Decomposition of inequality change into pro-poor growth and mobility components
dsginideco var0 var1 [weight] [if exp] [in range] [, parameters(numlist) format(%fmt) percentage percformat(%fmt) kakwani ]
aweights and fweights are allowed; see help weights.
dsginideco requires panel data, in wide form, on income in two time periods. var0 contains the measure of income in the initial period for each observation. var1 contains 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 define var0 or var1: see the Examples.
dsginideco decomposes 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 of v placing greater weight on inequality differences among poorer (lower ranked) observations. The conventional Gini coefficient corresponds to the case v = 2. The decomposition is of the form:
final-period inequality - initial-period inequality = R - P
where R is a measure of reranking, and P is 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.
parameters(numlist) specifies a value or values for v in G(v). The default value is 2, leading to a decomposition of the standard Gini coefficient. Multiple values of v can 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.
percentage requests that decomposition factors be reported as fractions of the initial-period G(v).
percformat(string) used in conjunction with percentage specifies a format for results expressed as a fraction of base-period Gini. The default is %4.1f.
kakwani requests 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.
r(sgini0) G(v) for initial period incomes
r(sgini1) G(v) for final period incomes
r(dsgini) Change in inequality: final-period G(v) - initial-period G(v)
r(pi) Average income growth between initial and final period
r(K) K, if requested
r(N) Number of observations
r(sum_w) Sum of weights
r(var0) The name of variable var0
r(var1) The name of variable var1
r(paramlist) The value(s) of v
r(coeffs) All estimates: G(v) for both periods, the change in G(v), P and R, and K if requested
r(parameters) Vector containing the value(s) of v
When the percentage option is specified, an additional set of results is returned, each prefixed by rel, containing the estimates expressed as a fraction of the initial-period G(v). Type return list after dsginideco to find out exactly what results are returned.
. 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)
Jenkins, 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]
Stephen P. Jenkins ISER, University of Essex, UK Philippe Van Kerm CEPS/INSTEAD, Luxembourg firstname.lastname@example.org