What Is the False Discovery Rate in Empirical Research?

A scientific discovery in empirical research, e.g., establishing a causal relationship between two variables, is typically based on rejecting a statistical null hypothesis of no relationship. What is the probability that such a rejection is a mistake? This probability is not controlled by the significance level of the test which is typically set at 5 percent. Statistically, the 'False Discovery Rate' (FDR) is the fraction of null rejections that are false. FDR depends on the significance level, the power of the test, and the prior probability that the null is true. All else equal, the higher the prior probability, the higher is the FDR. Economists have different views on how to assess this prior probability. I argue that for both statistical and economic reasons, the prior probability of the null should in general be quite high and, thus, the FDR in empirical economics is high, i.e., substantially higher than 5 percent. This may be a contributing factor behind the replication crisis that also haunts economics. Finally, I discuss conventional and newly proposed stricter significance thresholds and, more generally, the problems that passively observed economic and social science data pose for the traditional statistical testing paradigm.