Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances

Abstract

This study develops 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 GMM estimator suggested in Prucha (1998,1999) for the spatial autoregressive parameter in the disturbance process. We also define IV estimators for the regression parameters of the model and give results concerning the joint asymptotic distribution of those estimators and the GMM estimator. Much of the theory is kept general to cover a wide range of settings.

The more the merrier? Migration and convergence among European regions

“…In order not to induce serial correlation, the errors are assumed to correlate spatially only via contiguity. Kelejian and Prucha (2010) show that the parameter spaces for Λ and similarly R depend on the eigenvalues of W, W U , and the sample size. Maximum-row normalization constrains the parameter space of the eigenvalues to the interval (−1, 1).…”

Peer effects, fast food consumption and adolescent weight gain

“…It is important to note that, as in Kelejian and Prucha (1998), we assume that errors are homoscedastic. The estimation theory developed by Kelejian and Prucha (1998) under the assumption of homoscedastic errors does not apply if we assume heteroscedastic errors (Kelejian and Prucha, 2010).…”

In Tandem for Cohesion? Synergies and Conflicts between Regional and Agricultural Policies of the European Union

“…In the same way, the capacity of regional policies to target resources upon the weaker areas has still to be improved and such a capacity is certainly very much influenced by changes in the mechanisms of policy regulation. In table 5 the cross-sectional analysis of the relationship between structural disadvantage and allocated funds is re-assessed by means of a SARAR (Spatialautoregressive model with spatial-autoregressive disturbances) model (Kelejian and Prucha, 2010). In this model the funds allocated to region i depend also on spatiallyweighted average of the dependent variable observed for the other cross-sectional units (lambda parameter in table 5) as in the standard spatial-autoregressive (SAR) model.…”