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

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  • Xiaohong Chen
  • Timothy Christensen
  • Sid Kankanala

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.

Suggested Citation

  • Xiaohong Chen & Timothy Christensen & Sid Kankanala, 2025. "Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 92(1), pages 162-196.
    • Handle: RePEc:oup:restud:v:92:y:2025:i:1:p:162-196.
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    File URL: http://hdl.handle.net/10.1093/restud/rdae025
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    Cited by:

    1. Ming Chen & Linghao Yan, 2025. "Competition Policy and Corporate Labor Investment Efficiency: Evidence From China," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 46(7), pages 3729-3747, October.
    2. Sid Kankanala, 2025. "Generalized Bayes in Conditional Moment Restriction Models," Papers 2510.01036, arXiv.org.
    3. Xiaohong Chen & Wayne Yuan Gao, 2025. "Semiparametric Learning of Integral Functionals on Submanifolds," Cowles Foundation Discussion Papers 2450, Cowles Foundation for Research in Economics, Yale University.
    4. Xiaohong Chen & Wayne Yuan Gao, 2025. "Semiparametric Learning of Integral Functionals on Submanifolds," Papers 2507.12673, arXiv.org, revised Oct 2025.

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