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CONSISTENT SPECIFICATION TESTING UNDER SPATIAL DEPENDENCE

Published online by Cambridge University Press:  11 October 2022

Abhimanyu Gupta Open the ORCID record for Abhimanyu Gupta [Opens in a new window]  and
Xi Qu Open the ORCID record for Xi Qu [Opens in a new window]
Abhimanyu Gupta*
Affiliation:
University of Essex
Xi Qu
Affiliation:
Shanghai Jiao Tong University
*
Address correspondence to Abhimanyu Gupta, Department of Economics, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK; e-mail: a.gupta@essex.ac.uk.
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Abstract

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We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the “space” being of a general economic or social nature. Dependence can be parametric, parametric with increasing dimension, semiparametric or any combination thereof, thus covering a vast variety of settings. These include spatial error models of varying types and levels of complexity. Under a new smooth spatial dependence condition, our test statistic is asymptotically standard normal. To prove the latter property, we establish a central limit theorem for quadratic forms in linear processes in an increasing dimension setting. Finite sample performance is investigated in a simulation study, with a bootstrap method also justified and illustrated. Empirical examples illustrate the test with real-world data.

Type
ARTICLES
Information
Econometric Theory , Volume 40 , Issue 2 , April 2024 , pp. 278 - 319
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

We thank the Editor, the Co-Editor, and three referees for insightful comments that improved the paper. We are grateful to Swati Chandna, Miguel Delgado, Emmanuel Guerre, Fernando López Hernandéz, Hon Ho Kwok, Arthur Lewbel, Daisuke Murakami, Ryo Okui, and Amol Sasane for helpful comments, and audiences at YEAP 2018 (Shanghai University of Finance and Economics), NYU Shanghai, Carlos III Madrid, SEW 2018 (Dijon), Aarhus University, SEA 2018 (Vienna), EcoSta 2018 (Hong Kong), Hong Kong University, AFES 2018 (Cotonou), ESEM 2018 (Cologne), CFE 2018 (Pisa), University of York, Penn State, Michigan State, University of Michigan, Texas A&M, 1st Southampton Workshop on Econometrics and Statistics, and MEG 2019 (Columbus). We also thank Xifeng Wen from the Experiment and Data Center of Antai College of Economics and Management (SJTU) for expert computing assistance. The research of the first author was supported by ESRC grant ES/R006032/1. The research of the second author was supported by the National Natural Science Foundation of China (Project Nos. 72222007, 71973097, and 72031006).

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