Nonlinear Random Coefficients and Preference Heterogeneity

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Standard random coefficients models are either linear in regressors, or equal a transformation of a linear index of regressors (e.g., random coefficient logit models). In contrast, this paper shows identification of, and consistent estimators for, general nonlinear random coefficients models with unknown parameters. For example, we consider a model that includes interaction terms in regressors and nonlinear transformations of regressors, where each regressor has a random coefficient, and the joint distribution of the random coefficients is unknown. We then model unobserved preference heterogeneity in consumer demand as utility functions with random Barten scales. These Barten scales appear as random coefficients in nonlinear demand equations. Using Canadian data, we compare estimated energy demand functions with and without random Barten scales. We find that unobserved preference heterogeneity substantially affects the estimated consumer surplus costs of an energy tax.