Nonlinear Difference-in-Difference Treatment Effect Estimation: A Distributional Analysis

This chapter uses the nonlinear difference-in-difference (NL-DID) methodology developed by Athey and Imbens (2006) to estimate the effects of a treatment program on the entire distribution of an outcome variable. The NL-DID estimates the entire counterfactual distribution of an outcome variable that would have occurred in the absence of treatment. This chapter extends the Monte Carlo results in Athey and Imbens's (2006) to assess the efficacy of the NL-DID estimators in finite samples. Furthermore, the NL-DID methodology recovers the entire outcome distribution in the absence of treatment. Further, we consider the empirical size and power of tests statistics for equality of mean, medians, and complete distributions as suggested by Abadie (2002). The results show that the NL-DID estimator can effectively be used to recover the average treatment effect, as well as the entire distribution of the treatment effects when there is no selection during the treatment period in finite samples.