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USER MANUAL DASP version 2.1 DASP: Distributive Analysis Stata

1. Variable s of interest Decomposition approach 1 pecon95 pecon97 pecon99 pecon 1 Approach Jalan and Ravallion Censored incomes Parameters Parameter alpha 2 Poverty line z fi Size variable hs v W Bias correction Approach Analtic hd Survey settings 20 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 The results are displayed with 6 decimals this can be changed Main references e Jalan Jyotsna and Martin Ravallion 1998 Transient Poverty in Postreform Rural China Journal of Comparative Economics 26 2 pp 338 57 e Jean Yves Duclos amp Abdelkrim Araar amp John Giles 2006 Chronic and Transient Poverty Measurement and Estimation with Evidence from China Working Paper 0611 CIRPEE 15 5 Inequality decomposition by income sources diginis Analytical approach The diginis module decomposes the usual relative or the absolute Gini index by income sources The three available approaches
2. Here 2 DASP submenu ics User Window Help Data b Graphics E statistics tu s d Inequality gt Polarization gt Copyr ight 1984 2008 paver gt StataCorp Y 4905 Lakenay Drive ordi gt College Station Texas 77845 USA o m 800 STATA PC http uuu stata con Poverty and targeting policies f979 696 4600 statalstata con Poverty elasticities gt 979 696 4601 fax Decomposition b FGT Decomposition by groups Dominance b FGT Decomposition by income sources Curves gt FGT Growth and redistribution Distributive tools b FGT Decomposition into transient and chronic components Benefit analysis gt Generalised entropy Decomposition by groups Disaggregating data Gini Decomposition by groups Gini Decomposition by income sources gt DER Decomposition by population groups DER Decomposition by income sources To add the DASP sub menus the file profile do which is provided with the DASP package must be copied into the PERSONAL directory If the file profile do already exists add the contents of the DASP provided profile do file into that existing file and save it To check if the file profile do already exists type the command findfile profile do 4 DASP and data files DASP makes it possible to use simultaneously more than one data file The user should however initialize each data file before using it with DASP This initialization is done by 1 Labeling
3. y x with respect to x is given by 2 x The local linear approach is based on a local OLS estimation of the following functional form 18 4 2 Local linear approach K x y UOK A OK E a 2 v or alternatively of K x y aK x BK x x x Estimates are then given by dy E j E y x a 2 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 61 2 2 A 1 n 1 aci eh 2nhyhy Dwi 7 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 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 2 wi Ix lt X I y lt y Fay With this module the two variables of interest dimensions should be selected specific population subgroups can be selected surfaces showing the joint
4. gt difgt command Data inFile C DATA DKF98I dta z of the j R smi After clicking on SUBMIT the following should be displayed difgt exppcz exppc alphal ileliC DATA bkt9SI dta hsizellzizel filee C DATAYbKAS4 dta hzizedlsizel plinel 41099 plina l 41099 Poverty Index FGT Index Paraneter alpha 0 00 Est inate 10 LE UB F Line Distr ibut ion_1 0 267 027 0 431199 0 474156 4109900 Distr ibut ion 2 1 46 0 016124 0 412873 0 470256 41099 00 Difference 0 008113 0 019477 0 030062 0 046288 89 Q 3 Restrict the estimation to rural residents as follows o Select the option Condition s o Write ZONE in the field next to CONDITION 1 and type 1 in the next field Figure 21 Estimating differences in FGT indices E DASP Difference Between FGT Indices gt difgt command Confidence Interval Rests DatainFile C DATASDKSSI dta DatainFile C DATAAbKf94I dta 41099 Z of the z K cea After clicking on SUBMIT we should see Poverty Index FGT Index Paraneter alpha 0 00 Est inate sm LB IB P Line Distr ibution_1 LABH 0 01101 VAH 0 555149 41099 00 Distribution 0 5197 1 18 VAH 0 549755 41094 00 Difference 0 000153 0 023100 0 045427 0 045121 Q 4 90 Poverty Index oo FGT Index Faraneter alpha 0 00 Est inate Sm LE UB F Line Distribution 1 0 166
5. hy H u In addition the index by 2 to make its interval lie between 0 and 1 when the parameter a 1 PERCE ap pB bo is 0 6 0 6 jel k l 14 6 The Inaki 2008 polarization index ipoger Suppose that a population is split into N groups each one of sizen gt 0 The density function the mean and the population share of group iare denoted by f x u andz respectively U is the N N overall mean We therefore have that f f x 1 X oru u and Xa Using Inaki 2008 a i l i l social polarization index can be defined as P F SR F P i F where P G P pa e J fO Olx y ldydx and P i F u r u z EE od The module Stata dspol allows performing the decomposition of this index P F into group components The user can select a value for the parameter alpha 32 The user can use 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 the results in Excel format The results show The estimated population share of subgroup i 77 The estimated income share of subgroup i 77 44 U The estimated F i F index of subgroup i Theestimated P i F index of subgroup i The estimated F gt FP i F index The estimated P gt P i F index The
6. 102 Figure 33 Differences between FGT curves ioi Difference Between FGT Curves alpha 1 Burkina 1994 wo W o c M on Sig me o 2 lt o u a n t 0 20000 40000 _ 60000 80000 100000 Foverty line z Null Horizontal Line FGT_Urban FGT_Rural 23 5 Estimating FGT curves and differences between FGT curves with confidence intervals Is the poverty increase between 1994 and 1998 in Burkina Faso statistically significant 1 Using the file bkf94I dta draw the FGT curve and its confidence interval for the variable of interest exppc with a parameter a 0 b poverty line between 0 and 100 000 Franc CFA c size variable set to size 2 Using simultaneously the files bkf94I dta and bkf98I dta draw the difference between FGT curves and associated confidence intervals with a The variable of interest exppc for 1994 and exppcz for 1998 b parameter a 0 c poverty line between 0 and 100 000 Franc CFA d size variable set to size 3 Redo 2 with parametera 1 Answers 0 1 103 Steps Type use C data bkf941 dta clear To open the relevant dialog box type db cfgts Choose variables and parameters as in Figure 34 Drawing FGT curves with confidence interval EE DASP FGT Curve with Confidence Interval gt cfgts command After clicking SUBMIT the following appears 104 Figure 35 FGT curves w
7. 22 Appendices 22 1 Appendix A illustrative household surveys 22 1 1 The 1994 Burkina Faso survey of household expenditures bkf94I dta This is a nationally representative survey with sample selection using two stage stratified random sampling Seven strata were formed Five of these strata were rural and two were urban Primary sampling units were sampled from a list drawn from the 1985 census The last sampling units were households List of variables strata Stratum in which a household lives psu Primary sampling unit weight Sampling weight size Household size exp Total household expenditures expeq Total household expenditures per adult equivalent expcp Total household expenditures per capita gse Socio economic group of the household head 1 wage earner public sector 2 wage earner private sector 3 Artisan or trader 4 Other type of earner 5 Crop farmer 6 Subsistence farmer 7 Inactive sex Sex of household head 1 Male 2 Female zone Residential area 1 Rural 2 Urban 76 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
8. IR progressive if PR p Cy p Ly p gt 0 Vp 0 1 16 10 2 Checking the progressivity of a transfer vs a tax The module cprogbt allows checking for whether a given transfer is more progressive than a given tax The transfer B is more Tax Redistribution TR progressive than a tax T if PR p C p C p 2L p gt 0 Yp 0 1 The transfer B is more Income Redistribution TR progressive than a tax T if PR p Cx s p Cx p gt 0 Yp 0 1 17 Dominance 17 1 Poverty dominance dompov Distribution 1 dominates distribution 2 at order s over the range lz z if only if P a lt P a V Gel z z 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 and P G a forwhich P a P when sign P 1 a P 1 a sign P n a P 1n 0 for a small 77 The crossing points C can also be referred to as critical poverty lines The dompov module can be used to check for poverty dominance and compute critical values This module is mostly based on Araar 2006 57 Araar Abdelkrim 2006 Poverty Inequality and Stochastic Dominance Theory and Practice Illustration with Burkina Faso Surveys Working Paper 06 3
9. dimensions should be selected Conditions can be specified to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed 58 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 WSMS SY SY S SY If F y lt p lt F Y we define Q p Vea The normalized quantile is defined as O p Q p u Interested users are encouraged to consider the exercises that appear in Section 23 10 18 2 Income share and cumulative income share by percentile groups quinsh This module can be used to estimate the income shares as well as the cumulative income shares by groups or percentiles The user can indicate the number of group partitions For instance if the number is five quintile income shares are provided We can also
10. poorness with the dual approach 4 Using mex 98 2ml dta and mex 04 2ml dta estimate the pro poor indices of module ipropoor e Parameter alpha set to 1 e Poverty line equal to 600 Answer 0 1 Steps To open the relevant dialog box type db cpropoorp 133 Choose variables and parameters as in select the upper bounded option for the confidence interval Figure 61 Testing for pro poor growth primal approach ES DASP Pro poor curves primal approach gt cpropoorp command Datainfile C Documents and Settingst raa Data in file C Documents and Settingsk raa After clicking SUBMIT the following graph appears 134 Relative propoor curve o A Order s 1 Dif P_2 m2 m1 z a s 1 P_1 z a s 1 AAN A re ad Na Dl al te 2a J LO o LO T T T T T 1 0 600 1200 1800 2400 3000 Poverty line z Difference Upper bound of 95 confidence interval Null horizontal line Q 2 Steps To open the relevant dialog box type db cpropoord Choose variables and parameters as in with the lower bounded option for the confidence interval Figure 62 Testing for pro poor growth dual approach A 135 E DASP Pro poor curves dual approach gt cpropoord command Data in file C ADocuments and Settingst raa iny After clicking SUBMIT the following graph ap
11. 0 3 Choose variables and parameters as follows 95 Figure 25 Drawing FGT curves B DASP FGT Curves gt cfgt command Main Results Y Axis XAxis Title Caption Legend Overall Variable s of interest Type of curvefs exppe expeq T Type Normalised z T Difference No z Size variable size Group variable m Parameters Parameter alpha fo Minimum Maximum Poverty line 2 jo fi 00000 Cancel Submit To change the subtitle select the Title panel and write the subtitle Figure 26 Editing FGT curves E DASP FGT Curves gt cfgt command Main Results Y Axis X Axis Title Caption Legend Overall Title T Subtitle E Burkina 1884 Size Defaut z Justify Defaut x Size Defaut x Justify Defaut gt Color Defaut z Alignment Detaut x Color Defaut gt Alignment Defaut Position Defaut Margin HA Position Defaut x Margin H Orientation beat x Line gap Orientation Defaut CZ Line gap T Inside plot region T Inside plot region T Span width of graph T Span width of graph T Box Box Fill color Defaut z Fill color Default Line color Defaut z Line color Defaut z Marain s Margin s I Ignore text size F Ignore text size Cancel Submit After clicking SUBMIT the following graph appears 96 Figure 27 Gr
12. 4 1 Nadaraya Watson approach sseseesessssessessssseessessessessseessessrssessessrssressessrssees 6l 18 42 Locallinear approaches nan ane a nec ooo a oa ls 6l 18 5 DASP and joint density functions 5 idissi 5 sd as bassadse seandeieth Qeeaedegteaces se n dna 61 18 6 DASP and joint distribution functions eee 62 19 DASP ANG pro WOOT So Wh sinengitan i e ai e and hus dan 62 19 1 DASPARdpro Poor1ndiCES se suzs ee sie S cance 0a Snan ana E WB oso tag n d Heda cone 62 19 2 DASP and pro poor CUIVES z sicssiesscdsccessteceigpiadicckssteceusdsatcr ate riuneneasemae tetas 63 19 21 Primal pro DOOM CUIVES x Sais cited cts sa scenes doh anacade aa sea woacdia a i or 63 19 22 Dual pro poor CUE VCS aeeai aeaee esis tae tam eee ake 6 Be Books RE 64 20 DASP and Benefit Incidence AnalySis ccccessccsssecsseceseceeeecseneeescecsaeceseeseeeesseeesaeoees 65 201 BENETLIMNEIMENCE analysis asninn raan a Dodo Gn 65 20 2 Marginal benefit incidence analysis 3 sas cacascacisvesseundeasvceeestecuces deuccioeeas takes steaue vadseben 69 20 2 1 Derivative of the linear locally estimator approach 69 20 2 2 Ajwad and Quentin 2001 approach eee 69 21 Disaggregating CrOUpe ds AGA 35s3uses Hess sancashaaseus setin seesaisseauacohees cate Sucaas moeaae 71 22 PRPS CICS spots aaa a RO E a ERE a aN oo E E 76 22 1 Appendix A illustrative household SUrVeYS ccceseeseeeseeeeeeeeceseceseceeeseeeeeeeeaees 76 22 1 1 The 1994 Burkin
13. 41099 00 Distribut ion_2 0 10699 0 01306 0 070538 0 13345 41099 00 Difference 0 066388 0 022534 0 022222 0 110553 Q 6 91 We have that Lower Bound 0 0222 Upper Bound 0 1105 The null hypothesis is rejected since the lower bound of the 95 confidence interval is above zero 23 3 Estimating multidimensional poverty indices How much is bi dimensional poverty total expenditures and literacy in Peru in 1994 Using the peru94Ldta file 1 Estimate the Chakravarty et al 1998 index with parameter alpha 1 and Var of interest Pov line aj Dimension 1 exppc 400 1 Dimension 2 pliterate 0 90 1 2 Estimate the Bourguignon and Chakravarty 2003 index with parameters alpha beta gamma 1 and Var of interest Pov line Dimension 1 exppc 400 Dimension 2 literate 0 90 Q 1 Steps Type use C data peru94I dta clear To open the relevant dialog box type db imdpov Choose variables and parameters as in 92 Figure 23 Estimating multidimensional poverty indices A JE DASP Multidimensional poverty indices gt imdpov command fiese d fos After clicking SUBMIT the following results appear indpoy exppc pliterate heizelsize index 1 alphal0 a4 1 plit400 a li pl2i0 9 H D Poverty index Chakravarty et al 19981 Household size size Est inate opulat ion 0 416 Q 2 Steps Choose variables and pa
14. AH Cumulative income shares or Lorenz flp hd Total size fi 000 Percentage T Bottom group fic T Top group fic Number of obs fi oo fi 00 Distribution form Distribution Log normal M Adjustment IV Adjust the generated sample to match the aggregated data information M Saving the generated distribution File Browse m Plotting the Lorenz curves V Plot the Lorenz curves of the aggregated and generated data Cancel Submit Illustration with Burkina Faso household survey data In this example we use disaggregated data to generate aggregated information Then we compare the density curve of the true data with that of the data generated by the subsequent disaggregation procedure gen fw size weight gen y exppc r mean clorenz y hs size lres 1 L p 0233349 0576717 0991386 1480407 2051758 2729623 3565971 4657389 6213571 LS obuoata lt ibU 1 00000 Aggregated information Density functions without adjustment 15 Density functions with adjustment 2 4 Normalised per capita expenditures True distribition Uniform Generalized Quadratic LC Log Normal Beta LC SINGH amp MADALLA T T T 20 4 6 Normalised per capita expenditures True distribition Uniform Generalized Quadratic LC Log Normal Beta LC SINGH amp MADALLA T5
15. DASP Lorenz amp Concentration Curves gt clorenz command After clicking SUBMIT the following appears 112 Figure 42 Lorenz curves 5 Graph Graph Lorenz Curves 0 2 Steps Choose variables and parameters as in 113 Figure 43 Drawing concentration curves E DASP Lorenz amp Concentration Curves gt clorenz command X T B1B2B3 M as es a After clicking on SUBMIT the following appears 114 Figure 44 Lorenz and concentration curves t Graph Graph L p amp C P 4 line 45 Cip Bt Cp B2 Cip B3 0 3 Steps Type use C data bkf94I dta clear Choose variables and parameters as in 115 Figure 45 Drawing Lorenz curves E DASP Lorenz amp Concentration Curves gt clorenz command Main Results Axis X Axis Title Caption Legend Overall Variable s of interest Type of curve s Jexpeg v T Type Normalised by default z I Ranking Variable T Difference No v Range of percentiles p Size variable size Group variable zone v Minimum Maximum Ta Cancel Submit Figure 46 Lorenz curves 4 Graph Graph Lorenz Curves 116 23 9 Estimating Gini and concentration curves By how much do taxes and transfers affect inequality in Canada Using the can6 dta file 1 Estimate the Gini indices f
16. FGT curves cross a The variable of interest is exppc for 1994 and exppcz for 1998 b The poverty line should vary between 0 and 100 000 Franc CFA c The size variable should be set to size Answers 0 1 Steps To open the relevant dialog box type db dompov Choose variables and parameters as in 107 Figure 39 Testing for poverty dominance E DASP Poverty Dominance gt dompov command S x Main Results Distribution 1 M Distribution 2 DatainFile CADATANDKIS4 dta Browse Data in File m CADATASbkf98 dta Browse Variable of interest eee tt ss SCS Variable of interest eepe Size variable ze tst s sSOSCSCSCiswS Size variable iee T Condition s fi z T Condition s fi z Dominance order Second order o o Cancel Submit After clicking SUBMIT the following results appear Hunber of Crit ical Hin range of Ham range of Caze intersect ion pov line pov lines pov line 1 Fig a i 2 75 02 z E Hotes case A Before this intersection distribution 2 doninates distribution 1 Caze B Before this intersection distribution 1 doninates distribution 2 case C Ho doninance before this intersect ion 23 7 Decomposing FGT indices What is the contribution of different types of earners to total poverty in Burkina Faso 1 Open bkf94I dta and decompose the average poverty gap a with variable of interest exppc b wi
17. G A A P z a Z s P z a g g l where G is the number of population subgroups The results show The estimated FGT index of subgroup g P za g The estimated population share of subgroup 2 The estimated absolute contribution of subgroup g to total poverty o Plz a The estimated relative contribution of subgroup g to total poverty Hg Plz as g Ps 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 35 Figure 8 Decomposition of the FGT index by groups E DASP Decomposiotion of the FGT Index by Groups gt dfgtg command In x Main Results Variable of interest ji v gt 3 Type Not Normalised v Size variable v Group variable v Index option s Parameters Parameter alpha jo Poverty line z fi 0000 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 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
18. approach JGiniIndex 45 Thdinegs t b dep x nethod zero dregres 1 sun of ugt is 1 0000e 03 Source Hunber of obs 3000 FL 2 997 400 9 Hodel Prob gt F 200 Residual R squared LM Adj R squared D W Total Root HSE 606 9 x Pitt 95 Conf Interval t 1 00 ZANE 2 5506 b D 005 O cong 0 000 1H 116 8 Inequality regression based deconposition by predicted incone conponents using the Shapley value Execution tine 0 86 second s Inequality index Gini index Estinated inequality 0 508456 Sources Incone Absolute Relat ive Share Contribution Contribution level level 3 46 Example 2 E Inequality regression based decomposition by predicted components using the Shapley value rbe Main Results Regression and model specification Approach index and options Dependent Independent variables Approac Shapley approach x tb Index Generalised entropy v Theta 0 7 Model SemiLog linear logly XB e z Method Replace eliminated income source by its mean v Treatment of constant E Suppress constant term Size variable Cancel Submit Thdinegs t b depix index ge thetall nodel senilog dregres 0 Harning gt 115 are onitted Dependant variable should not be lt 0 with the senilog specif icat ion Inequality regression based deconposition by predicted incone conponents fu
19. confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 13 4 Difference between generalized entropy indices diengtropy This module estimates differences between the generalized entropy indices of two distributions For each of the two distributions One variable of interest should be selected Conditions can be specified to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 26 13 5 Atkinson index iatkinson Denote the Atkinson index of inequality for the group k by I g It can be expressed as follows n ns Wi yj I e Bree where u wi i l The Atkinson index of social welfare is as follows ahs l e 1 a l e k y AW ife l ande20 Wi i l i l E 1 n Exp W In y gt e 1 Wi i l i l The user can select more than one variable of interest simultaneously For example one can estimate inequality simultaneously for per capita consumption and for per capita income A group variable can be used to estimate inequality at the level of a categorical group Ifa group variable is selected only the first variable of inte
20. distribution function 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 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 62 _W z Wx 2 F z Index where Wp z is the Watts index for distribution D 1 2 and A z is the headcount for the first distribution both at poverty lines z 2 The Kakwani and Pernia pro poor index 2000 F 2 0 Py 2a R z a FR z 4 1w ha 3 The Kakwani Khandker and Son pro poor index 2003 Index F z a Py za Index g TOS P z a P 2 uy 14h a where average growth is g U 44 44 and where a second index is given by Index _2 Index l g One variable of interest should be selected for each distribution Conditions can be specified to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed A value for the parameter a can be chosen for each of the two distributions 19 2 DASP and pro p
21. distribution of benefits and not the expected change in participation with an expansion in a given public service Studies of marginal benefit incidence are devoted to respond to such problematic With cross section data to estimate the marginal benefit incidence that is who gains from an expansion in the program or service it is useful to exploit the geographic variation in access both between households and between regions as a source of information for understanding the diffusion process that generates access First assume that a given country with i 1 N regions Assume also that households are ranked by welfare indicator and assigned to one of q 1 income intervals Quintile for instance Then the ranking is done at regional level Let x be the benefit incidence or frequency of a program or service in household j belonging to interval g and living in region i The average benefit incidence in interval q for households in region i is denoted by X and the overall region average is i denoted by X If J is the number of households in interval q for region i the two averages are respectively equal to the following Jf Fa q q XISSI A 1 j l o Ji Q Lee A 2 q l j l q 1 20 2 1 Derivative of the linear locally estimator approach We use the LLE non parametrical approach which is defined in section 18 4 2 we simply estimate Ox q i lx i the derivative 20 2 2 Ajwad and Quentin 2001 approa
22. dk oases OAS doo oo o oo 123 Drawing non parametric regression CUIVES eseesseseeeseesreseessesresrrsseeseeseessreseese 124 Non parametric regression CUTVeS sesesessesessssesseeereseesstestestessetstesereseesessresseeseee 125 Drawing derivatives of non parametric regression CUIVES sssseseesesseseeeeseee 126 Derivatives of non parametric regression CUIVES eee 126 Plotting joint density FUNCTION wx j sccisd cecceseniecndssncescdusavesads hove ccosshigentavenessivseegvhdedacese 127 Plotting joint distribution Teton wg aiiwatepeeenadyynicareeees 129 Testing for bi dimensional poverty dominance eee 131 Testing the pro poor growth primal approach eee 134 Testing the pro poor growth dual approach A eee 135 Testing the pro poor growth dual approach B 137 Benefit incidence analysis 4 z3oiedk na st kdo e aes eet aah eaten 140 Benefit Incidence Analysis unit cost approach eee 142 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 intereste
23. 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 10 Difference between Quantile Share ratios dinineq This module estimates differences between the Quantile Share ratios 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 14 DASP and polarization indices 14 1 The DER index ipolder The Duclos Esteban and Ray 2004 DER polarization index can be expressed as DER a J f x 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 gt wif y ali DER a n wi i l The normalized DER estimated by this module is defined as DER a where 29 1 1 2y Wy wa 22 Wjyj W z a y u yi l i N wi ZW A Gaussian kernel estimator is used to estimate the density function The user can select more than one variable of interest simultaneously For example one
24. estimated total index P F To open the dialog box for module dspol type db dspol in the command window E Decomposition of the social polarisation index by groups gt dspol command Sj x Main Results v Parameter alpha fo 5 Use a fast approach for density estimation o of interest Parameter s and options Size variable Group variable Survey settings R 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 33 SIZE Household size INS_LEV Education level of the head of the household 1 Primary 2 Professional Training secondary and superior 3 Not responding We decompose the above social polarization index using the module dspol by splitting the Cameroonian population into three exclusive groups defined 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 Then open the dialog box by typing db dspol and choose variables and parameters as in E Decomposition of the social polarisation index by groups gt dspol command oj x Main Results Variable of interest Parameter s an
25. 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 X X Pg ZA and K x exp 0 5 4 x and A x l hJ2a i l 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 59 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 Bearse Canals and Rilstone 2007 A boundary corrected Kernel density estimator can then be written as Pag ZVK COK CO n wi i l where 1 X X K x exp 0 54 x and A x j 08 ee exp 0 5 A00 x and where the scalar K x is defined as Ki x yx P A x 2 s l pojeli W sw 2 2 6 1 I 1 w x M41 J K PO P0 h Ee Asm p Xam 0 0 0 min is the minimum bound and max is the maximum one A is the
26. r Size variable hse I Condition s fi z I Conditions fi z m Parameters and options Parameter alpha fi Poverty line 600 Type Normalised i Cancel Submit After clicking SUBMIT the following results appear Poverty line i 600 00 Faraneter alpha 1 00 Procpour ind ive ExLinalu 310 LB WB Grouth r telgl 0 559 0 14517 Li WA Chen amp Ravallion 2003 index 0 712285 1 00337 1265979 20054 Kakuani amp Pernia 2000 index 1 34 0 1044 1 415627 1 534 PEGE index 0 771879 0 137331 Le 1 1K FEGE g 0 19620 D S LME 1 286257 23 14 Benefit incidence analysis of public spending on education in Peru 1994 1 Using the peredu94I dta file estimate participation and coverage rates of two types of public spending on education when The standard of living is exppc The number of household members that benefit from education is fr prim for the primary sector and fr_sec for the secondary one The number of eligible household members is el prim for the primary sector and el_sec for the secondary one Social groups are quintiles 139 Answer Type db bian in the windows command and set variables and options as follows Figure 64 Benefit incidence analysis E DASP Benefit incidence analysis gt bian command After clicking on Submit the following appears 140 Benefit Incidence Analysis Educat ion Share by Quintile Groups Groups Pr in
27. the Data from the Demographic and Health Surveys Colombia 1995 that contain the following information for children aged 0 59 months List of variables hid Household id haz height for age waz weight for age whz weight for height sprob survival probability wght sampling weight Asset asset index 22 1 7 The 1996 Dominican Republic DHS survey Dominican republic19961 dta This sample is a part of the Data from the Demographic and Health Surveys Republic Dominican 1996 that contain the following information for children aged 0 59 months 78 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 labeling 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 the label command type help label in the command window delim To drop all label values label drop all To assign labels label var strata Stratum in which a household lives label var psu Primary sampling unit label var weight Sampling weight label var size Household size label var totexp Total household expenditures label var exppc Total household expenditures per capita label var expeq Total household expenditures per adult equivalent label var gse Socio economic group of the household head To define the l
28. yi a if s22 CD z 5 wi K z yj Ely ly z f if s 1 n i l where K is a kernel function and y is the j commodity Dominance of order s is checked by setting a s 1 The cdomc module draws such curves easily The module can draw more than one CD curve simultaneously whenever more than one component is selected draw the CD curves with confidence intervals estimate the impact of the 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 55 Figure 13 Consumption dominance curves E DASP Consumption Dominance Curves gt cdomc command Sj x Main Results Graphical Results Y Axis X Axis Title Caption Legend Overall Variable of interest Options and parameters Component vatiables fe Percentage of change in price fico Standard linvings v 7 Dominance order s gt 1 fi Normalised by the cost Not normalised hs Size variable Group var
29. 0 2 Difference between FGT indices difgt 0 0 0 ee eee ccceceteceseceeeeeeeeesseecaeceeeeeeeenseees 14 10 3 Watts poverty index iwatts essesssessssseesesstsetsesseseesssetstssestesesseseestsseesesseseesessese 15 10 4 Difference between Watts indices diwatts een 15 10 5 Sen Shorrocks Thon poverty index iSSU eee 15 10 6 Difference between Sen Shorrocks Thon indices disst eee 16 10 7 DASP and multidimensional poverty indices iMdpoV eee 16 11 DASP poverty and targeting POHCISS 3 gece cays Sescsdel oiactisiass acca nine Sad and nahoda 18 11 1 Poverty and targeting by population groups v eee 18 11 2 Poverty and targeting by income components eee 19 12 Marginal poverty impacts and poverty elasticitieS eee 20 12 1 FGT elasticity with respect to growth in average income efgtgr 20 12 2 FGT elasticity with respect to Gini inequality efgtined eee eeeeeeteeeeeeneeeeeees 21 12 3 FGT elasticities with respect to within between group components of inequality KS R A 509 POE RER ct cette teti tae O MO PO Gat ce a Rear L P O O aa 22 12 4 FGT elasticities with respect to within between income components of inequality ra EEE EE AEE A E 23 13 DASP and Inequality INGiCeS Sue ohn ters n a a a tate e Ra 25 13 1 Gini and concentration indices igini ssesesssesessseesseseossessesrsssessessrssressessrssressesse 25 13 2 Difference betw
30. 2008 An algorithm for computing the Shapley Value PEP and CIRPEE Tech Note Novembre 2008 http 132 203 59 36 DAD pdf files shap dec aj pd To open the dialog box for module dsginis type db dsginis in the command window Figure 10 Decomposition of the Gini index by income sources Shapley approach amp Decomposition of the Gini index by income components using the Shapley value gt dsginis command x Main Results r Variable s of interest sourcel sourceB v Size variable hhsize v Weight variable TEPLE Cancel Submit 42 15 6 Regression based decomposition of inequality by income sources A useful approach to show the contribution of income covariates to total inequality is by decomposing total inequality by the contributions of income covariates Formally denote total income by y and let the set of covariates be X x X Xp Using a linear model specification we have YS po BPA tat Pee tE where B and denote respectively the estimated constant and the residual term In general there tend to be two main approaches for the decomposition of total inequality by income sources 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 algebraical formulations of inequality indices that show the contribution of income sources to those indices W
31. 4 CIRPEE Department of Economics Universit Laval Interested users are encouraged to consider the exercises that appear in Section 23 6 17 2 Inequality dominance domineg Distribution 1 inequality dominates distribution 2 at the second order if and only if L p lt L p Y pe 0 1 The module domineg 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 be 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 1 2 The intersection bi dimensional FGT index for distribution D is estimated as Ma 2 k k mi fe yi d k 1 Il 1 Pp Z A wi i where Z zi Z and A a a are vectors of poverty lines and parameters respectively and x max x 0 Distribution 1 dominates distribution 2 at orders si S2 over the range O Z if and only if R Z A s lt B Z A s 1 V Ze 0 z x 0 z andfora 5 1 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
32. 73 0 016297 0 17533 0 196608 41099 00 Distribution 0 103604 0 013419 0 07709 0 1159 41099 00 Difference 0 060889 0 021111 0 019513 0 102265 One can see that the change in poverty was significant only for urban residents Q 5 Restrict the estimation to male headed urban residents as follows o Set the number of Condition s to 2 o Set sex in the field next to Condition 2 and type 1 in the next field Figure 22 FGT differences across years by gender and zone ES DASP Difference Between FGT Indices gt difgt command S x Main Confidence Interval Results Distribution 1 T Distribution 2 Data in File v J c DATASDKESSI dta Browse Data in File v C DATA bKFS4I dta Browse Variable of interest Jexppez Variable of interest Jexppe Size variable size Size variable size Poverty line Poverty line Absolute 41099 Absolute 41099 C Relative s54 72 ot the Mean z C Relative 504 Z of the Mean z IV Condition s 2 x IV Condition s 2 Condition I zone fee oo Condition fene jee o ano Condition 2 sex y zihi anD Condition 2k sex gt I ifi Parameters and Options Parameter alpha fo Type Normalised kad Cancel Submit After clicking on SUBMIT the following should be displayed Poverty Index oo FGT Index Faraneter alpha 0 00 Est inate ST LE WE F Line Distribution 1 0 17734 0 017701 0 1359 0 207179
33. 8 625 vars 9 31 Oct 2006 13 48 size 285 087 99 6 of memory free storage display value variable name type format label variable label weight float 9 0g Sampling weight size byte 8 0g Household size strata byte 8 0g Stratum in which a household lives psu byte 8 0g Primary sampling unit gse byte 29 0g gse Socio economic group of the household head sex byte 8 0g sex Sex of household head zone byte 8 0g zone Residential area exp double 10 0g Total household expenditures expeq double 10 0g Total household expenditures per adult equivalent exppc float 9 0g Total household expenditures per capita Typing label list we find zone 1 Rural 2 Urban 82 k Male Female N gse wage earner public sector wage earner private sector Artisan or trader Other type of earner Crop farmer Food farmer Inactive NOP WNP Q 2 You can set the sampling design with a dialog box as 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 pueight weight WE linearized Strata 1 strata SU 1 psu FPC 1 dzerot Hibs per Unit Stratun hits Hibs Hin Haan Hay F B B 0 3 Type bd ifgt to open the dialog box for the FGT poverty index and choose variables and parameters as indicated in the following window Click on SUBMIT 83 Figure 17 Estimating FGT indices E DASP FGT
34. Analysis 20 1 Benefit incidence analysis The main objective of using a benefit incidence approach is to analyse the distribution of benefits from the use of public services according to the distribution of living standards Two main sources of information are used The first informs on the access of household members to public services This information can be found in the usual household surveys The second deals with the amount of total public expenditures on each public service This information is usually available at the national level and sometimes in a more disaggregated format such as at the regional level The benefit incidence approach combines the use of these two sources of information to analyse the distribution of public benefits and its progressivity Formally let W be the sampling weight of observation 1 yi be the living standard of members belonging to observation i i e per capita income e 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 i provided by sector s gi be the socio economic group of eligible members of observation i typically classified by income percentiles 65 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 popula
35. Contribution Contribution 15 7 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 1 9 0Ps L g R gel Within Overlap nc __ Between where 48 9 is the population share of group g P is the income share of group g T is between group inequality when each individual is assigned the average income of his group R is the residual implied by group income overlap 15 8 Generalized entropy indices of inequality decomposition by population subgroups dentropyg The Generalized Entropy indices of inequality can be es as follows ice gt io 4 foo ick 6 16 1 where BO k is the proportion of the population found in subgroup k Bu k is the mean income of group k B I k 0 is ineguality within group k BI 0 is population ineguality if each individual in subgroup k is given the mean income of subgroup k p k 15 9 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 29 WRP B ec Within where P fa x f x dx e and y are respectively the population and income shares o
36. DKESBI dta After clicking SUBMIT the following information is obtained digini expegz expeg filel Cs databkfS8l dtal hzizellzizel Tile l datakbkt d dtal hzize sizel Est inate ST LE UE Dist ribut ion_1 GINT 0 44603 0 012016 0 419941 0 400755 Distr ibut ion Z GINT 0 505 0 008613 0 435116 0 46694 Difference 0 005492 0 015444 0 035762 0 024778 120 23 10 Using basic distributive tools What does the distribution of gross and net incomes look like in Canada Using the can6 dta file 1 Draw the density for gross income X and net income N The range for the x axis should be 0 60 000 2 Draw the quantile curves for gross income X and net income N The range of percentiles should be 0 0 8 3 Draw the expected tax benefit according to gross income X The range for the x axis should be 0 60 000 Use a local linear estimation approach 4 Estimate marginal rates for taxes and benefits according to gross income X The range for the x axis should be 0 60 000 Use a local linear estimation approach 0 1 Steps Type use C data can6 dta clear To open the relevant dialog box type db cdensity Choose variables and parameters as in Figure 50 Drawing densities J DASP Density Curves gt cdensity command In x Main Resuts Y Axis X Ais Title Caption Legend Overall r Variable s of interest M Parameters xN
37. F string where varlist is a list of variables Version 9 2 and higher Description Poverty FGT and EDE FGT indices Users should set their surveys sampling design before using this module and to save their data files If the sampling design is not set simple random sampling SRS will be automatically assigned by default with ifgt the following poverty indices and their standard errors will be estimated v DT indi mr Z 8 Applications and files in DASP Two main types of applications are provided in DASP For the first one the estimation procedures require only one data file In such cases the data file in memory is the one that is used or loaded it is from that file that the relevant variables must be specified by the user to perform the reguired estimation 11 Figure 5 Estimating FGT poverty with one distribution E DASP FGT and EDE FGT Index gt ifgt command ln x Main Confidence Interval Results r Variable s of interest Index options s l s Index FGT Index v Type Normalised Ke M Parameters Size variable a Parameter alpha jo Group variable x Poverty line Absolute fi 0000 C Relative 504 of the Mean z F group variable is used poverty line is relative to Survey settings The population z 20 Bal Cancel Submit For the second type of applications two distributions are neede
38. Interested users are encouraged to consider the exercises that appear in Section 23 8 16 5 Lorenz concentration curves with confidence intervals clorenzs The clorenzs module draws a Lorenz concentration curve and its confidence interval by taking sampling design into account The module can 53 draw a Lorenz concentration curve and two sided lower bounded or upper bounded confidence intervals condition the estimation on a population subgroup draw Lorenz concentration curves and generalized Lorenz concentration curves list or save the coordinates of the curves and their confidence interval save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs 16 6 Differences between Lorenz concentration curves with confidence interval clorenzs2d 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 recom
39. Relative 604 of the Median z Foroup variable is used poverty line is relative to 0 Cancel Submit Clicking on SUBMIT the following should appear ifgt exppc alphal0 hsizelsize horouplsesx plinel 41099 Poverty Index FGT Indes Household size size Sanpling weight weight Group variable sox Faraneter alpha 0 00 Group Est inate S10 LE IE l Hale 0 421 0 06633 0 419404 0 404367 Fonale 0 261350 DK 0 22411 0 357200 PULATION 0 444565 0 016124 0 412873 0 476256 Q 6 F Line 41099 00 41099 00 41099 00 Using the panel CONFIDENCE INTERVAL set the confidence level to 99 and set the number of decimals to 4 in the RESULTS panel 86 ifat exppc alphalO hsizelsize horouplsex decid Foverty Index Household size Sanpling weight z Group variable Faraneter alpha Group 1 Hale z Fonale POPULATION FGT Index size ue ight ZAM 0 00 Est inate 0 422 0 2619 0 4446 ST 0 0166 0 0 0 0464 87 leve lid9 pline 41099 LE UE 0 4004 1 462 0 2089 0 354 0 4028 0 4863 F Line 41099 00 41099 00 41099 00 23 2 Estimating differences between FGT indices Has poverty in Burkina Faso decreased between 1994 and 1998 1 Open the dialog box for the difference between FGT indices 2 Estimate the difference between headcount indices when a Distribution 1 is year 1998 and distribution 2 is year 1994 b The va
40. SP with a command window a5 Intercooled Stata 9 2 Results Oj x fm File Edit Prefs Data Graphics Statistics User Window Help s x S M OS AB S BE 0 8 Review use C DATASbK94I dta clear POP d f d f 7 9 2 Copyright 1984 2006 Stat ist ics Data Analysis StataCorp 4905 Lakeway Drive College Station Texas 77845 USA 800 STATA PC http uuu stata con 979 696 4600 statalstata con 979 696 4601 fax ariabl m x Pingle user Stata for Hindous perpetual license Serial nunber 1990520454 weight Licensed to Araar Abdelkrin size Universit Laval strata x psu gse commend zone ifgt exppc pline 41099 hsize size alpha 2 exppc iC data An alternative is to use dialog boxes For this the command db should be typed and followed by the name of the relevant DASP module 10 Example db ifgt 7 How can help be accessed for a given DASP module Type the command help followed by the name of the relevant DASP module Example help ifgt Figure 4 Accessing help on DASP Viewer 2 help ifgt O Back Refresh Search Help Contents What s New News Command help ifgt d j DASP Distributive Analysis Stata Package World Bank PEP and CIRPEE help for ifgt Dialog box ifgt FGT Poverty Indices ifgt varivst HSize varname HGroup varnaze PLine reas OPL string PROP ea PERC rea ALpha rea TrYPE string INDex string LEVEL ea CON
41. USER MANUAL DASP version 2 1 DASP Distributive Analysis Stata Package By Abdelkrim Araar Jean Yves Duclos Universit Laval PEP CIRP E World Bank and UNDP March 2009 Table of contents Table Of cont ntS is iania iea oK RT OaE AEE NOAR EE KERETE REA REAT ETA Te 2 Listof FIgUTE Senan a a aaa aaa aa aaaea ia aiis 5 t introduction oia e a E E Goa iro beg E oo E ono ooo ciate 7 Z lt DASP and Stata VerSiONS ainsin ri reae RE Na S E EAT E RE EERTE aias s 3 Installing and updating the DASP package ccesccesecesesseeeseeseeeseceaecueecseeeseeeeeeaeenaeenaeeaee 8 ork installing DASR m0 dtl Ose nnen a oo obr ooo ace 8 3 2 Adding the DASP submenu to Stata s main menu ooo eee een 9 A DASP and data fil s nisinsin seisin siirroissa s R Essare Tisa RAES anA Taat 9 5 Main variables for distributive analysis 0 cececccecsceceseceeeceeeeeeseecaeceeeeeeeenseecsaeenteeneees 10 6 How can DASP commands be invoked cs ycssicuscgsicesaicsaceusssseteses s n ease tances sis dodan a ee iecaeeess 10 7 How can help be accessed for a given DASP Module eee 11 oe Applhcations and filesin DASP riec tiai a a O E as SAR TEE Caia iiae 11 9 Basic Notation onari ne a a ad wp Sterns Bs Ss Sa e aiaa dead Sadu ode os a Sean es 13 10 DASP and poverty indices lt 3 ix ciscssccstiahsaiedeskevin dps sancease stenngey spate ota dsko dua k jha and anton 13 10 1 FGT and EDE FGT poverty indices ifgU ee eee eee 13 1
42. a Faso survey of household expenditures bkf94I dta 76 22 1 2 The 1998 Burkina Faso survey of household expenditures bkf98I dta TI 22 1 3 Canadian Survey of Consumer Finance a sub sample of 1000 observations CATA AUC A cs soa hen gcc atts ea wel O O date Coase O O ety ta hanes detested Ms dd 22 1 4 Peru LSMS survey 1994 A sample of 3623 household observations PEREDE OGRA cfesctiasusccsbanneusisnss aausecsds aise apa eatin gacat ates stusapaitud ecclesia E E 11 22 1 5 Peru LSMS survey 1994 A sample of 3623 household observations PERUA ita jeene n EN E EE E A R 78 22 1 6 The 1995 Colombia DHS survey columbial dta eee 78 22 1 7 The 1996 Dominican Republic DHS survey Dominican republic19961 dta 78 22 2 Appendix B labeling variables and values 2 eeeeeeeeeeeeeee eee 79 22 3 Appendix C setting the sampling design ee eee cesecneeeneeeeeeeeeeeceseceeeeeeeeeeees 80 23 Examples ad ex rcis8S zu 4 6Gaote ddd dash or aiaia Maa VSA hae seen nas 82 23 1 Estimation of FGT poverty Widices ys sseicasyaxcaissjaistacesavsttaalandecessdasvanajearanchoavedieadaaoneas 82 23 2 Estimating differences between FGT indices 0 0 ce eseeseeeeeeeeceseceeeeeeeseeeeeeeeaees 88 23 3 Estimating multidimensional poverty indices ee eee 92 23 4 Estimating FGT CUrVes 2 5 innare aus Boky Ea ee eels ll eal o 95 23 5 Estimating FGT curves and differences between FGT curves with confidence INSK ALS sask Std ooc
43. abel values that will be assigned to the categorical variable gse label define lvgse 1 wage earner public sector 2 wage earner private sector 3 Artisan or trader 4 Other type of earner 5 Crop farmer 6 Subsistence farmer 7 Inactive To assign the label values Ivgse to the variable gse label val gse lvgse label var sex Sex of household head 79 label def lvsex 1 Male 2 Female label val sex Ivsex label var zone Residential area label def lvzone 1 Rural 2 Urban label val zone lvzone 22 3 Appendix C setting the sampling design To set the sampling design for the data file bkf94 dta open the dialog box for the command svyset by typing the syntax db svyset in the command window In the Main panel set STRATA and SAMPLING UNITS as follows Figure 15 Survey data settings S svyset Survey data settings More Weights SE Poststatiication bu xfa Afo A In the Weights panel set SAMPLING WEIGHT VARIABLE as follows 80 Figure 16 Setting sampling weights S svyset Survey data settings Click on OK and save the data file To check if the sampling design has been well set type the command svydes The following will be displayed Survey Describing stage 1 sanpling units pueight weight WE linearized Strata 1 strata SU 1 peu FPE d lt zero gt H bz per Unit Stratun Whits Hibs Hin Hear Hay i 2 He 19 a a
44. and EDE FGT Index gt ifgt command The following results should then be displayed ifgt exppc expeg alphalO hzizelsizel plinel 41099 Poverty Index FGT Index Household size size Sanpling weight weight Paraneter alpha 0 00 War iab le Est inate ST LE UB BHD 0445 0 046124 0 412873 0 470256 ekipe 0 2540 WH 1 270006 0 281592 Q 4 Select RELATIVE for the poverty line and set the other parameters as above 84 F Line 41099 00 41099 00 Figure 18 Estimating FGT indices with relative poverty lines E DASP FGT and EDE FGT Index gt ifgt command After clicking on SUBMIT the following results should be displayed ifgt exppe alphalO heizelsize opl nedian propl li Poverty Index FGT Index Household size size anpling weight weight Faraneter alpha 0 00 Variable Est inate 1 LE IE epp 0 16243 DME 0 108386 12 0 5 Set the group variable to sex 85 F Lina 27046 71 Figure 19 FGT indices differentiated by gender E DASP FGT and EDE FGT Index gt ifgt command Main Confidence Interval Results exppc h of interest Size variable size v Group variable sex iw Survey settings M Index options s Index FGT Index x Type Normalised M Parameter s Parameter alpha fo gt Poverty line The population Absolute jan 099 C
45. ange 10d Survey settings Cancel Submit After clicking on SUBMIT the following should be displayed 22 efgtg income hgroup zone hsize hhsize alpha 0 pline 14897 prc l dec 3 Poverty and Inequality Indices intices Estimate Marginal Impact Elasticities By Groups Population Marginal Marginal Elasticity Share Impact on Ineq Impact on Pov South south H South east o g South west North central North east North west E ele NE NT CC C oo 12 4 FGT elasticities with respect to within between income components of inequality efgtc This module estimates the marginal FGT impact and FGT elasticity with respect to within between income components of inequality A list of income components must be provided This module is based on Araar and Duclos 2007 Araar A amp J Y Duclos 2010 Poverty and Inequality a Micro Framework Journal of African Economies doi 10 1093 jae ejg005 Link to Working Paper 07 35 http 132 203 59 36 CIRPEE cahierscirpee 2007 description descrip0735 htm To open the dialog box of this module type the command db efgtc 23 jE DASP FGT Poverty elasticities with respect to income sources inequalities gt efgtc command Truncated income components After clicking on SUBMIT the following should be displayed efgtc sourcel source6 tot income hsize hhsize alpha 0 pline 14897 prc l Pover
46. aph of FGT curves 5 Graph Graph lnx FGT Curves alpha 0 Burkina 1994 FGT z alpha 0 80000 100000 97 Q 4 Choose variables and parameters as in the following window Figure 28 FGT curves by zone E DASP FGT Curves gt cfgt command After clicking SUBMIT the following graph appears 98 Figure 29 Graph of FGT curves by zone 5 Graph Graph 2 5 x FGT Curves alpha 0 Burkina 1994 6 8 FGT z alpha 0 4 0 20000 s0000 100000 99 Choose the option DIFFERENCE and select WITH THE FIRST CURVE Indicate that the group variable is zone Select the Results panel and choose the option LIST in the COORDINATES quadrant Jn the GRAPH quadrant select the directory in which to save the graph in gph format and to export the graph in wmf format Figure 30 Differences of FGT curves E DASP FGT Curves gt cfgt command With the first curve home A Wihthefistouve xl 100 Figure 31 Listing coordinates E DASP FGT Curves gt cfgt command Ete genhsigaphtiwn Bone 101 After clicking SUBMIT the following appears Figure 32 Differences between FGT curves t Graph Graph Difference Between FGT Curves alpha 0 Burkina 1994 2 Differences 3 0 20000 0000 80000 100000 40000 B Foverty line z Null Horizontal Line FGT_Urban FGT_Rural Q 6
47. are e Rao s approach 1969 41 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 of separate income components The dsineqs Stata module estimates The share in total income of each income source k The absolute contribution of each source k to the Gini index The relative contribution of each source k to the Gini index For the Shapley decomposition the rule that is used to estimate the ineguality index for a subset of components is by suppressing the ineguality generated by the complement subset of components For this a counterfactual vector of income is generated which eguals the sum of components of the subset factors of the coalition in the Shapley decomposition terminology plus the average of the complement subset of components Note that the dsinegs ado file reguires 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
48. ary Secondary Quintile 1 Quint ile 2 Quintile 3 Quintile 4 Quintile 5 B BENRS All Groups Prinary Secondary Quintile 1 0 2 1 3225 Quintile 2 0 509 0 363 Quintile 3 0 772 0 323 Quintile 4 0 633 1 249 Quintile 5 0 472 0 147 All 01 69 0 207 2 To estimate total public expenditures on education by sector at the national level the following macro information was used Pre primary and primary public education expenditure as of all levels 1995 35 2 Secondary public education expenditure as ofall levels 1995 21 2 Tertiary public education expenditure as of all levels 1995 16 Public education expenditure as of GNP 1995 3 GDP per capita about 3 800 Using this information the following variables are generated cap drop _var1 gen varl size weight 3800 gui sum _var1 qui gen pri pub exp 0 03 0 352 r sum gui gen sec pub exp 0 03 0 212 r sum gui gen uni pub exp 0 03 0 160 r sum cap drop _var1 Total public expenditures on primary sector pri pub exp Total public expenditures 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 141 Figure 65 Benefit Incidence Analysis unit cost approach a DASP Benefit incidence analysis gt bian command Main Results Variable s of interest Stan
49. ations of the sample that was originally used to generate the aggregated data Because of this 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 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 Examples Notation NOBS number of total observations F vector of percentiles B_NOBS number of observations for the bottom group 72 T_NOBS number of observations for the top group For NOBS 1000 spread equally across all percentiles F 0 001 0 002 0 999 1 To avoid a value F 1 for the last generated observation one can 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 be easily
50. be changed The results are displayed with 6 decimals this can be changed Interested users are encouraged to consider the exercises that appear in Section 23 1 10 2 Difference between FGT indices difgt This module estimates differences between the FGT indices of two distributions For each of the two distributions There exist three ways of fixing the poverty line 1 Setting a deterministic poverty line 2 Setting the poverty line to a proportion of the mean 3 Setting the poverty line to a proportion of a quantile Q p One variable of interest should be selected Conditions can be specified to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed A level for the parameter can be chosen for each of the two distributions Interested users are encouraged to consider the exercises that appear in Section 23 2 14 10 3 Watts poverty index iwatts The Watts poverty index is estimated as 5 w In z yi P z n wi i where z is the poverty line and gis the number of the 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 grou
51. ble Frequency or Benefit here the use can indicate the number of household member that effectively use the service or the estimated monetary benefit form the public service 70 e The variable region this variable indicates the region integer value in which the household live It is recommended to select the appropriate level of spatial unit to ensure the representativeness of households at the regional level Example Using the Nigerian household survey of 2004 we estimate the MBI for the public primary school service based on Ajwad and Quentin 2001 approach E DASP Marginal Benefit Incidence gt imbi command i wile xj Main Results M Decomposition approach Welfare indicator pcexpdr Approach Parametric Ajwad amp Quentin 2001 Eligible group Je pr i Frequency Benefit u pr Areas Regions state hd Survey settings Cancel Submit inhi u pri e pri melfarelpcerpdr hregion state apprlagi drril Sanpling weight poput Regional variable state Hunber of regions 37 Harginal Benefit Incidence Estinated nith the Ajuad amp Quentin approach Group alpha beta HarginBen Quant ile_4 4 2679 1 14 1 153 Ouantile d 1 HAE 1 3347 Quant ile_3 1 115934 1 028162 1 02243 Quant ile_4 0 177103 0 934174 0 940037 Quant ile_5 0 2306 E 0 439100 21 Disaggregating grouped data 71 The ungroup DASP module generates disaggregated data from aggregate distribu
52. can estimate polarization by using simultaneously per capita consumption and per capita income A group variable can be used to estimate polarization at the level of a categorical group If a group variable is selected only the first variable of interest is then used Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed Main reference DUCLOS J Y J ESTEBAN AND D RAY 2004 Polarization Concepts Measurement Estimation Econometrica 72 1737 1772 14 2 Difference between DER polarization indices dipolder This module estimates differences between the DER indices of two distributions For each of the two distributions One variable of interest should be selected Conditions can be specified such as to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 14 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 r median The user can select more than one variable of in
53. ch The authors propose to regress the incidence in each of the intervals in the regions against the regional 69 means using Q regressions a Si X a pt E T e forg L 0 A 3 dw To avoid endogeneity means at regional level are for all households except for those belonging to interval q Pooling all observations from the various intervals together they estimate one regression QJ Q Q gt Xij D X Xa gt pt est e A 4 q 1 q 1 2 J q J q Since the average marginal increase in access from a unitary increase in mean access is one this implies the following restriction Q A I A 5 2 O 1 B Writing B the parameter for interval Q in relation to the other parameters yields the following Q ule gt F T a z To take a account the restriction A 6 A 4 is estimated with nonlinear least squares It can also be shown that a change in benefit incidence for the households belonging to quintile q in response to an increase in the aggregate incidence is as follows 6X Qf 6X Q 1 B o Bi A 6 A 7 The module imbi ado allows estimating the marginal benefit incidence with one of the presented two approaches above The user will indicate e The welfare indicator like the per capita expenditures e The variable eligible members For instance a household with two children aged between 6 and 11 years will have to members eligible to the primary school e The varia
54. cross time into transient and chronic components 39 The Jalan and Ravallion 1998 approach Let yt be the income of individual i in period t and u be average income over the T periods for that same individual i i 1 N Total poverty is defined as TN gt Z wi z yi TP a z Us T gt Wi i l The chronic poverty component is then defined as N a 2 wi z w CPC a z E N wi i l Transient poverty equals TPC a z TP a z CPC a z Duclos Araar and Giles 2006 approach Let yt be the income of individual i in period t and u be average income over the T periods for individual i Let a z be the egually distributed eguivalent EDE poverty gap such that T a z TP a aj Transient poverty is then defined as N 2 w 9 a z TPC a z x Wj i l T Va where 0 y a z y 1 z and By a z yb r 1 t and chronic poverty is given by CPC a z I a z TPC a z Note that the number of periods available for this type of exercise is generally small Because of this a bias correction is typically useful using either an analytical asymptotic or bootstrap approach 40 To open the dialog box for module dtcpov type db dtcpov in the command window Figure 9 Decomposition of poverty into transient and chronic components JS DASP Decomposition of the total poverty into transient and chronic poverty gt dtcpov command m oj x Main Results
55. d 2 73 1 19 8 a 3 M 183 19 7 0 Fal 4 183 19 19 9 al 5 i ih B 19 5 a 4 TA i 19 0 fal 7 a 1937 19 a 2l 7 as i 19 8 fal 81 23 Examples and exercises 23 1 Estimation of FGT poverty indices How poor was Burkina Faso in 1994 1 Open the bkf94 dta file and label variables and values using the information of Section 22 1 1 Type the describe command and then label list to list labels 2 Use the information of Section 22 1 1 to set the sampling design and then save the file 3 Estimate the headcount index using variables of interest expcc and expeg a You should set SIZE to household size in order to estimate poverty over the population of individuals b Use the so called 1994 official poverty line of 41099 Francs CFA per year 4 Estimate the headcount index using the same procedure as above except that the poverty line is now set to 60 of the median 5 Using the official poverty line how does the headcount index for male and female headed households compare 6 Can you draw a 99 confidence interval around the previous comparison Also set the number of decimals to 4 Answer Q 1 If bkf94 dta is saved in the directory c data type the following command to open it use C data bkf94 dta clear If lab bkf94 do is saved in the directory c do files type the following command to label variables and labels do C do files lab bkf94 do Typing the command describe we obtain obs
56. d 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 el x Main Confidence Interval Results Distribution 1 Distribution 2 Data in File C DATANDKIS4 dta Browse Variable of interest Variable of interest Size variable Size variable Poverty line Poverty line Absolute 10000 Absolute 10000 C Relative 503 of the Mean z C Relative s54 of the Mean z I Condition s fi s T Condition s fi z Data in Memory jk Parameters and Options Parameter alpha fo Type Normalised 20 Cancel Submit 12 Notes 1 DASP considers two distributions to be statistically dependent for statistical inference purposes if the same data set is used the same loaded data or data with the same path and filename for the two distributions 2 Ifthe option DATA IN FILE is chosen the keyboard must be used to type the name of the required variables 9 Basic Notation The following table presents the basic notation used in DASP s user manual Symbol Indication y variable of interest i observation number Ji value of the variable of interest for observation i hw sampling weight hw sampling weig
57. d in conducting distributive analysis with Stata In particular DASP is built to n Estimate the most popular statistics indices curves used for the analysis of poverty inequality social welfare and equity 7 Estimate the differences in such statistics n Estimate standard errors and confidence intervals by taking full account of survey design n Support distributive analysis on more than one data base n Perform the most popular poverty and decomposition procedures 7 Check for the ethical robustness of distributive comparisons n Unify syntax and parameter use across various estimation procedures for distributive analysis For each DASP module three types of files are provided ado This file contains the program of the module hlp This file contains help material for the given module dlg This file allows the user to perform the estimation using the module s dialog box The dlg files in particular makes the DASP package very user 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 9 2 or higher o ado files must be updated To update the executable file from 9 0 to 9 2 and the ado files see http www stata com support updates 3 Installing and updating th
58. d options expeg Parameter alpha o5 Size variable size Group variable Jins lev v Survey settings Cancel Submit After clicking SUBMIT the following results appear Deconposition of the social polarisation index by population groups Household size size Sanpling weight weight Group variable ins lev Paraneter alpha 0 50 Social polarisation index 0 65413204 0 00854258 Fopu lat ion Incone Hithin Group Betueen Group Share Share Conponerit Conponent ILH 1 200228 DK 0 021118 0 019042 0 004381 0 282791 0 41516 0 07714 0 021539 0 032054 0 005099 0 356762 1 252256 DEE 0 236 0 028543 0 027982 0 005985 0 020541 1 0000 1 000000 0 000000 0 000000 0 002360 0 010026 Main references 34 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 JAE Working Papers 736 08 Unitat de Fondaments de l An lisi Econ mica UAB and Institut d An lisi Econ mica CSIC 15 DASP and decompositions 15 1 FGT Poverty decomposition by population subgroups dfgtg The dgfgt module decomposes the FGT poverty index by population subgroups This decomposition takes the form A
59. dard living Label the public service Education Jexppe v Options Approach Unitcostbeneft Number of sectors 2 X Labels Sector 1 Primary Sector 2 Secondary Frequency fra prim firq_sec v Eligible HH members Jel prim had JeL sec hd Area indicator zl z Regional pub expenditures pri pub exp p sec pub exp ad Main Results DASP Benefit incidence analysis gt bian command M Result options Number of Decimals Social groups Group variable 3 Quintiles a Displayed results IV Average benefits IV Share and rate of participation IV Proportion of benefits After clicking on Submit the following appears Cancel Submit Cancel Submit Average Benefits by Quintile Groups at the level of eligible nenbers Groups Pr inary Secondary Quintile 1 276 936 43 356 Quintile 293 796 208 25 Quintile 3 20 211 90 Quintile 4 248 171 183 1 Quintile 5 171 520 95 228 All 4a 105 555 Groups Pr inary Secondary Quintile 1 M40 6 503 Quintile 2 33 446 656 563 Quintile 3 3 446 156 563 Quintile 4 33 4 6 503 Quintile 5 M24 156 563 All 33 46 6 503 Groups Pr inary Secondary Quintile 1 0 13 1 0 Quintile 2 0 144 1 0 Quintile 3 0 155 1 0 Quintile 4 0 127 0 075 Quintile 5 0 04 0 05 All 0 624 0 376 143
60. dence interval 1 0 eee 107 Figure 40 Testing for poverty dominance eee eee een 108 Figure 41 Decomposing FGT indices by EroupS eee 109 Figure 42 Lorenz and concentration CUIVES 0 cceccesceseceseeeeeseeeeeeecaeceeecaeeeseeeeeeseeeaeenaeeaee 112 Fig re43 Lorenz GUL VES coin rien an aye iin len cece oo i tat in o ob a aaia 113 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 Figure 63 Figure 64 Figure 65 Figure 66 Drawing concentration curves kudadsad sudo ee ssedecauckteedecstaree has ads ec dada ces 114 Lorenz and concentration CUTV S secissesscicsscesscdsnessieveserdecaacsdecutassesecdesedesnnasesdeceasetnes 115 Dr wing Lorenz curts uein oen rea a a u B b u oa a ce ents ol als 116 Loren CULV ES odds o ao s68 asd dave Va Saas do KK a A a acess od Wes dno odd P 116 Estimating Gini and concentration indices eee 118 Estimating concentration indices 3 44084x6a6su aid aida ob k t ao ees 119 Estimating differences in Gini and concentration indices 120 Drawing LOTUS TCS za her ot Ov Aaa david hig Tce la ee ooo ba G o oo tare ny 121 Density CU VES cates ese hah uit n E ta nae bond Ga Ret h zbo c te as Mac tetas 122 Drawing guantilecUrveS 3 32 neea ciao Bo caer ost uae somes 123 Quant es CHIVES data osa
61. e DASP package In general the ado files are saved in the following main directories Priority Directory Sources 1 UPDATES Official updates of Stata ado files 2 BASE ado files that come with the installed Stata software 3 SITE ado files downloaded from the net 4 PLUS 5 PERSONAL Personal ado files 3 1 installing DASP modules a Unzip the file dasp zip in the directory c b Make sure that you have c dasp dasp pkg or c dasp stata toc c Inthe Stata command windows type the syntax net from c dasp Figure 1 Ouput of net describe dasp Yersion version 2 0 Date June 2009 Stata Yersion Required 9 2 and higher Author DASP is conceived by Dr Abdelkrin Araar aabd ecn ulayal ca Dr Jean Yves Duclos jyyes ecn ulayal ca Before using nodules of this package users have to update the executable Stata file to Stata 9 2 or higher http uuu stata con support updates stata9 htnl update the ado files http uuu stata con support updates stata9 ado The tuo folluing sub packages nust be installed to run DASP PACKAGES you could net descr ibe dasp pl Distributive Analysis Stata Package PART I dasp_p2 Distributive Analysis Stata Package PART II d Type the syntax net install dasp_p1 pkg force replace net install dasp_p2 pkg force replace net install dasp_p3 pkg force replace 3 2 Adding the DASP submenu to Stata s main menu With Stata 9 sub menus can be added to the menu item User
62. e level of confidence used can be changed The results are displayed with 6 decimals this can be changed Interested users are encouraged to consider the exercises that appear in Section 23 9 13 2 Difference between Gini concentration indices digini This module estimates differences between the Gini concentration indices of two distributions For each of the two distributions 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 25 Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 13 3 Generalized entropy index ientropy The generalized entropy index is estimated as 1 P yvi Z 1 if 60 1 6 1 w i i l i 0 Zw to if 0 0 wi 1 i i l SE gl 2 if 0 1 gt w 1 u i l The user can select more than one variable of interest simultaneously For example one can estimate inequality simultaneously for per capita consumption and for per capita income A group variable can be used to estimate inequality at the level of a categorical group Ifa group variable is selected only the first variable of interest is then used Standard errors and confidence intervals with a
63. een Gini concentration indices digini 0 0 0 0 eee ee 25 13 3 Generalized entropy index ientropy ec eecceeceeeeesceceeeceeeeeeeeeseecseceeeneeeeeseees 26 13 4 Difference between generalized entropy indices diengtropy 26 13 5 Atkinson index iatkinson sic cccssscciscescva despues cosh ccnacavasvaces tessns ctna seceiatadevasesapeaetedieenz cits 27 13 6 Difference between Atkinson indices diatkinson eee 27 13 7 Coefficient of variation index icvar ooo eee ee cetcceseceeceeesceceseceeeneeeeeseecaeceeeeeeeenaeees 28 13 8 Difference between coefficients of variation diCVAT ee 28 13 9 Ouantile share ratio indices of inequality inineg sssesessssessessessesssesssssresseesees 28 13 10 Difference between Ouantile Share ratios dinineg eee 29 14 DASP and polarization indices s15 si s se hastecscotecenscanasuacusdesens aaviceastidevasevspvaneebemenseisa 29 141 gt The DER index 1O1EF 35 dass Mod u oa Vod dante a ecase odkud ear 29 14 2 Difference between DER polarization indices dipolder 30 14 3 The Foster and Wolfson 1992 polarization index ipolfW eee eeeeeeeneeeeeees 30 14 4 Difference between Foster and Wolfson 1992 polarization indices dipolfw 31 14 5 The Esteban Gardin and Ray 1999 polarization index ipoger eeeeeeeeees 31 14 6 The Inaki 2008 polarization index ipoger eee 32 15 DASP An decompo
64. ences across years by gender and Z0Ne eee 91 Figure 24 Estimating multidimensional poverty indices A 93 Figure 25 Estimating multidimensional poverty indices B eee 94 Figure 26xDrawing EGE CUTVESS ornidin athlete sob oo o ends lo oo lon 96 Figure 27 BGne PGTCUVES z cai victors sanan ysiseaas se anasiec sas ous Saas 66 Sensis Sousa ao ta a We dass 96 Fig re 28 Graph of MGW CUIVES sz sd civics adds only unease dan O Abeo ad aa ae 97 Fig re29 FGTc rves Dy ZoNe jis ead tav ka ncoacd ko p t sud dana sae wiaean kasta au alan Aiie 98 Figure 30 Graph of FGT curves by ZOMG o 5i4scce ccisevsesdsvecescuspnvcessecuzesstasus dn ns ds tron v es ola nada via 99 Figure 341 Ditterences of FGT CBS Sie Gg sta ea st soo EA laku a paste 100 Fig re 3 2 listne COOrdinateS z st lka Pasta oin ii iad iu a wine a T a 101 Figure 33 Differences between FGT CUrVES ccscsssssocssssorsetssesscessestesnssonsessessstensesseenssones 102 Figure 34 Differences between FGT CUrVeS sessessesessseseesesseseesrssereessestestsseseesssersesseseesesse 103 Figure 35 Drawing FGT curves with confidence interval 104 Figure 36 FGT curves with confidence interval eee 105 Figure 37 Drawing the difference between FGT curves with confidence interval 106 Figure 38 Difference between FGT curves with confidence interval a 0 106 Figure 39 Difference between FGT curves with confi
65. ensional poverty dominance Difference Lower bounded 0 5 r Upper bounded Us S RSL 0 2 131 To make a simple test of multidimensional dominance one should check if the lower bounded confidence interval surface is always above zero for all combinations of relevant poverty lines or conversely o For this click on the panel Confidence interval and select the option lower bounded o Click again on the button Submit After clicking SUBMIT the following graph is plotted interactively with Gnu Plot 4 2 Bi dimensional poverty dominance Lower bounded Dimension 1 2 gt 35 4 X 6 A 1 0 0 0 2 0 9 0 9 96 98 8 8 8 8 20 940 0 40 86 0 88 0 Dimension 2 132 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 2ml dta and mex 04 2ml dta test for absolute second order pro
66. entration curves with confidence intervals clorenzs 53 16 6 Differences between Lorenz concentration curves with confidence interval KADE ZS ZG EEE E E A T 54 16 7 Poverty curves cpoverty s ssssesssessesseesseesessresseessesersstessesersstessesstssressessessresseeseese 54 16 8 Consumption dominance curves cdomc sessssessesessssesseseresressessrssressessresresseeseese 55 16 9 Difference Ratio between consumption dominance curves cdomc2d 56 16 10 DASP and the progressivity curves isszez und kodu aSi neds temasas neska o kaodakdd oko d kd dan 56 16 101 Checking the progressivity Of taxes OF transfers we 56 16 10 2 Checking the progressivity ofa transfer VS a LaX we 57 17 VOTIVE CO sessu e a a R tan a e 57 17 1 Poverty dominance dompoV ssssssssessssssessessssresseesessressteseserssressesrrssressessrssressesse 57 17 2 Inequality dominance domineg sssessssessssessseessesessssessesersseessesstssessessrssresseeseese 58 17 3 DASP and bi dimensional poverty dominance dombdpov 58 18 Distributive tOGIS nien pih e a aa boze E ny 59 18 1 Quantile curves c guantile sirrini ai aa a aE AE SEAE RERNE ATEENAS 59 18 2 Income share and cumulative income share by percentile groups quinsh 59 18 3 D nsity curves cdensity ren a ooo oo eo 59 18 4 Non parametric regression curves CNPE ssssessesessssesseserssressessrssressessessresseeseese 6l 18
67. f group g T x denotes the local proportion of individuals belonging to group g and having income x 49 e P isthe DER polarization index when the within group polarization and inequality is ignored 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 Cahier de recherche 0806 CIRPEE 15 10 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 gt WCE k Ha d where CP jse a as and y are respectively the pseudo concentration index and a a l kk income share of income source k The dpolas module decomposes the DER index by income sources Reference s Abdelkrim Araar 2008 On the Decomposition of Polarization Indices Illustrations with Chinese and Nigerian Household Surveys Cahiers de recherche 0806 CIRPEE 16 DASP and curves 16 1 FGT CURVES cfgt FGT curves are useful distributive tools that can inter alia be used to 1 Show how the level of poverty varies with different poverty lines 2 Test for poverty dominance between two distributions 3 Test pro poor 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 simu
68. generated S 1 2 Generating an initial distribution of incomes The user must indicate a distributional form for the disaggregated data Normal and log normal distributions Assume that x follows a lognormal distribution with mean Z and variance o The Lorenz curve is defined as follows up o FB anne 0 2 o G We assume that Z 1 and we estimate the variance using the procedure suggested by Shorrrocks and Wan 2008 a value for the standard deviation of log incomes o is obtained by averaging the m 1 estimates of o p L p k 1 m1 where m is the number of classes and is the standard normal distribution function Aitchison and Brown 1957 Kolenikov and Shorrocks 2005 Appendix Generalized Ouadratic Lorenz Curve It is assumed that L I 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 2 0 5 We have O p b 2mp n mp tmp e 2 4 e a b c l m b 4a n 2be 4c Beta Lorenz Curve It is assumed that log p L log y log p 6 log 1 p After estimating the parameters we can generate quantiles as follows 73 See also Datt 1998 The Singh Maddala distribution The distribution function proposed by Singh and Maddala 1976 takes the following form 1 q4 FAI B a 0 b 0 q21 aa
69. he FGT index by groups eee 36 Figure 9 Decomposition of FGT by income componente Erreur Signet non d fini Figure 10 Decomposition of poverty into transient and chronic components 41 Figure 11 Decomposition of the Gini index by income sources Shapley approach 42 Figure T2 FGT CUVE Siasii soninig nean oea ieo ao A aa EES EERE AEREA Dee a bakes 51 Figure 13 Lorenz and concentration CUIVES sssssseesssseseesesseteessesttstsststesessesteseseesesseseesessese 53 Figure 14 Consumption dominance CUrVeS sseseseesesseseesesseseesstseestsststestsseseestsetsesseseesessese 56 Figure 5 u ngro p dialog Dox seereis ie aaa a Stan Pa atest es eas PaE aSa ia 75 Figure 16 Survey data settings sessesesseseesseseesesstsetsesststestssestesteseesessestestssesesteseesesseseesessese 80 Figure 17 S tti ng sampling W61PNTSx ei oad at age tao a Pal E 81 Figure 18 Estimating FGT indices ai oeceucs cc seacin yesloess eesnctactroseastandenste vSsacss sas sean eer ete 84 Figure 19 Estimating FGT indices with relative poverty liNeS eee 85 Figure 20 FGT indices differentiated by gender cic2 cocci ctasacsesgucdiisde saiarsadbedoncsabad sdacdiacta tans 86 Figure 21 Estimating differences between FGT iNndiCeS eee 89 Figure 22 Estimating differences in FGT indices 0 0 0 0 eecesecsteeneesseeeeeeeeeseceeecaeeeseeeeeeeeeaees 90 Figure 23 FGT differ
70. here 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 TaS u k 1 _ zf k z u k if a 0 The module itargetg allows to Estimate the impact of a marginal change in income of the group on poverty of the group and poverty of the total population Select the type of change constant or proportional to income the latter to keep inequality unchanged Draw curves of the impact according to a range of poverty lines Draw a two sided confidence interval of the impact curves or the lower or upper bound of this confidence interval Etc 18 Figure 7 Poverty and targeting by population groups six Main Results Graphical Results Y Axis Axis Title Caption Legend Overall Variable of interest Options and parameters Jexppc ba Parameter alpha fo Normalised by the cost Normalised Size variable size zl Targeting type Lump sum constant amount x Group variable zone bd Poverty line z 100000 Minimum Maximum C Range of pov line 0 10000 Cancel Submit Reference DUCLOS J Y AND A ARAAR 2006 Povert
71. ht for observation i hs size variable hsi size of observation i for example the size of household i Wi hwi hs hg group variable hgi group of observation i wi swik sw if hg k and 0 otherwise n sample size For example the mean of y is estimated by DASP as 1 10 DASP and poverty indices 10 1 FGT and EDE FGT poverty indices ifgt The non normalized Foster Greer Thorbecke or FGT index is estimated as n i Z w z n P za j F n ZW i where z is the poverty line and x max x 0 The usual normalized FGT index is estimated as Plz a Plc a z 13 The EDE FGT index is estimated as l a for a gt 0 EDE P z a Pe a There exist three ways of fixing the poverty line 1 Setting a deterministic poverty line 2 Setting the poverty line to a proportion of the mean 3 Setting the poverty line to a proportion of a quantile Q p The user can choose the value of parameter a The user can select more than one variable of interest 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
72. iable v Poverty line 2 10000 Minimum Maximum Range of pov line fo fi 0000 Cancel Submit 16 9 Difference Ratio between consumption dominance curves cdomc2d 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 to check whether taxes and transfers are progressive Let X be gross income T bea given tax and B be a given transfer The tax T is Tax Redistribution TR progressive if PR p Ly p C p gt 0 Yp 0 56 The transfer B is Tax Redistribution TR progressive if PR p C p L p gt 0 Yp 0 1 The tax T is Income Redistribution IR progressive if PR p Cy_ p Ly p gt 0 Vp 0 The transfer B is Income Redistribution
73. ith confidence interval FGT curve alpha 0 Burkina Faso T T T T l 0 20000 40000 60000 80000 100000 Poverty line z Confidence interval 95 Estimate 0 2 Steps To open the relevant dialog box type db cfgtsd2 Choose variables and parameters as in 105 Figure 36 Drawing the difference between FGT curves with confidence interval EE DASP Curve of difference between FGT Indices gt cfgts2d command Data in file v CADATASDKES4I dta Data in file v CADATASDKESSI dta fe a jn z p A NN a Figure 37 Difference between FGT curves with confidence interval o 0 Difference between FGT curves alpha 0 1 100000 T T T 40000 60000 80000 Poverty line z o T 20000 Confidence interval 95 Estimated difference 106 Figure 38 Difference between FGT curves with confidence interval a 1 Difference between FGT curves a alpha 1 T T T T 1 0 20000 40000 60000 80000 100000 Poverty line z Confidence interval 95 Estimated difference 23 6 Testing poverty dominance and estimating critical values Has the poverty increase in Burkina Faso between 1994 and 1998 been statistically significant 1 Using simultaneously files bkf94I dta and bkf98I dta check for second order poverty dominance and estimate the values of the poverty line at which the two
74. ith 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 regression model specifications e Linear 1 Bot Bx t Boxy tet Bory 8 e Semi Log Linear log y Bx ax By Xp With the analytic 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 5 5 8 5 Sp Where sis the estimated constant s 6 X and s is the estimated residual As discussed in Wang 2004 relative inequality indices are not defined when the average of the variable of interest equals zero such as in the case of the residual Also inequality indices are usually normalized to zero when the variable of interest is a constant 43 such as in the case of the estimated constant To deal with these two problems Wang 2004 proposes the following rules Let s S S t S and y s 5 5 then y cs I cs The contribution of the constant cs I y I The contribution of the residual cs 1 y I The Gini index Using the Rao s 1969 approach the relative Gini index can be decomposed as follows v Mk FA I y C H5 where u is the average
75. latins A asa ata VA dop AU Hooda ooo B che o o ten ees 103 23 6 Testing poverty dominance and estimating critical values 107 23 7 Decomposing FGT indices asi st edds aa k kto dizec s Ga dead tuze osad east dh gece Gees 108 23 8 Estimating Lorenz and concentration CUTVeS eee 111 23 9 Estimating Gini and concentration Curves eee 117 23 10 Using basic distributive LOOS 44 zs oka sca ou eect Me nasa A 121 23 11 Plotting the joint density and joint distribution functions 127 23 12 Testing the bi dimensional poverty dominance o 130 23 13 Testing for pro poorness of growth in Mexico 133 23 14 Benefit incidence analysis of public spending on education in Peru 1994 139 List of Figures Figure 1 Ouput Of net describe dasp ssc cas eiccts cnc iss nese ta detains ats eases ianens ass ghavasldedescnesNiseais sonsicnien 8 Fig r 2s DASP SUD MON ed hci et led tat elk weak aaa Nace tae se tana ees 9 Figure 3 Using DASP with a command WindOW eceeceeseceseceseeeeeseeeeeeseeeseceecaeeeaeeeeeeeeeaees 10 Figure 4 Accessing help on DASP i 0i03 ceccccassisctsscasty cessiceetadevescashveststeceracdsiyuasus tv date eb Vida sada dds kV 11 Figure 5 Estimating FGT poverty with one distribution eee 12 Figure 6 Estimating FGT poverty with two distributions eee 12 Figure 7 Poverty and the targeting by population groups sssssesessssesseserseessresseserssressessessressesse 19 Figure 8 Decomposition of t
76. lows PRE a X pi Plej ue jal k l where uj and p denote respectively the average income and the population share of group j The parameter a 1 1 6 reflects the sensitivity to polarization The first step of the estimation requires defining exhaustive and mutually exclusive groups p This can involve some degree of errors A measure of polarization proposed by Esteban et al 1999 is obtained after correcting the P a index with a measure of the grouping error This is done by selecting the partition that minimizes the Gini index value of within group inequality G f G p see Esteban et al 1999 The measure of polarization proposed by Esteban et al 1999 is then given by PER ap B S p ep lu u B G F G p jel k l 31 where B20 is a parameter for the assigned weight to the error term In Esteban et al 1999 the value used is B 1 The Stata module ipoegr ado estimates the Esteban et al 1999 polarization index In addition to the usual variables this routine offers the user three options 1 The number of groups Empirical studies often use two or three groups The user can select a number of groups The program then seeks the optimal income intervals for each group and G f G p G f displays them It also displays the error in percentage ie 100 2 The parameter a 3 The parameter To respect the scale invariance principle all incomes are divided by average income i e
77. ltaneously 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 50 list or save the coordinates of the curves save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs To open the dialog box of the module cfgt type the command db dfgt in the command window Figure 11 FGT curves E DASP FGT Curves gt cfgt command Se po oY ho Interested users are encouraged to consider the exercises that appear in Section 23 4 51 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 d
78. mation is obtained dfgtg exppc hgrouplgsel hzizelzizel alphalil plinel 41099 detd 0 typelnorl decid FGT Index Deconposition by Groups Group FGT Index Populat ion Absolute Relat ive Share Contribution Contribution uage earning public sector uage sarning private sector Artisan or trading Others activities Farners crop Farners food Inactive Z R5888 M2 DG Mi NH n np m1 130 POPULATION mm M mou m 110 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 bkf94I dta file 3 Draw Lorenz curves for rural and urban households a with variable of interest exppc b with size variable set to size c and using the group variable zone as residential area 0 1 Steps Type use C data can6 dta clear To open the relevant dialog box type db clorenz Choose variables and parameters as in 111 Figure 41 Lorenz and concentration curves E
79. mended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs 16 7 Poverty curves cpoverty The cpoverty module draws poverty gap and cumulative poverty gap curves o The poverty gap ata percentile p is G p z z Q p o The cumulative poverty gap at a percentile p noted by CPG p z is given by X w y SO p CPG p z EMs 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 54 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 n s 2 j 2 w Z Yj
80. module draws Lorenz and concentration curves simultaneously The module can 52 draw more than one Lorenz or concentration curve simultaneously whenever more than one variable of interest is selected draw more than one generalized or absolute Lorenz or concentration curve simultaneously whenever more than one variable of interest is selected draw more than one deficit share curve draw Lorenz and concentration curves for different population subgroups whenever a group variable is selected draw differences between Lorenz and concentration curves list or save the coordinates of the curves save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs To open the dialog box of the module clorenz type the command db clorenz in the command window Figure 12 Lorenz and concentration curves E DASP Lorenz amp Concentration Curves gt clorenz command 101 x Main Results Y Axis X Ais Title Caption Legend Overall Variable s of interest Type of curve s T Type Mormalised by default T Ranking Variable v T Difference No v Size variable v T Range of percentiles p Group variable S Minimum Maximum o 0 fi 0 20 Cancel Submit
81. nded FGT index anfa s Z A j l j 4 Tsui 2002 index b J z j P X Z i z 1 I min z X j 5 Intersection headcount index J PX Z Tz gt j l 6 Union headcount index J p X Z 1 1 z lt x jal 7 Bourguignon and Chakravarty bi dimensional 2003 index ma o ase y y ZT Xi Z272 e f L and Cz Z1 i Z2 ts imdpov estimates the above multidimensional poverty indices as well as their standard errors where 17 The user can select among the seven multidimensional poverty indices The number of dimensions can be selected 1 to 6 If applicable the user can choose parameter values relevant to a chosen index A group variable can be used to estimate the selected index at the level of a categorical group Standard errors and confidence intervals with a confidence level of 95 are 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 11 DASP poverty and targeting policies 11 1 Poverty and targeting by population groups The per capita dollar impact of the marginal addition of a constant amount of income to everyone within a group k called Lump Sum Targeting LST on the FGT poverty index P k z a is as follows aP k z a l if a21 LST f k z if a 0 w
82. ocuments o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs Interested users are encouraged to consider the exercises that appear in Section 23 5 16 3 Difference between FGT CURVES with confidence interval cfgts2d The cfgts2d module draws differences between FGT curves and their associated confidence interval by taking into account sampling design The module can draw differences between FGT curves and two sided lower bounded or upper bounded confidence intervals around these differences normalize or not the FGT curves by the poverty lines list or save the coordinates of the differences between the curves as well as the confidence intervals save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options 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 Pash show the level of inequality test for inequality dominance between two distributions test for welfare dominance between two distributions assess tax and benefit progressivity The clorenz
83. of the 1994 consumer price index to the 1998 consumer price index ipc_1994 ipc_1998 List of new variables expcpz Total household expenditures per capita deflated by z_1994 z_1998 expcpi Total expenditures per capita deflated by ipc_1994 ipc_1998 22 1 3 Canadian Survey of Consumer Finance a sub sample of 1000 observations can6 dta List of variables X Yearly gross income per adult eguivalent T Income taxes per adult eguivalent B1 Transfer 1 per adult eguivalent B2 Transfer 2 per adult eguivalent B3 Transfer 3 per adult eguivalent B Sum of transfers B1 B2 and B3 N Yearly net income per adult eguivalent X minus T plus B 22 1 4 Peru LSMS survey 1994 A sample of 3623 household observations PEREDE94I dta List of variables exppc Total expenditures per capita constant June 1994 soles per year weight Sampling weight 77 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
84. of y and G is the coefficient of concentration of s when Y is the ranking variable The sguared coefficient of variation index As shown by Shorrocks 1982 the sguared coefficient of variation index can be decomposed as lov j s 1G LAB 2 k l Decomposing with the Shapley approach As indicated above the Shapley approach is based on the expected marginal contribution of the various components to total ineguality 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 we replace it by its mean e With option method zero when a component is missing from a given set of components we replace it by zero As indicated above we cannot estimate relative ineguality for the residual component in a linear model e For the linear model the decomposition then takes the form I y cs where the contribution of the residual is cs I y I e For the log linear model the Shapley decomposition is applied to all components including the constant and the residual With the Shapley approach the user can use the log linear specification by specifying the income variable itself and not its log DASP then runs the regression with log y as dependent variable 44 Example 1 JE Inequality regression based decomposition by predicted components using the Shapley value rodini Shapley
85. on with DAD Berlin and Ottawa Springer and IDRC sec 12 12 Marginal poverty impacts and poverty elasticities 12 1 FGT elasticity with respect to growth in average income efgtgr The overall growth elasticity GREL of poverty when growth comes exclusively from growth within a group k namely growth is inequality neutral within that group is given by _ F k Z F z GREL 4 _ 7 a P k z P k z 1 P z a if a 0 if azl where z is the poverty line k is the population subgroup in which growth takes place f k z is the density function at level of income z of group k and F z is the headcount Araar A amp J Y Duclos 2010 Poverty and Inequality a Micro Framework Journal of African Economies doi 10 1093 jae ejg005 Link to Working Paper 07 35 http 132 203 59 36 CIRPEE cahierscirpee 2007 description descrip0735 htm Kakwani N 1993 Poverty and economic growth with application to C te D Ivoire Review of Income and Wealth 39 2 121 139 20 To estimate the FGT elasticity with respect to growth in average income of the group or of 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 inte
86. oor curves Pro poor curves can be drawn using either the primal or the dual approach The former uses income levels The latter is based on percentiles 19 2 1 Primal pro poor curves The change in the distribution from state 1 to state 2 is s order absolutely pro poor with standard cons if A z S P z cons a s l FA z a s 1 lt 0 Vze 0 2 The change in the distribution from state 1 to state 2 is s order relatively pro poor if A z s Pata s D R z a o vze 02 4 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 63 draw pro poor curves and their two sided lower bounded or upper bounded confidence intervals listor save the coordinates of the differences between the curves as well as those of the confidence intervals save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs Interested users are encouraged to consider the exercises that appear in Section 23 13 19 2 2 Dual pro poor curves Let Q p quantile at percentile p GL p Generalized Lorenz curve at percentile p U average living standards The change in the distribution from state 1 to state 2 is first
87. or gross income X and net income N 2 Estimate the concentration indices for variables T and N when the ranking variable is gross income X By how much has inequality changed in Burkina Faso between 1994 and 1998 Using the bkf94I dta file 3 Estimate the difference in Burkina Faso s Gini index between 1998 and 1994 a with variable of interest expegz for 1998 and expeg for 1994 b with size variable set to size 0 1 Steps Type use C data can6 dta clear To open the relevant dialog box type db igini Choose variables and parameters as in 117 Figure 47 Estimating Gini and concentration indices E DASP Gini amp Concentration Indices gt igini command After clicking SUBMIT the following results are obtained Variable Est inate ST i GHI X VE VH 2 GINIH 0 332355 0 012753 Q 2 Steps Choose variables and parameters as in 118 LB UB 04009 OA 0 1 0 757301 Figure 48 Estimating concentration indices E DASP Gini amp Concentration Indices gt igini command ME _ Variable Est inate 10 1 OH T 0 595359 1 12253 2 COHC H 1 VH 0 3 Steps To open the relevant dialog box type db digini Choose variables and parameters as in 119 Figure 49 Estimating differences in Gini and concentration indices E DASP Difference Between Gini Concentration Indices gt digini command Data in File o CNDATAS
88. order absolutely pro poor with standard cons 0 if A z 5 0 p 0 p gt 0 V pe 0 pt F z or equivalently if 0 p O p Ate gt 0v pel OP F z The change in the distribution from state 1 to state 2 is first order relatively pro poor if A z s LP 2 590 pefo p F c O p 4h The change in the distribution from state 1 to state 2 is second order absolutely pro poor if A z s GL p GL p gt 0 Y p e 0 p F z or equivalently if _ GL p GL p s GL p gt 0Vpe o p F z The change in the distribution from state 1 to state 2 is first order relatively pro poor if 64 G Alz s FP 259 v pefo pt F z GL p 4 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 listor save the coordinates of the differences between the curves as well as those of the confidence intervals save the graphs in different formats o gph Stata format o wmf typically recommended to insert graphs in Word documents o eps typically recommended to insert graphs in Tex Latex documents Many graphical options are available to change the appearance of the graphs Interested users are encouraged to consider the exercises that appear in Section 23 13 20 DASP and Benefit Incidence
89. 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 8 Difference between coefficients of variation dicvar This module estimates differences between the coefficients of variation 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 Ouantile share ratio indices of inequality inineq The quantile ratio is estimated as QP QR pi p2 QR p1 p2 aT where Q p denotes a p quantile and p and p gt are percentiles The share ratio is estimated as GL p2 GL p1 SR p1 p2 p3 p4 GL p4 GL p3 28 where GL p is the Generalized Lorenz curve and py p2 p3 and p4 are percentiles The user can select more than one variable of interest simultaneously For example one can estimate inequality simultaneously for per capita consumption and for per capita income A group variable can be used to estimate inequality at the level of a categorical group Ifa group variable is selected only the first variable of interest is then used Standard
90. p 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 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 5 Sen Shorrocks Thon poverty index isst The Sen Shorroks Thon poverty index is estimated as P z HP z 1 G 15 where z is the poverty line H is the headcount P z is the average poverty gap among the poor and G is the Gini index of poverty gaps among the 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 pover
91. pears Absolute propoor curves Order s 1 Dif Q_2 p Q_1 p mu 2 mu 1 m T T T T 0 184 368 552 736 92 Percentiles p Difference Lower bound of 95 confidence interval Null horizontal line Q 2 Steps 136 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 63 Testing for pro poor growth dual approach B E DASP Pro poor curves dual approach gt cpropoord command Datainfile C Documents and Settings araa Aa ae Datainfle C Documents and Settings araa n After clicking SUBMIT the following graph appears 137 Absolute propoor curves Order s 2 Dif GL_2 p GL_1 p GL_2 p T T 0 184 368 552 736 92 Percentiles p Difference Lower bound of 95 confidence interval Null horizontal line Q 4 Steps To open the relevant dialog box type db ipropoor Choose variables and parameters as 138 E DASP Pro poor indices gt difgt command In xj Main Confidence Interval Results Distribution 1 M Distribution 2 Data infile ZJ CADATAMexicovmex 98 2ml d Browse Datainfie J CADATAMexicotmex 04 2ml d Browse Variable of interest finc Variable of interest finc Size variable
92. rameters as in 93 Figure 24 Estimating multidimensional poverty indices B E DASP Multidimensional poverty indices gt imdpov command Bourguignon and Chakravarty 2003 bidimensional index E fo ee fs After clicking SUBMIT the following results appear indpoy exppe pliterate hsizelzizel index 7 alphall betald gannalil plil4 pl2 0 91 H D Poverty index Bourguignon and Chakravarty 2003 Household size size Est inate Populat ion 008 94 23 4 Estimating FGT curves How sensitive to the choice of a poverty line is the rural urban difference in poverty 1 Open bkf94I dta 2 Open the FGT curves dialog box 3 Draw FGT curves for variables of interest exppc and expeq with a parameter a 0 b poverty line between 0 and 100 000 Franc CFA c size variable set to size d subtitle of the figure set to Burkina 1994 4 Draw FGT curves for urban and rural residents with a variable of interest set to expcap b parameter a 0 c poverty line between 0 and 100 000 Franc CFA d size variable set to size 5 Draw the difference between these two curves and a save the graph in gph format to be plotted in Stata and in wmf format to be inserted in a Word document b List the coordinates of the graph 6 Redo the last graph witha 1 Answers Q 1 Open the file with use C data bkf941 dta clear 0 2 Open the dialog box by typing db difgt
93. re parameters to be estimated The income x is assumed to be equal or greater than zero The density function is defined as follows f x aq b 1 x b The quantile is defined as follows x b O p bl 1 We follow Jenkins 2008 approach for the estimation of parameters For this we maximize the likelihood function which is simply the product of density functions evaluated at the average income of the classes http stata press com journals stbcontents stb48 pdf STAGE II Adjusting the initial distribution to match the aggregated data optional This stage adjusts the initial vector of incomes using the procedure of Shorrocks and Wan 2008 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 74 Figure 14 ungroup dialog box amp Disaggregation of aggregated data gt ungroup command Basic information on the aggregated data Size of the generated distribution Percentiles p bo
94. rest is then used Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 12 2 FGT elasticity with respect to Gini inequality efgtineg The overall inequality elasticity INEL of poverty where the change in inequality comes exclusively from a change within a group k is given by k f k z u k z u 1 if a 0 INEL 2 F z HOHE C k Pze MH 2 2 Pa u Fazi P z p k u k C k 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 F z is the headcount and C k is the concentration coefficient of group k when the incomes of the rest of the population are preplaced by u k I denotes the Gini index Araar A amp J Y Duclos 2010 Poverty and Inequality a Micro Framework Journal of African Economies doi 10 1093 jae ejg005 Link to Working Paper 07 35 http 132 203 59 36 CIRPEE cahierscirpee 2007 description descrip0735 htm Kakwani N 1993 Poverty and economic growth with application to C te D Ivoire Review of Income and Wealth 39 2 121 139 To estimate FGT elasticity with respect to inequality among a group or among the whole population The user can select more than one variable of interest simultaneousl
95. rest is then used Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 13 6 Difference between Atkinson indices diatkinson This module estimates differences between the Atkinson indices of two distributions For each of the two distributions One variable of interest should be selected Conditions can be specified to focus on specific population subgroups Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 27 13 7 Coefficient of variation index icvar Denote the coefficient of variation index of inequality for group k by CV It can be expressed as follows 1 n n ae o Ewy zm _ i l i l CV 5 u The user can select more than one variable of interest simultaneously For example one can estimate inequality simultaneously for per capita consumption and for per capita income A group variable can be used to estimate inequality at the level of a categorical group Ifa group variable is selected only the first variable of interest is then used Standard errors and confidence intervals with a confidence level of 95 are provided B
96. riable of interest is exppc for 1994 and exppcz for 1998 c You should set size to household size in order to estimate poverty over the population of individuals d Use 41099 Francs CFA per year as the poverty line for both distributions 3 Estimate the difference between headcount indices when a Distribution 1 is rural residents in year 1998 and distribution 2 is rural residents in year 1994 The variable of interest is exppc for 1994 and exppcz for 1998 c You should set size to household size in order to estimate poverty over the population of individuals d Use 41099 Francs CFA per year as the poverty line for both distributions 4 Redo the last exercise for urban residents Redo the last exercise only for members of male headed households 6 Test if the estimated difference in the last exercise is significantly different from zero Thus test H AP z 41099 a 0 0 against H AP z 41099 a 0 0 Set the significance level to 5 and assume that the test statistics follows a normal distribution or Answers Q 1 Open the dialog box by typing db difgt 0 2 For distribution 1 choose the option DATA IN FILE instead of DATA IN MEMORY and click on BROWSE to specify the location of the file bkf98I dta Follow the same procedure for distribution 2 to specify the location of bkf94I dta Choose variables and parameters as follows 88 Figure 20 Estimating differences between FGT indices E DASP Difference Between FGT Indices
97. service from sector s that accrues to observations that belong to a group g is defined as PB n where B gt w Bili eg i l These statistics can be restricted to specific socio demographic groups e g rural urban by replacing I i g byl i c 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 freguency 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 guartiles guintiles or deciles 67 Generally public expenditures on a given service can vary from one geographical or administrative area to another When the information about public expenditures is available at the level of areas this information can be used with the bian module to estimate unit cost more accurately Example 1 Observationi HH Eligible HH Frequency Area indicator Total level of size members regional public expenditures 1 7 3 2 1 14000 2 4 2 2 1 14000 3 5 5 3 1 14000 4 6 3 2 2 12000 5 4 2 1 2 12000 In this example the fir
98. siness income source_5 Remittances received source_6 All other income The Stata data file is saved after initializing its sampling design with the command svyset e To open the dialog box for module dfgts type db dfgts in the command window Figure 1 Decomposition of the FGT index by income components amp Decomposition of the FGT index by income components using the Shapley value gt dfgts command XI Main Results Variable s of interest Parameters sourcel sourceB Parameter alpha jo Poverty line 2 fi Spoo Size variable hhsize z Weight variable Jweightea Cancel Submit e Indicate the varlist of the six income sources e Indicate that the poverty line is set to 15 000 N e Set the variable HOUSEHOLD SIZE 37 e Set the variable HOUSEHOLD WEIGHT e Click on the button SUBMIT The following results appear dfgts sourcel source plinel15000 heizefhhsize hueightl ueighteal Deconposition of the FGT index by incone conponents using the Shapley valued Execution tine 5 03 second s Paraneter alpha 0 00 Poverty line A 15000 00 FGT index 0 584910 Household size hheize Sanpling weight ueightea Sources Incore Absolute Relat ive Share Contribution Contribution z sourced source sourced z sourced z sourced ource level 3 level 4 source sourced source source4 source sourceb Source sourcel so
99. sing the Shapley value Execution tine 0 1 second s Inequality index Generalised entropy index Estinated inequality 0 368465 Incone Absolute Relat ive Share Contribution Contribution Harginal contr ibart ions Source lewsl 1 level level 3 1 p cons LM 4A ON pt 1 340 1 3530 1 3 pb Lest LHS D A With this specification we have y E xp s 5 5 S p Then e Anincome share cannot be straightforwardly provided with this non linear form 47 K e The contribution of the constant is nil since y E xp so J Exp s Exp s Adding a k l constant has no impact on relative inequality because of the exponential transformation Example 3 E Inequality regression based decomposition by predicted components using the Shapley value rbe Main Results M Regression and model specification Approach index and option s Dependent Independent variables Approac Analytic approach hd x tb Index Squared coefficient of varie Y Model r Treatment of constant JV Suppress constant term Size variable Cancel Submit Thdinegs t b depix indexlscvar apprlanalytic noconstant dregrezii Inequality regression based decomposition by predicted incone conponents Execution tine 0 16 second s Inequality index Squared coefficient of variation index Estinated inequality 1 613027 Sources Incore Absolute Felat ive Share
100. sition S nessen eninin i a a a a aeiia 35 15 1 FGT Poverty decomposition by population subgroups dfgtg 35 15 2 FGT Poverty decomposition by income components using the Shapley value dfgts 36 15 3 Decomposition of the variation in FGT indices into growth and redistribution components O BLOF errioan aa ar AEE E pclae E cad a gle decal 38 15 4 Decomposition of FGT poverty into transient and chronic poverty components LATENOV Safes atest a a E ER ues OE E E EA aac ad 39 15 5 Inequality decomposition by income sources diginis ee 41 15 6 Regression based decomposition of inequality by income sources 43 15 7 Gini index decomposition by population subgroups diginig cece 48 15 8 Generalized entropy indices of inequality decomposition by population suberoups dentropy8 s a sea acta deen in RA Saag a Add ida gtd a Se dada wet aaa ks 49 15 9 Polarization decomposition of the DER index by population groups dpolag 49 15 10 Polarization decomposition of the DER index by income sources dpolas 50 16 DASP and CUYVES idu stredu Sictos sine eiii aaia dua ss aai a i i ia ii 50 16 1 FGFGURVES efet denner na na asd ov Gry ab O EOR R R 50 16 2 FGT CURVE with confidence interval C EtS eee 52 16 3 Difference between FGT CURVES with confidence interval cfgts2d 52 16 4 Lorenz and concentration CURVES clorenz eee 52 16 5 Lorenz conc
101. st observation contains information on household 1 This household contains 7 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 costin 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 68 Interested users are encouraged to consider the exercises that appear in Section 23 14 20 2 Marginal benefit incidence analysis Despite the simplicity benefit incidence many researchers has addressed a serious criticisms to this approach when results are use to project the change in benefit incidence with an expansion in public spending Indeed BA describes the actual
102. terest simultaneously For example one can estimate polarization by using simultaneously per capita consumption and per capita income 30 A group variable can be used to estimate polarization at the level of a categorical group Ifa group variable is selected only the first variable of interest is then used Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed Main reference FOSTER J AND M WOLFSON 1992 Polarization and the Decline of the Middle Class Canada and the U S mimeo Vanderbilt University 14 4 Difference between Foster and Wolfson 1992 polarization indices dipolfw This module estimates differences between the Foster Wolfson 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 95 are provided Both the type of confidence intervals provided and the level of confidence used can be changed The results are displayed with 6 decimals this can be changed 14 5 The Esteban Gardin and Ray 1999 polarization index ipoger The measurement of polarization proposed by Esteban and Ray 1994 is defined as fol
103. term indicates that an income component reduces poverty Assume that there exist K income sources and that s denotes income source k The FGT index is defined as n a 1 3 n K Zn All P 3as y X Sp k Sw i l where w is the weight assigned to individual i 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 36 Note that the dfgts ado file requires the module shapar ado which is programmed to perform decompositions using the Shapley value algorithm developed by Araar and Duclos 2008 e Araar A and Duclos J Y 2008 An algorithm for computing the Shapley Value PEP and CIRPEE Tech Note Novembre 2008 http 132 203 59 36 DAD pdf files shap dec aj pd Empirical illustration with Nigerian household data 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 bu
104. th size variable set to size c atthe official poverty line of 41099 Francs CFA d and using the group variable gse Socio economic groups 2 Do the above exercise without standard errors and with the number of decimals set to 4 108 Answers 0 1 Steps Type use C data bkf941 dta clear To open the relevant dialog box type db dfgtg Choose variables and parameters as in Figure 40 Decomposing FGT indices by groups Normalised M After clicking SUBMIT the following information is provided 109 dfgta exppc haroupla el hzizelzizal alphald plinel 41044 typelnorl FGT Index Deconposit ion by Groups Group FGT Index Popu Lat ion Absolute Relat ive Share Contribution Contribution Hage earning public sector 0 4237 LMA 1 0 0 002571 0 003790 0 000117 Hage sarning private sector r rar 0 0060 0 010678 0 002164 0 000294 Artisan or trading 0 027741 Oj 0 00173 0 004653 0 004288 0 000325 Others activities 0 063053 OM OH 0 025805 0 001308 0 000170 Farners crop 0 13525 0 144 0 14358 0 011808 0 014896 0 002459 Farners food 0 16204 OG 0 1101 0 008843 0 016403 0 005823 Inactive 0 144916 0 075956 OH 0 014994 0 004839 0 001332 0 006520 POPULATION 0 139197 1 000 0 13919 0 006553 0 000000 0 006553 0 000000 Q 2 Using the RESULTS panel change the number of decimals and unselect the option DISPLAY STANDARD ERRORS After clicking SUBMIT the following infor
105. tion exclusive subgroups ES be total public expenditures on sector s in area r There are R areas the area here i refers to the geographical division which one can have reliable information on total public expenditures on the studied public service ES R be total public expenditures on sector s G gt l r 1 Here are some of the statistics that can be computed 1 The share ofag in sector s is defined as follows n gt wif i eg s _ i l SH a a gt wif i l G S Note that gt SH g l 2 The rate of participation of a group g in sector s is defined as follows wfc ceg _ isl CR n 3 weli eg i l This rate cannot exceed 100 since f lt ej 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 ES UC Ny S ZV jel where n is the number of sampled households in area r 4 The benefit of observation i from the use of public sector s is 5 The benefit of observation i from the use of the S public sectors is 66 S B XBi 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 gt wB eg ABE 8 n gt w el ieg i l The average benefit for those that use the service s and belong to a group g is defined as ba wB eg ABF gt wif lGeg i l The proportion of benefits from the
106. tive information Aggregate information is obtained from cumulative income shares or Lorenz curve ordinates at some percentiles For instance Percentile p 0 10 0 30 0 50 0 60 0 90 1 00 Lorenz values L p 0 02 0 10 0 20 0 30 0 70 1 00 The user must specify the total number of observations to be generated The user can also indicate the number of observations to be generated specifically at the top and or at the bottom of the distribution in which case the proportion in of the population found at the top or at the bottom must also be specified Remarks e If only the total number of observations is set the generated data are self weighted or uniformly distributed over population percentiles e Ifa number of observations is set for the bottom and or top tails the generated data are not self weighted and a weight variable is provided in addition to the generated income variable gt Example Assume that the total number of observations to be generated is set to 1900 but that we would like the bottom 10 of the population to be represented by 1000 observations In this case weights will equal 1 10000 for the bottom 1000 observations and 1 1000 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 takes the name of _W e The number of observations to be generated does not have to equal the number of observ
107. ty and Inequality Indices Marginal Impacts Elasticities of poverty with respect to the within between inequality in income components n k In case one is interested in changing some income component only among those individuals that are effectively active in some economic sectors the schemes nk T and A inthe paper mentioned above the user should select the approach Truncated income component 24 13 DASP and inequality indices 13 1 Gini and concentration indices igini The Gini index is estimated as EEA u where 2 2 k V V n y a Yi and V X Wh and y2 92 Yn 12 Yn i l v h i The concentration index for variable T when the ranking variable is Y is estimated as ICr 1 Sr HT where Ly is the average of variable T l amp gt al WP n l n and where V X wy and Y gt Y5 gt Yn gt n 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 Ifa group variable is selected only the first variable of interest is then used Standard errors and confidence intervals with a confidence level of 95 are provided Both the type of confidence intervals provided and th
108. ty 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 Sen Shorrocks Thon 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 10 7 DASP and multidimensional poverty indices imdpov The general form of an additive multidimensional poverty index is gt wP X Z P X Z 2 i l where p X Z is individual i s poverty function with vector of attributes X x jd J and vector of poverty lines Z Zi zy determiningil s contribution to total poverty P X Z 16 1 Chakravarty et al 1998 index J a PERES j l IOM 2 Extended Watts index J z p X Z X a In 2 7 min z x 3 Multiplicative exte
109. type db sjdistrub Choose variables and parameters as in 128 Figure 59 Plotting joint distribution function ES DASP Joint Distribution Surfaces gt sjdistrub command p foo gt reco a m After clicking SUBMIT the following graph is plotted interactively with Gnu Plot 4 2 Joint Distribution Function Fy 0 9 0 8 0 7 0 6 0 5 A 0 4 0 3 M 0 2 E VO ELIKLE LR RESO ATM TO paag OLR EES SOLS SLA LT Ars SS 5000 Migs Me SSS 350000 60000 ee 129 23 12 Testing the bi dimensional poverty dominance Using the columbia95I dta distribution 1 and the dominican republic95I dta distribution 2 files 1 Draw the difference between the bi dimensional multiplicative FGT surfaces and the confidence interval of that difference when Var of interest Range alpha_j Dimension 1 haz _ height for age 3 0 6 0 0 Dimension 2 sprob survival 0 7 1 0 0 probability 2 Test for bi dimensional poverty using the information above Answer 0 1 Steps To open the relevant dialog box type db dombdpov Choose variables and parameters as in 130 Figure 60 Testing for bi dimensional poverty dominance E DASP Difference Between Multiplicative FGT indices gt dombipov command After clicking SUBMIT the following graph is plotted interactively with Gnu Plot 4 2 Bi dim
110. urced source sourced sourced sourceb ch ch ch ch ch ch aha sha sa ah sh oh ERE level 6 A 15 3 Decomposition of the variation in FGT indices into growth and redistribution components dfgtgr Datt and Ravallion 1992 decompose the change in the FGT index between two periods t1 and t2 into growth and redistribution components as follows 38 P Pu n P a f P t n p nt R ref eei_ var iation Cl C2 BP Pau n Put xt l Pt n P a variation Cl C2 where variation difference in poverty between t1 and t2 C1 growth component C2 redistribution component R residual Ref period of reference P u 7 the FGT index of the first period Plu z the FGT index of the second period R ref 2 Pu 3 n the FGT index of the first period when all incomes y of the first period are multiplied by pt p Pu nt the FGT index of the second period when all incomes yi of the second period are multiplied by wt ha The Shapley value decomposes the variation in the FGT index between two periods t1 and t2 into growth and redistribution components as follows P gt P C C KV Variation l Cy peux Patt nth k peu 2 x 2 prut n 25 om Lou xp at lpqut t2 Put xt 15 4 Decomposition of FGT poverty into transient and chronic poverty components dtcpov This decomposes total poverty a
111. urves E DASP Non parametric regression gt cnpe command After clicking SUBMIT the following appears Figure 57 Derivatives of non parametric regression curves Non parametric derivative regression Linear Locally Estimation Approach Bandwidth 3699 26 dE Y X dX i 1 12000 24000 36000 48000 60000 126 23 11 Plotting the joint density and joint distribution functions What does the joint distribution of gross and net incomes look like in Canada Using the can6 dta file 4 Estimate the joint density function for gross income X and net income N o Xrange 0 60000 o N range 0 60000 5 Estimate the joint distribution function for gross income X and net income N o Xrange 0 60000 o N range 0 60000 Q 1 Steps Type use C data can6 dta clear To open the relevant dialog box type db sjdensity Choose variables and parameters as in Figure 58 Plotting joint density function EE DASP Joint Density Surfaces gt sjdensity command After clicking SUBMIT the following graph is plotted interactively with Gnu Plot 4 2 127 Joint Density Function f xy 3e 009 2 5e 009 2e 009 1 5e 009 1e 009 90000 lt 30000 40000 Dimension 1 LOT 40000 gt Dimension 2 50000 lt lt 50000 6000060000 Q 2 Steps To open the relevant dialog box
112. usual bandwidth This correction removes bias to order h DASP offers four options without correction and with correction of order 1 2 and 3 Refs e Jones M C 1993 Simply boundary correction for Kernel density estimation Statistics and Computing 3 135 146 e Bearse P Canals J and P Rilstone 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 _ DiwiKj x n 2 wi i l Koos k 2 ek ZAD zm f x Ref e Cwik and Mielniczuk 1993 Data dependent Bandwidth Choice for a Grade Density Kernel Estimate Statistics and Probability Letters 16 397 405 60 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 Di Wj Ki PORPP a From this the derivative of
113. v Minimum Maximum Range fo 60000 Size variable JV Override optimal bandwidth Group variable Bandwidth of 1 0 20 Cancel Submit 121 After clicking SUBMIT the following appears Figure 51 Density curves Density Curves 00002 00003 00004 00005 00001 0 Q 2 Steps To open the relevant dialog box type db c_quantile Choose variables and parameters as in 122 Figure 52 Drawing quantile curves 8 DASP Quantile amp Normalised Curves gt c_quantile command After clicking SUBMIT the following appears Figure 53 Quantile curves Quantile Curves T 123 Q 3 Steps To open the relevant dialog box type db cnpe Choose variables and parameters as in Figure 54 Drawing non parametric regression curves E DASP Non parametric regression gt cnpe command Local linear approach B After clicking SUBMIT the following appears 124 Figure 55 Non parametric regression curves Q 4 Steps Non parametric regression E Y X 10000 15000 20000 5000 ee Linear Locally Estimation Approach Bandwidth 3699 26 _ n o p t S 0 12000 24000 T 36000 X values Choose variables and parameters as in 125 T 1 48000 60000 Figure 56 Drawing derivatives of non parametric regression c
114. variables and values for categorical variables 2 Initializing the sampling design with the command svyset 3 Saving the initialized data file Users are recommended to consult appendices A B and C 5 Main variables for distributive analysis VARIABLE OF INTEREST This is the variable that usually captures living standards It can represent for instance income per capita expenditures per adult equivalent calorie intake normalized height for age scores for children or household wealth SIZE VARIABLE This refers to the ethical or physical size of the observation For the computation of many statistics we will indeed wish to take into account how many relevant individuals or statistical units are found in a given observation GROUP VARIABLE This should be used in combination with GROUP NUMBER It is often useful to focus one s analysis on some population subgroup We might for example wish to estimate poverty within a country s rural area or within female headed families One way to do this is to force DASP to focus on a population subgroup defined as those for whom some GROUP VARIABLE say area of residence equals a given GROUP NUMBER say 2 for rural area SAMPLING WEIGHT Sampling weights are the inverse of the sampling probability This variable should be set upon the initialization of the dataset 6 Howcan DASP commands be invoked Stata commands can be entered directly into a command window Figure 3 Using DA
115. y 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 21 12 3 FGT elasticities with respect to within between group components of inequality efgtg This module estimates the marginal FGT impact and the FGT elasticity with respect to within between group components of inequality A group variable must be provided This module is based on Araar and Duclos 2007 Araar A amp J Y Duclos 2010 Poverty and Inequality a Micro Framework Journal of African Economies doi 10 1093 jae ejg005 Link to Working Paper 07 35 http 132 203 59 36 CIRPEE cahierscirpee 2007 description descrip0735 htm To open the dialog box of this module type the command db efgtg JE DASP FGT Poverty elasticities with respect to population group inequalities gt efgtg command oj xj Main Results Parameters Variable of interest Jincome Parameter alpha jo Size variable hhsize z F Poverty line 2 fi 4897 Group variable zone Fercentage of ch
116. y 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 Poverty impact per 100 of proportional component change J Assume that total income Y is the sum of J income components with Y gt A Yj and where c is a j l factor that multiplies income component y and that can be subject to growth The derivative of the normalized FGT index with respect to A is given by OP z a On 1 hj Lj LJ CD z a where CD is the Consumption dominance curve of component j Change per of component The per capita dollar impact of growth in the j th component on the normalized FGT index of the k group is as follows 19 OP z a al ai dj CD z a ay where CD 1s the normalized consumption dominance curve of the component j The module itargetc allows to Estimate the impact of the marginal change in income component on poverty Select the option normalized or non normalized by the average of component Select the design of the change constant lump sum or proportional to income component to keep inequality within component unchanged Draw curves of the impact according to a range of poverty lines Draw two sided confidence intervals around impact curves or the lower or upper bound of such confidence intervals Reference DUCLOS J Y AND A ARAAR 2006 Poverty and Equity Measurement Policy and Estimati

USER MANUAL DASP version 2.1 DASP: Distributive Analysis Stata

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