Spatial econometric Monte Carlo studies: raising the bar

We discuss Monte Carlo methodology that can be used to explore alternative approaches to estimating spatial regression models. Our focus is on models that include spatial lags of the dependent variable, e.g., the SAR specification. A major point is that practitioners rely on scalar summary measures of direct and indirect effects estimates to interpret the impact of changes in explanatory variables on the dependent variable of interest. We argue that these should be the focus of Monte Carlo experiments. Since effects estimates reflect a nonlinear function of both \(\beta \) and \(\rho \), past studies’ focus exclusively on \(\beta \) and \(\rho \) parameter estimates may not provide useful information regarding statistical properties of effects estimates produced by alternative estimators. Since effects estimates have recently become the focus of inference regarding the significance of (scalar summary) direct and indirect impacts arising from changes in the explanatory variables, empirical measures of dispersion produced by simulating draws from the (estimated) variance–covariance matrix of the parameters \(\beta \) and \(\rho \) should be part of the Monte Carlo study. An implication is that differences in the quality of estimated variance–covariance matrices arising from alternative estimators also plays a role in determining the accuracy of inference. An applied illustration is used to demonstrate how these issues can impact conclusions regarding the performance of alternative estimators.