Bibliographic record
Abstract
"A popular measure to assess the likelihood of extreme and rare events—such as economic crises—is the tail index. Because of the small sample of extreme events, measuring the tail index precisely is difficult. Measuring changes to this likelihood over time is even more difficult. Under certain assumptions, using the variation across the population—a cross-section—at a given time offers a way to alleviate the problem posed by a small sample. For instance, to measure the tail index for a stock market, you could use the returns of the individual firms to imply the likelihood of a tail event for the market at a given time. Repeating this exercise for each time period produces a measure of the tail index over time. We show that these measurements contain a bias that fluctuates over time. Our theoretical results reveal that the bias: • results from trivial fluctuations that are common among the cross-section observations • moves the tail index estimates in the opposite direction for events that are extremely negative or extremely positive • is increasing in the number of extreme observations used in the measurement because the added observations are less extreme We provide two simple remedies. First, we devise a new estimator that averages the estimate for the extreme negative and positive events. Averaging the two estimates should cancel the bias present in both tails. Second, we subtract the cross-sectional average from each observation and repeat this at each point in time. To test for the presence, direction and size of the bias, we use monthly US stock returns and annual US Census county population data. We find that the bias plays an important role for stock returns, especially during crisis periods. However, the bias plays a small role for county population data due to the lack of common fluctuations in the population across counties."
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.043 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.026 | 0.004 |
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".