In this chapter, we consider the nonparametric estimation of the average treatment effect (ATE) based on direct estimation of the conditional treatment effect. We establish the asymptotic distribution of the proposed ATE estimator. We also consider consistent testing for a parametric functional...

We consider the Bayes estimation of a multivariate sample selection model with p pairs of selection and outcome variables. Each of the variables may be discrete or continuous with a parametric marginal distribution, and their dependence structure is modeled through a Gaussian copula function....

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...

A common approach to dealing with missing data is to estimate the model on the common subset of data, by necessity throwing away potentially useful data. We derive a new probit type estimator for models with missing covariate data where the dependent variable is binary. For the benchmark case of...

Observations in a dataset are rarely missing at random. One can control for this non-random selection of the data by introducing fixed effects or other nuisance parameters. This chapter deals with consistent estimation the presence of many nuisance parameters. It derives a new orthogonality...

This chapter proposes a simple procedure to estimate average derivatives in nonparametric regression models with incomplete responses. The method consists of replacing the responses with an appropriately weighted version and then use local polynomial estimation for the average derivatives. The...