The Envelope Theorem and Identification: Implications for Some Empirical Work in Finance and Economics

Abstract

This paper is about identification and endogeneity in models that estimate the effects of instrument choice on performance (or wealth or welfare) in situations where the instruments are chosen to optimize performance. Such models occur frequently in corporate finance, analysis of happiness and effectiveness of economic policy. The instruments are endogenous because of the optimization. We suggest an impossibility theorem: that identification is not possible for this class of models, and that in a well-specified model the expected values of estimated impacts of instruments choices will be exactly zero. This is a direct application of the envelope theorem. We follow with four applications to empirical work in economics and finance.