Long run consequence of p-hacking

We study the theoretical consequence of p-hacking on the accumulation of knowledge under the framework of mis-specified Bayesian learning. A sequence of researchers, in turn, choose projects that generate noisy information in a field. In choosing projects, researchers need to carefully balance as projects generates big information are less likely to succeed. In doing the project, a researcher p-hacks at intensity ε so that the success probability of a chosen project increases (unduly) by a constant ε. In interpreting previous results, researcher behaves as if there is no p-hacking because the intensity ε is unknown and presumably small. We show that over-incentivizing information provision leads to the failure of learning as long as ε≠ 0. If the incentives of information provision is properly provided, learning is correct almost surely as long as ε is small.