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Empirical Modeling Strategies for Spatial Interdependence: Omitted-Variable vs. Simultaneity Biases Hays, Jude Franzese, Robert Uploaded 07-24-2004 Keywords Spatial Lag Models Diffusion Omitted Variable Bias Simultaneity Bias Abstract Scholars recognize that time-series-cross-section data typically correlate across time and space, yet they tend to model temporal dependence directly while addressing spatial interdependence solely as nuisance to be “corrected” (FGLS) or to which to be “robust” (PCSE). We demonstrate that directly modeling spatial interdependence is methodologically superior, offering efficiency gains and generally helping avoid biased estimates even of “non-spatial” effects. We first specify empirical models representing two modern approaches to comparative and international political economy: (context-conditional) open-economy comparative political-economy (i.e., common stimuli, varying responses) and international political-economy, which implies interdependence (plus closed-economy and orthogonal-open-economy predecessors). Then we evaluate four estimators—non-spatial OLS, spatial OLS, spatial 2SLS-IV, and spatial ML—for analyzing such models in spatially interdependent data. Non-spatial OLS suffers from potentially severe omitted-variable bias, tending to inflate estimates of common-stimuli effects especially. Spatial OLS, which specifies interdependence directly via spatial lags, dramatically improves estimates but suffers a simultaneity bias, which can be appreciable under strong interdependence. Spatial 2SLS-IV, which instruments for spatial lags of dependent variables with spatial lags of independent variables, yields unbiased and reasonably efficient estimates of both common-stimuli and diffusion effects, when its conditions hold: large samples and fully exogenous instruments. A tradeoff thus arises in practice between biased-but-efficient spatial OLS and consistent- (or, at least, less-biased-) but-inefficient spatial 2SLS-IV. Spatial ML produces good estimates of non-spatial effects under all conditions but is computationally demanding and tends to underestimate the strength of interdependence, appreciably so in small-N samples and when the true diffusion-strength is modest. We also explore the standard-error estimates from these four procedures, finding sizable inaccuracies by each estimator under differing conditions, and PCSE’s do not necessarily reduce these inaccuracies. By an accuracy-of-reported-standard-errors criterion, 2SLS-IV seems to dominate. Finally, we explore the spatial 2SLS-IV estimator under varying patterns of interdependence and endogeneity, finding that its estimates of diffusion strength suffer only when a condition we call cross-spatial endogeneity, wherein dependent variables (y’s) in some units cause explanatory variables (x’s) in others, prevails.

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A Comparison of the Small-Sample Properties of Several Estimators for Spatial-Lag Count Models Hays, Jude Franzese, Robert Uploaded 07-22-2009 Keywords Interdependence Spatial Econometrics Spatial-Lag Models Count Data Poisson Nonlinear Least-Squares GMM Estimation Abstract Political scientists frequently encounter and analyze spatially interdependent count data. Applications include counts of coups in African countries, of state participation in militarized interstate disputes, and of bills sponsored by members of Congress, to name just a few. The extant empirical models for spatially interdependent counts and their corresponding estimators are, unfortunately, dauntingly complex, computationally costly, or both. They also generally tend 1) to treat spatial dependence as nuisance, 2) to stress spatial-error or spatial-heterogeneity models over spatial-lag models, and 3) to treat all observed spatial association as arising by one undifferentiated source. Prominent examples include the Winsorized count model of Kaiser and Cressie (1997) and Griffith�s spatially-filtered Poisson model (2002, 2003). Given the available options, the default approaches in most applied political-science research are to either to ignore spatial interdependence in count variables or to use spatially-lagged observed-counts as exogenous regressors, either of which leads to inconsistent estimates of causal relationships. We develop alternative nonlinear least-squares and method-of-moments estimators for the spatial-lag Poisson model that are consistent. We evaluate by Monte Carlo simulation the small sample performance of these relatively simple estimators against the naiive alternatives of current practice. Our results indicate substantial consistency improvements against minimal complexity and computational costs. We illustrate the model and estimators with an analysis of terrorist incidents around the world.