Testing for Spatial-Autoregressive Lag versus (Unobserved) Spatially Correlated Error-Components

One of the central challenges to empirical inference in the context of potentially interdependent observations, known as Galton’s Problem, is the difficulty distinguishing spatial correlation in outcomes due to the observed units’ exposure to spatially correlated shocks (‘common exposure’) from spatially dependent outcomes due to interdependence (‘spillovers’ or ‘contagion’) among units. The applied researcher’s first, and until recently only, defense against confusing these substantively importantly different processes empirically has been to control as best possible with observable regressors and/or groupwise dummy-variables for correlated-shocks processes when estimating interdependence models (spatial autoregression). Specifying empirical models and measures as precisely and powerfully as possible remains the optimal practice, but these strategies cannot guard fully against the possibility of exposure to unobserved exogenous shocks that are distributed spatially in some manner not fully common to some set of units (which fixed or random group effects could account) or fully controlled by observable exogenous factors (control variables), but are instead distributed across units more similarly to the pattern by which the outcome is contagious. This paper reviews recent developments in testing for three datagenerating processes (models) that span those possibilities: random effects by spatial units (‘groupwise [random or fixed] effects’), time-invariant group effects with interdependence across units (‘spatially interdependent group effects’), and time-varying spatial effects (i.e., the spatial-error or spatial-lag models.) The paper explores by Monte Carlo analyses how well Anselin et al. (1996)’s robust Lagrangemultiplier tests of spatial-autoregressive lag versus spatial-autoregressive error processes may distinguish these three models as well, and how effectively spatial-group dummy-variables or Griffith’s (2000) eigenvector spatial-filtering may control for them as alternatives in spatial-autoregressive models of interdependence. These analyses show the robust LM tests can be constructive and informative also in distinguishing these alternative sources of spatial association, and that eigenvector spatial-filtering offers an effective control in some conditions, and does so more generally than do spatial-group dummyvariables. (In fact, eigenvector spatial-filtering would seem to be a generalization that subsumes spatial dummy-variables, something not previously noticed in the literature.) The paper concludes with proposing an overall approach to empirical analysis of interdependence that includes as an important step using these tests and controls to provide direct answer to the question posed by Galton’s Problem: common exposure or contagion?