Identification of and Correction for Publication Bias

In empirical research, not all results are published; both researchers and journal editors make decisions which lead to publication probabilities which depend on empirical findings. Such selective publication potentially leads to biased estimators and distorted inference. We provide identification results which allow recovering conditional publication probabilities. Our first approach is based on replication experiments. Absent selectivity, initial and replication estimates would be symmetrically distributed; observed asymmetries allow to identify selectivity. Our second approach is based on meta-studies. Absent selectivity, the distribution of estimates for studies with higher standard errors would be a noised-up version of the distribution for studies with lower standard errors. Deviations from this equality again allow identifying selectivity. We also provide results for correct statistical inference when conditional publication probabilities are known. We propose median unbiased estimators and equal-tailed confidence intervals with correct coverage, allowing for the presence of nuisance parameters. The key ingredient for correct inference is a likelihood function reweighted by the inverse publication probability given latent parameters. We finally apply our results to a series of empirical fields, including experimental economics and experimental psychology, estimation of the effects of minimum wages, and the impact of de-worming programmes.