COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1732 Identification of a Heterogeneous Generalized Regression Model with Group Effects Steven T. Berry and Philip A. Haile October 2009 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. |
