Quasi Maximum Likelihood Estimation of Spatial Models with Heterogeneous Coefficients

64 Pages Posted: 14 Jul 2015

See all articles by Michele Aquaro

Michele Aquaro

European Commission, Joint Research Centre

Natalia Bailey

Monash University

M. Hashem Pesaran

University of Southern California - Department of Economics; University of Cambridge - Trinity College (Cambridge)

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Date Written: June 30, 2015

Abstract

This paper considers spatial autoregressive panel data models and extends their analysis to the case where the spatial coefficients differ across the spatial units. It derives conditions under which the spatial coefficients are identified and develops a quasi maximum likelihood (QML) estimation procedure. Under certain regularity conditions, it is shown that the QML estimators of individual spatial coefficients are consistent and asymptotically normally distributed when both the time and cross section dimensions of the panel are large. It derives the asymptotic covariance matrix of the QML estimators allowing for the possibility of non-Gaussian error processes. Small sample properties of the proposed estimators are investigated by Monte Carlo simulations for Gaussian and non-Gaussian errors, and with spatial weight matrices of differing degree of sparseness. The simulation results are in line with the paper’s key theoretical findings and show that the QML estimators have satisfactory small sample properties for panels with moderate time dimensions and irrespective of the number of cross section units in the panel, under certain sparsity conditions on the spatial weight matrix.

Keywords: spatial panel data models, heterogeneous spatial lag, coefficients, identification, quasi maximum likelihood (QML) estimators, non-Gaussian errors

JEL Classification: C210, C230

Suggested Citation

Aquaro, Michele and Bailey, Natalia and Pesaran, M. Hashem, Quasi Maximum Likelihood Estimation of Spatial Models with Heterogeneous Coefficients (June 30, 2015). CESifo Working Paper Series No. 5428, Available at SSRN: https://ssrn.com/abstract=2630546

Michele Aquaro

European Commission, Joint Research Centre ( email )

Via E. Fermi 2749
Ispra (VA), 21027
Italy

Natalia Bailey

Monash University ( email )

23 Innovation Walk
Wellington Road
Clayton, Victoria 3800
Australia

M. Hashem Pesaran (Contact Author)

University of Southern California - Department of Economics

3620 South Vermont Ave. Kaprielian (KAP) Hall 300
Los Angeles, CA 90089
United States

University of Cambridge - Trinity College (Cambridge) ( email )

United Kingdom

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