We consider identiﬁcation in a “generalized regression model” (Han, 1987) for panel settings in which each observation can be associated with a “group” whose members are subject to a common unobserved shock. Common examples of groups include markets, schools or cities. The model is fully nonparametric and allows for the endogeneity of group-speciﬁc observables, which might include prices, policies, and/or treatments. The model features heterogeneous responses to observables and unobservables, and arbitrary heteroskedasticity. We provide suﬀicient conditions for full identiﬁcation of the model, as well as weaker conditions suﬀicient for identiﬁcation of the latent group eﬀects and the distribution of outcomes conditional on covariates and the group eﬀect.
Berry, Steven T. and Haile, Philip A., "Identification of a Heterogeneous Generalized Regression Model with Group Effects" (2009). Cowles Foundation Discussion Papers. 2056.