Journal of Economic Literature (JEL) Code(s)
C13, C14, C36
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 rm exports and nd evidence against common parameterizations of the distribution of unobserved rm productivity.
Chen, Xiaohong; Christensen, Timothy M.; and Kankanala, Sid, "Adaptive Estimation and Uniform Confidence Bands for Nonparametric IV" (2021). Cowles Foundation Discussion Papers. 2630.