Time: Nov.23 (Tue.), 9：00 – 10：00
Title: Adaptive Estimation and Uniform Confidence Bands for Nonparametric IV
About the speaker:
Professor Xiaohong Chen currently serves as the Malcolm K. Brachman Professor of Economics at Yale University. She is a fellow of the Econometric Society and a laureate of the China Economics Prize. As one of the leading experts in econometrics, her research focuses on econometric theory, Semi/nonparametric estimation and inference methods, Sieve methods, Nonlinear time series, and Semi/nonparametric models. Professor Chen was elected to the American Academy of Arts and Sciences in 2019.
Abstract:
We introduce computationally simple, data-driven procedures for estimation and inference on a structural function h0 and its derivatives in nonparametric models using instrumental variables. Our first procedure is a bootstrap-based, data-driven choice of sieve dimension for sieve nonparametric instrumental variables (NPIV) estimators. When implemented with this data-driven choice, sieve NPIV estimators of h0 and its derivatives are adaptive: they converge at the best possible (i.e., minimax) sup-norm rate, without having to know the smoothness of h0, degree of endogeneity of the regressors, or instrument strength. Our second procedure is a data-driven approach for constructing honest and adaptive uniform confidence bands (UCBs) for h0 and its derivatives. Our data-driven UCBs guarantee coverage for h0 and its derivatives uniformly over a generic class of data-generating processes (honesty) and contract at, or within a logarithmic factor of, the minimax sup-norm rate (adaptivity). As such, our data-driven UCBs deliver asymptotic efficiency gains relative to UCBs constructed via the usual approach of undersmoothing. In addition, both our procedures apply to nonparametric regression as a special case. We use our procedures to estimate and perform inference on a nonparametric gravity equation for the intensive margin of firm exports and find evidence against common parameterizations of the distribution of unobserved firm productivity.
