  We propose a novel method for modeling data by using structural models based
on economic theory as regularizers for statistical models. We show that even if
a structural model is misspecified, as long as it is informative about the
data-generating mechanism, our method can outperform both the (misspecified)
structural model and un-structural-regularized statistical models. Our method
permits a Bayesian interpretation of theory as prior knowledge and can be used
both for statistical prediction and causal inference. It contributes to
transfer learning by showing how incorporating theory into statistical modeling
can significantly improve out-of-domain predictions and offers a way to
synthesize reduced-form and structural approaches for causal effect estimation.
Simulation experiments demonstrate the potential of our method in various
settings, including first-price auctions, dynamic models of entry and exit, and
demand estimation with instrumental variables. Our method has potential
applications not only in economics, but in other scientific disciplines whose
theoretical models offer important insight but are subject to significant
misspecification concerns.
