An m-STAR Model of Dynamic, Endogenous Interdependence – a.k.a. Network-Behavior Coevolution – in the Social Sciences

Spatial interdependence, the interdependence of outcomes across units, is theoretically and substantively ubiquitous and central across the social sciences. The empirical clustering or correlation of outcomes on some dimension(s), spatial association, is also obvious in most contexts. However, outcomes may exhibit spatial association for three distinct reasons. First, units may be responding similarly to similar exposure to similar exogenous internal/domestic or external/foreign stimuli (common exposure); second, 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 our previous work on specification, estimation, testing, and interpretation of the 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 as alternative substantive sources of observed spatial association, this paper extends those analyses, 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). As before, we stress substantivelytheoretically guided (i.e., structural) specifications that can support analyses of estimated spatiotemporal responses to stochastic or covariate shocks and that can distinguish the possible sources of spatial association, now three: common exposure, contagion, and selection. In addition to discussing estimation of m-STAR models, this paper compares the approach to extant longitudinal-network strategies [this work still pending as yet], and suggests how to calculate, interpret, and present the dynamic, endogenous coevolution of network structure and of contagion and common-exposure effects that emerges from such a system of nonlinear endogenous equations. We illustrate this approach to dynamic, endogenous interdependence—which parallels models of network and behavior coevolution in the dynamic or longitudinal networks literature—with an empirical application attempting to disentangle the roles of economic interdependence, correlated external and internal stimuli, and EU membership in shaping labor-market policies in recent years. * This research is supported in part by NSF grant #0318045. We thank Chris Achen, Jim Alt, Kenichi Ariga, Klaus Armingeon, Neal Beck, Jake Bowers, Jim Caporaso, Kerwin Charles, Bryce Corrigan, Tom Cusack, David Darmofal, Jakob de Haan, Scott De Marchi, John Dinardo, Zach Elkins, James Fowler, John Freeman, Fabrizio Gilardi, Kristian Gleditsch, Mark Hallerberg, John Jackson, Jonathan Katz, Mark Kayser, Achim Kemmerling, Gary King, Hasan Kirmanoglu, Herbert Kitschelt, Jim Kuklinski, Don Lacombe, Chris Lawrence, Tse-Min Lin, Xiaobo Lu, Scott McClurg, Walter Mebane, Covadonga Meseguer, Michael Peress, Thomas Pluemper, David Prosperi, Dennis Quinn, Megan Reif, Frances Rosenbluth, Ken Scheve, Phil Schrodt, Chuck Shipan, Beth Simmons, David Siroky, John D. Stephens, Duane Swank, Wendy Tam-Cho, Vera Troeger, Craig Volden, Michael Ward, Greg Wawro, and Erik Wibbels – and the many others we have surely forgotten – for useful comments on this and/or other work in our broader project on spatialeconometric models in political science. All remaining errors are ours alone.