Canada. Finite Sample Analysis of Two-Pass Cross-Sectional Regressions
Bibliographic record
Abstract
In this paper, we investigate finite sample properties of the two-pass cross-sectional regression (CSR) methodology, which is popular for estimation of risk premia and testing of beta pricing models. We find that the finite sample distribution of the estimated risk premium differs significantly from the asymptotic distribution. In particular, the risk premium estimates obtained from the second pass CSR of average returns on estimated betas can have serious bias even when the number of time series observations is reasonably large. In addition, the standard error of the estimated risk premium based on the asymptotic distribution overstates the actual standard error. A simple biasadjustment on the estimated zero-beta rate and risk premium is proposed and the adjusted version is shown to have better finite sample properties than the unadjusted one. In empirical asset pricing literature, the popular two-pass cross sectional regression (CSR) methodology developed by Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973) is often used for estimation of risk premia and testing of beta asset pricing models. Although there are many variations of this two-pass methodology, its basis setup always involves two steps. In the first pass, the betas of the test assets are estimated using the usual ordinary least squares (OLS) time series regression of returns on some common factors. In the second pass, the returns on test
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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 | 0.023 | 0.122 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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".