Identification-Robust Factor Pricing: Canadian Evidence
Bibliographic record
Abstract
We analyze factor models based on the Arbitrage Pricing Theory (APT). using identification-robust inference methods. Such models involve nonlinear reduced-rank restrictions whose identification may raise serious non-regularities and lead to a failure of standard asymptotic theory. We build confidence sets for structural parameters based on inverting Hotelling-type pivotal statistics. These confidence sets provide much more information than the corresponding tests. Our approach may be interpreted as a multivariate extension of the Fieller method for inference on mean ratios. We also introduce a formal definition for a redundant factor linking the presence of such factors to unbounded confidence sets, and we document their perverse effects on minimum-root-based model tests. Results are applied to multifactor asset-pricing models with Canadian data, the Fama-French-Carhart benchmarks and monthly returns of 25 portfolios from 1991 to 2010. Despite evidence of weak identification, several findings deserve notice when data are analyzed over ten-year subperiods. With equally weighted portfolios, the three-factor model is rejected before 2000, but weakly supported thereafter. In contrast, the three-factor model is not rejected with value-weighted portfolios. Interestingly in this case, the market factor is priced before 2000 along with size, while both Fama-French factors are priced thereafter. The momentum factor severely compromises identification, which calls for caution in interpreting existing work documenting momentum effects on the Canadian market. This empirical analysis underscores the practical usefulness of our analytical confidence sets.
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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 | 0.075 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.009 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 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".