Weighted-average least squares applied to spatial econometric models: A monte carlo investigation

Recently, model averaging techniques have been employed widely in empirical investigations as an alternative to the conventional model selection procedure, a procedure criticized because it disregards a major component of uncertainty, namely, uncertainty regarding the model itself, and, thus, it leads to the underestimation of uncertainty regarding the quantities of interest. Bayesian model averaging (BMA) is one of the most popular model averaging techniques. Some studies indicate that BMA has cumbersome aspects. One of the major practical issues of using BMA is its substantial computational burden, which obstructs the process of obtaining exact estimates. A simulation method, such as Markov chain Monte Carlo (MCMC), is required to resolve this problem. Weighted-average least squares (WALS) estimation has been proposed as an alternative to BMA. The computational burden of WALS estimation is negligible; therefore, it does not require the MCMC method. Furthermore, WALS estimation has theoretical advantages over BMA estimation. This article presents two contributions to the WALS literature. First, it applies WALS to spatial lag/error models in order to consider spatial dependence. Second, it extends WALS in order to consider explicitly the problem of multicollinearity by employing the technique of principal component regression. The small sample properties of the estimators of the proposed models are examined using Monte Carlo experiments; the results of these experiments suggest that the standard WALS may produce biased estimates when the underlying data-generating process is a spatial lag process. Results also indicate that when the correlation among the regressors is high, the standard WALS estimators may suffer from large variances and root mean squared errors. Both of these problems are significantly mitigated by using the proposed models.