Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities
This work addresses the challenge of reliable inference in econometric models for researchers and practitioners, offering improved methods for estimating structural functions and elasticities, though it is incremental in building on existing sieve two-stage least squares estimators.
The authors tackled the problem of optimal estimation and inference in nonparametric models using instrumental variables by introducing data-driven procedures for sieve dimension selection and uniform confidence bands, achieving minimax convergence rates in sup-norm and more efficient coverage than undersmoothing methods.
We introduce two data-driven procedures for optimal estimation and inference in nonparametric models using instrumental variables. The first is a data-driven choice of sieve dimension for a popular class of sieve two-stage least squares estimators. When implemented with this choice, estimators of both the structural function $h_0$ and its derivatives (such as elasticities) converge at the fastest possible (i.e., minimax) rates in sup-norm. The second is for constructing uniform confidence bands (UCBs) for $h_0$ and its derivatives. Our UCBs guarantee coverage over a generic class of data-generating processes and contract at the minimax rate, possibly up to a logarithmic factor. As such, our UCBs are asymptotically more efficient than UCBs based on the usual approach of undersmoothing. As an application, we estimate the elasticity of the intensive margin of firm exports in a monopolistic competition model of international trade. Simulations illustrate the good performance of our procedures in empirically calibrated designs. Our results provide evidence against common parameterizations of the distribution of unobserved firm heterogeneity.