Estimating Interdependence Across Space, Time and Outcomes in Binary Choice Models Using Pseudo Maximum Likelihood Estimators

Binary choice models, such as logit or probit, are frequently used in Political Science. However, such models have proven particularly difficult in dealing with interdependent data structures, including (1) spatial autocorrelation, (2) temporal autocorrelation, as well as (3) simultaneity arising from endogenous binary regressors in simultaneous equations. In each of these cases, the primary source of the estimation challenge is the fact that the jointly determined error terms in the reduced-form specification are analytically intractable due to an n-dimensional integral. To deal with this problem, simulation approaches have been proposed, but these are extremely computationally intensive and impractical for standard time-series-cross-sectional datasets with thousands of observations. As a way forward, in this paper, we demonstrate how to reduce computational burdens significantly by (i) introducing analytically tractable pseudo maximum likelihood estimators for spatial binary models that exhibit interdependence across space, time or outcomes, and by (ii) exploiting the (matrix-)sparseness in the interdependence structure for typical Political Science data. Monte-Carlo experiments demonstrate that (a) omitting interdependence induces severe bias in binary choice models, (b) our estimators are both consistent and more efficient, and (c) our estimators require only a fraction of the computational costs of simulation-based methods. We also demonstrate the usefulness of our approach in an empirical application of international environmental treaty ratification and compliance that captures all three types of interdependence. First, international cooperation suggests that "closer" countries should coordinate their decision making. Second, ratification and compliance tend to be temporally persistent." Third, strategic theory suggests that countries that are more likely to comply are also more likely to ratify to begin with, making it difficult to evaluate the effect of treaties.