Using Taylor’s Law to Estimate Variance in Annual Unemployment by State
Bibliographic record
Abstract
Taylor's law (TL) is a widely observed empirical pattern that relates variance to the the mean of a set of non-negative measurements via an approximate power function: varianceg ≈ a × (meang) b , where g indexes the group of measurements.While widely observed, we have not found an application of TL to annualized state unemployment data.Thus, in this paper, we construct a model using TL to estimate of the variance in the 2018 annualized number of employed by state using the mean number.Our "in-sample" set consists of 38 states with 25 or more counties.We then test the model by estimating the variance in the 2018 annualized number of employed by state using the mean number.Our "out-of-sample" test set consists of the 12 states with fewer than 25 counties.Variance in the numbers of annualized unemployed by county within each state is important because it is a summary measure of how disproportionate unemployment is spread across counties.This suggests that policy-based efforts to reduce unemployment inequality among counties in a given state might better serve a state with a high mean level of county unemployment than a state with a low mean level of county unemployment because Taylor's Law shows that there is a higher level of unemployment inequality in the former than in the latter.
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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 | 0.005 | 0.027 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".