Handling Endogenous Marketing Mix Regressors in Correlated Heterogeneous Panels with Copula Augmented Mean Group Estimation

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.