Diagnosing, Modeling, Interpreting, and Leveraging Spatial Relationships in Time-Series-Cross-Section Data

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

Social scientists recognize that observations in time-series-cross-section (TSCS) datasets will usually correlate across time and space. As Beck and Katz (1996) noted, their empirical analyses typically reflect one of two perspectives on these temporal and spatial dependencies. Some see such correlations as a nuisance. These analysts' concerns surround the drawing of accurate causal inferences about relations between other explanatory variables and the dependent variables; interest in temporal and spatial dependence arises only insofar as such dependence might jeopardize these theoretically more-central inferences. Given these goals, they do not always see a need to model spatial (or temporal) dependence directly. They argue, sometimes incorrectly, that the only cost of failing to do so lies in reduced efficiency, and that, therefore, estimation of standard errors robust to spatial (and temporal) correlation may suffice to ensure sound inferences. Others have more-substantive interest in spatial (and temporal) dependence and attempt to model these relationships directly. Standard practice in political science is now to model dynamics (i.e., temporal dependence) directly, typically with lags of the dependent variable, and to address spatial dependence solely by applying panel-corrected (robust) standard-errors. Thus, researchers commonly treat spatial dependence as a nuisance. In this project, the researchersargue, however, that direct modeling of spatial dependence (plus robust standard-errors perhaps) is always superior, regardless of the substantive interest in these relationships. Directly modeling spatial dependence enhances efficiency and, under many circumstances, is necessary to obtain unbiased coefficient estimates for non-spatial regressors. If, e.g., both dependent and independent variables correlate spatially, yet the statistical model ignores these correlations or relegates their role to adjusting standard-error estimates, the resulting inefficient coefficient estimates will also tend to misstate (i.e., bias) the direct effects of explanatory variables (adding to them the effects of spatial diffusion or of omitted stimuli that correlate across space). This also implies biased hypothesis tests, with null hypotheses rejected more or less often than truly warranted. Understandably, analysts uninterested in spatial relationships per se will want to employ simple proxies for more-complicated diffusion processes or omitted spatially correlated stimuli. The researchers investigate spatial lags and indicators as two such simple proxies. Those more directly interested in spatial dependence, contrarily, will prefer more sophisticated modeling techniques to estimate the possibly complex diffusion patterns in their data. For these purposes, the investigators explore spatial analogues to estimators from econometric approaches to dynamic-panel models (e.g., Hsiao 1986; Baltagi 1995). This sophisticated methodological investigation is addressed both to social-science researchers directly interested in spatial relationships (spatial substance) and to those primarily concerned to make optimal inferences regarding other substantive relationships given spatially dependent data (spatial nuisance). Building from analogies to similar, better-explored issues arising in temporal dependence and through analytic derivation and Monte Carlo experimentation, the investigators: (1) detail the conditions under which failing to model spatial dependence directly (or relegating its role to standard-error adjustment) renders other coefficient estimates biased or merely inefficient, exploring bias and inefficiency magnitudes under varying spatial-dependence conditions; (2) distinguish spatial diffusion from correlated responses to omitted spatially correlated factors conceptually and explore the properties of alternative approaches to making this distinction empirically; (3) develop and evaluate several non-, semi-, and parametric tests for and gauges of spatial correlation, with and without spatial lags in the model; (4) compare the properties of simple proxies for full models of the true spatial-diffusion or common omitted-factors--e.g., spatial dummies or symmetric spatial-lags comprised of averages of other cross-section units. dependent variables each time-period--to each other, to PCSE's alone, and to differing methods of estimating fuller models. The researchers will create and publish freely statistical-software algorithms to implement, and, where potentially useful, pedagogical modules, to teach, all of the techniques that they develop and explore