 3 Type bd ifgt to open the dialog box for the FGT poverty index and choose variables and parameters as indicated in the following window Click on SUBMIT 71 Figure 18 Estimating FGT indices E DASP FGT and EDE FGT Index gt ifgt command The following results should then be displayed ifgt exppc expeg alphalO hzizelsizel plinel 41099 Poverty Index FGT Index Household size size Sanpling weight weight Paraneter alpha 0 00 War iab le Est inate ST LE UB BHD 0445 0 046124 0 412873 0 470256 ekipe 0 2540 WH 1 270006 0 281592 Q 4 Select RELATIVE for the poverty line and set the other parameters as above 12 F Line 41099 00 41099 00 Figure 19 Estimating FGT indices with relative poverty lines E DASP FGT and EDE FGT Index gt ifgt command After clicking on SUBMIT the following results should be displayed ifgt exppe alphalO heizelsize opl nedian propl li Poverty Index FGT Index Household size size anpling weight weight Faraneter alpha 0 00 Variable Est inate 1 LE IE epp 0 16243 DME 0 108386 12
59. entile 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 n observations of living standards be ordered such that VSI SS S Yia Se Sy E FO lt psF y we define O p y The normalised quantile is defined as O p Q p u Interested users are encouraged to consider the exercises that appear in Section 23 10 18 2 Income share and cumulative income share by group quantiles quinsh This module can be used to estimate the income shares as well as the cumulative income shares by quantile groups The user can indicate the number of group partition For instance if the number is five the quintile income shares are provided We can also plot the graph bar of the estimated income shares 18 3 Density curves cdensity The Gaussian kernel estimator of a density function f x is defined by 49 Fee ee and K x l a i l exp 0 5 A x and A x where h is a bandwidth that acts as a smoothing parameter Interested users are encouraged to consider the exercises that appear in Section 23 10 Boundary bias correction 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 i
60. es a p quantile and p and pp are percentiles The share ratio is estimated as GL p2 GL p1 GL p4 GL p3 SR p1 p2 p3 p4 where GL p is the Generalised Lorenz curve and py p2 p3 and p4 are percentiles The user can select more than one variable of interest simultaneously For example one can estimate inequality simultaneously for per capita consumption and for per capita income A group variable can be used to estimate inequality at the level of a categorical group Ifa group variable is selected only the first variable of interest is then used Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 13 8 Difference between Quantile Share indices dinineq This module estimates differences between the Quantile Share indices of two distributions For each of the two distributions a One variable of interest should be selected Conditions can be specified to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 14 DASP and polarization indices 14 1 The DER index ipolder The Duclos Esteban and Ra
61. essresseeseese 46 16 9 Differences consumption dominance curves with confidence interval cdomc2d 47 17 Dominance se 205 ai sas e a e e A a a a Aea i ended 47 17 1 Poverty dominance dompoV sssssssessssssessessrsseesseesssresseesesesseessessesseessessrssressesse 47 17 2 Inequality dominance domineq sssesssssesssssesessesseseessssersessestesesseseessesersesseseesessese 48 17 3 DASP and bi dimensional poverty dominance dombdpov 48 18 Distributive tools inercias akana aii ia iai aR aaa 49 18 1 Ouantile curves Came Jazz osu ad k v e aa v cava onde dm n 49 18 2 Income share and cumulative income share by group quantiles guinsh 49 18 3 Density Curves cdensity sizes 5koa entada byo eedo pokus abaikoki von P s ded n ok Pe n aera 49 18 4 Non parametric regression curves CNPE cee eeecceeseeeseeceeceeeceeeeeeseeceueceeeeeeeenseees 51 18 4 1 Nadaraya Watson approach cece 056 ckivadesares blab ale dass odd Ska eno Mendel oeintee sats 51 18 42 Local near Gp progenies ccc0 55 asus SSV hist ta ys aati wader Sea Tae 51 18 5 DASP and joint density Unctons 3dad ba btodus saab vata ceed eodandnvsaccrepestanbneni eins 52 18 6 DASP and joint distribution functions z 52 19 DASP and pro poor STO WA sare eee ies ae a rae ao oe a ew SO 53 191 DASP andpro poorindices sz ainndusvancyu nese divaavaccacorand aviaaenevacdawace esse te n 53 19 2 DASP and pro poor CUTVeS e sssseseesessesessse
62. ference between FGT indices difgt eee 14 10 3 DASP and multidimensional poverty indices iIMAPOV eee 15 11 DASP poverty and targeting DOHCIES c2isdiccincsis naseedonctadassqeavandsans cade rinesbansvaes naval asy 16 11 1 Poverty and targeting by population groups eee 16 11 2 Poverty and targeting by income components eee 17 12 Marginal poverty impacts and poverty elasticities ee eeeeeeseeceseceecneeeeeeeeeeeeaees 18 12 1 FGT elasticity s with respect to the average income growth efgtgr 18 12 2 FGT elasticity s with respect to Gini inequality efgtineg ee 19 12 3 FGT elasticities with respect to within between group components of inequality GE Jeho Soon va veins pa atlas oa botnets O Da o C EEA 20 12 4 FGT elasticities with respect to within between income components of inequality efote ha Arto aea dicen sd olea obal s Ak tb tt NA So tana ie outa dol G bony 21 13 DASP and inequality indices sss ss la ose n dobude Sed aus n co ds bd sss dd ads K bed bk dns ena 23 13 1 Gini and concentration indices igini ssesesseesessseessesessseseesersseessessrssressessessresseese 23 13 2 Difference between Gini concentration indices digini 2 0 0 0 eee ee 23 13 3 Generalised entropy index ientropy sssessessssessesessssesseserssressessrssressessrssresseesees 24 13 4 Difference between generalized entropy indices diengtropy 24 13 5 Atkinson index TA
63. g the precise demarcation between different groups To address this problem Esteban et al 1999 follow the methodology proposed by Aghevli and Mehran 1981 and Davies and Shorrocks 1989 in order to find the optimal partition of the distribution in a given number of groups p This means selecting the partition that minimises the Gini index value of within group ineguality Error G f G p see Esteban et al 1999 The measure of generalised polarisation proposed by Esteban et al 1999 therefore is given by PPR a p p V pp lu 1 B G f G p jel k l where B20 is a parameter that informs about the assigned weight to the error term In the study of Esteban et al 1999 the used value where 1 The Stata module ipoegr ado estimates the generalised form of the Esteban et al 1999 polarisation index In addition to the usual variables that the user can indicate this routine offers to the user three following options 1 The number of groups Empirical studies use two or three groups The user can select the number of groups According to this number the program seeks for the optimal income interval for each group and displays them It also displays the error in percentage ie G f G p G f 2 The parameter a 100 3 The parameter To respect the scale invariance principle we divide beforehand all incomes by the average income i e 4 u In addition we divide the index by the scalar 2
64. gph C Stata_graphs graph1 wmf 89 After clicking SUBMIT the following appears Figure 33 Differences between FGT curves t Graph Graph Difference Between FGT Curves alpha 0 Burkina 1994 2 Differences 3 0 20000 0000 80000 100000 40000 B Foverty line z Null Horizontal Line FGT_Urban FGT_Rural Q 6 90 Figure 34 Differences between FGT curves ioi Difference Between FGT Curves alpha 1 Burkina 1994 wo W o c M on Sig me o 2 lt o u a n t 0 20000 40000 _ 60000 80000 100000 Foverty line z Null Horizontal Line FGT_Urban FGT_Rural 23 5 Estimating FGT curves and differences between FGT curves with confidence intervals Is the poverty increase between 1994 and 1998 in Burkina Faso statistically significant 1 Using the file bkf94I dta draw the FGT curve and its confidence interval for the variable of interest exppc with a parameter a 0 b poverty line between 0 and 100 000 Franc CFA c size variable set to size 2 Using simultaneously the files bkf94I dta and bkf98I dta draw the difference between FGT curves and associated confidence intervals with a The variable of interest exppc for 1994 and exppcz for 1998 b parameter a 0 c poverty line between 0 and 100 000 Franc CFA d size variable set to size 3 Redo 2 with parametera 1 Answers 0 1 91
65. gts ado file requires the module shapar ado which is programmed to perform decompositions using the Shapley value algorithm developed by Araar and Duclos 2008 e Araar A and Duclos J Y 2008 An algorithm for computing the Shapley Value PEP and CIRPEE Tech Note Novembre 2008 http 132 203 59 36 DAD pdf files shap dec aj pd 33 Empirical illustration with the Nigerian household survey We use a survey of Nigerian households NLSS using 17764 observations carried out between September 2003 and August 2004 to illustrate the use of the dfgts module We use per capita total household income as a measure of individual living standards Household observations are weighted by household size and sampling weights to assess poverty over all individuals The six main income components are source_1 Employment income source_2 Agricultural income source_3 Fish processing income source_4 Non farm business income source_5 Remittances received source_6 All other income The Stata data file is saved after initializing its sampling design with the command svyset To open the dialog box for module dfgts type db dfgts in the command window Figure 9 Decomposition of FGT by income components E Decomposition of the FGT index by income components using the Shapley value gt dfgts command In x Main Results Variable s of interest Parameters source sourceb Parameter alpha jo Poverty li
66. he clorenz2d module draws differences between Lorenz concentration curves and their associated confidence intervals by taking sampling design into account The module can draw differences between Lorenz concentration curves and associated two sided lower bounded or upper bounded confidence intervals list or save the coordinates of the differences and their confidence intervals save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs 16 7 Poverty curves cpoverty The cpoverty module draws the poverty gap or the cumulative poverty gap curves o The poverty gap ata percentile p is G p z z Q p o The cumulative poverty gap at a percentile p noted by CPG p z is given by X w y 10 lt OCP CPG p z TM The module can thus draw more than one poverty gap or cumulative poverty gap curves simultaneously whenever more than one variable of interest is selected draw poverty gap or cumulative poverty gap curves for different population subgroups whenever a group variable is selected 45 draw differences between poverty gap or cumulative poverty gap curves list or save the coordinates of the curves save the graphs in different formats o gph Stata format o wmf typic
67. he name of the relevant DASP module Example help ifgt Figure 4 Accessing help on DASP Viewer 2 help ifgt O Back Refresh Search Help Contents What s New News Command help ifgt d j DASP Distributive Analysis Stata Package World Bank PEP and CIRPEE help for ifgt Dialog box ifgt FGT Poverty Indices ifgt varivst HSize varname HGroup varnaze PLine reas OPL string PROP ea PERC rea ALpha rea TrYPE string INDex string LEVEL ea CONF string where varlist is a list of variables Version 9 2 and higher Description Poverty FGT and EDE FGT indices Users should set their surveys sampling design before using this module and to save their data files If the sampling design is not set simple random sampling SRS will be automatically assigned by default with ifgt the following poverty indices and their standard errors will be estimated v DT indi mr Z 8 Applications and files in DASP Two main types of applications are provided in DASP For the first one the estimation procedures require only one data file In such cases the data file in memory is the one that is used or loaded it is from that file that the relevant variables must be specified by the user to perform the reguired estimation 11 Figure 5 Estimating FGT poverty with one distribution E DASP FGT and EDE FGT Index gt ifgt command Main Confidence Interval Results r
68. iendly and easy to learn When these dialog boxes are used the associated program syntax is also generated and showed in the review window The user can save the contents of this window in a do file to be subsequently used in another session 2 DASP and Stata versions DASP requires o Stata version 9 2 or higher o ado files must be updated To update the executable file from 9 0 to 9 2 and the ado files see http www stata com support updates 3 Installing and updating the DASP package In general the ado files are saved in the following main directories Priority Directory Sources 1 UPDATES Official updates of Stata ado files 2 BASE ado files that come with the installed Stata software 3 SITE ado files downloaded from the net 4 PLUS 5 PERSONAL Personal ado files 3 1 installing DASP modules a Unzip the file dasp zip in the directory c b Make sure that you have c dasp dasp pkg or c dasp stata toc c Inthe Stata command windows type the syntax net from c dasp Figure 1 Ouput of net describe dasp Yersion version 2 0 Date June 2009 Stata Yersion Required 9 2 and higher Author DASP is conceived by Dr Abdelkrin Araar aabd ecn ulayal ca Dr Jean Yves Duclos jyyes ecn ulayal ca Before using nodules of this package users have to update the executable Stata file to Stata 9 2 or higher http uuu stata con support updates stata9 htnl update the ado files http uuu
69. in Results Variable s of interest source source Size variable hhsize nd Weight variable REFUGE Cancel Submit 39 15 6 Gini index decomposition by population subgroups diginig The diginig module decomposes the usual relative or the absolute Gini index by population subgroups Let there be G population subgroups We wish to determine the contribution of every one of those subgroups to total population inequality The Gini index can be decomposed as follows G I 200 1 1 R g l Within Overlap Between where 9 the population share of group g P the income share of group g T between group ineguality when each individual is assigned the average income of his group R The residue implied by group income overlap 15 7 Generalized entropy indices of inequality decomposition by population subgroups dentropyg The Generalised Entropy indices of inequality can be decomposed as follows se ji i gt iio ick 0 106 k 1 u where BO k is the proportion of the population found in subgroup k Bu k is the mean income of group k B I k 0 is ineguality within group k BI 0 is population ineguality if each individual in subgroup k is given the mean income of subgroup k p k 15 8 Polarization decomposition of the DER index by population groups dpolag As proposed by Araar 2008 the Duclos Esteban and Ray index can be decomposed as follows Between
70. information L p 0233349 0576717 0991386 1480407 2051758 2729623 3565971 4657389 6213571 1 00000 PODNRDAUAWNHED 4 2 Normalised per capita expenditures True distribition Uniform Generalized Quadratic LC Log Normal Beta LC SINGH amp MADALLA 63 Density functions with adjustment 13 0 2 4 Normalised per capita expenditures True distribition Log Normal Uniform Beta LC Generalized Quadratic LC SINGH amp MADALLA 22 Appendices 22 1 Appendix A illustrative household surveys 22 1 1 The 1994 Burkina Faso survey of household expenditures bkf94I dta This is a nationally representative survey with sample selection using two stage stratified random sampling Seven strata were formed Five of these strata were rural and two were urban Primary sampling units were sampled from a list drawn from the 1985 census The last sampling units were households List of variables strata Stratum in which a household lives psu Primary sampling unit weight Sampling weight size Household size exp Total household expenditures expeq Total household expenditures per adult equivalent expcp Total household expenditures per capita gse Socio economic group of the household head 1 wage earner public sector 2 wage earner private sector 3 Artisan or trader 4 Other type of earner 5 Crop farmer 6 Subsistence farmer 7 Inactive sex Sex
71. ion E Y X 10000 15000 20000 5000 ee Linear Locally Estimation Approach Bandwidth 3699 26 _ n o p t S 0 12000 24000 T 36000 X values Choose variables and parameters as in 113 T 1 48000 60000 Figure 57 Drawing derivatives of non parametric regression curves E DASP Non parametric regression gt cnpe command After clicking SUBMIT the following appears Figure 58 Derivatives of non parametric regression curves Non parametric derivative regression Linear Locally Estimation Approach Bandwidth 3699 26 dE Y X dX i 1 12000 24000 36000 48000 60000 114 23 11 Plotting the joint density and joint distribution function What does the joint distribution of gross and net incomes look like in Canada Using the can6 dta file 4 Estimate the joint density function for gross income X and net income N o Xrange 0 60000 o N range 0 60000 5 Estimate the joint distribution function for gross income X and net income N o Xrange 0 60000 o N range 0 60000 Q 1 Steps Type use C data can6 dta clear To open the relevant dialog box type db sjdensity Choose variables and parameters as in Figure 59 Plotting joint density function E DASP Joint Density Surfaces gt sjdensity command 1 After clicking SUBMIT
72. is intersection distribution 1 doninates distribution case C Ho doninance before this intersect ion 23 7 Decomposing FGT indices What is the contribution of different types of earners to total poverty in Burkina Faso 1 Open bkf94I dta and decompose the average poverty gap with variable of interest exppc with size variable set to size at the official poverty line of 41099 Francs CFA and using the group variable gse Socio economic groups an oP 2 Do the above exercise without standard errors and with the number of decimals set to 4 96 Answers 0 1 Steps Type use C data bkf941 dta clear To open the relevant dialog box type db dfgtg Choose variables and parameters as in Figure 41 Decomposing FGT indices by groups DASP Decomposiotion of the FGT Index by Groups gt dfgtg command Normalised E After clicking SUBMIT the following information is provided 97 dfgta exppc haroupla el hzizelzizal alphald plinel 41044 typelnorl FGT Index Deconposit ion by Groups Group FGT Index Popu Lat ion Absolute Relat ive Share Contribution Contribution Hage earning public sector 0 4237 LMA 1 0 0 002571 0 003790 0 000117 Hage sarning private sector r rar 0 0060 0 010678 0 002164 0 000294 Artisan or trading 0 027741 Oj 0 00173 0 004653 0 004288 0 000325 Others activities 0 063053 OM OH 0 025805 0 001308 0 000170 Farners crop 0 13
73. kf94I dta file 3 Draw Lorenz curves for rural and urban households a with variable of interest exppc b with size variable set to size c and using the group variable zone as residential area 0 1 Steps Type use C data can6 dta clear To open the relevant dialog box type db clorenz Choose variables and parameters as in 99 Figure 42 Lorenz and concentration curves E DASP Lorenz amp Concentration Curves gt clorenz command After clicking SUBMIT the following appears 100 Figure 43 Lorenz curves 5 Graph Graph Lorenz Curves 0 2 Steps Choose variables and parameters as in 101 Figure 44 Drawing concentration curves E DASP Lorenz amp Concentration Curves gt clorenz command X T B1B2B3 After clicking on SUBMIT the following appears 102 Figure 45 Lorenz and concentration curves t Graph Graph L p amp C P 4 line 45 Cip Bt Cp B2 Cip B3 0 3 Steps Type use C data bkf94I dta clear Choose variables and parameters as in 103 Figure 46 Drawing Lorenz curves E DASP Lorenz amp Concentration Curves gt clorenz command Main Results Y Axis X Axis Tite Caption Legend Overall Variable s of interest Type of curve s Jexpeq T Type Normalised by default z T Ranking Variable T Difference No v
74. l This would occur when the information on public expenditures is only available at the national level 58 Example 2 Observationi HH Eligible Frequency Area indicator Regional public size members expenditures 1 7 3 2 1 28000 2 4 2 2 1 28000 3 5 5 3 1 28000 4 6 3 2 1 28000 5 4 2 1 1 28000 The unit cost benefit at the national level equals 28000 10 2800 Interested users are encouraged to consider the exercises that appear in Section 23 14 59 21 Disaggregating the grouped data The ungroup DASP module generates disaggregated data from aggregate distributive information Aggregate information is obtained from cumulative income shares or Lorenz curve ordinates at some percentiles For instance Percentile p 0 10 0 30 0 50 0 60 0 90 1 00 Lorenz values L p 0 02 0 10 0 13 0 30 0 70 1 00 The user must specify the total number of observations to be generated The user can also indicate the number of observations to be generated specifically at the top and or at the bottom of the distribution in which case the proportion in of the population found at the top or at the bottom must also be specified Remarks If only the total number of observations is set the generated data are self weighted or uniformly distributed over percentiles If a number of observations is set for the bottom and or top tails the generated data are not self weighted and a weight variable is provided in addition t
75. l a l a D Re 2 P Ws R k P 8 Within 40 where Ja x 2 f a de p da DF de e 9 andy are respectively the population and income shares of group g R 8 e z x denotes the local proportion of individuals belonging to group g and having incomex e P is the DER polarization index when the within group polarization or inequality is ignored o The dpolas module decomposes the DER index by population subgroups Reference s Abdelkrim Araar 2008 On the Decomposition of Polarization Indices Illustrations with Chinese and Nigerian Household Surveys Cahiers de recherche 0806 CIRPEE 15 9 Polarization decomposition of the DER index by income sources dpolas As proposed by Araar 2008 the Duclos Esteban and Ray index can be decomposed as follows P y CP k Ha Where CP J Fox ae and y are respectively the pseudo concentration index and Ved income share of income source k The dpolas module decomposes the DER index by income sources Reference s Abdelkrim Araar 2008 On the Decomposition of Polarization Indices Illustrations with Chinese and Nigerian Household Surveys Cahiers de recherche 0806 CIRPEE 41 16 DASP and curves 16 1 FGT CURVES cfgt FGT curves are useful distributive tools that can inter alia be used to 1 Show how the level of poverty varies with different poverty lines 2 Test for poverty dominance between two distributions 3 Test pro poor gr
76. last observation since the chosen functional form forces the curve to go through 1 1 b 2mp n mp np e M We have Q p 2 4 e a b c l m b 4a n 2be Ac 61 Beta Lorenz Curve It is assumed that log p L log vlog p 6 log 1 p After estimating the parameters we can generate quantiles as follows O p 0 p 1 JF cal See also Datt 1998 The Singh Maddala distribution The distribution function proposed by Singh and Maddala 1976 takes the following form 1 q4 FA iy a20 b20 q21 aare parameters to be estimated The income x is assumed to be equal or greater than zero The density function is defined as follows F x aq b 1 x by _ The quantile is defined as follows x b 1 0 Va 0 p b i p 1 We follow Jenkins 2008 approach for the estimation of parameters For this we maximize the likelihood function which is simply the product of density functions evaluated at the average income of classes http stata press com journals stbcontents stb48 pdf STAGE II Adjusting the initial distribution to match the aggregated data optional This stage adjusts the initial vector of incomes using the Shorrocks and Wan 2008 procedure This procedure proceeds with two successive adjustments e Adjustment 1 Correcting the initial income vector to ensure that each income group has its original mean income e Adjustment 2 Smoothing the inter class dist
77. line how does the headcount index for male and female headed households compare 6 Can you draw a 99 confidence interval around the previous comparison Also set the number of decimals to 4 Answer Q 1 If bkf94 dta is saved in the directory c data type the following command to open it use C data bkf94 dta clear If lab bkf94 do is saved in the directory c do files type the following command to label variables and labels do C do files lab bkf94 do Typing the command describe we obtain obs 8 625 vars 9 31 Oct 2006 13 48 size 285 087 99 6 of memory free storage display value variable name type format label variable label weight float 9 0g Sampling weight size byte 8 0g Household size strata byte 8 0g Stratum in which a household lives psu byte 8 0g Primary sampling unit gse byte 29 0g gse Socio economic group of the household head sex byte 8 0g sex Sex of household head zone byte 8 0g zone Residential area exp double 10 0g Total household expenditures expeq double 10 0g Total household expenditures per adult equivalent exppc float 9 0g Total household expenditures per capita Typing label list we find zone 1 Rural 2 Urban 70 k Male Female N gse wage earner public sector wage earner private sector Artisan or trader Other type of earner Crop farmer Food farmer Inactive NOP WNP Q 2 You can set the sampling design with a dialog box as indicat
78. mation to analyse the distribution of public benefits and its progressivity 55 Formally let Wi be the sampling weight of observation 1 be the living standard of members belonging to observation 1 i e per capita income be the number of eligible members of observation i i e members that need the public service provided by sector s There are S sectors be the number of members of observation i that effectively use the public service provided by sector s be the socio economic group of eligible members of observation i typically classified by income percentiles be a subgroup indicator for observation i e g 1 for a rural resident and 2 for an urban resident Eligible members can thus be grouped into population exclusive subgroups be total public expenditures on sector s in area r There are R areas the area here refers to the geographical division which one can have reliable information on total public expenditures on the studied public service R be total public expenditures on sector s G p r l Here are some of the statistics that can be computed The share of ag in sector s is defined as follows n gt wi ffl eg s isl SH X wif i l G s Note that gt SH g l The rate of participation of a group g insector s is defined as follows gt wif leg i l Che Dwell sg i l This rate cannot exceed 100 since ff Sej Vi 56 3 The unit cost of a benefit in
79. more than one variable of interest simultaneously where each variable represents income for one period The user can select one of the two approaches presented above Small T bias corrections can be applied using either an analytical asymptotic or a bootstrap approach Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed Main references e Jalan Jyotsna and Martin Ravallion 1998 Transient Poverty in Postreform Rural China Journal of Comparative Economics 26 2 pp 338 57 e Jean Yves Duclos amp Abdelkrim Araar amp John Giles 2006 Chronic and Transient Poverty Measurement and Estimation with Evidence from China Working Paper 0611 CIRPEE 15 5 Inequality decomposition by income sources diginis Analytical approach The diginis module decomposes the usual relative or the absolute Gini index by income sources The three available approaches are e Rao s approach 1969 e Lerman and Yitzhaki s approach 1985 e Araar s approach 2006 38 Reference s e Lerman R I and S Yitzhaki Income Inequality Effects by Income Source A New Approach and Applications to the United States Review of Economics and Statistics 67 1985 151 56 e Araar Abdelkrim 2006 On the Decomposition of the Gini Coefficient a
80. multaneously For example one can estimate poverty by using simultaneously per capita consumption and per capita income A group variable can be used to estimate poverty at the level of a categorical group If a group variable is selected only the first variable of interest is then used Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed Interested users are encouraged to consider the exercises that appear in Section 23 1 10 2 Difference between FGT indices difgt This module estimates differences between the FGT indices of two distributions For each of the two distributions There exist three ways of fixing the poverty line 1 Setting a deterministic poverty line 2 Setting the poverty line to a proportion of the mean 3 Setting the poverty line to a proportion of a quantile Q p One variable of interest should be selected Conditions can be specified to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed A level for the parameter can be chosen for each of the two distributions Interested
81. n Exact Approach with an Illustration Using Cameroonian Data Working paper 02 06 CIRPEE Shapley approach The dsginis module decomposes the Gini inequality into a sum of the contributions generated by separate income components The dsginis Stata module estimates The share in total income of each income source k The absolute contribution of each source k to the Gini index The relative contribution of each source k to the Gini index For the Shapley decomposition the rule that is used to estimate the Gini index for a subset of components is by suppressing the inequality generated by the complement subset of components For this we generate a counterfactual vector of income which equals to the sum of components of the subset factors of the coalition plus the average of the complement subset Note that the dsginis ado file requires the module shapar ado which is programmed to perform decompositions using the Shapley value algorithm developed by Araar and Duclos 2008 e Araar A and Duclos J Y 2008 An algorithm for computing the Shapley Value PEP and CIRPEE Tech Note Novembre 2008 http 132 203 59 36 DAD pdf files shap dec aj pdf To open the dialog box for module dsginis type db dsginis in the command window Figure 11 Decomposition of the Gini index by income sources Shapley approach amp Decomposition of the Gini index by income components using the Shapley value gt dsginis command In x Ma
82. ndices eee en 107 Figure 50 Estimating differences in Gini and concentration indices ee 108 Fig r 51 Drawing densities n sic Aea react alas eee aac celal a rs ooo nl 109 Pisute 520 Density CUIVES cnc une neti oa uvede ou a Me Rae RRs 110 Figure 53 Drawing quantile CUE VES bida odad akad oak asd coins dose tone Atos de ts d 111 Figure 54 Quantile Curry eS aha ovo eo eat asad eee abba dou Woe de apenas 111 Figure 55 Drawing non parametric regression CUIVES eee 112 Figure 56 Non parametric regression CUIVES ccccsscesecsseesseeseeseeesecaeceeecaeeeseeseeeaeeeaeenaeeaee 113 Figure 57 Drawing derivatives of non parametric regression CUIVES ssceeseeeeceteeeeeeeee 114 Figure 58 Derivatives of non parametric regression CUIVES ee 114 Figure 59 Plotting joint density FUNCTION ee eee eee een 115 Figure 60 Plotting joint distribution function c ccccssesssecconserseesssencsorserssenseeaceaorsnesenee 117 Figure 61 Testing for bi dimensional poverty dominance u 119 Figure 62 Testing the pro poor growth primal approach 122 Figure 63 Testing the pro poor growth dual approach A 123 Figure 64 Testing the pro poor growth dual approach B 125 Figure 65 Benefit incidence analysis s ccissivssdiesecs cstennsvsniacesaneensuneods vaecanionegendededesctanevaeudasocnes 128 Figure 66 Benefit Incidence Analysis unit Cost approach 130 1 Introduction The Stata sof
83. ne 2 fi EM Size variable hhsize Weight variable Jweightea Cancel Submit Indicate the varlist of the six income sources Indicate that the poverty line is set to 15 000 N Set the variable HOUSEHOLD SIZE Set the variable HOUSEHOLD WEIGHT Click on the button SUBMIT The following results appear 34 digts sourcel source plinel15000 hzizelhhsize hueightl ueighteal Deconposition of the FGT index by incone conponents using the Shapley valued Execution tine 5 03 second s Paraneter alpha 0 00 Poverty line 15000 00 FGT index 0 584910 Household size hhe ize Sanpling weight ueightea Sources Incore Share Absolute Contr ibut ion Relat ive Contr ibut ion z sourced z source sourced sourced z sourced source level 2 level 3 level 4 level 5 Source sourcel 0 0328 0 022837 0 0238 0 021734 0 021085 source D M 0 04 0 05221 0 05637 0 source3 0 001848 0 0019 3 0 0018 0 001971 1 sourced 0 559 0 05661 1 02544H 0 0501 0 sources 0 001297 0 001494 0 001597 0 001636 0 source 0 003113 0 003378 0 00306 0 03535 0 level 6 sourcel sourced source sourced sourced sourceb an 15 3 Decomposition of the variation in FGT indices into growth and redistribution components dfgtgr Datt and Ravallion 1992 decompose the change in the FGT index between two periods t1 and t2 into g
84. nfidence interval by taking into account sampling design The module can draw an FGT curve and two sided lower bounded or upper bounded confidence intervals around that curve condition the estimation on a population subgroup draw a FGT curve that is not normalized by the poverty lines list or save the coordinates of the curve and of its confidence interval save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs Interested users are encouraged to consider the exercises that appear in Section 23 5 16 3 Difference between FGT CURVES with confidence interval cfgts2d The cfgts2d module draws differences between FGT curves and their associated confidence interval by taking into account sampling design The module can draw differences between FGT curves and two sided lower bounded or upper bounded confidence intervals around these differences normalize or not the FGT curves by the poverty lines list or save the coordinates of the differences between the curves as well as the confidence intervals save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options ar
85. o the generated income variable gt Example Assume that the total number of observations to be generated is set to 1900 but that we would like the bottom 10 of the population to be represented by 1000 observations In this case weights will equal 1 1000 for the bottom 1000 observations and 1 100 for the remaining observations the sum of weights being normalized to one The generated income vector takes the name of y and the vector weight w The number of observations to be generated does not have to equal the number of observations of the sample that was originally used to generate the aggregated data The ungroup module cannot in itself serve to estimate the sampling errors that would have occurred had the original sample data been used to estimate poverty and or inequality estimates The user can select any sample size that exceeds number of classes 1 but it may be more appropriate for statistical bias reduction purposes to select relatively large sizes STAGE I Generating an initial distribution of incomes and percentiles S 1 1 Generating a vector of percentiles Starting from information on the importance of bottom and top groups and on the number of observations to be generated we first generate a vector of percentiles 60 Examples Notations NOBS number of total observations F vector of percentiles B_NOBS number of observations for the bottom group T_NOBS number of observations for the top group For NOBS 1
86. of household head 1 Male 2 Female zone Residential area 1 Rural 2 Urban 64 22 1 2 The 1998 Burkina Faso survey of household expenditures bkf98I dta This survey is similar to the 1994 one although ten strata were used instead of seven for 1994 To express 1998 data in 1994 prices two alternative procedures have been used First 1998 expenditure data were multiplied by the ratio of the 1994 official poverty line to the 1998 official poverty line z_1994 z_1998 Second 1998 expenditure data were multiplied by the ratio of the 1994 consumer price index to the 1998 consumer price index ipc_1994 ipc_1998 List of new variables expcpz Total household expenditures per capita deflated by z_1994 z_1998 expcpi Total expenditures per capita deflated by ipc_1994 ipc_1998 22 1 3 Canadian Survey of Consumer Finance a sub sample of 1000 observations can6 dta List of variables X Yearly gross income per adult eguivalent T Income taxes per adult eguivalent B1 Transfer 1 per adult eguivalent B2 Transfer 2 per adult eguivalent B3 Transfer 3 per adult eguivalent B Sum of transfers B1 B2 and B3 N Yearly net income per adult eguivalent X minus T plus B 22 1 4 Peru LSMS survey 1994 A sample of 3623 household observations PEREDE94I dta List of variables exppc Total expenditures per capita constant June 1994 soles per year weight Sampling weight 65 size Household size npubprim Number of household members in
87. ollows a normal distribution or Answers Q 1 Open the dialog box by typing db difgt 0 2 For distribution 1 choose the option DATA IN FILE instead of DATA IN MEMORY and click on BROWSE to specify the location of the file bkf98I dta Follow the same procedure for distribution 2 to specify the location of bkf94I dta Choose variables and parameters as follows 76 Figure 21 Estimating differences between FGT indices jE DASP Difference Between FGT Indices gt difgt command Normalised ha K Cancel Submit After clicking on SUBMIT the following should be displayed difgt exppez exppe alphal filedC ATR kt9G1 dta heizellsize fileZiC A DATA bkt dtal heizeelsize plinel 41099 pl ined 41099 Poverty Index oo FGT Index Paraneter alpha 0 00 Est inate Distribution 1 Ur istribut ion 0 46 Difference 0 008113 bal LE UB P Line 0 027 0 431199 0 474156 41099 00 0 116124 0 42873 0476256 41099 00 0 01947 0 030062 0 046288 11 Q 3 Restrict the estimation to rural residents as follows o Select the option Condition s o Write ZONE in the field next to CONDITION 1 and type 1 in the next field Figure 22 Estimating differences in FGT indices E DASP Difference Between FGT Indices gt difgt command DatainFile _ C DATA bKf98I dta 41099 41099 Z of the E of the 4 K e
88. ominance and estimating critical values Has the poverty increase in Burkina Faso between 1994 and 1998 been statistically significant 1 Using simultaneously files bkf94I dta and bkf98I dta check for second order poverty dominance and estimate the values of the poverty line at which the two FGT curves cross a The variable of interest is exppc for 1994 and exppcz for 1998 b The poverty line should vary between 0 and 100 000 Franc CFA c The size variable should be set to size Answers 0 1 Steps To open the relevant dialog box type db dompov Choose variables and parameters as in 95 Figure 40 Testing for poverty dominance E DASP Poverty Dominance gt dompov command S x Main Results Distribution 1 Distribution 2 DatainFie CADATANDKIS4 dta Browse DatainFie v CADATASbkf98l dta Browse Variable of interest eee st C CO OC Variable of interest epp SOSOS S Size variable see Size variable ze t i SsSSCSCSwS I Condition s fi z T Condition s fi z Second order Dominance order Cancel Submit After clicking SUBMIT the following results appear Hunbar of Crit ical Hin range of Han range of Caze intersect ion pov line pov lines pov line 1 Fig a al P 2 75 02 i i E Hotes z case A Before this intersection distribution 2 doninates distribution 1 case B Before th
89. ommand and set variables and options as follows Figure 65 Benefit incidence analysis E DASP Benefit incidence analysis gt bian command After clicking on Submit the following appears 128 Benefit Incidence Analysis Education Share by Quintile Groups Groups Pr inary Secondary Quintile 1 0 218 0 155 Quintile 2 1 276 0 216 Quintile 3 1 220 0 274 Quintile 4 0 197 0 251 Quintile 5 0 139 0 173 All 1 00 1 000 Rate of Participation by Quintile Groups Groups Fr inary Secondary Quintile 1 1 7 0 455 Quintile 2 1 35 0 641 Quintile 3 1a 0 663 Quintile 4 0 723 0 687 Quintile 5 0 56 0 511 All 0 730 0 592 2 To estimate total public expenditures on education by sector at the national level the following macro information was used Pre primary and primary public education expenditure as of all levels 1995 35 2 Secondary public education expenditure as of all levels 1995 21 2 Tertiary public education expenditure as of all levels 1995 16 Public education expenditure as of GNP 1995 3 GDP per capita about 3 800 Using this information the following variables are generated cap drop _var1 gen varl size weight 3800 qui sum _var1 qui gen pri pub exp 0 03 0 352 r sum gui gen sec pub exp 0 03 0 212 r sum gui gen uni pub exp 0 03 0 160 r sum cap drop _var1 Total public expenditures on primary sector pri pub exp Total public expenditures
90. or tax and transfer progressivity by comparing Lorenz and concentration curves 17 3 DASP and bi dimensional poverty dominance dombdpov Let two dimensions of well being be denoted by k 1 2 The intersection bi dimensional FGT index for distribution D is estimated as Pp Z A I Ma 2 n d l k l n ZW i l where Z z z and A a a are vectors of poverty lines and parameters c respectively and x max x 0 Distribution 1 dominates distribution 2 at orders Sis S2 over the range 0 Z if and only if 48 R Z A s 1 lt P Z A s 1 V Ze 0 z x 0 z and fora s 1 5 1 The DASP dombdpov module can be used to check for such dominance For each of the two distributions The two variables of interest dimensions should be selected Conditions can be specified to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed Surfaces showing the difference the lower bound and the upper bound of the confidence surfaces are plotted interactively with the GnuPlot tool Coordinates can be listed Coordinates can be saved in Stata or GnuPlot ASCII format Interested users are encouraged to consider the exercises that appear in Section 23 12 18 Distributive tools 18 1 Quantile curves c_quantile The quantile at a perc
91. owth conditions FGT curves are also called primal dominance curves The cfgt module draws such curves easily The module can draw more than one FGT curve simultaneously whenever more than one variable of interest is selected draw FGT curves for different population subgroups whenever a group variable is selected draw FGT curves that are not normalized by the poverty lines a draw differences between FGT curves list or save the coordinates of the curves save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs To open the dialog box of the module cfgt type the command db dfgt in the command window Figure 12 FGT curves E DASP FGT Curves gt cfgt command 5 x Main Results Y Axis Axis Title Caption Legend Overall Variable s of interest Type of curve s _ lt z a Type Normalised I Difference No m Size variable o Group variable PE Parameters Parameter alpha B Minimum Maximum Poverty line 2 0 fioooo 2 R Cancel Submit Interested users are encouraged to consider the exercises that appear in Section 23 4 42 FGT CURVE with confidence interval cfgts The cfgts module draws an FGT curve and its co
92. rea or within female headed families One way to do this is to force DASP to focus on a population subgroup defined as those for whom some GROUP VARIABLE say area of residence equals a given GROUP NUMBER say 2 for rural area SAMPLING WEIGHT Sampling weights are the inverse of the sampling probability This variable should be set upon the initialization of the dataset 6 Howcan DASP commands be invoked Stata commands can be entered directly into a command window Figure 3 Using DASP with a command window a5 Intercooled Stata 9 2 Results Oj x fm File Edit Prefs Data Graphics Statistics User Window Help s x S M OS AB S BE 0 8 Review use C DATASbK94I dta clear POP d f d f 7 9 2 Copyright 1984 2006 Stat ist ics Data Analysis StataCorp 4905 Lakeway Drive College Station Texas 77845 USA 800 STATA PC http uuu stata con 979 696 4600 statalstata con 979 696 4601 fax ariabl m x Pingle user Stata for Hindous perpetual license Serial nunber 1990520454 weight Licensed to Araar Abdelkrin size Universit Laval strata x psu gse commend zone ifgt exppc pline 41099 hsize size alpha 2 exppc iC data An alternative is to use dialog boxes For this the command db should be typed and followed by the name of the relevant DASP module 10 Example db ifgt 7 How can help be accessed for a given DASP module Type the command help followed by t
93. ributions The generated sample is saved automatically in a new Stata data file called by default ungroup data dta names and directories can be changed The user can also plot the Lorenz curves of the aggregated when we assume that each individual has the average income of his group and generated data Dialog box of the ungroup module 62 Figure 15 ungroup dialog box amp Disaggregation of aggregated data gt ungroup command Basic information on the aggregated data Cumulative income shares or Lorenz flp Percentiles p 5 v Y Distribution form Distribution Log normal M Adjustment data information IV Adjust the generated sample to match the aggregated Size of the generated distribution Total size fi ooo Percentage Number of obs T Bottom group fio fioo I Top group fio fioo M Saving the generated distribution File Poo Browse M Plotting the Lorenz curves V Plot the Lorenz curves of the aggregated and generated data Cancel Submit Illustration with Burkina Faso household survey data In this example we use disaggregated data to generate aggregated information Then we compare the density curve of true data with those of the generated with the disaggregation of aggregated data gen fw size weight gen y exppc r mean clorenz y hs size lres 1 Density functions without adjustment 1 Aggregated
94. rovided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 3 decimals this can be also changed Users are encouraged to consider the exercises that appear in Section 23 3 11 DASP poverty and targeting policies 11 1 Poverty and targeting by population groups 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 a is as follows aP k z a 1 if a21 LST f 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 The per capita dollar impact of a proportional marginal variation of income within a group k called Inequality Neutral Targeting on the FGT poverty index P k z a is as follows P k z a zP k z a 1 Fas w K 1 _ zf k z u k if a 0 16 The module itargetg allows to Estimate the impact of marginal change in income of the group on poverty of the group and that of the population Select the design of change constant or proportional to income to keep inequality unchanged Draw curves of impact according for a range of poverty lines Draw the confidence interval of impact curves or the lower or upper bound of confidence interval Etc
95. rowth and redistribution components as follows 35 P P n Pat sn f Pa nl R ref var iation Cl C2 PoP Pat 2 p y nt ee Pu P a var iation I C2 where variation difference in poverty between t1 and t2 C1 growth component C2 redistribution component R residual Ref period of reference P u 2 the FGT index of the first period P u 7t the FGT index of the second period R ref 2 P u nil the FGT index of the first period when all incomes y of the first period are multiplied P t nt the FGT index of the second period when all incomes v of the second period are multiplied by u ult The Shapley value decomposes the variation in the FGT Index between two periods t1 and t2 into growth and redistribution components as follows P gt P C C E V Variation one pq x Pat as Put n Put n 2 l C2 putt 2 Pett at Pat P a 15 4 Decomposition of FGT poverty by transient and chronic poverty components dtcpov This decomposes total poverty across time into transient and chronic components 36 The Jalan and Ravallion 1998 approach Let yt be the income of individual i in period t and u be average income over the T periods for that same individual i i 1 N Total poverty is defined as T N ka wi z yi _ t li 1 TP a z N T pa Wi i l The chronic poverty component is then defined as N
96. s positive usual kernel estimation of the density close to these two bounds will be biased A similar problem occurs with non parametric regressions Renormalisation approach 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 Pag i vKi OK n 2 wi i l where 1 X X K x expl 0 5A x and A x 08 pl 0 5 A00 x and where the scalar K x is defined as Ki x yx P A x 2 s l PA I A OS ee 2 6 1 I 1 w x M71 K PQ IPRA L a B l 1 0 0 0 min is the minimum bound and max is the maximum one is the usual bandwidth This correction removes bias to order h DASP offers four options without correction and with correction of order 1 2 and 3 Refs e Jones M C 1993 simply boundary correction for Kernel density estimation Statistics and Computing 3 135 146 e Bearse P Canals J and Rilstone P Efficient Semi parametric Estimation of Duration Models With Unobserved Heterogeneity Econometric Theory 23 2007 281 308 50 Reflection approach The reflection estimator approaches the boundary estimator by reflecting the data at the boundaries f x i EA 2 wi i l Kroos k 2 Jex ZAZ Km Refs e Cwik and Mielniczuk 1993 Data dependent Bandwidth Choice for a Gr
97. sector s for observation j which refers to the household members that live in area r ES UC gt wjf jel where n is the number of sampled households in area r 4 The benefit of observation i from the use of public sector s is B f UC 5 The benefit of observation i from the use of the S public sectors is S B XBi s 1 6 The average benefit at the level of those eligible to a service from sector s and for those observations that belong to a group g is defined as ba w B I i eg ABE 8 n wli eg i l 7 The average benefit for those that use the service s and belong to a group g is defined as by w B l i eg ABF n gt wifi eg i l 8 The proportion of benefits from the service from sector s that accrues to observations that belong to a group g is defined as n where B X w Billie g i l These statistics can be restricted to specific socio demographic groups e g rural urban by replacing I i g byI i c The bian ado module allows the computation of these different statistics 57 Some characteristics of the module o Possibility of selecting between one and six sectors o Possibility of using frequency data approach when information about the level of total public expenditures is not available o Generation of benefit variables by the type of public services ex primary secondary and tertiary education levels and by sector o Generation of unit cost v
98. setsesseststsseseesssetstssestestssesesttseesessestesessese 53 19 21 B imal PrO POer CUVE S soaren a E ooo a a enone 54 19 22 lt gt Dial pro poor curve Sean asd vas save eE dead Va SAV E ia AE i PE NiE 54 20 DASP and Benefit Incidence AnalySis ecceccceesseesseesseceseeeeeeceeeeeeseecaeceeeeeeeenseeenaeenes 55 20 1 Benefit mcidence anal ysis cosisr edu ace advese Gane nia a a ade 55 21 Disaggregating the grouped data ss o jsiccassivsecaxvacenianssiseescheacpines sauvscaveaasuadsoinnnseweasdvacagnne 60 22 PAPI CIC SEERE prenos og oko o ooo o oo ooo oo oo 64 22 1 Appendix A illustrative household SUrVeyS ccsceseeseeseeeeeeeecesecesecneeeseeeeeeeeeaees 64 22 1 1 The 1994 Burkina Faso survey of household expenditures bkf94I dta 64 22 1 2 The 1998 Burkina Faso survey of household expenditures bkf98I dta 65 22 1 3 Canadian Survey of Consumer Finance a sub sample of 1000 observations cano CA kenen aaa ta ASA OKO ach clinic begat s 8 oa kata 65 22 1 4 Peru LSMS survey 1994 A sample of 3623 household observations PEREDEVPETA sea a a A SVA RO totals phan o o oD oo oo ngs 65 22 1 5 Peru LSMS survey 1994 A sample of 3623 household observations PERU Ae Eta z dea sata stealer oin a ua u ARR yd KAR dk da 66 22 1 6 The 1995 Colombia DHS survey columbial dta eee 66 22 1 7 The 1996 Dominican Republic DHS survey Dominican republic19961 dta 66 22 2 Appendix B labelling variables and Values
99. sonsicnien 8 Fig r 2s DASP SUD MON ed hci et led tat elk weak aaa Nace tae se tana ees 9 Figure 3 Using DASP with a command WindOW eceeceeseceseceseeeeeseeeeeeseeeseceecaeeeaeeeeeeeeeaees 10 Figure 4 Accessing help on DASP i 0i03 ceccccassisctsscasty cessiceetadevescashveststeceracdsiyuasus tv date eb Vida sada dds kV 11 Figure 5 Estimating FGT poverty with one distribution 12 Figure 6 Estimating FGT poverty with two distributions eee 12 Figure 7 Poverty and the targeting by population groups ssssessssssessessrseessessesressressessessressesse 17 Figure 8 Decomposition of the FGT index by groups eee 30 Figure 9 Decomposition of FGT by income COMponentS eee 34 Figure 10 Decomposition of poverty into transient and chronic components 38 Figure 11 Decomposition of the Gini index by income sources Shapley approach 39 Figure T2 FGT CUVE Sissies siberateataesenees near oeaan a a E ES Eae a atana a a habeas 2 42 Figure 13 Lorenz and concentration CUIVES sssseseesesseseesesseteesstststsststesessestestsetsessesesessese 44 Figure 14 Consumption dominance CUrVeS sssseseesesseseesesseseessesetstsststestssesesesetsesseseesessese 47 Figure 5 unsroup dialog Dox ss ereinen i ie aa a Stas Pa Eae E es ea oo dass ESTESE 63 Figure 16 Survey data settings s i 3 cdsscsecacgssaducaeentesenjosaduccussdesnantestecancuteceaasuadedteentetepacdectussdetves
100. t of Economics Universit Laval Kakwani N 1993 Poverty and economic growth with application to C te D Ivoire Review of Income and Wealth 39 2 121 139 To estimate the FGT elasticity s with respect average income growth the group or the whole population The user can select more than one variable of interest simultaneously For example one can estimate poverty by using simultaneously per capita consumption and per capita income A group variable can be used to estimate poverty at the level of a categorical group If a group variable is selected only the first variable of interest is then used Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 12 2 FGT elasticity s with respect to Gini inequality efgtineq The overall growth elasticity INEL of poverty when growth comes exclusively from growth within a group k namely within that group inequality neutral is given by Kk f k 2 w K z b k uk C k F z u I a Pk za UO 2 PE za D Hu CO P z a u I if a 0 INEL if azl where z is the poverty line k is the population subgroup in which growth takes place f k z is the density function at level of income z of group k and F z is the headcount C k is the concentration coefficient of group k
101. the command window delim To drop all label values label drop all To assign labels label var strata Stratum in which a household lives label var psu Primary sampling unit label var weight Sampling weight label var size Household size label var totexp Total household expenditures label var exppc Total household expenditures per capita label var expeq Total household expenditures per adult equivalent label var gse Socio economic group of the household head To define the label values that will be assigned to the categorical variable gse label define lvgse 1 wage earner public sector 2 wage earner private sector 3 Artisan or trader 4 Other type of earner 5 Crop farmer 6 Subsistence farmer 7 Inactive To assign the label values Ivgse to the variable gse label val gse lvgse label var sex Sex of household head 67 label def lvsex 1 Male 2 Female label val sex Ivsex label var zone Residential area label def lvzone 1 Rural 2 Urban label val zone lvzone 22 3 Appendix C setting the sampling design To set the sampling design for the data file bkf94 dta open the dialog box for the command svyset by typing the syntax db svyset in the command window In the Main panel set STRATA and SAMPLING UNITS as follows Figure 16 Survey data settings S svyset Survey data settings More Weights SE Poststatiication
102. the following graph is plotted interactively with Gnu Plot 4 2 115 Joint Density Function f xy SEES 10000 20000 lt 2 30000 40000 Dimension 1 40000 ZZ Dimension 2 50000 ZS 50000 6000060000 0 2 Steps To open the relevant dialog box type db sjdistrub Choose variables and parameters as in 116 Figure 60 Plotting joint distribution function ES DASP Joint Distribution Surfaces gt sjdistrub command After clicking SUBMIT the following graph is plotted interactively with Gnu Plot 4 2 Joint Distribution Function Fy ik ERS n LEE SASS ASS 40000 lt 2 SSS SSS 117 23 12 Testing the bi dimensional poverty dominance Using the columbia95I dta distribution 1 and the dominican republic95I dta distribution 2 files 1 Draw the difference between the bi dimensional multiplicative FGT surfaces and the confidence interval of that difference when Var of interest Range alpha_j Dimension 1 haz _ height for age 3 0 6 0 0 Dimension 2 sprob survival 0 7 1 0 0 probability 2 Test for bi dimensional poverty using the information above Answer 0 1 Steps To open the relevant dialog box type db dombdpov Choose variables and parameters as in 118 Figure 61 Testing for bi dimensional poverty dominance DASP Difference Between Multiplicative FGT indices gt dombipov command
103. tware has become a very popular tool to transform and process data It comes with a large number of basic data management modules that are highly efficient for transformation of large datasets The flexibility of Stata also enables programmers to provide specialized ado routines to add to the power of the software This is indeed how DASP interacts with Stata DASP which stands for Distributive Analysis Stata Package is mainly designed to assist researchers and policy analysts interested in conducting distributive analysis with Stata In particular DASP is built to n Estimate the most popular statistics indices curves used for the analysis of poverty inequality social welfare and equity 7 Estimate the differences in such statistics n Estimate standard errors and confidence intervals by taking full account of survey design n Support distributive analysis on more than one data base n Perform the most popular poverty and decomposition procedures 7 Check for the ethical robustness of distributive comparisons n Unify syntax and parameter use across various estimation procedures for distributive analysis For each DASP module three types of files are provided ado This file contains the program of the module hlp This file contains help material for the given module dlg This file allows the user to perform the estimation using the module s dialog box The dlg files in particular makes the DASP package very user fr
104. y 2004 DER polarization index can be expressed as DER a J f x f y y x dydx 26 where f x denotes the density function at x The discrete formula that is used to estimate this index is as follows n wf y aly DER a F ZW i l The normalized DER estimated by this module is defined as DER 2 where 1 i l 2X Wj Wj 2D Wij Wii j l j l a yi u yi N l N X wi yw The Gaussian kernel estimator is used to estimate the density function The user can select more than one variable of interest simultaneously For example one can estimate polarization by using simultaneously per capita consumption and per capita income A group variable can be used to estimate polarization at the level of a categorical group If a group variable is selected only the first variable of interest is then used Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed Main reference DUCLOS J Y J ESTEBAN AND D RAY 2004 Polarization Concepts Measurement Estimation Econometrica 72 1737 1772 14 2 Difference between DER polarization indices dipolder This module estimates differences between the DER indices of two distributions For each of the two distributions One variable of interest should be selected
105. y income components using the Shapley value dfgts The dfgts module decomposes the total alleviation of FGT poverty into a sum of the contributions generated by separate income components Total alleviation is maximal when all individuals have an income greater than or equal to the poverty line A negative sign on a decomposition term indicates that an income component reduces poverty Assume that there exist K income sources and that s denotes income source k The FGT index is defined as n a s K 2 wi I a A Pza sa m t wi i l where w is the weight assigned to individual 7 and n is sample size The dfgts Stata module estimates The share in total income of each income source k The absolute contribution of each source k to the value of P 1 The relative contribution of each source k to the value of P 1 Note that the dfgts ado file requires the module shapar ado which is programmed to perform decompositions using the Shapley value algorithm developed by Araar and Duclos 2008 e Araar A and Duclos J Y 2008 An algorithm for computing the Shapley Value PEP and CIRPEE Tech Note Novembre 2008 http 132 203 59 36 DAD pdf files shap dec aj pd Empirical illustration with the Nigerian household survey We use a Survey of Nigerian households NLSS using 17764 observations carried out between September 2003 and August 2004 to illustrate the use of the dfgts module We use per capita total household

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