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GEL estimation and tests of spatial autoregressive models

Fei Jin and Lung-Fei Lee ()

Journal of Econometrics, 2019, vol. 208, issue 2, 585-612

Abstract: This paper considers the generalized empirical likelihood (GEL) estimation and tests of high order spatial autoregressive (SAR) models by exploring an inherent martingale structure. The GEL estimator has the same asymptotic distribution as the generalized method of moments estimator explored with same moment conditions for estimation, but circumvents a first step estimation of the optimal weighting matrix with a preliminary estimator, and thus can be robust to unknown heteroskedasticity and non-normality. While the GEL removes the asymptotic bias from the preliminary estimator and partially removes the bias due to the correlation between the moment conditions and their Jacobian, the empirical likelihood as a special member of GELs further partially removes the bias from estimating the second moment matrix. We also formulate the GEL overidentification test, Moran’s I test, and GEL ratio tests for parameter restrictions and non-nested hypotheses. While some of the conventional tests might not be robust to non-normality and/or unknown heteroskedasticity, the corresponding GEL tests can be robust.

Keywords: Spatial autoregressive model; Empirical likelihood; Higher order asymptotic bias; Unknown heteroskedasticity; Non-normality; EL ratio test (search for similar items in EconPapers)
JEL-codes: C12 C13 C14 C21 C52 (search for similar items in EconPapers)
Date: 2019
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Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

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