Working Paper: NBER ID: w13357
Authors: A Craig Burnside
Abstract: The risk factors in many consumption-based asset pricing models display statistically weak correlation with the returns being priced. Some GMM-based procedures used to test these models have very low power to reject proposed stochastic discount factors (SDFs) when they are misspecified and the covariance matrix of the asset returns with the risk factors has less than full column rank. Consequently, these estimators provide potentially misleading positive assessments of the SDFs. Working with SDFs specified in terms of demeaned risk factors improves the performance of GMM but the power to reject misspecified SDFs may remain low. Two summary tests for failure of the rank condition have reasonable power, and lead to no Type I errors in Monte Carlo experiments.
Keywords: empirical asset pricing; stochastic discount factors; generalized method of moments; risk factors
JEL Codes: C33; F31; G12
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| SDFs specified using raw risk factors (C29) | estimated parameters converge in probability to a nonzero limit (C51) |
| estimated parameters converge in probability to a nonzero limit (C51) | SDF is uncorrelated with the returns (C29) |
| SDF is uncorrelated with the returns (C29) | associated risk factors help price the assets (G19) |
| R² measure of model fit converges in probability to 1 (C52) | strong fit of the model under this normalization (C52) |
| t-statistics associated with any parameter of the SDF diverge in probability to 1 (C46) | significance for at least one risk factor (I12) |
| rank condition fails (C29) | parameters of the SDF become asymptotically unidentified (C51) |
| failure of the rank condition (C62) | proposed consumption-based SDFs are false (C43) |
| failure of the rank condition and falsehood of the proposed SDF (C62) | lack of robustness across normalizations (C20) |
| normalization affects statistical significance of the parameters (C20) | significant differences observed between the two normalizations (C52) |