Essays on weak identification, model selection and hypothesis testing in econometrics
Bibliographic record
Abstract
This thesis makes contributions to weak identification, model selection and hypothesis testing in econometrics.It consists of the following essays.In Chapter 1, we study likelihood-based inference in models with possible identification failure.The results rely heavily on the properties of the mapping from structural parameters to generalized reduced-form parameters (which are identified by construction).We establish an asymptotic chi-square bound on the likelihood ratio (LR) statistic for testing restrictions on the possibly unidentified structural parameters with degrees of freedom equal to the dimension of the reduced form parameter vector through which the tested parameters enter the likelihood function.We also propose pivotal C(α)-type statistics that are robust to potential identification failure and are flexible in incorporating a wide class of estimators of the (strongly identified) nuisance parameters.Furthermore, we develop a generalized version of the classical Anderson-Rubin (AR)-type statistic in linear simultaneous equations and an identification-robust pretest-based inference procedure.Our simulations suggest that the likelihood-based tests control the level more accurately and the generalized AR test exhibits good power when compared to their identification-robust minimum distance counterparts.Finally, the proposed methods are used for inference in the hybrid New Keynesian Phillips Curve (NKPC) model.In Chapter 2, we study the invariance properties of various test criteria which have been proposed for hypothesis testing in the context of incompletely specified models, such as models which are formulated in terms of estimating functions (Godambe, 1960, Ann.Math.Stat.) or moment conditions and are estimated by generalized method of moments (GMM) procedures (Hansen, 1982, Econometrica), and models estimated by pseudo-likelihood (Gouriéroux, Monfort and Trognon, 1984, Econometrica) and M-estimation methods.The invariance properties considered include invariance to (possibly nonlinear) hypothesis reformulations and reparameterizations.The test statistics examined include Wald-type, LRtype, LM-type, score-type, and C(α)-type criteria.Extending the approach used in Dagenais and Dufour (1991, Econometrica), we show first that all these test statistics except the Wald-type ones are invariant to equivalent hypothesis reformulations (under usual regularity conditions), but all five of them are not generally invariant to model reparameterizations, including measurement unit changes in nonlinear models.In other words, testing i I am very grateful to my advisors, Jean-Marie Dufour and Victoria Zinde-Walsh for their guidance and support through my graduate years.I have benefitted greatly from Professor Dufour's immense knowledge, scholarly wisdom, vision and attitude toward research.Being his student has been an eye-opening experience.Professor Zinde-Walsh has always kept her office open to me and offered generous support.I would like to
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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 | 0.020 | 0.068 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.011 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.008 |
| Insufficient payload (model declined to judge) | 0.006 | 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".