Essays in Nonparametric Econometrics

This dissertation studies three topics in nonparametric econometrics. The first chapter proposes a unique approach for constructing nonparametric confidence bands in quantile regression. The second chapter investigates nonparametric identification of a dynamic model of entry. The final chapter studies identification of interaction terms in a static model of entry in which firm-specific private information is correlated.;(Chapter 1: A Bootstrap Procedure for Pointwise Confidence Bands in Nonparametric Quantile Regression). The construction of nonparametric confidence bands for Kernel-based regression functions is complicated by the presence of asymptotic bias when the bandwidth sequence is chosen to minimize some form of Lp error. Conventional methods which address the bias problem in the context of mean regression are typically aimed at bias reduction, either by undersmoothing or by explicit bias correction. Many of these methods perform poorly in practice and often require the selection of a nonstandard tuning parameter - the choice of which is, in many cases, intractable provided a single data set. (We point out in Chapter 1 that recent developments in the literature on explicit bias correction by Calonico, Cattaneo & Farrell (2015) may allow for more tractable choice of nonstandard smoothing parameters, and improved performance of bias correction in the context of mean regression). Hall & Horowitz (2013) suggests a simple bootstrap-based procedure for constructing pointwise confidence bands in mean regression, which does not rely on the ad hoc choice of nonstandard tuning parameters. In this paper, we follow Hall & Horowitz (2013) closely to suggest a similar bootstrap-based procedure for quantile regression functions. Our method yields relatively narrow bands, which perform well in practice (in terms of coverage probability), and requires only the choice of the initial bandwidth sequence.;(Chapter 2: Nonparametric Identification of a Two-Firm Dynamic Entry Game with Incomplete Information). The existing literature on identification and estimation of dynamic games typically makes strong parametric assumptions on the shape of period profits as well as the distribution of unobservables. This chapter explores nonparametric identification of dynamic games with incomplete information. In particular, we study games in which per-period profit functions and the distribution of unobserved heterogeneity are unknown. We present both partial identification and point identification results for the setting in which the universe of data is limited to a single market of observed interaction between firms. In an Appendix to this chapter (Appendix B.11), we extend the analysis to the more common data environment in which the econometrician observes several markets. The discussion of multiple equilibria is fundamental to the identification strategy.;(Chapter 3: Identification of Signs of Interaction Terms in Simple Bayesian Coordination Games with Correlated Private Information). In empirical game theory, understanding how decisions of opponents impact firm payoffs is crucial to the identification and estimation of profit functions. This chapter discusses identification of the signs of these strategic interaction terms in two-player Bayesian coordination games, where private information across firms may be correlated. We obtain sufficient conditions on the support of covariates, which deliver sign identification.