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User Manual for Stata Package DASP: Version 2.3

1. siee tal hci 25 12 6 FGT elasticities with respect to within between income components of inequality ford 26 13 DASPandnequalit IHIlI68s uni e do eto Mesi ete oe on on oou t ond se und 28 13 1 Gini and concentration indices igini oo ccc ccccccccccccceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeees 28 13 2 Difference between Gini concentration indices digini 28 13 3 Generalised entropy index ientropy ssesssessssssssseeccsreeereesssssssssssseeeerrerereessssssssssss 29 13 4 Difference between generalized entropy indices diengtropy 29 13 5 JATKINSON MdEX TAEKINSON pessecessseessenatcde casey te e ex Eee oU pue ek rota EV ted pesas ebbe ee od 30 13 6 Difference between Atkinson indices diatkinson eeeeeeeees 30 13 7 Coefficient of variation index icvar ccccccccccccccccsssccccccsssssssseesssssscecceceesseeeaeeees 31 13 8 Difference between coefficient of variation dicvar eeeeeeeeeeees 31 13 9 Quantile share ratio indices of inequality inineq eseeeeeeeeeeeeese 31 13 10 Difference between Quantile Share indices dinineq 32 13 11 The Araar 2009 multidimensional inequality index
2. eene 138 Testing the pro poor growth primal approach esses 141 Testing the pro poor growth dual approach A esses 142 Testing the pro poor growth dual approach B esses 144 benefi incidence analysis vpisni cite niet OR DH ERES IEEE HEURE KT rOn EH HUS UH E ADE aiaiai 147 Benefit Incidence Analysis unit cost approach esses 149 1 Introduction The Stata software 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 m Estimate the most popular statistics indices curves used for the analysis of poverty inequality social welfare and equity m Estimate the differences in such statistics m Estimate standard errors and confidence intervals by taking full account of survey design m Support distributive analysis on more than one data bas
3. sss 101 Drawing FG CURVES usado eigen dcn DO DONNE EC DR OM ONE EE DEN 103 Editino FG CU VeS detained nvrn ec Le c rte LES EI 103 Graph ol BGT CUEVES aetatis raten a eut isatus Vet oi ea lubet t na Mm Ga pelett 104 PGT elins dorAvAv cce 105 Graph orFGT Curves DV ZONE sso t ire hn vade ADR ON es 106 Differences ot EGT CUEVOS uiae eio obtenue c Luar n 107 Listing Coordinate S aio aU ER MAMMA DE 108 Differences between FOT CUEVOS uento oeil foto etes tondere sweet peer cuero teta 109 Differences between PG DEUEPVS cone idee E e cete a tto inea ned 110 Drawing FGT curves with confidence interval sese 111 FGT curves with confidence interval eese nere tn tenent tnnt 112 Drawing the difference between FGT curves with confidence interval 113 Difference between FGT curves with confidence interval a 0 113 Difference between FGT curves with confidence interval a 1 114 Testing Tor poverty dominan e 5 c acide pcenis eee SR DRUNE LEONE 115 Decomposing PGT Indices DY SEOUDS sustinuti fee a interiret att 116 Lorenz and concentration CUIVES eese nene teret tarte tetas niaaa 119 Figure 44 Figure 45 Figure 46 Figure 47 Figure 48 Figure 49 Figure 50 Figure 51 Figure 52 Figure 53 Figure 54 Figure 55 Figure 56 Figure 57 Figure 58 Figure 59 Figure 60 Figure 61 Figure 62
4. 32 14 DASPand polarization Indice S eoe e ERE RI n a eie dede eet eoe 32 141 The DER midex 1D OIG CF reete opi etas oe tie e eo pod taraen ti deha eoe peo doe epe etae evo ete cts 32 14 2 Difference between DER polarization indices dipolder 33 14 3 The Foster and Wolfson 1992 polarization index ipolfw 34 14 4 Difference between Foster and Wolfson 1992 polarization indices dipolfw 34 14 5 The Generalised Esteban Gradin and Ray 1999 polarisation index ipoger 34 14 6 The Inaki 2008 polarisation index ipoger eeeeeeeeeeeenenn 36 15 DASP and CECOMPOSIUIONS i cedoseto tocco a dot brodo Puce a deovat o iu en erp pA ads 39 15 1 FGT Poverty decomposition by population subgroups dfgtg 39 15 2 FGT Poverty decomposition by income components using the Shapley value dfgts 40 15 3 Alkire and Foster 2011 MD index of poverty decomposition by population S boroupsAdmadale hyse oia T a a 42 15 4 Alkire and Foster 2011 decomposition by dimensions using the Shapley value eb 0 6 20 ty Meet e P 42 15 5 FGT Poverty decomposition by income components using the Shapley value dfgts 43 15 6 Decomposition of the variation in FGT indices into growth and redistribution components GTP LE os aae etta asistente mtetuedienq tl uqeiuecte diat deme dad qeu eu ei ute n tai 45 15 7 Decompo
5. Cancel Submit After clicking on SUBMIT the following should be displayed difgt exppcz exppc alphalll filellC SDATASbktSSI dtal heizellsize file C ADATASbkfS4I dtal hzized size plined 44099 pline2l 44099 Poverty Index FGT Index Paraneter alpha 0 00 Est inate a Tl LB UB P Line Distr ibut ion 1 1 2677 0 0 0 431199 0 474156 41099 00 Distribution 0 44605 0 06174 1 112873 I 4726256 41099 00 Difference 0 008113 0 019477 0 030062 0 046234 mss 96 Q 3 Restrict the estimation to rural residents as follows o Selectthe option Condition s o Write ZONE in the field next to CONDITION 1 and type 1 in the next field Figure 23 Estimating differences in FGT indices ES DASP Difference Between FGT Indices gt difgt command B x Main Confidence Interval Results Distribution z Data in File C ADATA DK ESI dta Browse Variable of interest Jexppe Size variable size Poverty line f Absolute 41083 C Relative 5024 nf the Mean Iv Condition s 1 Condition 1 zone li Distribution 1 Data in File CNDATASDKISEI dta Browse Variable of interest Jexppez Size variable size Poverty line Absolute 33 C Relative zm of the Mean M Condition s Condition 1 zone f Parameters and Options Parameter alpha jo Type Mormalised Cancel Submit After clicking on SUBM
6. 0 000988 4A D sourced A A Dk D H DA EEA sources ALO 0 01 0 01597 41 06 0 sourceh J R 7 0 4 005 0 003536 0 0 level 6 sourcel 0 007 source i e sources 0 08 sourced 1 023076 sources 16d spurceb NEM 15 3 Alkire and Foster 2011 MD index of poverty decomposition by population subgroups dmdafg The dmdafg module decomposes the MD Alkire and Foster index of poverty index by population subgroups This decomposition takes the form The results show The estimated Alkire and Foster index of each subgroup The estimated population share of subgroup The estimated absolute contribution of subgroup g to total poverty The estimated relative contribution of subgroup g to total poverty An asymptotic standard error is provided for each of these statistics 15 4 Alkire and Foster 2011 decomposition by dimensions using the Shapley value dmdafs The dmdafs module decomposes the Alkire and Foster 2011 multidimensional poverty indices into a sum of the contributions generated by each of the poverty dimensions It uses the Shapley characteristic function The non presence of a given factor dimension is obtained by setting the level of that dimension to its specific poverty line thus ensuring the non contribution of this dimension to the AF 2011 indices Note that the dmdafs ado file requires the module shapar ado which is programmed to perform decompositions using the Shapley value
7. Q 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 90 Figure 19 Estimating FGT indices ES DASP FGT and EDE FGT Index gt ifgt command E aj x Main Confidence Interval Results Varable s of interest exppc expe rar Index Normalised T Farameter a Size valable size Parameter alpha E Group variable ha Poverty line Absolute 41088 Relative zm of the Mean IF group variable ie used poverty line 1s relative bor Survey settings The population The following results should then be displayed ifgt exppc expeg alphalll hsizelsize plinel 41099 Poyerty Index FGT Index Household size size Sanpling weight ueight Paraneter alpha 0 00 Mar Labla Est inata STL LE UE P Line EHDE 0 44605 0 016124 0 412873 0 476256 41099 00 BHT 0 4540 0 013376 1 223218 0 291507 41099 00 Q 4 Select RELATIVE for the poverty line and set the other parameters as above 9 Figure 20 Estimating FGT indices with relative poverty lines ES DASP FGT and EDE FGT Index gt ifgt command E aj x Main Confidence Interval Results Varable s of interest exppc FET Index Normalized m Farameter a Size valable size y l Farameter alpha Group variable ha Poverty line C Absolute
8. Main Confidence Interval Number of dimensions Size variable size l Group variable Common parameters alpha U Variable s af interest Poverty line s Parameter s a_j Dimension 1 exppc 400 1 Dimension_ pliterate 09 1 Bs After clicking SUBMIT the following results appear indpoy exppc pliterate heizelsize index 1 alphat allil plil4uu a2 1 plerd 9 H D Poverty indes Chakravarty et al 1998 Household size size Est inate opulat ion 0 418 Q 2 To open the relevant dialog box type db imdp_cmr Steps Choose variables and parameters as in 100 Figure 26 Estimating multidimensional poverty indices B DASP Bourguignon and Chakravarty 2003 bidimensional poverty index gt imdp bci command Confidence Interval Number of dimensions 2 Common parameters Size variable size alpha 1 gamma 1 Group variable Variable s of interest Poverty line s Dimension 1 exppc A 400 Dimension 2 pliterate A 0 9 Fam ee iy After clicking SUBMIT the following results appear indpoy exppc pliterate hzizelzizel index alphald betall gannald pliidil pl2t 9 H D Poverty indes Bourguignon and Chakravarty 2003 Household size size Est inate Populat ion 0 098 101 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 Openthe FGT curves
9. n 2 Wi i where z is the poverty line and q the number of poor 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 10 4 Difference between Watts indices diwatts This module estimates differences between the Watts 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 9596 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 a can be chosen for each of the two distributions 16 10 5 Sen Shorrocks Thon poverty index isst The Sen Shorroks Thon poverty index is estimated as Z gt K P z HP z a 1 G where z is the poverty li
10. C2 redistribution component R residual Ref period of reference P u xz the FGT index of the first period P u 2 the FGT index ofthe second period 45 P u ri the FGT index of the first period when all incomes y of the first period are multiplied t2 tl by p p P uH ni the FGT index of the second period when all incomes y of the second period are multiplied by ut ju The Shapley value decomposes the variation in the FGT Index between two periods t1 and tZ into growth and redistribution components as follows P P C C Ucx Y Variation Ci 1a pute jpe Patt n y Cy 1p patat qi pq 15 7 Decomposition of change in FGT poverty by poverty and population group components sectoral decomposition dfgtgZd Additive poverty measures like the FGT indices can be expressed as a sum of the poverty contributions of the various subgroups of population Each subgroup contributes by its population share and poverty level Thus the change in poverty across time depends on the change in these two components Denoting the population share of group k in period L by A the change in poverty between two periods can be expressed as see Huppi 1991 and Duclos and Araar 2006 P za P na amp gt Piana Pina k withim gFoup poverty effects E 2 Pr kaja a k amp k cemegraphir oF general effects P2218 Pina 5 5 0 QR
11. Figure 63 Figure 64 Figure 65 Figure 66 Figure 67 LOLenz ibV6953505 an cda een cree eee tenn eee Reese treet eee 120 Drawing concentration CUEVES saisonnier amine REVISE RM REV ONERE UN Ee 121 Lorenzand concentration CUYOS e nete ve ani Vacante dn is ida 122 Drawing Lorenz CUEVES sanas isi tar i Ee pu eive d icu suh t cap Uk ex PUN REN EMG 123 Lorenz COTY CS cesses co cach ue mM ADI E A 123 Estimating Gini and concentration indices eene nentes 125 Estimating concentration Indices oiii i a tcu a 126 Estimating differences in Gini and concentration indices 127 Drawing del SH eS sete dui Eee a 128 Density GUT VS o o cea Tere emmy nar ct ny enor MM EE EMEN A Mes 129 Drawing guantile CUEVeSs us atn RHEIN 130 Duae CU FV CS ocimieisamiti ees Ra ede inccr talento r n odan aair on ovr el Fk en or da 130 Drawing non parametric regression CUFrVes eessssseseeenenenntetetntntntntntntntntnns 131 Non parametric resressiom CUFVS ua pbi erepta np et ix eap ta HE Ur ru eon FU Pe URBE 132 Drawing derivatives of non parametric regression curves eee 133 Derivatives of non parametric regression cCUrves esee netnnennntntenns 133 Plottine JOME density TUITCELOTEs sc eie oic oo o er a S MED 134 Plotting joint distribution function essere nennen nnne nnne nennen 136 Testing for bi dimensional poverty dominance
12. Oo Oo We assume that u and we estimate the variance using the procedure suggested by Shorrrocks and Wan 20089 a value for the standard deviation of log incomes o is obtained by averaging the m 1 estimates of o Q p 9 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 L a p L bL p 1 c p L We can regress L 1 L on p L L p 1 and p L without an intercept dropping the last observation since the chosen functional form forces the curve to go through 1 1 2 2 5 0 5 We have Q p Bik ir I 80 e at b ctl m b 4a n 2be 4c Beta Lorenz Curve Itis assumed that log p L log 0 y log p log l p After estimating the parameters we can generate quantiles as follows olp 0 p t py Z t See also Datt 1998 The Singh Maddala distribution The distribution function proposed by Singh and Maddala 1976 takes the following form 1 q Fa 1 where a2 0 b20 q21 aare parameters to be estimated The income x is assumed to be equal to or greater than zero The density function is defined as follows f x aq b 1 x b xb Quantiles are defined as follows ET l a Q p b 1 p 1 We follow Jenkins 2008 s approach for the estimation of parameter
13. cdomcZd The cdomc2d module draws difference or ratio 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 16 10 DASP and the progressivity curves 16 10 1 Checking the progressivity of taxes or transfers The module cprog allows checking whether taxes or transfers are progressive Let X bea gross income T be a given tax and D be a given transfer The tax T is Tax Redistribution TR progressive if PR p L p C p 0 Vp e J0 1 66 The transfer B is Tax Redistribution TR progressive if PR p C p L p 0 Yp 0 1 The tax 7 is Income Redistribution IR progressive if PR p C p L p 0 vp e 0 1 The transfer B is Income Redistribution IR progressive if PR p C p L p 0 Vp e 0 1 16 10 2 Checking the progressivity of transfer vs tax The module cprogbt allows checking whether a given transfer is more progressive
14. tererccolow Cer 06 This decomposition use the initial period as the one If the reference period is the final the decomposition takes the form P zya P zy a E A k P an a P ki e a k Witte group poverty ef Prem E are e K e 8 k demographic er gerceral effec D gt PA na PG na P409 9900 Pee ea ee Denm 06 To remove the arbitrarness in selecting the reference period we can use the Shapley decomposition approach finding P za P a a E UP Pi k n a Pe a a a Y F kona G 5 6 0 lk demegrashic er szctorul effects 07 where k is the average population share 5 7 K k and P ky 2 a m GEP kn a P ka a The DASP module dfgtg2d performs this sectoral decomposition and this by selecting the reference period of the Shapley approach see the following dialog box 47 Figure 10 Sectoral decomposition of FGT DASP Sectoral Decomposition of the FGT Indices gt dfgtg2d command Distribution 1 Distribution 2 Daainfie C data blf94l dta Datainfle C data bkf98l dta Variable of interest exppc Variable of interest exppcz Size variable size Size variable size Parameters and options Group variable gse Parameter alpha Poverty line z Reference ley approach LC O dfgtg2d exppc exppcz alpha 0 hgroup gse pline 41099 filel C data bkf94I dta hsizel size file2 C
15. 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 is 69 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 f x 24 Wik x Kj x n 2 Wi i where l X X K x expl 0 52 x and A x 08 exp 053 097 x and where the scalar K x is defined as K x w x P A x 2 s l P A 1 A MA 2 s 1 1 mi w x 2 M f keorceoro a l fea pa 1 0 0 0 min is the minimum bound and max is the maximum one h is the usual bandwidth This correction removes bias to order h DASP offers four options without correction and with correction of order 1 2 and 3 Refs e Jones M C 1993 simply boundary correction
16. 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 79 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 gt For NOBS 1000 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 1 2 Generating an initial distribution of incomes The user must indicate the form of distribution of the disaggregated data Normal and log normal distributions Assume that x follows a lognormal distribution with mean 4 and variance o The Lorenz curve is defined as follows Up o Beaters e 160 4
17. 1l x 2 Wi i l T l a where Q y a z vi Lz and By a z b a e Jn i t 49 and chronic poverty is given by CPC a z 2I o 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 Figure 11 Decomposition of poverty into transient and chronic components E DASP Decomposition of the total poverty into transient and chronic poverty gt dEcpov command ial x Main Results V ariable s of interest Decomposition approach pecansb5 pecon pecon33 pecanl1 Approach Jalan and Ravallion 1998 Censored incomes Parameters Parameter alpha Size variable hz Poverty line z v Bias correction Approach Analytic i Survey settings Cancel Submit The user can select 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 T
18. 35 pres asp p od 3s A hiatt a j l k m 14 6 The Inaki 2008 polarisation index ipoger Let a population be split into N groups each one of size n gt 0 The density function the mean and the population share of group i are denoted by f x 4 and z respectively 4 is the overall mean N N We therefore have that f x 1 gt Gb u and by Using Inaki 2008 a social i l i polarisation index can be defined as P F SIr i F P i F where j Baren r D 09 QUE x y dyds and Pia am u am i iis G9dx 1 f ie ood The module Stata dspol allows performing the decomposition of the social polarisation index P F into group components The user can select the parameter alpha The user can select the use of a faster approach for the estimation of the density function Standard errors are provided for all estimated indices They take into account the full sampling design The results are displayed with 6 decimals by default this can be changed The user can save results in Excel format The results show The estimated population share of subgroup i z The estimated income share of subgroup i 7 4 4 The estimated FP i F index of subgroup i The estimated P i F index of subgroup 1 Theestimated P gt P i F index The estimated P 2 P i F index The estimated total index P 36 To open the dialog box for module dsp
19. 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 of household head 1 Male 2 Female Zone Residential area 1 Rural 2 Urban 83 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 1999 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 equivalent T Income taxes per adult e
20. bini index Estinated inequality 0 508456 Sources Tncone Absolute Relat ive Share Contr ibut ion Contr ibut ion Harginal contribut ions Source loyal 1 level 2 leve 3 1 p cons DH A 32 ES e pt A673 1 375 1 648 3 pb 1 11ME6 OO 56 Example 2 Inequality regression based decomposition by predicted components using the Shapley value rbdineqs CF E ioj x M ain Results Regression and model specification Dependent Independent variables p tb Model SemiLog linear lag v 2 XB e Treatment af constant Suppress constant berm Size variable Approach index and eption s Appraac Shapley approach Index Generalised entropy Theta 0 7 Method Replace eliminated income source by its mean L ancel Submit Th lineqs t b deptx index ge thetalll 7 nodellsenilog dregres 0 Harnimg 115 OBS are onitted Dependant variable should not be lt D uith the senilog specificat ion Inequality regression based deconposition by predicted incone conponents using the Shapley value Execution tine O41 second s Inequality index Generalised entropy index Est inated inequality 0 306465 Sources Incone Hbsalute Relat ive Share Contr ibut ion Contr ibut ion Harginal contribut ions Source lewe 1 lewe level 3 1 p cans LN A 6 e opt Lee 1 3155300 1A 3 pb Le 0 DINE With this specification we have y E xp s
21. 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 13 FGT curves BS DASP FGT Curves gt cfgt command l I al x Main Results v wis Meis Title Caption Legend Overall V ariable s of interest Type of curve s Difference Ma Ln Size variable Group variable Parameters Parameter alpha o Minimum hd animum Poverty line z o 10000 Cancel Submit Interested users are encouraged to consider the exercises that appear in Section 23 4 61 FGT CURVE with confidence interval cfgts The cfgts module draws an FGT curve and its confidence 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 us
22. sourceb plinel 15000 hsizelhhsize hueightl ueighteal leaconposition of the FGT index by incone conponents using the Shapley value Execution tine 0 03 second s Paraneter alpha 0 00 Poverty line 15000 00 FGT index 0 584910 Household size hhsize Sanpling weight ueightea Sources Incone Hbsolute Relat ive Share Contr ibut ion Contr ibut ion snurcal sources sources sourced sources sourceb 44 arginal contribut ions Source level 1 tm im PI ro tm tm I a level 4 lewe 5 source 4 023228 Aa ALE LEA LUZ source J H D H DAA 05637 ILI S9 2H sources 0 0 D 0 00008 DA LENTES sourced 41 025759 1 025661 4 044 DA eE sourceb 0 001297 0044 0 01597 41 06 0 sourceh ALM I A 4 005 0 003536 70S level 6 sourcel 0 007 source mex sources 0 08 sourced 1 023376 sources 6d sourceh 0 0361 15 6 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 growth and redistribution components as follows P P Pu n1 P u 7 n e P u n2 P a R ref I variation C1 C2 Pp P PK 2 P u nt 2 22 P R ref 2 sg var lation mm Cl CC ME 03 where variation difference in poverty between t1 and t2 C1 growth component
23. y U x K x WOOK x x x v or alternatively of K 3 y a K x BK x x x v Estimates are then given by dy E j E y x a 2 x 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 71 2 2 x n X x Vox f Xw exp E E E E 2nhyh wi b 2 y i l With this module 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 Y wi Kx x I y y F x y El n Wi i l 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 coordinates can be
24. 0 000291 0 007 0 000325 0 0K 0 000170 0 014355 0 002459 0 110012 0 005623 0 010995 0 001332 0 139197 0 006553 dfgtg exppc hgrouplgse heizelsize alphald plinel41099 dstd 0 typelnor decidi FGT Index Deconposition by Groups Hage earning public sector Hage earning private sector Hrtisan or trading Others activities Farners crop Farners fond Tract ive POPULATION Popu lat ion 117 Share E 2838528 Absolute Contr ibut ion Relat ive Contr ibut ion 0 00 0 000640 0 016980 0 Sond 0 019015 0 078973 0 005520 1 000000 0 000000 Relat ive Contr ibut ion 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 bkf94Ldta 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 Q 1 Steps Type use C data can6 dta cle
25. 7 SS SOS 50000 ZLS ane 136 23 12 Testing the bi dimensional poverty dominance Using the columbia95IL dta distribution 1 and the dominican republic95I dta distribution 2 files m Answer Q 1 Steps Draw the difference between the bi dimensional multiplicative FGT surfaces and the confidence interval of that difference when Varofinteest Range alphaj haz _ height for age 30 60 0 Dimension 2 sprob survival 0 7 1 0 probability Test for bi dimensional poverty using the information above To open the relevant dialog box type db dombdpov Choose variables and parameters as in 137 co ooo er aa oOo ODO o C N OLE cO m 5 D565 o 2 ban x E a El id d un ES CN x ex Q 3 z 45 d 5 a 5 o o AV Qo 5 E My i iy MM e E c A MIA WMA AU Ca D VA i M VA TRAY e z S E l QA S SE E D gt MMR AWO V p EE E VIDEOR 3 gt NON Ka WU Y gt E g i AA QAO W Q PE S hs OCA AARON NS eo LE e ADAMS o n G S AAA IS V n Y e 4 2 3 WAR P e A C AOR WIV 1 K h A AXI S F E QUA i Aa eo EE 5 V MORE ois ak m LU XE DESIRES fe E 5 j TAX QS i i c me j e 2 5 S ig E ES Hos Y SE a E 5 i a gt 2 en c r1 Ss C Ek Gls A E A ON I SE v Soo EE og L o E 2 tz Li lt 138 Q 2 To make a simple test of multidimensional dominance one should check if the lower bounded co
26. Back Refresh Search Help Contents whats Mew Mews Command fhelpift 000000000000000 Lil DASP Distributive Analysis 5tata Package World Bank PEP and CIRPEE help for ifgt Dialog box idifqgt FGT Poverty Indices ifgt va 7 7 st HStze earsare Horoup arsare PLine esa7 OPL sivrag PROP neal PERC real ALpha s37 TrPE sierag InDex siriag LEVEL 237 CONF 5 577539 Where warlist is a list of variables wersion 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 Tiles If the sampling design is nat set simple random sampling CSRS will be automatically assigned by default with ifgt the following poverty indices and their standard errors will be estimated TE anda m mrm 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 required estimation 12 Figure 5 Estimating FGT poverty with one distribution ES DASP FGT and EDE FGT Index gt ifgt command Bl x Main Confidence Interval Results Index optionala Index FGT Index Type Normalized id Farameter s
27. Figure 33 Figure 34 Figure 35 Figure 36 Figure 37 Figure 38 Figure 39 Figure 40 Figure 41 Figure 42 Figure 43 SectoraldecompositoD zof FG T uei ten da iiiv d ence etit me dad 48 Decomposition of poverty into transient and chronic components 50 Decomposition of the Gini index by income sources Shapley approach 52 ek OC 60 ih seer me ore rere ee ari ert rarer te te meia MM IMMER 61 Lorenz and Concentration CUIVES acuit iti eere trier ie n HEU EM ERE REL E nd 63 Consumption GON Aan CE CuEVeS ea cti aio inc ib tati itus FU tens 66 npgroup dialog DO Xctautestextiiuteotibumletei elt rebua uns dt Lees ule a 92 SUEVeV OE d SOLLIDIBS cori caen iini ruta d aseo di s EE Ed rH ogee nse aes 87 Setups sampine welgHEs usse ce eee ie ee en el tn Lad 88 Esthmating BOT MIGICES uinea itor anu DE ADV IMS er 91 Estimating FGT indices with relative poverty lines sse 92 PGT indices ditrerentated Dy gender sa asaaeteditasde bd ngo ORE Oh blend aiia acc 93 Estimating differences between FGT indices eee 96 Estimating differences in FGT indices eese nennen 97 FGT differences across years by gender and zone 1 sss 98 Estimating multidimensional poverty indices A sess 100 Estimating multidimensional poverty indices B
28. a P P z a X g P z og B where G is the number of population subgroups The results show The estimated FGT index of subgroup 2 P z a g The estimated population share of subgroup g Ag The estimated absolute contribution of subgroup g to total poverty g P z A g The estimated relative contribution of subgroup g to total poverty Xe Pc a g P 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 ES DASP Decomposiotion of the FGT Index by Groups gt dfgtg command a x Main Results Indes aptian s Variable of interest Type Mat Normalized Size variable Group variable Parameters Parameter alpha ja Poverty line z i DOC Survey settings 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 39 15 2 FGT 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 equal to the poverty line A negative sign on a decomposition term indicates that an incom
29. 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 dad ecn ulaval ca pdf files shap dec aj pd 42 15 5 FGT 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 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 Qa z K aM 7 P ses gt ar k Y w i where w is the weight assigned to individual 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 dad ecn ulaval ca pdf files shap
30. all components including the constant and the residual With the Shapley approach the user can use the log linear specification However the user must indicate the income variable and not the log of that variable DASP automatically runs the regression with log y as the dependent variable Example 1 ESI Inequality regression based decomposition by predicted components using the Shapley value gt rbdineqs comman 1 rl x M ain Results Regression and model specification Dependent Independent variables Fk zl 1 d Model Linear y kB e M Treatment af constant Suppress constant berm Size variable Approach index and eptien s Appraac Shapley approach Index Gini Index m Method Replace eliminated income source by zero Cancel Submit 54 ESI Inequality regression based decomposition by predicted components using Ehe Shapley value rbdineqs command Mej x 55 Th lineqs t b deptx nethod zero dregrest1 sun of ugt is 1 00613 Source Hunber of obs 3000 FL 2 997 AM Hodel Prob gt F 0 000 Residual R squared 0 978 Adj R squared 0 977 Total Root ASE 526 9 P iti 957 Conf Interval t NNI 2M 2 5059026 b DO 6pdK5 704206 cons 0 0 TA 11626 98 Inequalitu regression based deconposition by predicted incone conponents using the Shapley valual Execution tine O66 second s Inequalitu index
31. 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 30 13 7 Coefficient of variation index icvar Denote the coefficient of variation index of inequality for the group k by CV It can be expressed as follows 1 n n 9 _ Xwy Xxw CV 1 1 1 1 2 T 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 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 9596 are provided Both the type of confidence int
32. 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 ia 1 if a 21 LST l 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 f u k azl _ z f k z u k if a 0 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 Ete 20 Figure 7 Poverty and the targeting by population groups DASP Poverty amp Targeting by Population Groups gt itargetg command ioj xj Main Results Graphical Results EHE Anis Title Caption Legend Overall Options and parameters Farameter alpha fo Normalized b
33. 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 9596 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 elasticities with respect to average income growth with different approaches efgtgro The overall growth elasticity of poverty is estimated using one approach among the following list e The counterfactual approach e The marginal approach e The parameterized approach e The numerical approach The module efgtgro allows the estimation of a poverty elasticity or semi elasticity with respect to growth with the different approaches mentioned above For more details on these approaches see Abdelkrim Araar 2012 Expected Poverty Changes with Economic Growth and Redistribution Cahiers de recherche 1222 CIRPEE To estimate a FGT elasticity semi elasticity with respect to average income growth in a group or in an entire population A group variable can be used to estimate
34. 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 expcap b parameter a 0 c poverty line between 0 and 100 000 Franc CFA d size variable set to size 5 Drawthe 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 Listthe coordinates of the graph 6 Redo the last graph witha 1 Answers Q 1 Open the file with use C data bkf94I dta clear Q 2 Open the dialog box by typing db difgt Q 3 Choose variables and parameters as follows 102 Figure 27 Drawing FGT curves E DASP FGT Curves gt cigt command z joi xl Main Results Y axis Anis Tithe Caption Legend Overall Type af curve s Type Normalised Difference Ma r V ariable s of interest exppc expe Size variable size Group variable Parameters Parameter alpha jo Minimum hd asinum Poverty line z jo f DODOL L ancel Submit To change the subtitle select the Title panel and write the subtitle Figure 28 Editing FGT curves E DASP FGT Curves gt cfgk command l E lox Main Results Anis Axis Tit
35. 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 Savingthe initialized data file Users are recommended to consult appendices A B and C 10 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 area or within female headed families One way to do this is to force DASP to f
36. f Relative eo X of the Median IF group variable is used poverty line is relative bo Survey settings The population After clicking on SUBMIT the following results should be displayed ifgt exppc alphalll hsizelsize opllnedian propt l Poverty Index FGT Index Household size size Sanpling weight ueight Paraneter alpha 0 00 Mar iabla Est inate STL LE UE P Lina eXxppc 0 155243 D ESS 76 0 1053 D a 2M 74 Q 5 Set the group variable to sex 92 Figure 21 FGT indices differentiated by gender ES DASP FGT and EDE FGT Index gt ifgt command al xj Main Confidence Interval Results Varable s of interest exppe rar Indes Normalised T Farameter a Size valable size Parameter alpha E Group variable zex Poverty line Absolute 41083 Relative EE of the Median IF group variable ts used poverty lineis relative bor Survey settings The population Cancel Submit Clicking on SUBMIT the following should appear ifgt ewppc alphall hsizelsize hgrouplsex pline 41099 Poverty Indes FGT Index Household size size Sanpling weight weight Group variable sex Paraneter alpha 0 00 Group Est inate STD LE UE P Line l Hale 0 621 1 016533 0 41484 1 454067 41099 00 3 Fenale 1 2810 II riral i 1 226111 1 33729 41099 00 OPULATION 0 444565 U 016124 0 412873 0 476256 41099 00 Q 6 Using the panel C
37. 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 parameter q 1 Answers Q 1 110 Steps Type use C data bkf94I dta clear To open the relevant dialog box type db cfgts Choose variables and parameters as in Figure 36 Drawing FGT curves with confidence interval I DA5SP FGT Curve with Confidence Interval gt cfgEs command After clicking SUBMIT the following appears 111 Figure 37 FGT curves with confidence interval FGT curve alpha 0 Burkina Faso 0 20000 40000 60000 80000 100000 Poverty line z Confidence interval 95 Estimate Q 2 Steps To open the relevant dialog box type db cfgtsd2 Choose variables and parameters as in 112 Figure 38 Drawing the difference between FGT curves with confidence interval ES DASP Curve of difference between FGT Indices gt cfgts2d command E 15 x Main Confid
38. is defined as B Sige Po S where B gt wBil Eg i These statistics can be restricted to specific socio demographic groups e g rural urban by replacing I 1 g byI 1ec The bian ado module allows the computation of these different statistics Some characteristics of the module O Possibility of selecting between one and six sectors Possibility of using frequency data approach when information about the level of total public expenditures is not available Generation of benefit variables by the type of public services ex primary secondary and tertiary education levels and by sector Generation of unit cost variables for each sector Possibility of computing statistics according to groups of observations Generation of statistics according to social demographic groups such as quartiles quintiles or deciles TI Public expenditures on a given service often vary from one geographical or administrative area to another When 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 This household contains 7
39. poverty at the level of a categorical group If a group variable is selected only the first variable of interest is then used The results are displayed with 6 decimals this can be changed 12 3 FGT elasticity with respect to Gini inequality efgtineq The overall growth elasticity INEL of poverty when growth comes exclusively from change in inequality within a group k is given by 23 9k f k z u k z Auk COO F z u I Poesia 09 7 2 z Pk zia 7D aout cao P z u I if a 0 INEL if 21 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 for group k and F z is the headcount C K is the concentration coefficient of group k when incomes of the complement group are replaced by u k J 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 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 a FGT elasticity with respect to average income growth in a group or in an entire 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
40. the lower bounded option for the confidence interval Figure 65 Testing the pro poor growth dual approach B ES DASP Pro poor curves dual approach gt cpropoord command Datainfle v C Documents and SettingsV raa Daaintle v C Documents and Settings Vira Inc Inc GL zIp GL T pl GL Tip After clicking SUBMIT the following graph appears 144 Absolute propoor curves Order s 2 Dif GL 2 p GL 1 p GL 2 p 0 184 368 552 36 92 Percentiles p Q 4 Steps To open the relevant dialog box type db ipropoor Choose variables and parameters as 145 BB DASP Pro poor indices gt difgt command 15 x Main Confidence Interval Results Distribution 1 Data in file csp amp TAsM excowmex 38 2ml d Browse Variable of interes inc hhsz Conditions 1 n Distribution 2 Data in file c DA TAM exco mex 4 Zml d Browse Variable of interest linc hhsz Size variable Size variable Condition s Parameters and options Parameter alpha i Poverty line 600 Type Marmalized m Cancel Submit After clicking SUBMIT the following results appear Poverty line 600 00 Paraneter alpha 1 00 Pru puur indices Esl ingale aT LE UB brouth ratelg 0 557359 1 12551 IL 336361 1 825357 Chen amp Ravallion 2003 index 0 H2205 1 06337 L2659M e O04 Kakuani amp P
41. 00218 000930 001222 001731 000768 001380 002417 000610 000234 000700 000930 010387 029328 005992 013963 012648 014336 016127 018726 001724 011681 002932 004317 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 E Wage earner public sector Wage earner private sector Artisan or trader Other type of earner Crop farmer Subsistence farmer D O 769 O OOO OG O OOOO Inactive SOO O CX OGO O O O OOGO 0D 48 15 8 Decomposition of FGT poverty by transient and chronic poverty components dtcpov This decomposes total poverty across time into transient and chronic components The Jalan and Ravallion 1998 approach Let yi 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 LN t a 2 25 wi z yi _ t li l TP a z x T gt Wi i The chronic poverty component is then defined as N X wiz niX CPC a z El x 2 Wi i l Transient poverty equals TPC a z TP a z CPC a z Duclos Araar and Giles 2006 approach Let y be the income of individual i in period t and u be average income over the T periods for individual i Let I a z be the equally distributed equivalent EDE poverty gap such that I o z TP o z Transient poverty is then defined as N 2 W409 0 2 TPC a z
42. 0945 CIRPEE http Aideas repec org p lvl lacicr 0945 html 14 DASP and polarization indices 14 1 The DER index ipolder 32 The Duclos Esteban and Ray 2004 DER polarization index can be expressed as DER a f x f y y x dydx where f x denotes the density function at x The discrete formula that is used to estimate this index is as follows 5 wif y a y DER a 2 Wi i The normalized DER estimated by this module is defined as ee DER DER a oe where 1 i l 2 Wj Wi 2 Wipe a j l j l a y j M Yi EXE A GG zi N 2 Wi 2 Wi 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 9596 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 indic
43. 128 23 11 Plotting the joint density and joint distribution function 134 23 12 Testing the bi dimensional poverty dominance seeeeeeuuseeee 137 23 13 Testing for pro poorness of growth in Mexico eeeeeeenene 140 23 14 Benefit incidence analysis of public spending on education in Peru 1994 146 List of Figures Figure 1 Ouput of net dQescrIDe dOSD 3uidncusa nct iet A 9 Pigure2 DASP SUD CMU eerte icm E A AEEA ETAN AERE SE ARRA EEUU ENEN 10 Figure 3 Using DASP with a command windoOW eese entente nnne tentent 11 FIgure 4 ACCESSING help On DA Potest wai divo eric e e E ix dati ipu c o beret 12 Figure 5 Estimating FGT poverty with one distribution eene 13 Figure 6 Estimating FGT poverty with two distributions eene 13 Figure 7 Poverty and the targeting by population groups essere renes 21 Figure 8 Decomposition of the FGT index by groups eene nennen tentent nn nnnns 39 Figure 9 Decomposition of FGT by income components essere tenente nnns 44 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 Figure 25 Figure 26 Figure 27 Figure 28 Figure 29 Figure 30 Figure 31 Figure 32
44. 5 5 FF s 5 Then e Wecannotestimate the income share no linear form 57 K e The contribution of the constant is nil y E xp s E xp s E xp s Adding a k l constant will have not any impact Example 3 Inequality regression based decomposition by predicted components using the Shapley value rbdineqs cor ioj x Main Results Regression and model specification Dependent Independent variables Fk zl 4 m Model Linear p eB e h Treatment af constant Iv Suppress constant term Size variable Approach index and options Approac Analytic approach Indes Squared coefficient of vari Cancel Submit Thdinegs t b depix index scvar apprianalyt ic noconstant dregres 0 Inequality regression based deconposition by predicted incone conponents Execution tine 0 1 second s Inequality indes Squared coefficient of variation index Estinated inequality 1 613027 Sources Incane Absolute Relat ive Share Contr ibut ion Contr ibut ion 15 11 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 5 9 1 uM R g l Within Overlap wr Between
45. 96 of all levels 1995 35 200 Secondary public education expenditure as 96 of all levels 1995 21 2 Tertiary public education expenditure as 96 of all levels 1995 1696 Public education expenditure as 96 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 expz0 03 0 352 r sum qui gen sec pub expz0 03 0 212 r sum qui gen uni pub exp 20 03 0 160 r sum cap drop _var1 Total public expenditures on primary sector pri pub exp Total public expenditures 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 Set variables and options as follows 148 Figure 67 Benefit Incidence Analysis unit cost approach ES DASP Benefit incidence analysis gt bian command B ioj x Main Results Label the public service Education Options Approach Unit cost benefit m V ariable s of interest Standard living Jexppe Number of sectors 2 Labels Frequency Eligible HH members Area indicator Regional pub expenditures Sector 1 Primary frq prim el prim pri pub exp Sector 2 Secondary ita sec 8l sec sec pub exp BS DASP Benefit incidence analysis gt bia
46. C data can6 dta clear To open the relevant dialog box type db cdensity Choose variables and parameters as in Figure 52 Drawing densities ES DASP Density Curves gt cdensity command l n x Main Results Anis xAxis Title Caption Legend Overall V ariable s of interest Parameters AM Minimum Masimum Hange o ponon Size variable v Override optimal bandwidth Group variable Bandwidth of fia Cancel Submit 128 After clicking SUBMIT the following appears Figure 53 Density curves Density Curves 00005 N 00001 00002 00003 00004 A 7 0 0 12000 24000 36000 Q 2 Steps To open the relevant dialog box type db c_quantile Choose variables and parameters as in 129 o 8 Figure 54 Drawing quantile curves B DASP Quantile amp Normalised Curves gt c quantile command After clicking SUBMIT the following appears Figure 55 Quantile curves Quantile Curves co 7 P dd d os m CN A C O pea aI O _ O 7 m d T T P r a A S 0 2 6 8 130 Q 3 Steps To open the relevant dialog box type db cnpe Choose variables and parameters as in Figure 56 Drawing non parametric regression curves LE i DASP Non parametric regression gt cnpe command Non parametric regression 7 Local linear appro
47. IT we should see Poverty Index FGT Indes Paraneter alpha 0 00 Est inate STL LE UE P Line Distribut ion 1 1 510344 0 0100 1 845 0 553149 41099 00 Distribution 0 5109 0 01995 1 423 1 54735 41099 00 Difference 0 000153 0 023100 0 045427 0 045121 Q 4 97 Poverty Index FGT Indes Paraneter alpha 0 00 Est inate aT LE UB P Line listribut ion 1 0 16573 0 016297 1 345 0 19008 41099 00 Distribution 2 D 103654 0 013419 0 07739 D 1359 41099 00 Difference 0 060889 0 021111 0 019513 0 102265 Mem 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 Setthe number of Condition s to 2 o Setsexin the field next to Condition 2 and type 1 in the next field Figure 24 FGT differences across years by gender and zone ES DASP Difference Between FGT Indices gt difgt command al x Main Confidence Interval Results Distribution 1 Distribution 2 Data in File C DATANDKFSBI dta Browse Data in File C DATANDK FSAI dta Browse Variable of interest Jexppez Variable of interest Jexppe Size variable size Size variable size Poverty line Poverty line Absolute 099 Absolute 099 C Relative tt the Mean z C Relative sH Zaf the Mean M Condition s Iv Condition s Condition 1 zone 2 Condition 1 zone AND C
48. ONFIDENCE INTERVAL set the confidence level to 99 and set the number of decimals to 4 in the RESULTS panel 93 ifgt exppc alphall hsizelsize hgrouplsex decid Poyarty Index Household size Sanplirng weight broup variable Paraneter alpha Group i Hale d Fenale POPULATION FGT Index size ua ight EB 0 00 Est inate 0 422 0 2619 0 4446 oT 0 1166 0 023 0 0161 94 level 99 plinel 41099 LE UE 0 4081 0 482 0 2009 0 38 0 4026 0 4603 P Line 41099 00 41099 00 41099 00 23 2 Estimating differences between FGT indices Has poverty Burkina Faso decreased between 1994 and 1998 1 Openthe 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 pov
49. PERU 2 Ota Em 85 22 1 6 The 1995 Colombia DHS survey columbial dta ssseeesssssss 85 22 1 7 The 1996 Dominican Republic DHS survey Dominican republic1996lI dta 85 22 2 Appendix B labelling variables and values sssseeeeesuueuuuees 86 22 3 Appendix C setting the sampling design sssesssseeeeeeeeeeeeeerennnnnnnns 87 23 Examples dnd exercISOSrzssec vid tees dtr E uiia Nu ee bt ders 89 23 1 EStimation of PGT poverty INGICES onset tette beet See oi ete de fee reste aas 89 23 2 Estimating differences between FGT indices eeeseeueesuuse 95 23 3 Estimating multidimensional poverty indices cccccseesessesssssesssssssesssssseseeeees 99 29 4 Bstimiatinp EG CUEVES cseteris No eta tete toi bat id dehet a Dude die Pu d es 102 23 5 Estimating FGT curves and differences between FGT curves with confidence DONG Vel is ecu neu a uut M i eae NE E ELE 110 23 6 Testing poverty dominance and estimating critical values 114 23 7 DECOMPOSING PGP IMC CES eesi AE SESER 115 23 8 Estimating Lorenz and concentration CUIVES cccccceeessessssesssssessesssessssessssseeeees 118 23 9 Estimating Gini and concentration curves cceeessssseeceeeeeeeeeeeeeeeeseseeeeeeesttaaeees 124 2910 Using Dasic dIStEIDUULIVE LOOMS su eres PE na beue Ua un Po Up ie oe ant iode eee bi ineduut
50. 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 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 ES a x Main Results Parameters Variable af interest income Parameter alpha jo Size variable hhsize r Poverty line z f 4837 Group variable zone Percentage af change 100 Survey settings Cancel 5 ubmit After clicking on SUBMIT the following should be displayed 25 efgtg income hgroup zone hsize hhsize alpha pline l4897 proil dec 3 Poverty and Inequality Indices FGT 0 585 Gini 0 617 Marginal Impact amp 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 12 6 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 inequ
51. USER MANUAL DASP version 2 3 DASP Distributive Analysis Stata Package By Abdelkrim Araar Jean Yves Duclos Universit Laval PEP CIRP E and World Bank june 2013 Table of contents flee 0 eke if ote alee 4h eee ere Nene eRe een ENT ee SRP Eee ENON RUT LT SE ARP SE OEE t S 2 IF EO 0 Bb i624 6 eee ere ene nee Re Te enn ME IU GER Ac M eer eee eee ee ee OD re 6 eA Odu EMO A ge ETE 8 yams BY AVS aaies 010 Stata VESON S enn ee ee ee ee 8 3 Installing and updating the DASP package 0c cccccccccccccsceeccceeececeeceeeceeeeeeeeeeeceeeeeeeeeeeeeeeeees 9 3 1 instalhng DASP MO Gules o5 did eei ES RET dumque ido VERE En bes Udo to usta dasenaeas 9 3 2 Adding the DASP submenu to Stata s main menu seesseeseeeeeeeeeeeerererns 10 A AST AMAA BUC ecce stcettbetietuien iecur ADSL E 10 5 Main variables for distributive analysis eesssssssssseeeeeeennen nnn 11 6 How can DASP commands be invoked eeeeeeeeenes 11 7 Howcan help be accessed for a given DASP module ssessssesseeeeeeereerr 12 o JApphcatons and TESA DAS omiin oot d ORE ro to nvi dosis a odd indo ossa eM 12 LN riori loatlente 14 1 DASP and poverty WACICES sistat eost vit onda iuro r Ete iis Abs 14 10 1 FGT and EDE FGT poverty indices if8t cc cccccccsceeeeeeeeeeeeeeeeeeeeeeseeeeeeeeeeees 14 10 2 Difference between FGT indices Cifgt ccc ccccccccceeceeeeeee
52. Unit atraturn Hlnits bs nin Hean Hay 1 Ea zm 19 21 i Pa d M fas 17 19 8 zt 3 05 1950 19 1 0 A 4 5 103 19 19 9 Pa n ob 1226 13 19 5 Pa 4 Hn 1 19 0 zt 7 97 1937 19 2i i ul 7 435 00 5 1 19 8 Pa 88 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 Usethe 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 expeq a You should set SIZE to household size in order to estimate poverty over the population of individuals b Usethe 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 6096 of the median 5 Using the official poverty 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_
53. Users abara AppData Local Temp STDOc Multidimensional inequality gt gt Pro poor curves dual approach 2 do C Users abara AppData Local Temp NSTDO cC Polarization gt 146 3 _daspmenu Poverty 7 Multidimensional poverty d window menu append item Benefit analysis Pro poor gt gt Benefit incidence analysis db Poverty and targeting policies gt 147 window menu append item Benefit analysis ME Marginal benefit incidence analysi Poverty elasticities gt 148 Decomposition gt FGT Decomposition by groups Dominance gt FGT Decomposition by income sources f 2st Curves d FGT Growth and redistribution Distributive tools d FGT Sectoral decomposition fe Benefit analysis gt FGT Decomposition into transient and chronic components dl Disaggregating data gt Foster and Alkire 2007 index by groups Variables Hypothesis tests gt Foster and Alkire 2007 index by dimensions using the Shapley approach Variable Label There are no items to show Generalized entropy Decomposition by groups Gini Decomposition by groups Gini Decomposition by income sources gt Inequality decomposition by income sources Regression based decomposition of inequality DER Decomposition by population groups DER Decomposition by income sources daspmenu To add the DASP sub menus the file profile do which is provided with the DASP package must be copied into the PERSONAL directory If the file profile do already
54. V ariable s of interest Po Size variable l Farameter alpha Group variable Poverty line Absolute 10000 C Relative sH Z of the Mean IF group variable ie used poweri line ie relative Far Survey settings The population Cancel Submit 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 E ioj x Main Confidence Interval Results Distribution Z Data in Merncry T Data in File E DATAsbkf94 dta Browse Variable of interest Variable of interest Size variable Size variable Poverty line Poverty line Absolute 10000 Absolute 10000 C Relative sH 5 n the Mean C Relative co Bai the Mean Condition s Condition s Distribution 1 Parameters and Options Parameter alpha ja Type Normalised Cancel Submit 13 Notes 1 DASP considers two distributions to be statistically dependent for statistical inference purposes if the same data set is used the same loaded data or data with the same path and filename for the two distributions 2 Ifthe option DATAIN FILE is chosen the keyboard must be used to type the name o
55. a Faso 1 Open bkf94Ldta and decompose the average poverty gap a with variable of interest exppc b with size variable set to size c atthe official poverty line of 41099 Francs CFA d andusing the group variable gse Socio economic groups 2 Dothe above exercise without standard errors and with the number of decimals set to 4 115 Answers Q 1 Steps Type use C data bkf94I dta clear To open the relevant dialog box type db dfgtg Choose variables and parameters as in a Normalised 0 0 0 O m After clicking SUBMIT the following information is provided 116 dfgtg exppc hgrouplgse heizelsize alphald plinel41099 tupelnar FGT Index Deconposition by Groups Hage earning public sector Hage earning private sector Artisan or trading thers activities Farners crop Farners food Tract ive POPULATION Q 2 Using the RESULTS panel change the number of decimals and unselect the option DISPLAY STANDARD ERRORS 0 004237 0 002571 D 022176 0 010678 D E 0 004653 0 15 0 025805 0 137525 D 11818 0 162094 0 00643 0 144916 0 014994 0 139197 0 006553 Fopulat ion Share 0 042071 0 005790 0 005 0 002164 0 0 004206 0 000050 D 001308 0 10442 0 014696 0 65065895 0 016403 0 075056 0 004639 1 00000 0 000000 After clicking SUBMIT the following information is obtained Abszolute Contr ibut ion 0 0 HS 0 000117 0 0S9
56. ach 7 After clicking SUBMIT the following appears 131 Figure 57 Non parametric regression curves Non parametric regression Linear Locally Estimation Approach Bandwidth 3699 26 E Y X 10000 15000 20000 5000 0 12000 24000 36000 48000 X values Q 4 Steps Choose variables and parameters as in 132 Figure 58 Drawing derivatives of non parametric regression curves BS DASP Non parametric regression gt cnpe command 2 al x Main Results v Awis Meis Title Caption Legend Overall V ariable s of interest Regression and approach options v Regression Derivatives of non parametric regression v Approach Local linear approach m Parameters Minimum Masimum Size variable Hange jo E0000 Group variable v Override optimal bandwidth Bandwidth of f lH Cancel Submit After clicking SUBMIT the following appears Figure 59 Derivatives of non parametric regression curves Non parametric derivative regression Linear Locally Estimation Approach Bandwidth 3699 26 LO gt lt S pen Xo 7 07x T id p ui sc RENNES Nd ec P ad LLI d O P d A A LO Pd A 0 12000 24000 36000 48000 60000 X values b 133 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
57. ain Confidence Interval Results Distribution 1 Distribution 2 Data in Fie CNDATANDKIS8L dta O Browse Data in File m CADATANDKAS4 dta Browse Variable of interest Uc II Variable of interest epee Ranking War ER Ranking Var o Um Size variable fize CiS Size variable ize Condition s Conditions L ancel Submit After clicking SUBMIT the following information is obtained digini expagz expeq filell data bkfUBI dtal hzizellzizel file C data bkfU4I dtal hzizeg zizel Est inate 5 TI LE UE Distribution 1 GTHTI 0 44665 0 012616 0 419371 0 469755 Distribution 2 GTHT 0 45055 0 009618 0 433116 1 466004 Difference 1 0054972 0 015444 0 035762 0 024778 127 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 Drawthe 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 Usea 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 Usea local linear estimation approach Q 1 Steps Type use
58. ality 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 CIRPEE Department of Economics Universit Laval To open the dialog box of this module type the command db efgtc 26 ES DASP FGT Poverty elasticities with respect Eo income sources inequalities efgtc command ol x Main Results V ariable s of interest Income components sourcel sourceb Total income income Decomposition approach Approach Won truncated income components Non truncated Income components Truncated income components Parameters Parameter alpha o Size variable hhsize Poverty line z f 4387 Percentage of change f j Survey settings L ancel Submit After clicking on SUBMIT the following should be displayed efgtc sourcel sources tot income hsize hhsize alpha 0 pline 14897 prc l Poverty and Inequality Indices oe omm FGT 8 584667 Gini 0 616503 Marginal Impacts amp Elasticities of poverty with respect to the within between inequality in income components Source Income Impact on Impact on Elasticity Share Inequality Poverty sourcel 0 352966 0 097233 0 385605 n k i Sourcez 0 199865 06 0 032419 0 5317610 Source3 0 023131 l 0 002508 0 211784 sourced 0 344093
59. and its confidence interval by taking sampling design into account The module can 63 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 clorenzsZd The 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 cp
60. ant the case of the estimated constant To deal with these two problems Wang 2004 proposes the following basic rules Let Y s S 5 4 5 and Y s s t s then y 2 es I y cs The contribution of the constant cs y I The contribution of the residual cs y I y The Gini index Using Rao 1969 s approach the relative Gini index can be decomposed as follows wy Hi A I y C H where 44 is the average of y and C is the coefficient of concentration of s when y isthe ranking variable The Squared coefficient of variation index As shown by Shorrocks 1982 the squared coefficient of variation index can be decomposed as y wiCowy s i5 Od k l Shapley decompositions The Shapley approach is built around the expected marginal contribution of a component The user can select among two methods to define the impact of missing a given component e With option method mean when a component is missing from a given set of components it is replaced by its mean e With option method zero when a component is missing from a given set of components it is replaced by zero As indicated above we cannot estimate relative inequality for the residual component 53 e For the linear model the decomposition takes the following form y y cs where r the contribution of the residual is cs I y I y e For the Semi log linear model the Shapley decomposition is applied to
61. ar To open the relevant dialog box type db clorenz Choose variables and parameters as in 118 Figure 43 Lorenz and concentration curves ES DASP Lorenz amp Concentration Curves gt clorenz command After clicking SUBMIT the following appears 119 Figure 44 Lorenz curves R Graph Graph EN ioj x Lorenz Curves Q 2 Steps Choose variables and parameters as in 120 Figure 45 Drawing concentration curves ES DASP Lorenz amp Concentration Curves gt clorenz command After clicking on SUBMIT the following appears 121 Figure 46 Lorenz and concentration curves R Graph Graph E ioj x Lorenz and Concentration Curves T EL un m mms oee f ae ee zc ea ae QC m ad QE E B e ad n N eso 7 E a ea eS E D a ra fe S Pa E d al oo Lua id i n r SU a um a di p m T m 6 p p o p xu E ee eet ae O 2 4 B Fercentiles ip line 45 Cipi Hl Cip B2 Cipi BS Q 3 Steps Type use C data bkf94I dta clear Choose variables and parameters as in 122 Figure 47 Drawing Lorenz curves E DASP Lorenz amp Concentration Curves gt clorenz command Figure 48 Lorenz curves F Graph Graph Lorenz Curves LM MET E weer M 123 23 9 Estimating Gini and concentration curves By how much do taxes and transfers affect inequa
62. are R areas the area here T refers to the geographical division which one can have reliable information on total public expenditures on the studied public service E5 be total public expenditures on sectors G 93 3 r Here are some of the statistics that can be computed 1 The share of ag in sector s is defined as follows n wf eg S _ i l SH REIN RD gt wif i G P S Note that gt SH zl g l 2 Therate of participation of a group g in sector s is defined as follows wif la Eg S _ i l CR EL gt weil Eg i This rate cannot exceed 100 since f ei Vi 3 The unit cost of a benefit in sector s for observation j which refers to the household members that live in area r E UC Dr S 2 wifi j l where n is the number of sampled households in area r 4 The benefit of observation 1 from the use of public sector s is 5 The benefit of observation 1 from the use of the S public sectors is 76 S B Bi s l 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 2 4Bi I1 e g ABE El 2 w eil ie g i l The average benefit for those that use the service s and belong to a group g is defined as w BiI ie g ABF gt wif ICi eg i l The proportion of benefits from the service from sector s that accrues to observations that belong to a group g
63. ategorical 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 9596 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 a can be chosen for each of the two distributions Interested users are encouraged to consider the exercises that appear in Section 23 2 15 10 3 Watts poverty index iwatts The Watts poverty index is estimated as J w In z yj P z E
64. 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 069 0g Sampling weight size byte 8 0g Household size strata byte 098 0g Stratum in which a household lives psu byte 8 0g Primary sampling unit gse byte 0629 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 89 Sex m 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 indicated 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 puaight meight NCE Linearized Strata 1 strata ol 1 psu FPE 1 zeros bs per Unit Stratun Hlnits Hbs Hin Hear Har 1 cra zm 19 70 0 A d M H3 17 19 8 zt 3 05 1950 19 2i i 2 4 5 13 19 19 9 21 n bb 1226 13 19 5 Pa 4 Tr 1 19 0 zt 7 97 1937 19 1 0 A 7 45 0075 1 19 8 Pa
65. ceived source 6 All other income The Stata data file is saved after initializing its sampling design with the command svyset e loopen the dialog box for module dfgts type db dfgts in the command window 40 Figure 1 Decomposition of the FGT index by income components G Decomposition of the FGT index by income components using the Shapley value gt dfgts command O x Main Results V ariable s of interest Parameters source seurceG Parameter alpha D 15000 Size variable hhsize Weight variable weightea Poverty line z 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 dfgtz sourcel sourceb plinal 15000 hsizelhhsize hueightl ueighteal leconposition of the FGT index by incone conponents using the Shapley value Execution tine 0 03 second s Paraneter alpha 0 00 Poverty line 15000 00 FT index 0 554910 Household size hhsize Sanpling weight ueightea Sources Incone Absolute Relat ive Share Contr ibut ion Contr ibut ion s urcal sourced sources sourced sourced source 41 arginal contribut ions loyal 1 leyal 2 lewel 3 level 4 lewe 5 sourced ALIAS D Ae DEH LUZ RS ource J H D H DAA 05637 4 594 sources ALO D
66. composition the rule that is used to estimate the inequality 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 that equals the sum of the components of the subset plus the average of the complement subset Note that the dsineqs 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 dad ecn ulaval ca pdf files shap dec aj pd To open the dialog box for module dsginis type db dsginis in the command window 5 Figure 12 Decomposition of the Gini index by income sources Shapley approach Ex Decomposition of the Gini index by income components using Ehe Shapley value gt dsginis command as oO x Main Results V ariable s of interest source source Size variable hhsize Weight variable Cancel Submit 15 10 Regression based decomposition of inequality by income sources A useful approach to show the contribution of income covariates to total inequality is by decomposing the latter by the predicted contributions of covariates Formally denote total income by y andthe set of covariates by X Duo giu bel Using a linear model specification w
67. d the level of confidence used can be changed 68 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 percentile p of a continuous population is given by Q p F p where p F y is the cumulative distribution function at y For a discrete distribution let n observations of living standards be ordered such that VY Sy SS Yi S Yia Sosy HF lt p SF Yni we define Q p y The normalised quantile is defined as Q 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 f x 2 sK 0 and K x cu l 2 exp 0 54 x7 and A 9 hd 27 i
68. data bkf98I dta hsize2 size ref 0 Decomposition of the FGT index by groups Group variable gse Parameter alpha 0 00 Population shares and FGT indices Initial Final Final Difference in FGT index Pop share FGT index FGT index 042971 003790 026598 002164 062640 004288 006650 001308 104402 014896 680885 016403 075856 004839 022406 012599 067271 024093 097548 014712 194481 060817 500707 034911 514999 021132 414986 035336 041403 003927 029035 002624 055795 004666 005689 000923 167806 014125 653552 015083 046719 003354 Population 000000 444565 000000 452677 008113 000000 016124 000000 010927 019477 Decomposition components 059094 023396 111283 023087 126776 018202 293404 089680 424391 024457 533956 011572 386852 032340 036688 026573 044012 033369 029228 023404 098923 108357 076316 042625 018957 024093 028134 047901 Wage earner public sector Wage earner private sector Artisan or trader Other type of earner Crop farmer Subsistence farmer 3 Oo CQ C C C C C C Oo 5 Oo Inactive CO O O UCM ED SD CY SD O O CO OD oC IS OOS HOD IS OOS OOO C 0C D CX C CX O O IOS OG CO OS SS OS OS O GOG cO C CX cC o o0 O Poverty Population Interaction Component Component Component 001548 000064 001117 001931 001224 0
69. dec aj pd Empirical illustration with a 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 43 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 G Decomposition of the FGT index by income components using the Shapley value gt dfgts command f oO xl Main Results V ariable s of interest Parameters source seurceG Parameter alpha D 15000 Size variable hhsize Weight variable weightea Poverty line z 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 dfgtz sourcel
70. dta file 4 Estimate the joint density function for gross income X and net income N o Xrange 0 60000 o Nrange 0 60000 5 Estimate the joint distribution function for gross income X and net income N o Xrange 0 60000 o Nrange 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 60 Plotting joint density function ES DASP Joint Density Surfaces gt sjdensity command 2l x Main Resulta Parameters Minimum Masimum H of partitions Range Dum 1 0 E0000 30 Range Dim 2 E E0000 a V ariable s of interest Dim 1 variable Dum 2 variable v Override optimal bandwidths Bandwidth of kernel Dim 1 f Bandwidth of kernel Dim 2 f O Size variable Group variable Group number Cancel Submit After clicking SUBMIT the following graph is plotted interactively with Gnu Plot 4 2 134 Joint Density Function 3e 009 2 5e 009 2e 009 1 5e 009 1e 009 5e 010 0 Dimension 1 Dimension 2 6000060000 Q 2 Steps To open the relevant dialog box type db sjdistrub Choose variables and parameters as in 135 Figure 61 Plotting joint distribution function After clicking SUBMIT the following graph is plotted interactively with Gnu Plot 4 2 Joint Distribution Function F x y i UNS SRS EES SS
71. e m Perform the most popular poverty and decomposition procedures m Check for the ethical robustness of distributive comparisons 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 friendly 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 10 0 or higher o ado files must be updated To update the executable file from 10 0 to 10 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 Make sure
72. e component reduces poverty Assume that there exist K income sources and that s denotes income source k The FGT index is defined as n Qa r K gt wi t 7 Pl zay 3 amp J 5 i where w is the weight assigned to individual 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 dad ecn ulaval ca pdf files shap dec aj pd Empirical illustration with a 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 re
73. e have y f Bat By Bx t Bexg t where and denote respectively the estimated constant term and the residual Two approaches for the decomposition of total inequality by income sources are used 1 The Shapley approach This approach is based on the expected marginal contribution of income sources to total inequality 2 The Analytical approach This approach is based on algebraic developments that express total inequality as a sum of inequality contributions of income sources With the Shapley approach e The user can select among the following relative inequality indices e Gini index e Atkinson index e Generalized entropy index e Coefficient variation index e The user can select among the following model specifications e Linear y B Bx Boxy tt Bux e Semi Log Linear log y B Bx Bx desse oe E 22 With the Analytical approach e The user can select among the following relative inequality indices e Gini index e Squared coefficient variation index e The model specification is linear Decomposing total inequality with the analytical approach Total income equals y 5S 5 5 5 8 Where s is the estimated constant s D X and s is the estimated residual As reported by Wang 2004 relative inequality indices are not defined when the average of the variable of interest equals zero the case of the residual Also inequality indices equal zero when the variable of interest is a const
74. e 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 96 of the population found at the top or at the bottom must also be specified Remarks e If only the total number of observations is set the generated data are self weighted or uniformly distributed over percentiles e Ifanumber 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 to the generated income variable Example Assume that the total number of observations to be generated is set to 1900 but that we would like the bottom 1096 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 e The generated income vector takes the name of y and the vector weight w e 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 e The user can select any sample size that exceeds number of classes
75. eeeeeeeeeeeeseeeeeeeeeeees 15 10 3 Watts poverty index 1WAIIS 4st eI eb Ue bred atdas obe edt e E ee taba m ied so 16 10 4 Difference between Watts indices diwatts sssssseeeennen 16 10 5 Sen Shorrocks Thon poverty index isst eesssseeeennnnn 17 10 6 Difference between Sen Shorrocks Thon indices disst 17 10 7 DASP and multidimensional poverty indices ssssssseeeen 17 10 8 Multiple overlapping deprivation analysis MODA indices 19 11 DASP poverty and tarsetine polle Sina ate e HO n mt me eeu 20 11 1 Poverty and targeting by population groups seseeeeeeeeernr 20 11 2 Poverty and targeting by income components ssseeeeeeeeeerrrrrrerrreerennn 21 12 Marginal poverty impacts and poverty elasticities eeeeeeeeeeeeeeeeeeeeeee 22 12 1 FGT elasticity s with respect to the average income growth efgtgr 22 12 2 FGT elasticities with respect to average income growth with different approaches OTO LErO E E ecc E 25 12 3 FGT elasticity with respect to Gini inequality efgtineq eeesssses 23 12 4 FGT elasticity with respect to Gini inequality with different approaches efgtine 24 12 5 FGT elasticities with respect to within between group components of inequality iorbg e
76. ence interval Line options Results Anis Anis Title Caption Legend Overall Distribution 2 Data in file EDATAsbktS8L dta Browse Variable of interest Jexpped Size variable size Condition z 1 Distribution 1 Data in File E DATA bk dta Browse Variable of interest Jexppe Size variable size Condition z 1 Parameters and options Parameter alpha E Type Normalized m Minimum Maximum E f oooga Poverty line z L ancel Submit Figure 39 Difference between FGT curves with confidence interval o 0 Difference between FGT curves alpha 0 ES oO jf cc ww ww cs Ne X ws A ws A M ws ws A A ws ws ws ws ws M LO e 0 20000 40000 60000 80000 100000 Poverty line z Confidence interval 95 Estimated difference 113 Figure 40 Difference between FGT curves with confidence interval a 1 Difference between FGT curves alpha 1 e oO cg ce ce ws cs cs cs cs cs cs cs cs cs cs ss cs CN e Y e 0 20000 40000 60000 80000 100000 Poverty line z Confidence interval 95 Estimated difference 23 6 Testing poverty dominance and estimating critical values Has the poverty increase in Burkina Faso between 1994 and 1998 been statistically si
77. entration curves with confidence interval fendi A EE 64 T6 7 Poverty curves CDOVOFPEY esee ied ov bove pietate E bi etsupta tuto eo tiri e tbe vasa eds 64 16 8 Consumption dominance curves cdomc sssssssesseeeeerresesssssssssssssrsrrrerrreressssssssse 65 16 9 Difference Ratio between consumption dominance curves cdomc2d 66 16 10 DASP and the progressivity curves cccccccccccccseeeeeceeeeeeeeeceeeceeeeeseeeseeeeeeeeeeeeeeeeees 66 16 10 1 Checking the progressivity of taxes or transfers essere 66 16 10 2 Checking the progressivity of transfer vs tax esses 67 17 PDO UU ATV CO venei dread a cre ani an E den cerro ep crinem euni N 67 17 1 Povertydommance dOmbpoY ec B RU i Ha a patet eS 67 17 2 Anequality dominance domllieq usus ne inte or aede mda 68 17 3 DASP and bi dimensional poverty dominance dombdpov 68 18 DUS Gr IDULIVE TOONS odit et t dein eee i NM MIN eens eee 69 TIST Quannmlecurves cquahule csset e bri bv a a 69 18 2 Income share and cumulative income share by group quantiles quinsh 69 19 3 J Densibcuryes cdensity osos ote ES SaEu d co NR V YER Un e ORUI T LOU ETE EEUU UR cS 69 18 4 Non parametric regression curves cnpe ssesesseeeeeeeeerreneerennennnnnnnnnnnnnns 71 18 4 1 Nadaraya Watson approach sss nnne nennen enne nnn nnns 71 t342 iLocabimeardpDDEOGUDl cse eae aa
78. er alpha Survey settings Cancel Submit After clicking SUBMIT the following results appear laconpazition of the social polarisation index by population groups Household size size Sahpling ueight weight Group variable inz lew Paraneter alpha 0 50 Social polarisation index 65413204 0 00854255 Batueen lroup L anponent Hithin broup Conponarit Popu lat ian Incone Share share Main references D MA 0 021118 0 202791 0 021539 D 366762 0 026543 1 00 0 000000 1 200271 0 019042 0 61516 0 032054 1 262255 0 027982 1 0000 0 000000 DKA 0 004381 0 027714 0 005099 D 0290 0 005965 0 0478 0 002360 1 2135 0 01522 0 119772 0 009773 0 2 0 020541 0 50954 0 010026 1 DUCLOS J Y J ESTEBAN AND D RAY 2004 Polarization Concepts Measurement Estimation Econometrica 72 1737 1772 2 Tian Z amp all 1999 Fast Density Estimation Using CF kernel for Very Large Databases http portal acm org citation cfm id 312266 3 I aki Permanyer 2008 The Measurement of Social Polarization in a Multi group Context UFAE and IAE Working Papers 736 08 Unitat de Fonaments de l An lisi Econ mica UAB and Institut d Analisi Economica CSIC 38 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 zs G
79. erche 0806 CIRPEE 15 14 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 l where CP OAOT and y are respectively the pseudo concentration index and a a l Wi My income share of income sourcek 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 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 Testfor poverty dominance between two distributions 60 3 Test pro poor growth 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 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
80. erest 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 Figure 14 Lorenz and concentration curves ES DASP Lorenz amp Concentration Curves gt clorenz command i Ioj x Main Results v Awis M Awis Title Caption Legend Overall Type of curve s Type ormalised by default Difference Ma V ariable s of interest Range of percentiles p Size variable Group variable Maximum Minimum 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
81. ernia 2000 index 1 325436 03TH 1 115627 1 53524 PEGE index 1 771879 1 137331 LA 1 PEGR q 0 199520 0 040357 LHA 1 206257 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 146 Answer Type db bian in the windows command and set variables and options as follows Figure 66 Benefit incidence analysis ES DA SP Benefit incidence analysis gt bian command pin E sm E Send mnes m folsec m After clicking on Submit the following appears 147 Benefit Incidence Analysis Education Share by Quintile Groups Groups Prinary Secondary Quintile 1 Quintile Quintile 3 Quint ile 4 Quintile 5 All Groups Prinary secondary Quintile 1 l 762 1 325 Quintile 2 0 0 0 363 Quintile 3 D 772 1 33 Quintile 4 1 683 1 279 Quintile 5 1 472 0 14 All 1 500 1 287 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
82. ers are encouraged to consider the exercises that appear in Section 23 5 16 3 Difference between FGT CURVES with confidence interval cfgtsZd 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 are 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 meo quc 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 62 draw more than one Lorenz or concentration curve simultaneously whenever more than one variable of int
83. erty 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 20 Set the significance level to 5 and assume that the test statistics follows a normal distribution a Answers Q 1 Open the dialog box by typing db difgt Q 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 95 Figure 22 Estimating differences between FGT indices ES DASP Difference Between FGT Indices gt difgt command Main Confidence Interval Results Distribution 1 Data in File E DATA bKE981 dta Browse Variable of interest Jexppez 15 x Distribution 2 Data in File EADATASbKESAL dta Browse Variable of interest Jexppe size 41088 zm D the Mean Condition s 1 size HE 502 x otthe Mean 7 ESTE Size variable Size variable Poverty line Poverty line f Absolute f Absolute Relative C Relative Condition s Parameters and Options Parameter alpha jo Type Mormalised
84. ervals 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 coefficient of variation dicvar This module estimates differences between coefficient of variation 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 13 9 Quantile share ratio indices of inequality inineq The quantile ratio is estimated as Q pi QR pi p3 2 p1 p2 p where Q p denotes a p quantile and p and p are percentiles The share ratio is estimated as GL p2 GL p1 SR pl p2 p3 p4 cae GL p4 GL p3 3l where GL p is the Generalised Lorenz curve and p4 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 If a group variable is selected only the first variable of interest is then used Standard errors and confidence inter
85. es 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 Conditions can be specified such as to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 9596 are provided Both the type of confidence intervals provided and the level of confidence used can be changed 33 The results are displayed with 6 decimals this can be changed 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 F 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 Unive
86. f 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 Vi value of the variable of interest for observation i hw sampling weight hw sampling weight for observation i hs size variable hs size of observation i for example the size of household i Wi hw hs hg group variable hgi group of observation i wik swik sw if hgi k and 0 otherwise n sample size For example the mean of y is estimated by DASP as i 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 2 Wi e Yi E P z g gt Wi i l where z is the poverty line and x max x 0 The usual normalised FGT index is estimated as P z a P z a z 14 The EDE FGT index is estimated as EDE P z Qa P a for 0 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 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 c
87. 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 Reflection approach The reflection estimator approaches the boundary estimator by reflecting the data at the boundaries f x 25 wisi x 2 Wi i K x K 2 Eton AX one h h h Refs e Cwik and Mielniczuk 1993 Data dependent Bandwidth Choice for a Grade Density Kernel Estimate Statistics and probability Letters 16 397 405 70 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 24 Wi Ki x yj Eje 019 n CO From this the derivative of y x with respect to x is given by 2 ae The local linear approach is based on a local OLS estimation of the following functional form 18 4 2 Local linear approach K x
88. 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 an optimal partition of the distribution for a given number of groups p This means selecting the partition that minimises the Gini index value of within group inequality Error G f G p see Esteban et al 1999 The measure of polarisation proposed by Esteban et al 1999 is therefore given by PER f ap B Y Spip Ih puy PB G G j l k l where B20 is a parameter that informs about the weight assigned to the error term In the study of Esteban et al 1999 the value used is B 1 The Stata module ipoegr ado estimates the generalised form of the Esteban et al 1999 polarisation index In addition to the usual variables this routine offers the 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 searches 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 Q 100 3 The parameterp To respect the scale invariance principle all incomes are divided by average income i e pp u In addition we divide the index by the scalar 2 to make its interval lie between 0 and 1 when a I
89. ge 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 Af Rz jen F z GREL P P k z P k z 1 Fazi P z a 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 22 Araar Abdelkrim and Jean Yves Duclos 2007 Poverty and inequality components a micro framework Working Paper 07 35 CIRPEE Department 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
90. ged 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 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 28 Standard errors and confidence intervals with a confidence level of 9596 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 2 yw 2 1 if 620 n 0 0 1 X w i i i 0 a Ewig f if 0 0 Y w 1 1 i Qoi it 0 1 w 1 H i 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 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 B
91. gnificant 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 Q 1 Steps To open the relevant dialog box type db dompov Choose variables and parameters as in 114 Figure 41 Testing for poverty dominance EB DASP Poverty Dominance gt dompov command a x Main Results Distribution 1 Data in File CADATAMbKISA dta Browse Variable of interest Jexppe Size variable size Distribution 2 Data in File C DATASDKESBI dta Browse Variable of interest esppde Size variable size Condition z Condition z Dominance order Second order Cancel Submit After clicking SUBMIT the following results appear Hunber of Critical Hin range of Has range of Case intersect ion pow line pov lines pow line 1 2262 8 n i 675 052 B Hotes case A Before this intersection distribution doninates distribution 1 rase B Before this intersection distribution 1 doninates distribution rase C Mo doninance before this intersect ion 23 7 Decomposing FGT indices What is the contribution of different types of earners to total poverty in Burkin
92. gt 0 Y p e 0 p F or equivalently if Q p Qi p Sad d Q p 1 gt 0 v pe 0 p F z The change in the distribution from state 1 to state 2 is first order relatively pro poor if Q p u Az Goo pe 0 p 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 0 V p e 0 p F z or equivalently if _GL p GL p TP gt 0 Y pe 0 p F z A z s The change in the distribution from state 1 to state 2 is first order relatively pro poor if 74 A z s GL p 5 gt 0 Y p e 0 p F z GL p 44 The module 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 list or 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
93. he results are displayed with 6 decimals this can be changed References Jalan Jyotsna and Martin Ravallion 1998 Transient Poverty in Postreform Rural China Journal of Comparative Economics 26 2 pp 338 57 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 50 15 9 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 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 an Exact Approach with an Illustration Using Cameroonian Data Working paper 02 06 CIRPEE Shapley approach The dsineqs module decomposes inequality indices into a sum of the contributions generated by separate income components The dsineqs Stata module estimates The share in total income of each income source kK 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 de
94. ic and Health Surveys Republic Dominican_1996 witch contains the following information for children aged 0 59 months 85 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 the command window 8 delim Todropalllabel 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 nactive J To assign the label values Ivgse to the variable gse label val gse lvgse label var sex Sex of household head 86 label def lvsex 1 Male 2 Female
95. individuals Three individuals in this household are eligible to the public service Only 2 among the 3 eligible individuals benefit from the public service 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 level This would occur when the information on public expenditures is only available at the national level 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 78 21 Disaggregating 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 010 030 0 50 0 60 0 90 1 00 Lorenz values L p The user must specify th
96. ion Plotting the Lorenz curves v Plot the Lorenz curves of the aggregated and generated data vw Adjust the generated sample to match the aggregated 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 the true data with those of the data generated through disaggregation of the previously aggregated data gen fw size weight Aggregated information gen y exppc r mean p Lp o o clorenz y hs size lres 1 1 0233349 2 0576717 3 0991386 A 1480407 5 2051758 6 2729623 7 3565971 8 4657389 9 6213571 1 1 00000 Density functions Density functions without adjustment with adjustment aet Normalised per capita expenditures Normalised per capita expenditures True distribition Log Normal True distribition Log Normal Uniform Beta LC Uniform Beta LC Generalized Quadratic LC SINGH amp MADALLA Generalized Quadratic LC SINGH amp MADALLA 82 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
97. ion 2 at the second order if and only if L p lt L p v pel 0 The module domineq can be used to check for such inequality dominance It is based mainly 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 Intersections between curves can be estimated with this module It can also used to check for 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 21 2 The intersection bi dimensional FGT index for distribution D is estimated as n Z k k a w oy i Pp Z A LE 2 Wj i where Z Zi Z2 and A a At are vectors of poverty lines and parameters respectively and x max x 0 Distribution 1 dominates distribution 2 at orders 5 5 over the range 0 Z if and only if P Z A s 1 lt P Z A s l V Ze 0 z x Oz andforg s 1l a s 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 an
98. label val sex lvsex label var zone Residential area label def Ivzone 1 Rural 2 Urban J 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 17 Survey data settings ojx Main More Weights SE Poststratification Number of stages fi Clear settings Sampling units Strata Finite pap correction Stage 1 psu strata Mate Empty ar n in Sampling units above indicates sampling of observations Cancel Submit In the Weights panel set SAMPLING WEIGHT VARIABLE as follows 87 Figure 18 Setting sampling weights Plies Md ain More Weights SE Poststratification Weight type Help weights C Mane Sampling weight variable weight C Importance weight variable rare weight Balanced repeated replicate BRA weight variables Fay s adjustment Jackkrnife replicate weight variables Cancel Submit 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 puaight meight NCE limearized Strata 1 strata ol 1 psu FPE 1 zeros bs per
99. le Caption Legend Overall Title Subtitle Size Defaut Justify Defaut v Size Defaut Justify Defaut Color Deta gt Alignment Defaut Color Defaut gt Alignment Defaut Position Defaut gt Margin H Position Defaut gt Margin zl Orientation Defaut gt Line gap Orientation Defaut Line gap Inside plot region Inside plot region Span width of graph Span width of graph Box Bow Fill color Default Fillcolor Default Line color Defaut Line colar Defaut z lara hv arai Ignore test size Ignore test size After clicking SUBMIT the following graph appears 103 Figure 29 Graph of FGT curves R Graph Graph FGT Curves alpha 0 Burkina 1994 oo 5 m ud II a m a 7 T d um ms Fal i DU T n Fd LL 2 C4 a s z UU i T 20000 4000 0000 s0000 Poverty line z 5 x 100000 104 Q 4 Choose variables and parameters as in the following window Figure 30 FGT curves by zone ES DASP FGT Curves gt chot command After clicking SUBMIT the following graph appears 105 Figure 31 Graph of FGT curves by zone s Graph Graph FGT Curves alpha 0 Burkina 1994 B 40000 Bo000 S0000 Poverty line z FisT z alpha a 5 x 100000 106 Choose the option DIFFERENCE and select WITH THE FIRST CURVE Indicate that
100. lity 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 bkf941 dta file 3 Estimate the difference in Burkina Faso s Gini index between 1998 and 1994 a with variable of interest expeqz for 1998 and expeq for 1994 b with size variable set to size Q 1 Steps Type use C data can6 dta clear To open the relevant dialog box type db igini Choose variables and parameters as in 124 Figure 49 Estimating Gini and concentration indices After clicking SUBMIT the following results are obtained Variable Est inate STD LE UB 1 GHI X 0 IE 0 06734 0 476500 0 54113 2 GHI H 0 3355 0 1258 307318 3257391 Q 2 Steps Choose variables and parameters as in 125 Figure 50 Estimating concentration indices ES DASP Gini amp Concentration Indices gt igini command Mar Lab le Est inate STU LE UB 1 OHE T 1 595330 1 02293 1 554140 0 64 IES zz CONCH 3060 0 013268 1 290114 0 330187 Q 3 Steps To open the relevant dialog box type db digini Choose variables and parameters as in 126 Figure 51 Estimating differences in Gini and concentration indices ES DASP Difference Between Gini Concentration Indices gt digini command 3 x M
101. n command BE x Main Results Result options Number of Decimals 32 Social groups Quintiles Y C Group variable Displayed results Share and rate of participation v Average benefits v Proportion of benefits Cancel Submit After clicking on Submit the following appears 149 Average Benef its by Quintile Groups at the level of eligible nenbers Groups Prinary secondary Quintile 1 276 036 213 306 Quintile 203 P6 235 235 Quintile 3 201 60 211 999 Quintile 4 205 121 183 199 Quintile 5 1 521 06 228 All 254 21 195 595 Groups Prinary secondary Quintile 1 353 446 656 563 Quintile 353 446 656 563 Quintile 3 353 446 656 563 Quintile 4 303 446 656 563 Quintile 5 353 446 656 563 All 353 446 656 563 Groups Prinary secondary Quint ile 1 1 136 0 065 Quint ile 0 14 0 095 Quintile 3 0 1355 1 055 Quint ile 4 1 127 1 073 Quint ile 5 1 084 0 035 All 1 624 1 376 150
102. ne H is the headcount P z amp the poverty gap estimated at the level of X poor group and Go the Gini index of poverty gaps z y z 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 10 6 Difference between Sen Shorrocks Thon indices disst This module estimates differences between the Watts 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 9596 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 Alevelfor the parameter a can be chosen for each of the two distributions 10 7DASP and multidimensional poverty indices The general form of an additive multidimen
103. nfidence 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 0 1 0 15 0 2 0 25 uw VS Dimension 1 2094096099 0 9 5 0820 840 86088 09 Dimension 2 139 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 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 Zml 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 Q 1 Steps To
104. objective of benefit incidence 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 access of household members to public services This information can be found in 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 information to analyse the distribution of public benefits and its progressivity Formally let W be the sampling weight of observation 1 y be the living standard of members belonging to observation 1 i e per capita income es 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 fs be the number of members of observation i that effectively use the public service provided by sector s g be the socio economic group of eligible members of observation i typically classified by income percentiles 75 C 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 E be total public expenditures on sector s in area r There
105. ocus on a population subgroup defined as those for whom some GROUP VARIABLE say area of residence equals a given GROUP NUMBER say Z 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 How can DASP commands be invoked Stata commands can be entered directly into a command window Figure 3 Using DASP with a command window af Intercooled Stata 9 2 Results Ioj x wa File Edit Prefs Data Graphics Statistics User Window Help x eH 4 8 w B g9p m EE 0 Review use L ADATASBEKP3AIL dta clear o _ F Po P P P P 92 Copyright 1984 2006 Stat ist ics Data Analysis Statalorp 4905 Lakeuau Drive College Station Texas 77845 USA SU0 5 TATH PC httpz uuu stata can 979 646 4600 stat al st at a con 079 696 4601 fax Variabl m x Pingle user Stata for Hindous perpetual licenze Hue Serial number 1990520454 weight a Licensed to Araar Abdelkrin size llniversit Lawal strata psu ge zone ifgt exppc pline 41099 hsize size alpha 11 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 Example db ifgt 7 How can help be accessed for a given DASP module Type the command help followed by the name of the relevant DASP module Example help ifgt Figure 4 Accessing help on DASP x
106. ol type db dspol in the command window Ex Decomposition of the social polarisation index by groups gt dspol command n x Main Results Yanable of interest Size variable Group variable Parameter s and options Farameter alpha 0 5 Use a fast approach for density estimation Survey settings Cancel Submit Example For illustrative purposes we use a 1996 Cameroonian household survey which is made of approximately 1700 households The variables used are Variables STRATA Stratum in which a household lives PSU Primary sampling unit of the household WEIGHT Sampling weight SIZE Household size INS LEV Education level of the head of the household 1 Primary 2 Professional Training secondary and superior 3 Notresponding We decompose the above social polarization index using the module dspol by splitting the Cameroonian population into three exclusive groups according to the education level of the household head We first initialize the sampling design of the survey with the dialog box svyset as shown in what follows 37 After that open the dialog box by typing db dspol and choose variables and parameters as in O x Ex Decomposition of the social polarisation index by groups gt dspol command Main Results V ariable of interest expeq Size variable size Group variable ins lev Parameter s and options a Faramet
107. ondition 2h sex i AND Condition 2h sex j f Parameters and Option Parameter alpha jo Normalised m Cancel Submit Type After clicking on SUBMIT the following should be displayed Poverty Index Fol Index Paraneter alpha 0 00 Est inate STI LE UE P Line Distribution 1 0 17234 0 01741 0 13490 AN 41099 00 Distr ibut ion 0 1069 0 016 0 07538 0 145 41 95 00 Difference 0 066398 0 022534 22222 0 110553 see Q 6 98 We have that Lower Bound 0 0222 Upper Bound 0 1105 The null hypothesis is rejected since the lower bound of the 9596 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 peru94I dta file 1 Estimate the Chakravarty et al 1998 index with parameter alpha 1 and Varofintees Pov line aj Dimensiont expe 409 1i pliterate 2 Estimate the Bourguignon and Chakravarty 2003 index with parameters alpha beta gamma 1 and Var ofinterest Dimension2 literate 0 90 Q 1 Steps Type use C data peru94 A L dta clear To open the relevant dialog box type db imdp bci Choose variables and parameters as in 99 Figure 25 Estimating multidimensional poverty indices A amp DASP Chakravarty Mukherjee and Ranade 1998 multidimensional poverty index gt imdp cmr command
108. open the relevant dialog box type db cpropoorp 140 Choose variables and parameters as in select the upper bounded option for the confidence interval Figure 63 Testing the pro poor growth primal approach ES DASP Pro poor curves primal approach gt cpropoorp command Datainfle v C Documents and SettingssAraa Daainfle v C Documents and SellingsViraa Inc Inc L z Relatives T After clicking SUBMIT the following graph appears 141 Relative propoor curve Order s 1 Dif P 2 m2 m1 z a s 1 P_1 z a s 1 05 0 600 1200 1800 2400 3000 Poverty line Z 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 confidence interval Figure 64 Testing the pro poor growth dual approach A 142 ES DASP Pro poor curves dual approach gt cpropoord command Daaintie v C Documents and SellingsV raa Daaintie m C Documents and SetingeViraa Inc Inc al g m z Hd apl p Mu z Mu 1 After clicking SUBMIT the following graph appears Absolute propoor curves Order s 1 Dif Q 2 p Q_1 p mu 2 mu 1 MJ N e addidi UN pno ee ae Ti T eS SON ge A IN V NA v A V Y 0 184 368 552 136 92 Percentiles p Q 2 Steps 143 To open the relevant dialog box type db cpropoord Choose variables and parameters as in with
109. oth 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 29 13 5 Atkinson index iatkinson Denote the Atkinson index of inequality for the group k by I z It can be expressed as follows ve 86 gun I g EL where mo u w i The Atkinson index of social welfare is as follows I amp l s Wi yi 1fgzzl andg20 W 1 1 i l e l n Exp T pz w In y gt e Y W 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 If a group variable is selected only the first variable of interest is then used Standard errors
110. overty 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 lt yal SQ CPG p z d l 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 64 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 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 8 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_ wi z Yi if 22 2 Wi CD z s EY Y wi K z yi yf E y yez fG e EL if sel 2 Wi i where K is a kernel function and y is the Jj commodity Dominance of order s is checked by se
111. pproach 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 l A z a s 1 lt 0 Vze FO The change in the distribution from state 1 to state 2 is s order relatively pro poor if A z s nea s l P z a 2E Vze 0 2 4h 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 73 draw pro poor curves and their two sided lower bounded or upper bounded confidence intervals list or 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 Q p
112. quivalent B1 Transfer 1 per adult equivalent B2 Transfer 2 per adult equivalent B3 Transfer 3 per adult equivalent B Sum of transfers B1 B2 and B3 N Yearly net income per adult equivalent 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 84 size Household size npubprim Number of household members in 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_republic1996I dta This sample is a part of the Data from the Demograph
113. rsity 14 4 Difference between Foster and Wolfson 1992 polarization indices dipolfw This module estimates differences between the FW indices of two distributions For each 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 9596 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 Gradin and Ray 1999 polarisation index ipoger The proposed measurement of polarisation by Esteban and Ray 1994 is defined as follows 34 PPR fa Y pp ii Hl j l kel where p and p denote respectively the average income and the population share of group j The parameter a L1 6 reflects sensitivity of society to polarisation The first step for the estimation requires to define exhaustive and mutually exclusive groups p This will involve some degree of error Taking into account this idea the measure of 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
114. s For this we maximize the likelihood function which is simply the product of density functions evaluated at the average income of each class 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 distributions 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 8 1 Figure 16 ungroup dialog box G Disaggregation of aggregated data gt ungroup command ioj x Size of the generated distribution Total size li O00 Percentage umber of alis Bottom group fic 100 Top group E 100 Basic information on the aggregated data Percentiles p lb Cumulative income shares or Lorenz flp vi Distribution Form Distribution Loa normal Adjustment Saving the generated distribution File Browse data informat
115. 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 72 Mi z Wo z F z Index where Wp z is the Watts index for distribution D e 1 2 and F z is the headcount for index for the first distribution both with poverty lines z 2 The Kakwani and Pernia pro poor index 2000 RB z a P za P z P 2 7 4h a 3 The Kakwani Khandker and Son pro poor index 2003 Index B za P za Index l2 g B za P z 14 4h a where the average growth is g 4 44 4j and where a second index is given by Index _2 Index 1 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 a can be chosen for each of the two distributions 19 2 DASP and pro poor curves Pro poor curves can be drawn using either the primal or the dual a
116. sional poverty index is 17 2 wp Z P X Z n 2 Wi i l where p X Z is individual I s poverty function with vector of attributes X E Xi J and vector of poverty lines Z z NE determining s contribution to total poverty P X Z 1 Chakravarty et al 1998 index imdp_cmr J E D d p X Z Ma a j l tj jJ 2 Extended Watts index imdp ew ej i p X Z 5 a ln Ye min z x eur Y 3 Multiplicative extended FGT index a a Za j l J 4 4 Tsui 2002 index imdp twu b J e j wati j l 5 Intersection headcount index imdp ihi J P X Z I s gt x j l 6 Union headcount index imdp uni J j l 7 Bourguignon and Chakravarty bi dimensional 2003 index imdp bci 18 P X Z c af y y p Ail Z2 Xi C and C_ e a lt 2 8 Alkire and Foster 2011 index imdp afi where a X ee yea ee Ur m d P Y 1 Ne To J z 1 C J J where W J and d denotes the number of dimensions in which the individual i is deprived j l d denotes the normative dimensional cut off The modules presented above can be used to estimate the multidimensional poverty indices as well as their standard errors The user can select among the seven multidimensional poverty indices The number of dimensions can be selected 1 to 10 If applicable the user can choose parameter values relevant to a chosen inde
117. sition of change in FGT poverty by poverty and population group components sectoral decomposition dfgtg2d eeseeeseeeeeeeeeeel 46 15 8 Decomposition of FGT poverty by transient and chronic poverty components AEDO EN ETUR 49 15 9 Inequality decomposition by income sources diginis 51 15 10 Regression based decomposition of inequality by income sources 52 15 11 Gini index decomposition by population subgroups diginig 58 15 12 Generalized entropy indices of inequality decomposition by population SUDPFOUDSTUe IE ODVE coectetuer Nese mene eer eer sorde iia Nese Net ANCE Sts sen cot ere ae mere Ne ere E 59 15 13 Polarization decomposition of the DER index by population groups dpolag 59 15 14 Polarization decomposition of the DER index by income sources dpolas 60 16 IAS aL ON Soe cesta peace du itii diii iua etu utem Eia 60 teL S OTCURVISTSISE estates mara Re totem eot atte tete Md 60 16 2 FGT CURVE with confidence interval CfEts oo cccccceeceeeeeeeeeeeeeeeeeeeeeeeeeeeees 62 16 3 Difference between FGT CURVES with confidence interval cfgts2d 62 16 4 Lorenz and concentration CURVES clorenZ eeeeeseeeeeeessssssesssssereserererrersssssesssss 62 16 5 Lorenz concentration curves with confidence intervals clorenzs 63 16 6 Differences between Lorenz conc
118. t aaaetostieats aod ELEM S DUO 71 I9 5 DASP and joint density TUNCUONS iiiv adici E ene aap eas 71 18 6 DASP and joint distribution functions 0 00 ccecccsssttsssseeeeeeeeeeeecceeeeeeeeeeeaaaaas 12 19 DASP and prospoor gEOWULUDS des etos t e Oe eee ae ee 72 POLL DASP and pro pOOE IHOlICOS sese encase toan EO i bo aute ped as 72 19 2 DASP and pro DOOE CUEVOS ea e edes bu es qe a a cape ttu anaes dest 73 19 21 Brmnialprospoor Curves imet oet hie n tt E A 73 1922 DudbDro DOOEF CUL VOS usssorqsee testet td ote tei need mat tute UE Cir apetece da ede mae S 74 20 DASP and Benefit Incidence Analysis sssssssseeeeeeenennne nennen 75 20 1 iBenentU incidence analysis x55 aho ti ete eet os Dr nate 75 21 Disaggregating grouped data essssssesseeeeeeeeee E E En 79 22 ADDEHGIGBS aarin epoca cd D cd anm ten orc a ee la conet OO eT ae 83 22 1 Appendix A illustrative household SurveyS ccccceeessssssssssesssssssssssssssssseeseeeees 83 22 1 1 The 1994 Burkina Faso survey of household expenditures bkf94I dta 83 22 1 2 The 1998 Burkina Faso survey of household expenditures bkf98I dta 84 22 1 35 Canadian Survey of Consumer Finance a sub sample of 1000 observations ALSE NE Y e RRR ln AEE E ro E A A N ee ee 84 22 1 4 Peru LSMS survey 1994 A sample of 3623 household observations PEREDE YALALA orena r E EAE 84 22 1 5 Peru LSMS survey 1994 A sample of 3623 household observations
119. than a given tax The transfer B is more Tax Redistribution TR progressive than a tax if PR p C p C p 2L p 0 Vp e J0 1 The transfer B is more Income Redistribution TR progressive than a tax 7 if PR p Cy p C p 0 Vp e J0 1 17 Dominance 17 1 Poverty dominance dompov Distribution 1 dominates distribution 2 at order s over the range lz l z if only if B Ga B m v e z c fora s l This involves comparing stochastic dominance curves at order s or FGT curves with s 1 This application estimates the points at which there is a reversal of the ranking of the curves Said differently it provides the crossing points of the dominance curves that is the values of C and F 6 a for which F 45a P a when sign Fj 1 a P C m a sign P 6 5 0 P ma for a small 7 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 67 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 domineq Distribution 1 inequality dominates distribut
120. 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 Vers ion version 2 0 lata June eL Stata Merzion Required 9 2 and higher Author DASP is conceived by Ur Abdelkrin Araar aabd ecnulayval ca Ur Jean wes Duclos jyvesPechulayal ca Before using nodules of this package users have to update the executable Stata file to Stata 9 2 or higher http Hun stata con support updatezs st at a8 htrnl update the ado files http Hun stata con support updatez st ata ado The tua follwing sub packages nust be installed to run DRSP PACKAGES you could met describe dasp pi Distributive Analysis Stata Package PART I dasp pe 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 net install dasp p4 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 Figure 2 DASP submenu File Edit Data Graphics Statistics User Window Help ES il d IEE REAA ERA B Data NE Graphics gt I Y 2 Xx 144 Filter commands here Statistics gt o9 window menu append item Pro poor Pro poor curves primal approach DASP gt I T Command oo 145 window menu append item Pro poor 1 do C
121. 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 32 Differences of FGT curves 107 Figure 33 Listing coordinates 5tata graphs qgraphl gph 5tata graphs graph wmf 108 After clicking SUBMIT the following appears Figure 34 Differences between FGT curves R Graph Graph i x Difference Between FGT Curves alpha 0 Burkina 1994 e n E z D amp r s XE 3s C s E E RE s b w eee mdi Te _o JL Mu D 20000 40000 5000D 80000 100000 Poverty line z Mull Horizontal Line FGT Urban FGT Rural Q 6 109 Figure 35 Differences between FGT curves R Graph Graph l ol xl Difference Between FGT Curves alpha 1 Burkina 1994 NES Ps a kani a m i 7 EN ui M qu m E E m 4 E g NEM Ci b Ten e Se ot D 20000 40000 5000D 80000 100000 Poverty line z Mull 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 bkf94L dta draw the FGT curve and its confidence interval
122. tting ao 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 command window 65 Figure 15 Consumption dominance curves Ex DASP Consumption Dominance Curves gt cdomc command z ml x Main Results Graphical Results mls Anis Title Caption Legend Overall Option and parameters Percentage of change in price i j Dominance order 25 21 1 Normalized by the cost Not normalized Poverty line z f DOO Minimum Masimu C Range of pov line fo 10000 Variable of interest Component variables Standard linvings Size variable S Group variable Cancel Submit 16 9 Difference Ratio between consumption dominance curves
123. 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 9596 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 4 FGT elasticity with respect to Gini inequality with different approaches efgtine The overall Gini inequality elasticity of poverty can be estimated by using one approach among the following list e The counterfactual approach e The marginal approach e The parameterized approach e The numerical approach The module efgtine allows the estimation of a poverty elasticity or semi elasticity with respect to inequality with the different approaches mentioned above For more details on these approaches see Abdelkrim Araar 2012 Expected Poverty Changes with Economic Growth and Redistribution Cahiers de recherche 1222 CIRPEE 24 To estimate a FGT elasticity semi elasticity with respect to inequality 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 The results are displayed with 6 decimals this can be changed 12 5 FGT elasticities with respect to within between group components of inequality efgtg
124. vals 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 10 Difference between Quantile Share indices dinineq This module estimates differences between the Quantile Share 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 9596 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 11 The Araar 2009 multidimensional inequality index The Araar 2009 the multidimensional inequality index for the K dimensions of wellbeing takes the following form K M 4 4l 1 4 C i where is the weight attributed to the dimension k may take the same value across the dimensions or can depend on the averages of the wellbeing dimensions 7 C are respectively the relative absolute Gini and concentration indices of component k The normative parameter A controls the sensitivity of the index to the inter correlation between dimensions For more details see Abdelkrim Araar 2009 The Hybrid Multidimensional Index of Inequality Cahiers de recherche
125. where 58 D the population share of group g Q the income share of group g I between group inequality when each individual is assigned the average income of his group R The residue implied by group income overlap 15 12 Generalized entropy indices of inequality decomposition by population subgroups dentropyg The Generalised Entropy indices of inequality can be a as follows k ioa XU J k 0 1 where B k is the proportion of the population found in subgroup k B u k is the mean income of group k B I k 0 is inequality within group k BI 0 is population inequality if each individual in subgroup k is given the mean income of subgroup k u k 15 13 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 P 2 9 WRP P Between Within where y dar G f G9 di g 9 p 1 a x f x d e and y are respectively the population and income shares of group g 59 e z x denotes the local proportion of individuals belonging to group g and having income x e P isthe DER polarization index when the within group polarization or inequality is ignored e 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 rech
126. x 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 provided 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 10 8 Multiple overlapping deprivation analysis MODA indices The imoda DASP module produces a series of multidimensional poverty indices in order to show the incidence of deprivation in each dimension Further this application estimates the incidence of multi deprivation in the different combinations of dimensions In this application the number of dimensions is set to three Further the multidimensional poverty is measured by the headcount union and intersection headcount indices and the Alkire and Foster 2011 MO index for different levels of the dimensional cut off 19 The number of dimensions is three A group variable can be used to estimate the MODA indices at the level of a categorical group 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 3 decimals this can be also changed 11 DASP poverty and targeting policies 11 1 Poverty
127. x 384 0 067828 0 311798 sources 0 024588 0 002247 171358 source6 0 054758 0 005368 180533 I In case one is interested in changing some income component only among those individuals that are effectively active in some economic sectors schemes n k t and A in the paper mentioned above the user should select the approach Truncated income component 27 13 DASP and inequality indices 13 1 Gini and concentration indices igini The Gini index is estimated as jp u where 2 2 AR V V n Y nc y and V 2 Y w and YixY52 Yn IxYn i lV h i The concentration index for the variable T when the ranking variable is Y is estimated as IC yep or HT where y is the average of variable T amp E Ma e mM n and where V gt wp and y gt Y5 gt Yn 1 gt Yn h i The user can select more than one variable of interest simultaneously For example one can estimate 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 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 9596 are provided Both the type of confidence intervals provided and the level of confidence used can be chan
128. y the cost Normalised E Targeting type Lump sum constant amount bd f Poverty line z f OO000 Minimum hd asinum C Range of pov line 0 10000 Vanable of interest Jexppe Size variable size Group variable zone L ancel 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 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 A is given by OP z a O J DuzLjebeJ CD Z a where CDj is the Consumption dominance curve of component j Change per of component The per capita dollar impact of growth in the j component on the normalized FGT index of the k group is as follows 21 OP z a OY eas 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 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 chan

User Manual for Stata Package DASP: Version 2.3

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