How to use economic theory to improve estimators

This appendix provides some additional discussion and results, supplementing the manuscript of “How to use economic theory to improve estimators.” In Section A of this appendix,we consider two additional applications of our proposed approach, to a general equilibrium model of financial markets, and to structural models of (consumer) preferences. Our theoretical results suggest that the proposed empirical Bayes estimators should uniformly outperform unrestricted estimators and outperform structural (restricted) estimators for most parameter values. In Section C, we discuss some Monte Carlo simulations which do indeed confirm these predictions. In section 3.1 of the manuscript we consider estimation of labor demand systems, shrinking toward the predictions of a CES production function model. In Section D of this appendix, we review CES production functions and derive from them the wage regressions considered in the manuscript. In section 3.3 of the manuscript, we consider empirical Bayes estimators for choice probabilities, where estimation of the hyper-parameters involves maximization of a Dirichlet-multinomial likelihood subject to a set of linear inequality constraints. In Section E of this appendix, we discuss methods for the numerical solution of such maximization problems.