Assessing Misspecified Asset Pricing Models with Empirical Likelihood Estimators

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