Heteroskedasticity and Spatiotemporal Dependence Robust Inference for Linear Panel Models with Fixed Effects
Bibliographic record
Abstract
This paper studies robust inference for linear panel models with fixed effects in the presence of heteroskedasticity and spatiotemporal dependence of unknown forms. We propose a bivariate kernel covariance estimator, which is flexible to nest existing estimators as special cases with certain choices of bandwidths. For distributional approximations, we consider two different types of asymptotics. When the level of smoothing is assumed to increase with the sample size, the proposed estimator is consistent and the associated Wald statistic converges to a χ2 distribution. We show that our covariance estimator improves upon existing estimators in terms of robustness and efficiency. When we assume the level of smoothing to be held fixed, the covariance estimator has a random limit and we show by asymptotic expansion that the limiting distribution of the test statistic depends on the bandwidth parameters, the kernel function, and the number of restrictions being tested. As this distribution is nonstandard, we establish the validity of an F-approximation to this distribution, which greatly facilitates the test. For optimal bandwidth selection, we propose a procedure based on the upper bound of asymptotic mean square error criterion. The flexibility of our estimator and proposed bandwidth selection procedure make our estimator adaptive to the dependence structure in data. This adaptiveness automates the selection of covariance estimator. That is, our estimator reduces to the existing estimators which are designed to cope with the particular dependence structures. Simulation results show that the F-approximation and the adaptiveness work reasonably well.
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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 | 0.014 | 0.071 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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".