Information-Theoretic Deconvolution Approximation of Treatment Effect Distribution

This study proposes an information-theoretic deconvolution method to approximate the entire distribution of individual treatment effect. This method uses higher-order information implied by the standard average treatment effect estimator to construct a maximum entropy approximation to the treatment effect distribution. This method is able to approximate the underlying distribution even if it is entirely random or dependent on unobservable covariates. The asymptotic properties of the proposed estimator is discussed. This estimator is shown to minimize the Kullback-Leibler distance between the underlying distribution and the approximations. Monte Carlo simulations and experiments with real data demonstrate the efficacy and flexibility of the proposed deconvolution estimator. This method is applied to data from the U.S. Job Training Partnership Act (JTPA) program to estimate the distribution of its impact on individual earnings.