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Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities

Christensen, Timothy; Chen, Xiaohong; Kankanala, Sid; (2024) Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities. The Review of Economic Studies , Article rdae025. 10.1093/restud/rdae025. (In press).

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Abstract

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 h0 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 h0 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.

Type: Article
Title: Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities
DOI: 10.1093/restud/rdae025
Publisher version: https://doi.org/10.1093/restud/rdae025
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.
Keywords: Honest and adaptive uniform confidence bands, Minimax rate-adaptive estimation, Nonparametric instrumental variables, Nonparametric estimation of elasticities, International trade
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/10184559
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