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Abstract
Estimation of the causal effect of a binary treatment on outcomes often requires conditioning on covariates to address selection concerning observed variables. This is not straightforward when one or more of the covariates are measured with error. Here, we present a new semi-parametric estimator that addresses this issue. In particular, we focus on inverse propensity score weighting estimators when the propensity score is of an unknown functional form and some covariates are subject to classical measurement error. Our proposed solution involves deconvolution kernel estimators of the propensity score and the regression function weighted by a deconvolution kernel density estimator. Simulations and replication of a study examining the impact of two financial literacy interventions on the business practices of entrepreneurs show our estimator to be valuable to empirical researchers.
Highlights
Empirical researchers in economics, finance, management, and other disciplines are often interested in the causal effect of a binary treatment on outcomes
We focus on the case when the propensity score is of an unknown functional form and some covariates are subject to classical measurement error
Each observation is characterized by the quadruple {Yj, Tj, Xj, Zj}, where Yj is the observed outcome, Tj is a binary indicator of the treatment received, Xj is a scalar covariate, and Zj is a d-dimensional vector of covariates
Summary
Finance, management, and other disciplines are often interested in the causal effect of a binary treatment on outcomes. We consider the case where adjustment for observed covariates is performed to recover an unbiased estimate of the effect of a treatment. The econometric and statistics literature on the estimation of causal effects in the case of selection on observed variables has grown tremendously of late.. The study by Drexler et al (2014) addresses this issue by exploring the impact of different types of financial literacy training on firm success. Despite training being randomly assigned, the authors control (via regression) for several covariates to increase the precision of the treatment effect estimates.
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