Causal heterogeneity in comparative research: A Bayesian hierarchical modelling approach

Pooled cross-sectional time-series models in comparative politics typically constrain the effects of variables to be identical across countries. These models conflict with general principles of comparative analysis and theories of comparative political economy that the models are designed to test. In contrast, Bayesian hierarchical models allow time-series coefficients to vary across countries, and time-series effects can be related to cross-national variation in institutions. While allowing causal complexity into comparative analysis, the hierarchical model also provides: (1) more accurate forecasts than rival models, (2) more accurate estimates of time-series effects than unpooled analysis; and (3) a more realistic accounting of uncertainty than conventional pooled analysis. In addition, Bayesian theory for the hierarchical model helps specify the concept of "comparability" in comparative research. These ideas are illustrated in a reanalysis of a model of the political determinants of economic growth studied by Alvarez, Garrett, and Lange (1991).