Correcting Endogeneity via Nonparametric Copula Control Functions
Bibliographic record
Abstract
We propose a new framework that addresses endogenous regressors using a novel conditional copula endogeneity model to capture the regressor-error dependence unexplained by exogenous regressors.Building on the model, we develop a two-stage nonparametric copula control function approach (2sCOPEnp) for endogeneity correction without relying on instrumental variables.The method relaxes the restrictive assumption of the Gaussian copula regressor-error dependence structure and eliminates the need to model regressors.It unifies and generalizes existing copulabased endogeneity correction methods, while minimizing assumptions about the first-stage auxiliary dependence structures among regressors.Specifically, 2sCOPEnp constructs control functions using nonparametric estimates of the conditional cumulative distribution functions (CDFs) of endogenous regressors given exogenous variables, enhancing the accuracy and robustness of endogeneity correction.Unlike existing copula control function methods, 2sCOPEnp applies to broader dependence structures and can handle discrete endogenous regressors (e.g., binary or count) by leveraging relevant exogenous control variables to smooth discrete conditional CDFs.We demonstrate the robustness and broad applicability of the proposed method compared to existing copula-based endogeneity correction methods.Simulation studies demonstrate that the proposed method outperforms existing methods.We illustrate its usage and advantages in two empirical examples: store sales estimation and return to education.
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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) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".