Handling Endogenous Marketing Mix Regressors in Correlated Heterogeneous Panels with Copula Augmented Mean Group Estimation
Bibliographic record
Abstract
Endogeneity is a primary concern when evaluating causal effects using observational panel data.While unit-specific intercepts control for unobserved time-invariant confounders, dependence between (i) regressors (e.g., marketing mix strategy of interests) and the current error term (regressor endogeneity) and/or between (ii) regressors and heterogeneous slopes (slope endogeneity) can introduce significant endogeneity bias.This paper proposes a two-stage copula endogeneity correction mean group (2sCOPE-MG) estimator for panel models, simultaneously addressing both endogeneity concerns.We generalize the IV-free copula control function, employing a general location Gaussian copula that effectively captures the panel structure.The heterogeneous coefficients are treated as unit-specific parameters without distributional assumptions.Consequently, 2sCOPE-MG allows for arbitrary dependence structure between heterogeneous coefficients and regressors.Compared with Haschka (2022), 2sCOPE-MG is more general (permitting correlated random coefficients), more robust (allowing for heterogeneity in the variance-covariance matrix of the Gaussian copula), and easier to implement.We extend 2sCOPE-MG to dynamic panels, where intertemporal dependence in the outcome process can be suitably captured.We derive its asymptotic properties and an analytical variance formula for inference without bootstrapping.We demonstrate its usage by simulations and a marketing mix response application across 21 categories accounting for both endogeneities in store-sales panel data.
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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 | 0.037 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".