Working Paper: NBER ID: w16634
Authors: Craig Burnside
Abstract: When excess returns are used to estimate linear stochastic discount factor (SDF) models, researchers often adopt a normalization of the SDF that sets its mean to 1, or one that sets its intercept to 1. These normalizations are often treated as equivalent, but they are subtly different both in population, and in finite samples. Standard asymptotic inference relies on rank conditions that differ across the two normalizations, and which can fail to differing degrees. I first establish that failure of the rank conditions is a genuine concern for many well known SDF models in the literature. I also describe how failure of the rank conditions can affect inference, both in population and in finite samples. I propose using tests of the rank conditions not only as a diagnostic device, but also for model reduction. I show that this model reduction procedure has desirable size and power properties in a Monte Carlo experiment with a calibrated model.
Keywords: stochastic discount factor; asset pricing; model identification
JEL Codes: C3; G12
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| failure of rank conditions in SDF models (C52) | nonstandard asymptotic distributions (C46) |
| failure of rank conditions in SDF models (C52) | issues with inference (C20) |
| rank of the covariance matrix of excess returns (cov(re, f)) < number of risk factors (k) (C10) | model is not identified (C52) |
| rank of the covariance matrix of excess returns (cov(re, f)) = k and rank of the expected excess returns (ere(f)) = k (C10) | model is identified (C52) |
| model is identified (C52) | standard asymptotic properties apply (C51) |
| using rank tests as part of a model reduction procedure (C52) | eliminate models dominated by spurious factors (C52) |
| using rank tests as part of a model reduction procedure (C52) | improve inference (C20) |