Approximating an Infinite Horizon Model in the Presence of Optimal Experimentation
Bibliographic record
Abstract
In an recent article Amman and Tucci (2020) make a comparison of the two dominant approaches for solving models with optimal experimentation in economics; the value function approach and an approximation approach. The approximation approach goes back to engineering literature in the 1970ties (cf. Tse & Bar-Shalom, 1973). Kendrick (1981) introduces this approach in economics. By using the same model and dataset as in Beck and Wieland (2002), Amman and Tucci conclude that differences may be small between the both approaches. In the previous paper we did not present the derivation of the approximation approach for this class of models. Hence, here we will present all derivations of the approximation approach for the case where there is an infinite horizon as is most common in economic models. By presenting the derivations, a better understanding and insight is obtained by the reader on how the value function is adequately approximated.
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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 | 0.006 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.004 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 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".