Maximum Simulated Likelihood Estimation with Spatially Correlated Observations: A Comparison of Simulation Techniques

Econometric models are a powerful tool for analyzing regional issues. Complex models are normally intractable and require special estimation methods. Maximum simulated likelihood estimation (MSLE) techniques have become popular in recent years, and are being included in new software releases (such as STATA and Limdep). It is important that analysts understand the relative performance of different simulation techniques under various data circumstances. This especially true in regional studies, where observations are often spatially correlated. This paper studies the performance of several simulation techniques with spatially correlated observations. Quasi Monte-Carlo (QMC) methods are found to impose a strong periodic correlation pattern across observations. While some forms of sequencing, such as scrambled Halton, Sobol and Faure, can sever correlations across dimensions of error-term integration, they cannot remove the correlation that exists across observations. When a data set’s true correlation patterns clearly differ from the simulated patterns, model estimation may become inefficient; and, with finite samples, statistical identification of parameters may suffer. Fortunately, here we find that, at least within the mixed logit framework, even when observations are correlated, QMCs and hybrid methods are typically preferred to pseudo Monte-Carlo methods, thanks to their better coverage. These findings offer an important supplement to existing studies of spatial model estimation and should prove valuable for future work that requires simulated likelihoods with spatially correlated observations.