Berkson errors are commonplace in empirical microeconomics. In consumer demand, this form of measurement error occurs when the price an individual pays is measured by the (weighted) average price paid by individuals in a group (e.g., a county) rather than the true transaction price. We show the importance of Berkson errors for demand estimation with nonseparable unobserved heterogeneity. We develop a consistent estimator using external information on the true price distribution. Examining gasoline demand in the United States, we document substantial within-market price variability. Accounting for Berkson errors is quantitatively important. Imposing the Slutsky shape constraint reduces sensitivity to Berkson errors.

We measure selection among high-skilled emigrants from Germany using predicted earnings. Migrants to less equal countries are positively selected relative to nonmigrants, while migrants to more equal countries are negatively selected, consistent with the prediction in Borjas (1987). Positive selection to less equal countries reflects university quality and grades, and negative selection to more equal countries reflects university subject and gender. Migrants to the United States are highly positively selected and concentrated in STEM fields. Our results highlight the relevance of the Borjas model for high-skilled individuals when credit constraints and other migration barriers are unlikely to be binding.

We present a method for consistent nonparametric estimation of a demand function with nonseparable unobserved taste heterogeneity subject to the shape restriction implied by the Slutsky inequality. We use the method to estimate gasoline demand in the United States. The results reveal differences in behavior between heavy and moderate gasoline users. They also reveal variation in the responsiveness of demand to plausible changes in prices across the income distribution. We extend our estimation method to permit endogeneity of prices. The empirical results illustrate the improvements in finite-sample performance of a nonparametric estimator from imposing shape restrictions based on economic theory.