Missing(s) in Space: Monte Carlo Simulations and a Bayesian Approach to Missing Data in Spatial Econometric Models

Missing data is a common concern to researchers in the social sciences. Whereas this issue has received increasing attention in sociological research based on survey data (Allison, 2001; Rubin, 1987), researchers face additional challenges when addressing missing data in spatial econometric models. Unlike in the non-spatial case, ignoring missing data is not only a problem in terms of introducing bias when the missing process is at random (`selection on observables'; MAR) or not at random (the reason of missingness is related to missing values; MNAR – Allison, 2001), but also if missings are completely at random (MCAR – Kelejian and Prucha, 2010). Due to the interdependence between units and the corresponding spatial multipliers, ignoring missing data introduces bias in spatial econometric models in any of the three cases (LeSage and Pace, 2009; Wang and Lee, 2013).

Using Monte-Carlo simulations and an empirical application from the field of political science, this paper addresses the outlined problem by means of a Bayesian framework. It can be demonstrated how the amount of bias introduced in parameter estimates is almost independent of the nature of the missing process, although it is marginally lower in the case of missings completely at random. Additionally, the amount of bias generally increases with the strength of the underlying spatial association across all different specifications. Finally, allowing for the simultaneous imputation of missing values and model estimation, the pursued Bayesian approach – although computationally intensive – offers an adequate framework to address this bias introduced in models with spatially lagged variables (and/or errors).