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Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroscedastic Disturbances (2006)
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BibTeX
@MISC{Kelejian06specificationand,
author = {Harry H. Kelejian and Ingmar R. Prucha},
title = {Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroscedastic Disturbances},
year = {2006}
}
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Abstract
One important goal of this study is to develop a methodology of inference for a widely used Cliff-Ord type spatial model containing spatial lags in the dependent variable, exogenous variables, and the disturbance terms, while allowing for unknown heteroskedasticity in the innovations. We first generalize the generalized moments (GM) estimator suggested in Kelejian and Prucha (1998,1999) for the spatial autoregressive parameter in the disturbance process. We prove the consistency of our estimator; unlike in our earlier paper we also determine its asymptotic distribution, and discuss issues of efficiency. We then define instrumental variable (IV) estimators for the regression parameters of the model and give results concerning the joint asymptotic distribution of those estimators and the GM estimator under reasonable conditions. Much of the theory is kept general to cover a wide range of settings. We note the estimation theory developed by Kelejian and Prucha (1998, 1999) for GM and IV estimators and by Lee (2004) for the quasi-maximum likelihood estimator under the assumption of homoskedastic innovations does not carry over to the case of heteroskedastic innovations. The paper also provides a critical discussion of the usual specification of the parameter space.
Keyphrases
heteroscedastic disturbance spatial autoregressive model joint asymptotic distribution cliff-ord type spatial model give result spatial lag wide range homoskedastic innovation usual specification reasonable condition important goal critical discussion spatial autoregressive parameter heteroskedastic innovation quasi-maximum likelihood estimator dependent variable asymptotic distribution disturbance term discus issue iv estimator unknown heteroskedasticity estimation theory gm estimator regression parameter instrumental variable parameter space exogenous variable disturbance process generalized moment
