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CONTINUOUSLY UPDATED INDIRECT INFERENCE IN HETEROSKEDASTIC SPATIAL MODELS

Published online by Cambridge University Press:  22 September 2021

Maria Kyriacou ,
Peter C.B. Phillips  and
Francesca Rossi
Maria Kyriacou*
Affiliation:
University of Southampton
Peter C.B. Phillips
Affiliation:
Yale University University of Auckland University of Southampton Singapore Management University
Francesca Rossi
Affiliation:
University of Verona
*
Address correspondence to Maria Kyriacou, Department of Economics, University of Southampton, Southampton, UK; e-mail: [email protected].
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Abstract

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Spatial units typically vary over many of their characteristics, introducing potential unobserved heterogeneity which invalidates commonly used homoskedasticity conditions. In the presence of unobserved heteroskedasticity, methods based on the quasi-likelihood function generally produce inconsistent estimates of both the spatial parameter and the coefficients of the exogenous regressors. A robust generalized method of moments estimator as well as a modified likelihood method have been proposed in the literature to address this issue. The present paper constructs an alternative indirect inference (II) approach which relies on a simple ordinary least squares procedure as its starting point. Heteroskedasticity is accommodated by utilizing a new version of continuous updating that is applied within the II procedure to take account of the parameterization of the variance–covariance matrix of the disturbances. Finite-sample performance of the new estimator is assessed in a Monte Carlo study. The approach is implemented in an empirical application to house price data in the Boston area, where it is found that spatial effects in house price determination are much more significant under robustification to heterogeneity in the equation errors.

Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 1 , February 2023 , pp. 107 - 145
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), 2021. Published by Cambridge University Press

Footnotes

We thank the Co-Editor, Dennis Kristensen, and two anonymous referees for helpful comments and suggestions that have improved the quality of the paper. Phillips acknowledges research support from the NSF under Grant No. SES 18-50860 and a Kelly Fellowship at the University of Auckland. Rossi acknowledges research support from MIUR under the Rita Levi Montalcini scheme.

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