Explaining Rare Events in International Relations

Many of the most signiŽ cant events in international relations—wars, coups, revolutions, massive economic depressions, economic shocks—are rare events. They occur infrequently but are considered of great importance. In international relations, as in other disciplines, rare events—that is, binary dependent variables characterized by dozens to thousands of times fewer 1’s (events such as wars or coups) than 0’s (nonevents)—have proven difŽ cult to explain and predict. Though scholars have made substantial efforts to quantify rare events, they have devoted less attention to how these events are analyzed.We show that problems in explaining and predicting rare events stem primarily from two sources: popular statistical procedures that underestimate the probability of rare events and inefŽ cient data-collection strategies. We analyze the issues involved, cite examples from the international relations literature, and offer some solutions. The Ž rst source of problems in rare-event analysis is researchers’ reliance on logit coefŽ cients, which are biased in small samples (those with fewer than two hundred observations), as the statistical literature well documents. Not as widely understood is that the biases in probabilities can be substantivelymeaningful when sample sizes are in the thousands and are always in the same direction: estimated event probabilities are always too small. A separate, often overlooked problem is that the almost universally used method of computing probabilities of events in logit analysis is suboptimal in Ž nite samples of rare-events data, leading to errors in the