Assessing Misspecified Asset Pricing Models with Empirical Likelihood Estimators

44 Pages Posted: 16 Feb 2009 Last revised: 1 Jun 2021

See all articles by Caio Almeida

Caio Almeida

Princeton University

René Garcia

Université de Montréal - CIREQ - Département de sciences économiques; University of Montreal

Multiple version iconThere are 2 versions of this paper

Date Written: February 13, 2009


Hansen and Jagannathan (1997) compare misspecified asset pricing models based on least-square projections on a family of admissible stochastic discount factors. We extend their fundamental contribution by considering Minimum Discrepancy (MD) projections where misspecification is measured by convex functions that can explicitly take into account higher moments of asset returns. The MD problems are solved on dual spaces with the interpretation of optimal portfolio problems based on HARA utility functions, producing a family of estimators that captures the least-square problem as a particular case. We use our proposed methodology to test the Consumption Asset Pricing Model and illustrate, under several different discrepancy functions and regions of the parametric space, the relation between the parametric proxy model, and the closest admissible SDF. On the estimation problem, not surprisingly, all MD estimators clearly reject the CCAPM model. However, some of these estimators lead to admissible SDFs that are very distinct from the one implied by the least-square solution. By their pricing implications, this rich set of optimal MD SDFs represent useful tools to diagnose missing factors in asset pricing models.

Keywords: Stochastic Discount Factor, Euler Equations, Generalized Minimum Contrast Estimators, Model Selection, Cressie Read Discrepancies

JEL Classification: C1,C5,G1

Suggested Citation

Almeida, Caio and Garcia, René, Assessing Misspecified Asset Pricing Models with Empirical Likelihood Estimators (February 13, 2009). EFA 2009 Bergen Meetings Paper, Journal of Econometrics, Vol. 170, No. 2, 2012, Available at SSRN: or

Caio Almeida

Princeton University ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States

René Garcia (Contact Author)

Université de Montréal - CIREQ - Département de sciences économiques ( email )

C.P. 6128, succursale Centre-Ville
3150, rue Jean-Brillant, bureau C-6027
Montreal, Quebec H3C 3J7
514-985-4014 (Phone)

University of Montreal ( email )

United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics