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

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: CESifo Working Paper ; No. 2448

Classification and Topics

• Classification: Wirtschaft ; Single Equation Models; Single Variables: Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions ; Multiple or Simultaneous Equation Models: Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
• Subject: Spatial dependence ; heteroskedasticity ; Cliff-Ord model ; two-stage least squares ; generalized moments estimation ; asymptotics ; Räumliche Interaktion ; Autokorrelation ; Momentenmethode ; Schätztheorie ; Autokorrelation ; Heteroskedastizität ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Kelejian, Harry H. ; Prucha, Ingmar R.
• Event: Veröffentlichung
• (who): Center for Economic Studies and ifo Institute (CESifo)
• (where): Munich
• (when): 2008

Further information

• Handle: http://hdl.handle.net/10419/26493
• Last update: 10.03.2025, 11:44 AM CET