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ALGORITHMIC SUBSAMPLING UNDER MULTIWAY CLUSTERING

Published online by Cambridge University Press:  11 July 2023

Harold D. Chiang ,
Jiatong Li  and
Yuya Sasaki
Harold D. Chiang*
Affiliation:
University of Wisconsin–Madison
Jiatong Li
Affiliation:
Vanderbilt University
Yuya Sasaki
Affiliation:
Vanderbilt University
*
Address correspondence to Harold D. Chiang, Department of Economics, University of Wisconsin–Madison, Madison, WI 53706, USA; e-mail: hdchiang@wisc.edu.
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Abstract

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This paper proposes a novel method of algorithmic subsampling (data sketching) for multiway cluster-dependent data. We establish a new uniform weak law of large numbers and a new central limit theorem for multiway algorithmic subsample means. We show that algorithmic subsampling allows for robustness against potential degeneracy, and even non-Gaussian degeneracy, of the asymptotic distribution under multiway clustering at the cost of efficiency and power loss due to algorithmic subsampling. Simulation studies support this novel result, and demonstrate that inference with algorithmic subsampling entails more accuracy than that without algorithmic subsampling. We derive the consistency and the asymptotic normality for multiway algorithmic subsampling generalized method of moments estimator and for multiway algorithmic subsampling M-estimator. We illustrate with an application to scanner data for the analysis of differentiated products markets.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 44
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), 2023. Published by Cambridge University Press

Footnotes

We benefited from very useful comments by Peter C. B. Phillips (the Editor), Matias Cattaneo (the Co-Editor), Sokbae (Simon) Lee, three anonymous referees, and participants in the 2021 North American Summer Meeting, International Association for Applied Econometrics, 2021 Asian Meeting, 2021 China Meeting of the Econometric Society, 26th International Panel Data Conference, 2021 Australasia Meeting of the Econometric Society, 2021 European Summer Meeting, and New York Camp Econometrics XVI. The usual disclaimer applies. We thank James M. Kilts Center, University of Chicago Booth School of Business for allowing us to use scanner data from the Dominicks Finer Foods (DFF) retail chain. H. 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.

References

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