  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 $\varepsilon$ so that the success probability
of a chosen project increases (unduly) by a constant $\varepsilon$. In
interpreting previous results, researcher behaves as if there is no p-hacking
because the intensity $\varepsilon$ is unknown and presumably small. We show
that over-incentivizing information provision leads to the failure of learning
as long as $\varepsilon\neq 0$. If the incentives of information provision is
properly provided, learning is correct almost surely as long as $\varepsilon$
is small.
