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HETEROSKEDASTICITY ROBUST SPECIFICATION TESTING IN SPATIAL AUTOREGRESSION

Published online by Cambridge University Press:  21 May 2024

Jungyoon Lee Open the ORCID record for Jungyoon Lee [Opens in a new window] ,
Peter C. B. Phillips Open the ORCID record for Peter C. B. Phillips [Opens in a new window]  and
Francesca Rossi Open the ORCID record for Francesca Rossi [Opens in a new window]
Jungyoon Lee*
Affiliation:
Royal Holloway, University of London
Peter C. B. Phillips
Affiliation:
Yale University, University of Auckland, and Singapore Management University
Francesca Rossi
Affiliation:
University of Verona
*
Address correspondence to Jungyoon Lee, Department of Economics, Royal Holloway, University of London, Egham, United Kingdom; e-mail: Jungyoon.Lee@rhul.ac.uk.
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Abstract

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Spatial autoregressive (SAR) and related models offer flexible yet parsimonious ways to model spatial and network interactions. SAR specifications typically rely on a particular parametric functional form and an exogenous choice of the so-called spatial weight matrix with only limited guidance from theory in making these specifications. Also, the choice of a SAR model over other alternatives, such as spatial Durbin (SD) or spatial lagged X (SLX) models, is often arbitrary, raising issues of potential specification error. To address such issues, this paper develops a new specification test within the SAR framework that can detect general forms of misspecification including that of the spatial weight matrix, the functional form and the model itself. The test is robust to the presence of heteroskedasticity of unknown form in the disturbances and the approach relates to the conditional moment test framework of Bierens ([1982, Journal of Econometrics 20, 105–134], [1990, Econometrica 58, 1443–1458]). The Bierens test is shown to be inconsistent in general against spatial alternatives and the new test introduces modifications to achieve test consistency in the spatial setting. A central element is the infinite-dimensional endogeneity induced by spatial linkages. This complexity is addressed by introducing a new component to the omnibus test that captures the effects of potential spatial matrix misspecification. With this modification, the approach leads to a simple pivotal test procedure with standard critical values that is the first test in the literature to have power against misspecifications in the spatial linkages. We derive the asymptotic distribution of the test under the null hypothesis of correct SAR specification and prove consistency. A Monte Carlo study is conducted to study its finite sample performance. An empirical illustration on the performance of the test in modeling tax competition in Finland is included.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 41 , Issue 5 , October 2025 , pp. 995 - 1043
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), 2024. Published by Cambridge University Press

Footnotes

Phillips acknowledges research support from the NSF under Grant No. SES 18-50860 and the Kelly Fund at the University of Auckland. Lee and Rossi acknowledge research support from the ESRC Grant No. ES/P011705/1. We are indebted to Teemu Lyytikäinen for sharing his dataset.

References

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