Abstract
In this study, I investigate the necessary condition for the consistency of the maximum likelihood estimator (MLE) of spatial models with a spatial moving average process in the disturbance term. I show that the MLE of spatial autoregressive and spatial moving average parameters is generally inconsistent when heteroskedasticity is not considered in the estimation. I also show that the MLE of parameters of exogenous variables is inconsistent and determine its asymptotic bias. I provide simulation results to evaluate the performance of the MLE. The simulation results indicate that the MLE imposes a substantial amount of bias on both autoregressive and moving average parameters.
Highlights
The spatial dependence among the disturbance terms of a spatial model is generally assumed to take the form of a spatial autoregressive process
The analytical results show that when heteroskedasticity is not considered in the estimation, the necessary condition for the consistency of the maximum likelihood estimator (MLE) is generally not satisfied for both the SARMA(1,1) and SARMA(0,1) models
I show that the MLE of the spatial autoregressive and moving average parameters for the SARMA(1,1) specification is generally inconsistent in the presence of heteroskedastic disturbances
Summary
The spatial dependence among the disturbance terms of a spatial model is generally assumed to take the form of a spatial autoregressive process. The spatial model that has a spatial lag in the dependent variable and an autoregressive process in the disturbance term is known as the SARARmodel. The autoregressive process is not the correct specification when the effects of Econometrics 2015, 3 shocks are contained within a small region and are not transmitted to other regions. An alternative to an autoregressive process is a spatial moving average process, where the effects of shocks are more localized. The spatial model that contains a spatial lag of the dependent variable and a spatial moving average process for the disturbance term is known as the SARMA model
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