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Identification and estimation of interventions using changes in inequality measures

By Sergio Pinheiro Firpo

Abstract

This paper presents semiparametric estimators of changes in inequality measures of adependent variable distribution taking into account the possible changes on the distribu-tions of covariates. When we do not impose parametric assumptions on the conditionaldistribution of the dependent variable given covariates, this problem becomes equivalent toestimation of distributional impacts of interventions (treatment) when selection to the pro-gram is based on observable characteristics. The distributional impacts of a treatment willbe calculated as di¤erences in inequality measures of the potential outcomes of receivingand not receiving the treatment. These differences are called here Inequality TreatmentEffects (ITE). The estimation procedure involves a first non-parametric step in whichthe 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 inequalitymeasures are computed. Root-N consistency, asymptotic normality and semiparametrice¢ ciency are shown for the semiparametric estimators proposed. A Monte Carlo exerciseis performed to investigate the behavior in finite samples of the estimator derived in thepaper. We also apply our method to the evaluation of a job training program.

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