Identification and estimation of interventions using changes in inequality measures




This paper presents semiparametric estimators of changes in inequality measures of a dependent variable distribution taking into account the possible changes on the distribu- tions of covariates. When we do not impose parametric assumptions on the conditional distribution of the dependent variable given covariates, this problem becomes equivalent to estimation of distributional impacts of interventions (treatment) when selection to the pro- gram is based on observable characteristics. The distributional impacts of a treatment will be calculated as di¤erences in inequality measures of the potential outcomes of receiving and not receiving the treatment. These differences are called here Inequality Treatment Effects (ITE). The estimation procedure involves a first non-parametric step in which the probability of receiving treatment given covariates, the propensity-score, is estimated. Using the inverse probability weighting method to estimate parameters of the marginal dis- tribution of potential outcomes, in the second step weighted sample versions of inequality measures are computed. Root-N consistency, asymptotic normality and semiparametric e¢ ciency are shown for the semiparametric estimators proposed. A Monte Carlo exercise is performed to investigate the behavior in finite samples of the estimator derived in the paper. We also apply our method to the evaluation of a job training program.


inequality measures, treatment effects, semiparametric e¢ ciency, reweighting estimator

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