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

Xiaohong Chen, Timothy Christensen, Sid Kankanala

arXiv 25 Jul 2021 · Econometrics · publishedThe Review of Economic Studies (2024) · 24 citations (OpenAlex)

arXiv:2107.11869 · PDF · DOI · OpenAlex · Extracted main text

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 $h_0$ 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.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Chaney, T (2008) Distorted gravity: The intensive and extensive margins of international trade0.9507386%
2Head, K., T. Mayer, and M. Thoenig (2014) Welfare and trade without Pareto0.9416383%
3Chernozhukov, V., D. Chetverikov, and K. Kato (2014) Anti-concentration and honest, adaptive confidence bands0.92843100%
4Blundell, R., X. Chen, and D. Kristensen (2007) Semi-nonparametric IV estimation of shape-invariant Engel curves0.8746367%
5Adao, R., C. Arkolakis, and S. Ganapati (2020) Aggregate implications of firm heterogeneity: A nonparametric analysis of monopolistic competition trade models0.87452100%
6Chen, X. and T. M. Christensen (2018) Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression self0.79416550%
7Giné, E. and R. Nickl (2016) Mathematical foundations of infinite-dimensional statistical models0.7946350%
8Melitz, M. J (2003) The impact of trade on intra-industry reallocations and aggregate industry productivity0.7373367%
9Eaton, J., S. Kortum, and F. Kramarz (2011) An anatomy of international trade: Evidence from french firms0.73732100%
10Melitz, M. J. and S. J. Redding (2015) New trade models, new welfare implications0.73732100%

Showing the top 10 of 55 scored citations.

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