We propose to use economic theories to construct estimators in empirical microeconomics that perform well when the theories' empirical implications are approximately correct, but perform no worse than unrestricted estimators if the theories' implications do not hold. We describe a construction of such estimators using the empirical Bayes paradigm. We implement this construction in various settings, including labor demand and wage inequality, and estimation of consumer demand. We provide theoretical characterizations of the behavior of the proposed estimators, and evaluate them using Monte Carlo simulations. 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.