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APPLICATIONS OF FUNCTIONAL DEPENDENCE TO SPATIAL ECONOMETRICS

Published online by Cambridge University Press:  31 May 2024

Zeqi Wu Open the ORCID record for Zeqi Wu [Opens in a new window] ,
Wen Jiang Open the ORCID record for Wen Jiang [Opens in a new window]  and
Xingbai Xu Open the ORCID record for Xingbai Xu [Opens in a new window]
Zeqi Wu
Affiliation:
Renmin University of China
Wen Jiang
Affiliation:
Minjiang University
Xingbai Xu*
Affiliation:
Xiamen University
*
Address correspondence to Xingbai Xu, Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, China, e-mail: [email protected]. Zeqi Wu and Wen Jiang are the co-first authors.
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Abstract

In this paper, we generalize the concept of functional dependence (FD) from time series (see Wu [2005, Proceedings of the National Academy of Sciences 102, 14150–14154]) and stationary random fields (see El Machkouri, Volný, and Wu [2013, Stochastic Processes and Their Applications 123, 1–14]) to nonstationary spatial processes. Within conventional settings in spatial econometrics, we define the concept of spatial FD measure and establish a moment inequality, an exponential inequality, a Nagaev-type inequality, a law of large numbers, and a central limit theorem. We show that the dependent variables generated by some common spatial econometric models, including spatial autoregressive (SAR) models, threshold SAR models, and spatial panel data models, are functionally dependent under regular conditions. Furthermore, we investigate the properties of FD measures under various transformations, which are useful in applications. Moreover, we compare spatial FD with the spatial mixing and spatial near-epoch dependence proposed in Jenish and Prucha ([2009, Journal of Econometrics 150, 86–98], [2012, Journal of Econometrics 170, 178–190]), and we illustrate its advantages.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 36
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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Footnotes

We sincerely thank the Editor (Peter C. B. Phillips), the Co-Editor (Liangjun Su), and three anonymous referees for their helpful comments and suggestions on the earlier version of this paper. Xu gratefully acknowledges the financial support from the NSFC (Grant Nos. 72073110 and 72333001), Basic Scientific Center Project 71988101 of the NSFC, and the 111 Project (B13028).

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