PRACTITIONER'S CORNER*: A Simulation Alternative to the Comparative R2 Approach to Decomposing Inequality
| Author | Richard H. Sabot,Jere R. Behrman,John B. Knight |
| Published date | 01 August 1983 |
| DOI | http://doi.org/10.1111/j.1468-0084.1983.mp45003006.x |
| Date | 01 August 1983 |
PRACTITIONER'S CORNER*
A Simulation Alternative to the Comparative R2
Approach to Decomposing Inequality
Jere R. Behrman, John B. Knight and Richard H. Sabot
Decompositions of inequality measures are of interest in understanding
the sources of inequality and the impact of various demographic,
economic and policy changes on inequality. Several authors have
advocated and utilized a 'comparative R2' regression procedure for
identifying the relative contributions of different factors to inequality
of income (or of similar variables). Wise (p. 359), for example, claims
that 'an idea of the relative contribution of academic versus non-
academic variables in the "determination" of salary may be obtained by
comparing values of R2 obtained when different groups of variables are
included in the regression. .. . A high estimate of the contribution of
academic variables is the proportion of remaining variance explained
when they are added to the regression in the absence of non-academic
variables; a low estimate is the addition to the proportion explained
when they are added after the non-academic variables'. Fields and
Schultz (pp. 458-62) use a similar procedure to establish bounds on
regional and other contributions to income inequality.
In this note we argue that the comparative R2 procedure is often less
satisfactory for decomposing inequality than is simulation with the
estimated 'true' relation determining the distribution of interest. There-
fore we conclude that the latter is often a preferred procedure.
THE COMPARATIVE R2 PROCEDURE
Let the true relation determining ln income1 be:
Ya1X+U (1)
where Y is ln income; X are a set of independent variables with X0 a
constant; a are unknown parameters; U is a stochastic term distributed
independently of all X, with mean zero and constant variance u.
* The purpose of Practitioner's Corner is to publish brief methodological notes of interest to
applied economists. The Editors welcome submissions of this sort.
'We use in income in this illustration since the lognormal is a better approximation than the
normal for most empirical income (and related) distributions.
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