On the Empirical Saddlepoint Approximation with Application to Asset Pricing

Abstract

Moment-based estimation often yields instable estimates, such as the RRA (relative risk aversion) estimate in consumption-based asset pricing. This paper establishes novel theoretical results for the ESP (empirical saddlepoint) approximation, and then use them to investigate this instability. We prove that there exists an intensity distribution of the solutions to empirical moment conditions, and approximate it with the integral of the ESP approximation, calling the result the ESP intensity. Global consistency and asymptotic normality of the ESP intensity are proved. The application provides an explanation for the instability of the RRA estimates reported in the literature (fat and long right tail of the ESP approximation), and it suggests that consumption-based asset-pricing theory is more consistent with data than standard inference approaches indicate.

Keywords: Saddlepoint approximation; Moment-based estimation; Multiple roots to estimating equations; Schmetterer-Jennrich lemma; Empirical consumption-based asset pricing

JEL Classification: C1, G12