How to use economic theory to improve estimators: Shrinking toward theoretical restrictions

We propose to use economic theories to construct shrinkage estimators that perform well when the theories' empirical implications are approximately correct, but perform no worse than unrestricted estimators when the theories' implications do not hold. We implement this construction in various settings, including labor demand and wage inequality, and estimation of consumer demand. We provide asymptotic and finite sample characterizations of the behavior of the proposed estimators. Our approach is an alternative to the use of theory as something to be tested or to be imposed on estimates. Our approach complements uses of theory for identification and extrapolation.