Empirical Asset Pricing: The Beta Method versus the Stochastic Discount Factor Method,” working paper
Bibliographic record
Abstract
Canada. In a simple standardized factor model, Kan and Zhou (1999) show that the estimate of the parameter in the stochastic discount factor (SDF) method is much less efficient than the risk premium estimate in the beta method, when both are estimated using the generalized method of moments (GMM). Jagannathan and Wang (2001) and Cochrane (2000a,b) debate this conclusion in a nonstandardized factor model where the factor mean and variance have to be estimated, but their analysis relies on joint normality assumption for both the asset returns and the factors in an unconditional model. We make four contributions in this paper. First, we show that once the restrictive normality assumption is relaxed, the variance of the GMM estimate of the SDF parameter is highly sensitive to factor skewness and kurtosis whereas the variance of the GMM estimate of the risk premium is not. Second, we show that provide results for the general case and show that inference about the SDF parameter is highly sensitive to factor skewness and kurtosis, whereas inference about the factor premium is not. Therefore, even when the mean and the variance of the factor are unknown, inference based on the SDF parameter can still be less reliable
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.042 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".