EXPRESS: Correcting omitted-variable bias without instruments: An ICA-based alternative to Gaussian copula methods

This paper proposes an instrument-free correction for omitted-variable bias and overcomes a key limitation of Gaussian copula control function (GCCF) approaches. Omitted-variable bias is the most common source of endogeneity in marketing, and many articles apply GCCF to address it. Yet GCCF require a nonlinear regressor-error relation, whereas textbooks assume linear, additive relationships between regressors and omitted variables. The authors prove that GCCF is biased in classical omitted-variable settings. Extant articles that address omitted-variables with GCCF also show language cues implicitly assuming linear relationships, which invalidate the use of GCCF. The proposed endogeneity correction is tailored to this prominent case, utilizing independent component analysis (ICA). It assumes a latent normally distributed component that additively influences both the endogenous regressor and the error. This can be interpreted as the sum of omitted variables, which, according to the Central Limit Theorem, add up to a normal distribution. Through ICA, this component is identified and extracted from the endogenous regressor, rendering the regression model free of endogeneity and enabling causal inference. The paper proves that the model is point-identified despite endogeneity due to omitted variables, that the proposed estimator is consistent and asymptotically normal, and that Jackknife resampling yields valid standard errors.