Abstract
Consumption-based asset pricing and other areas have been a challenge to existing inference theories. In this paper, we develop a classical moment-based inference framework with Bayesian properties to tackle this challenge. We prove that there exists an intensity distribution of the solutions to empirical moment conditions over the parameter space. We approximate it thanks to the empirical saddlepoint (ESP) technique. We call the result the ESP intensity. A higher ESP intensity value indicates a higher estimated probability weight of being a solution to the empirical moment conditions. We propose to use the ESP intensity in the same way as posteriors are used in Bayesian inference to obtain point estimators, confidence regions, and define tests. We call this the ESP approach, and explain the rationale behind it. We prove the counterpart of Doob's theorem (i.e., consistency) and Bernstein-von Mises' theorem (i.e., asymptotic normality) for the ESP intensity. The ESP approach provides a unique answer to multiple concerns especially acute in consumption-based asset pricing, such as lack of identification and multiple hypothesis testing on the same data set. It also sheds a new light on consumption-based asset pricing, and, in particular, indicates that consumption-based asset pricing theory is more consistent with data than existing inference approaches suggest.