Is peace a missing value or a zero? On selection models in political science

Sample selection models, variants of which are the Heckman and Heckit models, are increasingly used by political scientists to accommodate data in which censoring of the dependent variable raises concerns of sample selectivity bias. Beyond demonstrating several pitfalls in the calculation of marginal effects and associated levels of statistical significance derived from these models, we argue that many of the empirical questions addressed by political scientists would – for both substantive and statistical reasons – be more appropriately addressed using an alternative but closely related procedure referred to as the two-part model (2 PM). Aside from being simple to estimate, one key advantage of the 2 PM is its less onerous identification requirements. Specifically, the model does not require the specification of so-called exclusion restrictions, variables that are included in the selection equation of the Heckit model but omitted from the outcome equation. Moreover, we argue that the interpretation of the marginal effects from the 2 PM, which are in terms of actual outcomes, are more appropriate for the questions typically addressed by political scientists than the potential outcomes ascribed to the Heckit results. Drawing on data from the Correlates of War database, we present an empirical analysis of conflict intensity illustrating that the choice between the sample selection model and 2 PM can bear fundamentally on the conclusions drawn.