Addressing Endogeneity Using a Two-Stage Copula Generated Regressor Approach
Bibliographic record
Abstract
The ubiquitous presence of endogenous regressors presents a significant challenge when drawing causal inferences using observational data. The classical econometric method used to handle regressor endogeneity requires instrumental variables (IVs) that must satisfy the stringent condition of exclusion restriction, rendering it unfeasible in many settings. Herein, the authors propose a new IV-free method that uses copulas to address the endogeneity problem. Existing copula correction methods require nonnormal endogenous regressors: Normally or nearly normally distributed endogenous regressors cause model nonidentification or significant finite-sample bias. Furthermore, existing copula control function methods presume the independence of exogenous regressors and endogenous regressors. The authors' generalized two-stage copula endogeneity-correction (2sCOPE) method simultaneously relaxes the two key identification requirements while maintaining the Gaussian copula regressor-error dependence structure. They prove that under the Gaussian copula dependence structure, 2sCOPE yields consistent causal-effect estimates with correlated endogenous and exogenous regressors as well as normally distributed endogenous regressors. In addition to relaxing the identification requirements, 2sCOPE has superior finite-sample performance and addresses the significant finite-sample bias problem due to insufficient regressor nonnormality. Moreover, 2sCOPE employs generated regressors derived from existing regressors to control for endogeneity, and can thus considerably increase the ease and broaden the applicability of IV-free methods for handling regressor endogeneity. The authors further demonstrate 2sCOPE's performance using simulation studies and illustrate its use in an empirical application.
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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 | 0.024 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".