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POST-SELECTION INFERENCE IN THREE-DIMENSIONAL PANEL DATA

Published online by Cambridge University Press:  15 March 2022

Harold D. Chiang ,
Joel Rodrigue  and
Yuya Sasaki
Harold D. Chiang
Affiliation:
University of Wisconsin-Madison
Joel Rodrigue
Affiliation:
Vanderbilt University
Yuya Sasaki*
Affiliation:
Vanderbilt University
*
Address correspondence to Yuya Sasaki, Department of Economics, Vanderbilt University, VU Station B #351819, 2301 Vanderbilt Place, Nashville, TN 37235-1819, USA; e-mail: yuya.sasaki@vanderbilt.edu.
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Abstract

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Three-dimensional panel models are widely used in empirical analysis. Researchers use various combinations of fixed effects for three-dimensional panels while the correct specification is unknown. When one imposes a parsimonious model and the true model is rich in complexity, the fitted model inevitably incurs the consequences of misspecification including potential bias. When a richly specified model is employed and the true model is parsimonious, then the consequences typically include a poor fit with larger standard errors than necessary. It is therefore useful for researchers to have good model selection techniques that assist in determining the “true” model or a satisfactory approximation. In this light, Lu, Miao, and Su (2021, Econometric Reviews 40, 867–898) propose methods of model selection. We advance this literature by proposing a method of post-selection inference for regression parameters. Despite our use of the lasso technique as the means of model selection, our assumptions allow for many and even all fixed effects to be nonzero. This property is important to avoid a degenerate distribution of fixed effects which often reflect economic sizes of countries in gravity analyses of trade. Using an international trade database, we document evidence that our key assumption of approximately sparse fixed effects is plausibly satisfied for gravity analyses of trade. We also establish the uniform size control over alternative data generating processes of fixed effects. Simulation studies demonstrate that the proposed method is less biased than under-fitting fixed effect estimators, is more efficient than over-fitting fixed effect estimators, and robustly allows for inference that is as accurate as the oracle estimator.

Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 3 , June 2023 , pp. 623 - 658
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

First arXiv version: March 30, 2019. We benefited from very useful comments by Peter C.B. Phillips (editor), Liangjun Su (co-editor), three anonymous referees, Antonio Galvao, Hiro Kasahara, Kengo Kato, Carlos Lamarche, Whitney Newey, participants in 2019 Cemmap/WISE Workshop on Advances in Econometrics and 2019 University of Tokyo Workshop on Advances in Econometrics. All remaining errors are ours. Code files are available upon request from the authors. Chiang is supported by the Office of the Vice Chancellor for Research and Graduate Education at the University of Wisconsin–Madison with funding from the Wisconsin Alumni Research Foundation.

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