Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances

Harry H. Kelejian and Ingmar Prucha

No 2448, CESifo Working Paper Series from CESifo

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.

Keywords: spatial dependence; heteroskedasticity; Cliff-Ord model; two-stage least squares; generalized moments estimation; asymptotics (search for similar items in EconPapers)
JEL-codes: C21 C31 (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

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Related works:
Journal Article: Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:ces:ceswps:_2448

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