Debopam Bhattacharya (Oxford)

“Nonparametric Welfare Analysis for Discrete Choice”

Abstract

We consider empirical measurement of exact equivalent/compensating variation resulting from price-change of a discrete good, using individual-level data. Our set-up comprises utility functions which include unobserved heterogeneity of unknown dimension and are not required to be quasi-linear, parametrically specified or smooth — thus allowing for extremely general preference-distributions. We show that for binary and multinomial choice, the marginal distribution of EV/CV are nonparametrically point-identified solely from average demand-functions, even when the distribution and dimension of unobserved heterogeneity are neither specified nor identified. We express welfare distributions as closed-form functionals of average demand and show that average EV for price-rise equals the change in average consumer surplus and is smaller than average CV for a normal good. Our point-identification results for multinomial choice complement Hausman-Newey’s (2013) partial identification results for welfare distributions resulting from price change of a continuous good.