Estimating the anomaly base rate

The anomaly zoo has caused many to question whether researchers are using the right tests of statistical significance. But even if researchers are using the right tests, they will still draw the wrong conclusions from their econometric analyses if they start out with the wrong priors (i.e., if they start out with incorrect beliefs about the ex ante probability of encountering a tradable anomaly, the “anomaly base rate”). We propose a way to estimate it by combining two key insights: Empirical Bayes methods capture the implicit process by which researchers form priors about the likelihood that a new variable is a tradable anomaly based on their past experience, and under certain conditions, a one-to-one mapping exists between these prior beliefs and the best-fit tuning parameter in a penalized regression. The anomaly base rate varies substantially over time, and we study trading-strategy performance to verify our estimation results.