Applying Benford’s Law to Examine the Quality of Reported Income Numbers of Unlisted Firms
Bibliographic record
Abstract
The present study makes an attempt to examine the quality of reported income numbers of unlisted firms in India. The Benford’s Law is applied to examine the digital occurrence of reported income numbers of unlisted firms. The analysis is based on 43,996 reported annual income numbers of 22,147 sample firms during the financial years from 2000-01 to 2011-12. Further, the results are analyzed under four different scenarios viz., ownership, size, age and nature of industry. The empirical results show that the observed proportionate occurrence of zero is significantly less than the expected proportionate occurrence. These results are contrary to the findings of the related studies of listed companies. The results indicate lower quality of reported income numbers of unlisted firms. Based on the scenario analysis, the empirical results indicate that the proportionate occurrence of second single digits of state-owned unlisted firms confirm the Benford’s Law. The present study contributes to the literature by examining the quality of reported income numbers of unlisted firms using the Benford’s Law.
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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 | 0.009 | 0.072 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.007 | 0.011 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".