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There is a growing literature in nonparametric econometrics in the recent two decades. Given the space limitation, it is impossible to survey all the important recent developments in nonparametric econometrics. Therefore, we choose to limit our focus on the following areas. In Section 2, we review the recent developments of nonparametric estimation and testing of regression functions with mixed discrete and continuous covariates. We discuss nonparametric estimation and testing of econometric models for nonstationary data in Section 3. Section 4 is devoted to surveying the literature of nonparametric instrumental variable (IV) models. We review nonparametric estimation of quantile regression models in Section 5. In Sections 2–5, we also point out some open research problems, which might be useful for graduate students to review the important research papers in this field and to search for their own research interests, particularly dissertation topics for doctoral students. Finally, in Section 6 we highlight some important research areas that are not covered in this paper due to space limitation. We plan to write a separate survey paper to discuss some of the omitted topics.

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 form for the conditional treatment effect function. A small-scale Monte Carlo simulation study is reported to examine the finite sample performance of the proposed estimator.

“The Elephant in the Corner: A Cautionary Tale About Measurement Error in Treatment Effects Models” by Daniel L. Millimet discusses the current use of the unobserved-outcome framework to estimate population-averaged treatment effects, and it exposes the sensitivity of these estimators to assumption of no measurement error. The Monte Carlo simulation evidence in this chapter indicates that “nonclassical measurement error in the covariates, mean-reverting measurement error in the outcome, and simultaneous measurement errors in the outcome, treatment assignment, and covariates have a dramatic, adverse effect on the performance of the various estimators even with relatively small and infrequent errors” (Millimet article, p. 1–39). To some extent, all the estimators analyzed by Millimet are based on weak functional form assumptions and use semiparametric or nonparametric methods. Millimet's results indicate the need for measurement error models be they parametric or nonparametric models, see Schennach (2007), Hu and Schennach (2008), and Matzkin (2007) for some recent research in nonparametric approaches. Chapter 7 develops a Bayesian estimator that can handle some of the measurement errors discussed in this chapter.

Identification and inference are central to applied analysis, and two papers examine these issues, the first being theoretical in nature and the second being simulation based.