------------------------------------------------------------------------------- help fordsginidecoJenkins and Van Kerm (February 2009) -------------------------------------------------------------------------------

Decomposition of inequality change into pro-poor growth and mobility components

dsginidecovar0 var1[weight] [ifexp] [inrange] [,parameters(numlist)format(%fmt)percentagepercformat(%fmt)kakwani]

aweightsandfweightsare allowed; see help weights.

dsginidecorequires panel data, in wide form, on income in two time periods.var0contains the measure of income in the initial period for each observation.var1contains the measure of income in the final period for each observation. If the data are held in long form, time-series operators may be used to definevar0orvar1: see the Examples.

Description

dsginidecodecomposes the change in income inequality between two time periods into two components, one representing the progressivity (pro-poorness) of income growth, and the other representing reranking. Inequality is measured using the generalized Gini coefficient, also known as the S-Gini,G(v). This is a distributionally-sensitive inequality index, with larger values ofvplacing greater weight on inequality differences among poorer (lower ranked) observations. The conventional Gini coefficient corresponds to the casev= 2. The decomposition is of the form:final-period inequality - initial-period inequality =

R-Pwhere

Ris a measure of reranking, andPis a measure of the progressivity of income growth.For full details of the decomposition and an application, see Jenkins and Van Kerm (2006). For an application to the related topic of cross-country convergence, see O'Neill and Van Kerm (2008).

See the online manual for additional discussion and examples.

Options

parameters(numlist)specifies a value or values forvinG(v). The default value is 2, leading to a decomposition of the standard Gini coefficient. Multiple values ofvcan be given but every value specified must be greater than 1.

format(string)specifies a format for the displayed results. The default is %5.3f.

percentagerequests that decomposition factors be reported as fractions of the initial-periodG(v).

percformat(string)used in conjunction withpercentagespecifies a format for results expressed as a fraction of base-period Gini. The default is %4.1f.

kakwanirequests reporting of the Kakwani-type measure of progressivity of income growth,K. (See Jenkins and Van Kerm 2006 for the definition.) This statistic is meaningful only when average income growth is not close to zero.

Saved ResultsScalars:

r(sgini0)G(v) for initial period incomes

r(sgini1)G(v) for final period incomes

r(dsgini)Change in inequality: final-periodG(v) - initial-periodG(v)

r(pi)Average income growth between initial and final period

r(P)P

r(R)R

r(K)K, if requested

r(N)Number of observations

r(sum_w)Sum of weightsMacros:

r(var0)The name of variablevar0

r(var1)The name of variablevar1

r(paramlist)The value(s) ofvMatrices:

r(coeffs)All estimates:G(v) for both periods, the change inG(v),PandR, andKif requested

r(parameters)Vector containing the value(s) ofvWhen the

percentageoption is specified, an additional set of results is returned, each prefixed byrel, containing the estimates expressed as a fraction of the initial-periodG(v). Typereturn listafterdsginidecoto find out exactly what results are returned.

Examples. use http://www.stata-press.com/data/r9/nlswork , clear

. tsset idcode year

. gen w = exp(ln_wage)

. dsginideco L.w w

. dsginideco L.w w , percentage parameters(1.5 2 3 4) kakwani

. gen newid = idcode

. tsset newid year

. bootstrap dG=r(dsgini) R=r(R) P=r(P) ///

, cluster(idcode) idcluster(newid) reps(250) nodots: ///

dsginideco L.w w if !mi(L.w) & !mi(w)

. jackknife dG=r(dsgini) R=r(R) P=r(P) ///

, cluster(idcode) idcluster(newid) rclass nodots: ///

dsginideco L.w w if !mi(L.w) & !mi(w)

ReferencesJenkins, S.P. and Van Kerm, P. (2006). Trends in income inequality, pro-poor income growth and income mobility.

Oxford Economic Papers, 58(3): 531-548. [link]O'Neill, D. and Van Kerm, P. (2008). An integrated framework for analysing income convergence.

The Manchester School. 76(1): 1-20. [link]

Authors

Stephen P. Jenkins ISER, University of Essex, UK Philippe Van Kerm CEPS/INSTEAD, Luxembourg philippe.vankerm@ceps.lu