  Catalytic prior distributions provide general, easy-to-use, and interpretable
specifications of prior distributions for Bayesian analysis. They are
particularly beneficial when the observed data are inadequate to stably
estimate a complex target model. A catalytic prior distribution is constructed
by augmenting the observed data with synthetic data that are sampled from the
predictive distribution of a simpler model estimated from the observed data. We
illustrate the usefulness of the catalytic prior approach using an example from
labor economics. In the example, the resulting Bayesian inference reflects many
important aspects of the observed data, and the estimation accuracy and
predictive performance of the inference based on the catalytic prior are
superior to, or comparable to, that of other commonly used prior distributions.
We further explore the connection between the catalytic prior approach and a
few popular regularization methods. We expect the catalytic prior approach to
be useful in many applications.
