A Practical Guide to Endogeneity Correction Using Copulas
Bibliographic record
Abstract
Causal inference is of central interests in many empirical applications yet often challenging because of the presence of endogenous regressors.The classical approach to the problem requires using instrumental variables that must satisfy the stringent condition of exclusion restriction.At the forefront of recent research, instrument-free copula methods have been increasingly used to handle endogenous regressors.This article aims to provide a practical guide for how to handle endogeneity using copulas.The authors give an overview of copula endogeneity correction and its usage in marketing research, discuss recent advances that broaden the understanding, applicability, and robustness of copula correction, and examine implementation challenges of copula correction such as construction of copula control functions and handling of higher-order terms of endogenous regressors.To facilitate the appropriate usage of copula correction, the authors detail a process of checking data requirements and identification assumptions to determine when and how to use copula correction methods, and illustrate its usage using empirical examples.
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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 | 0.007 | 0.041 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.048 | 0.026 |
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".