mpi A Stata command for the Alkire-Foster methodology Christoph Jindra 9 November 2015 OPHI Seminar Series - Michaelmas 2015

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1 mpi A Stata command for the Alkire-Foster methodology Christoph Jindra OPHI Seminar Series - Michaelmas November 2015 Christoph Jindra (Research Officer) 9 November / 30

2 Outline What and why Data and indicators for examples The syntax General syntax Minimal expression Missing values Options Weights Multidimensional FGT class Raw and censored headcounts and dimensional breakdown Subgroup analysis Saved results Dominance approach using graphs To do list Literature Christoph Jindra (Research Officer) 9 November / 30

3 What and why What and why What mpi is a flexible Stata command for the estimation of the Alkire-Foster (2011) class of multidimensional poverty measures Allows the estimation of all indices of the class and the most important partial indices alongside their standard errors Subgroup analysis and dimensional breakdown Why In principle easy to calculate, in practice error prone assure quality Existing ado-files do not make the most out of the method (IMDP_AFI by Abdelkrim and Duclos (2013) calculates the multidimensional FGT class but does not offer any decomposition) To provide practitioners with a comprehensive command that facilitates the most important steps in the creation of an MPI steps in the analysis of poverty based on the AF-method Christoph Jindra (Research Officer) 9 November / 30

4 Data and indicators for examples Data All examples use a dataset that is installed with Stata nlsw88: 1988 data, extracted from the National Longitudinal Survey of Young Woman (US) Ages in 1968 Number of cases: 2246 Can be loaded using sysuse nlsw88 as long as Stata is installed Christoph Jindra (Research Officer) 9 November / 30

5 Data and indicators for examples Indicators, cutoffs and missing values Three indicators (dimensions) for all the examples Indicator Variable Cutoff Hourly wage wage deprived if hourly wage below 70% of median (rounded z Wage = 4) College graduate collgrad deprived if not a college graduate (0) Usual hours worked hours deprived if less than 26 hours Missing values on the indicators. mdesc collgrad wage hours Variable Missing Total Percent Missing collgrad 0 2, wage 0 2, hours 4 2, Christoph Jindra (Research Officer) 9 November / 30

6 The syntax General syntax General syntax of mpi command mpi syntax so far: mpi varlist [if] [in] [pweight aweight iweight], z(numlist) ks(numlist) [weights(numlist) hraw cardinal malpha(numlist) dcontribution group(varlist) groupcont groupdcontribution] As always: Expressions in the brackets are optional Underlining denotes the shortest allowed abbreviation A minimal expression would be (unidimensional case): mpi v1, z(z_v1) ks(1) Three-dimensional case: mpi v1 v2 v3, z(z_v1 z_v2 z_v3) ks(1) Christoph Jindra (Research Officer) 9 November / 30

7 The syntax Minimal expression Indicators, deprivation cutoffs z j and poverty cutoff(s) k Each time you use the mpi command, you have to minimally specify 1. The indicators in varlist (at least one) 2. The deprivation cutoffs for each indicator (z j ) specified in z(numlist) Have to have exactly the same order as in varlist! Deprived if xij < z j, non-deprived otherwise 3. At least one poverty cutoff k in ks(numlist) The command assumes: normalized weights: w j > 1 and d w j = 1 0 < k 1 j=1 Syntax: mpi v1 v2 v3 v4, z(z_v1 z_v2 z_v2 z_v4) /// ks( ) Christoph Jindra (Research Officer) 9 November / 30

8 The syntax Minimal expression Calculation of M 0, H and A Without any additional options, mpi calculates M 0, H and A: mpi creates various temporary variables, the most important are: rho_ k : One identifier of the poor for each poverty cutoff k c0k_ k : One censored deprivation score for each poverty cutoff k H = 1 n ρ k i mean of rho_ k n A = 1 q M 0 = 1 n i=1 q i=1 n i=1 c i (k) mean of c0k_ k if rho_ k == 1 c i (k) mean of c0k_ k Christoph Jindra (Research Officer) 9 November / 30

9 The syntax Minimal expression Most basic command. // Basic mpi command. mpi wage collgrad hours, z( ) ks(0.333) Results for Alkire-Foster dual cutoff method Dimensions: wage collgrad hours Number of indicators d: 3 Respective weights w_j: 1/3 1/3 1/3 Deprivation cutoffs z: Poverty cutoffs k:.333 Number of observations: 2242 M0, H and A: k M0 se M0 H se H A se A // Number of cases in dataset. count 2246 Christoph Jindra (Research Officer) 9 November / 30

10 The syntax Minimal expression Several poverty cutoffs. // Several poverty cutoffs (command allows for numlist in ks()). mpi wage collgrad hours, z( ) ks(0.1(0.1)1) Results for Alkire-Foster dual cutoff method (... output omitted...) Poverty cutoffs k: M0, H and A: k M0 se M0 H se H A se A Christoph Jindra (Research Officer) 9 November / 30

11 The syntax Missing values Treatment of missing values Sample restrictions/ exclusion of observations: those that have missing on any of the variables in varlist those excluded by if and in restrictions those for which (sampling) weight = 0 Stata: marksample If subgroup analysis touse all with missing on subgroup variable! Stata: if " group "!= "" markout touse /// group, strok strok allows for string variables Christoph Jindra (Research Officer) 9 November / 30

12 Options Weights Weights Indicator specific weights are optional (weights(numlist)) Default is equal weights (w 1 = w 2 =... = w d ) Weights can be specified, however: ( d ) 1. mpi assume normalized weights w j = 1 Weights in j=1 weights(numlist) have to sum up to one 2. Have to have the same order as the indicators in varlist Syntax: mpi v1 v2 v3 v4, z(z_v1 z_v2 z_v2 z_v4) /// ks(0.3) weights(w_v1 w_v2 w_v3 w_v4) Christoph Jindra (Research Officer) 9 November / 30

13 Options Weights Weights. // Weights. mpi wage collgrad hours, z( ) ks( ) /// > weights( ) Results for Alkire-Foster dual cutoff method (... output omitted...) Respective weights w_j: Poverty cutoffs k: M0, H and A: k M0 se M0 H se H A se A Christoph Jindra (Research Officer) 9 November / 30

14 Options Multidimensional FGT class Multidimensional FGT class Let g α ij be g α ij = ( (zj x ij ) z j ) α α = 1 normalized gaps; α = 2 squared normalized gaps Adjusted poverty gap measure: Adjusted FGT measure: Adjusted FGT class: M 1 = 1 n M 2 = 1 n M α = 1 n n n d i=1 j=1 n d i=1 j=1 d i=1 j=1 w j g 1 ij (k) w j g 2 ij (k) w j g α ij (k); α 0 Christoph Jindra (Research Officer) 9 November / 30

15 Options Multidimensional FGT class Multidimensional FGT class - estimation Let ci α (k) be d w jg α j=1 ij (k) Adjusted FGT class as: M α = 1 n n i=1 cα i (k); α 0 cardinal option 1. Creates temporary variables: 1.1 c1k k = One censored weighted rowtotal of gaps for each k 1.2 c2k k = One censored weighted rowtotal of squared gaps for each k 2. Calculates 2.1 Adjusted gap measure M Adjusted FGT measure M 2 malpha(numlist) 1. creates temporary variable: 1.1 cak k = One censored weighted rowtotal of normalized gaps to the power of α for each k 2. Calculates 2.1 Adjusted FGT class Christoph Jindra (Research Officer) 9 November / 30

16 Options Multidimensional FGT class Multidimensional FGT class. // Adjusted poverty gap, adjusted FGT measure and adjusted FGT class. mpi wage collgrad hours, z( ) ks(0.3333) cardinal /// > malpha(3) Results for Alkire-Foster dual cutoff method (... output omitted...) M0, H and A: k M0 se M0 H se H A se A M1 and M2: k M1 se M1 M2 se M M_alpha (alpha = 3) k M(Alpha) se MAlpha Christoph Jindra (Research Officer) 9 November / 30

17 Options Raw and censored headcounts and dimensional breakdown Raw headcount ratios Raw (uncensored) headcount ratios: h j = 1 n n i=1 g 0 i. Show the share of people deprived in each dimension/indicator. // Raw headcount ratio with hraw option. mpi wage collgrad hours, z( ) ks(0.3333) hraw Results for Alkire-Foster dual cutoff method (...ouput omitted...) M0, H and A: k M0 se M0 H se H A se A Raw (uncensored) headcount ratios: h_j wage.1949 collgrad.7632 hours.1517 Christoph Jindra (Research Officer) 9 November / 30

18 Options Raw and censored headcounts and dimensional breakdown Censored headcount ratios and dimensional breakdown Censored headcount ratios: h j (k) = 1 n n i=1 g 0 i.(k) Show the share of people deprived in each dimension/indicator who are at the same time multidimensionally poor M 0 can be expressed in terms of censored headcounts: M 0 = 1 n n d i=1 j=1 w j g 0 ij (k) = [ d 1 n w j n j=1 i=1 The contribution of each dimension to M 0 : φ 0 j (k) = w j h j (k) M 0 g 0 ij (k) ] d = w j h j (k) j=1 Contribution depends on wj and h j (k) Whenever φ 0 j (k) is much larger than w j, the poor are more likely to be deprived on that indicator Christoph Jindra (Research Officer) 9 November / 30

19 Options Raw and censored headcounts and dimensional breakdown Censored headcounts and percentage contribution. // Censored headcounts and dimensional contribution with dcontribution. mpi wage collgrad hours, z( ) ks( ) dcontribution Results for Alkire-Foster dual cutoff method (... output omitted...) Dimensional breakdown Censored headcount ratios: k wage collgrad hours Percentage contribution to M0 by dimensions: k wage collgrad hours Christoph Jindra (Research Officer) 9 November / 30

20 Options Subgroup analysis Subgroup decomposition population subgroup decomposability has proved particularly useful in poverty measurement Means that overall poverty can be expressed as a population-share weighted sum of subgroup poverty levels Holds for M 0 as well: M 0 (X) = m l=1 n l n M 0(X l ) We can further calculate the percentage contribution to overall poverty by group: D 0 l = n l M 0 (X l ) n M 0 (X) If contribution of certain group exceeds population share suggests unequal distribution of poverty Christoph Jindra (Research Officer) 9 November / 30

21 Options Subgroup analysis Subgroup decomposition (shown for M 0 only). // Subgroup analysis. mpi wage collgrad hours, z( ) ks( ) group(married) Results for Alkire-Foster dual cutoff method (... output omitted...) Results for subgroup decomposition: for M0 k Obs single married Overall M se M se M se Christoph Jindra (Research Officer) 9 November / 30

22 Options Subgroup analysis Subgroup contribution to M 0. // Subgroup analysis. mpi wage collgrad hours, z( ) ks( ) group(married) /// > groupc Results for Alkire-Foster dual cutoff method Dimensions: wage collgrad hours Number of indicators d: 3 Respective weights w_j: 1/3 1/3 1/3 Deprivation cutoffs z: Poverty cutoffs k: Number of observations: 2242 Subgroup contribution to M0 in % for all k: k married Percent N single married Christoph Jindra (Research Officer) 9 November / 30

23 Options Saved results Saved results mpi is e-class command ereturn list shows all saved results All the results are saved in matrices for further usage. quietly mpi wage collgrad hours, z( ) ks( ( )1) /// > group(union). ereturn list scalars: macros: matrices: functions: e(n) = 1877 e(d) = 3 e(cmd) : "mpi" e(m0ha) : 3 x 6 e(group_a) : 3 x 7 e(group_h) : 3 x 7 e(group_m0) : 3 x 7 e(sample) Christoph Jindra (Research Officer) 9 November / 30

24 Options Dominance approach using graphs Dominance analysis. quietly mpi wage collgrad hours, z( ) ks( ) /// > group(union). mat temp = e(group_m0). mat list temp temp[3,7] M0_nonunion se_nonunion M0_union se_union M0_overall se_overa k clear. svmat temp, names(col) number of observations will be reset to 3 Press any key to continue, or Break to abort obs was 0, now 3. // most basic form:. graph twoway (connected M0_nonunion k) (connected M0_union k) Christoph Jindra (Research Officer) 9 November / 30

25 Options Dominance approach using graphs M 0 dominance k M0_nonunion M0_union Christoph Jindra (Research Officer) 9 November / 30

26 Options Dominance approach using graphs M 0 dominance M 0 dominance over union membership Alongside 95% confidence interval M Poverty cutoff k Non union Union Christoph Jindra (Research Officer) 9 November / 30

27 To do list do s More options if necessary (creating actual variables)? Warnings Complete list of returned results Rounding and precision Testing/verification based on Gould (2001) Testing procedures for M 0, H and A M 1 and M 2 Raw headcounts and censored headcounts already implemented But needs to be implemented for all elements Complex survey design Will be implemented using svy option Will use the default: linearized variance estimator Christoph Jindra (Research Officer) 9 November / 30

28 To do list don ts: Bootstrapping Often applied, but is it really that easy? Examples where the bootstrap fails are abundant [...]. Complex survey data is one such example (Kolenikov, 2010) In case of only few PSUs per stratum, naive bootstrapping can lead to biased and inconsistent variance estimates Replicate weights have to be used for correct estimation (Asparouhov and Muthén, 2010; Kolenikov, 2010) bootstrap samples that can be used to assess the variability of the estimates Often not delivered with dataset Can theoretically be calculated if one understands the sampling procedure correctly (package bsweights) In Stata: svy bootstrap requires that the bootstrap replicate weights be identified (StataCorp, 2013, p. 74) No option, but can theoretically be calculated Christoph Jindra (Research Officer) 9 November / 30

29 To do list Bootstrapping without complex survey design Christoph Jindra (Research Officer) 9 November / 30

30 Literature Literature I Abdelkrim, A. and J.-Y. Duclos (2013). User Manual for Stata Package DASP: Version 2.3. PEP, World Bank, UNDP and University Laval. Alkire, S. and J. Foster (2011). Counting and multidimensional poverty measurement. Journal of Public Economics 95(7-8), Asparouhov, T. and B. O. Muthén (2010). Resampling Methods in Mplus for Complex Survey Data. Gould, W. (2001). Statistical software certification. The Stata Journal 1(1), Kolenikov, S. (2010). Resampling variance estimation for complex survey data. The Stata Journal 10(2), StataCorp (2013). Stata Survey Data Reference Manual - Release 13. College Station, Texas: Stata Press. Christoph Jindra (Research Officer) 9 November / 30