A web appendex is also available. Data to replicate and code to implement estimation and interpretation procedures in the text are available from the authors' web pages or upon request.


Spatial interdependence, the interdependence of outcomes across units, is theoretically and substantively ubiquitous and central across the social sciences. The empirical clustering of outcomes on some dimension(s), spatial association, is also obvious in most contexts. However, outcomes may exhibit spatial association for three distinct reasons. Units may be responding similarly to similar exposure to similar exogenous internal/domestic or external/foreign stimuli (common exposure), and/or units’ responses may depend on others’ responses (contagion). A third possibility arises when the putative outcome affects the variable along which clustering occurs (selection: e.g., homophily). Severe empirical difficulties confront the accurate estimation and distinction of these alternative sources of spatial association. After brief review of spatial and spatiotemporal autoregressive (SAR and STAR) models, which reflect interdependence directly and so can address Galton’s Problem of distinguishing common exposure from contagion, this paper extends those models, proposing to apply the multiparametric spatiotemporal autoregressive (m-STAR) model as a simple approach to estimating jointly the pattern of connectivity and the strength of contagion by that pattern, including the case where connectivity is endogenous to the dependent variable (i.e., selection). This paper introduces the m-STAR model, compares the approach to extant longitudinal-network strategies, and suggests how to calculate, interpret, and present the dynamic, endogenous coevolution of network structure and of contagion and common-exposure effects in such systems of nonlinear endogenous equations. We illustrate with an empirical application attempting to disentangle the roles of economic interdependence, correlated external and internal stimuli, and EU membership in shaping recent OECD labor-market policies.

HaysKachiFranzese.PolNet09.WebAppendix.pdf (570 kB)
Web appendix to Hays, Kachi, & Franzese. Data & code also available at our web pages or upon request.