TESTING LINEAR RESTRICTIONS ON COINTEGRATING VECTORS: SIZES AND POWERS OF WALD AND LIKELIHOOD RATIO TESTS IN FINITE SAMPLES
Bibliographic record
Abstract
The Wald test for linear restrictions on cointegrating vectors is compared in finite samples using the Monte Carlo method. The Wald test is calculated within the vector error-correction based estimation methods of Bewley, Orden, Yang, and Fisher (1994, Journal of Econometrics 64, 3–27) and of Johansen (1991, Econometrica 59, 1551–1580), the canonical cointegration method of Park (1992, Econometrica 60, 119–143), the dynamic ordinary least squares method of Phillips and Loretan (1991, Review of Economic Studies 58, 407–436), Saikkonen (1991, Econometric Theory 7, 1–21), and Stock and Watson (1993, Econometrica 61, 783–820), the fully modified ordinary least squares method of Phillips and Hansen (1990, Review of Economic Studies 57, 99–125), and the band spectral techniques of Phillips (1991, in W. Barnett, J. Powell, & G. E. Tauchen (eds.), Nonparametric and Semiparametric Methods in Economics and Statistics , pp. 413–435). The Wald test performance is also compared to that of the likelihood ratio test suggested by Johansen and Juselius (1990, Oxford Bulletin of Economics and Statistics 52, 169–210) and to a Bartlett correction of that test as proposed by Johansen (1998, A Small Sample Test for Tests of Hypotheses on Cointegrating Vectors, European University Institute).
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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 | 0.127 | 0.571 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.005 | 0.005 |
| Bibliometrics | 0.013 | 0.010 |
| Science and technology studies | 0.001 | 0.012 |
| Scholarly communication | 0.007 | 0.027 |
| Open science | 0.004 | 0.006 |
| Research integrity | 0.005 | 0.005 |
| Insufficient payload (model declined to judge) | 0.012 | 0.002 |
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".