Nonparametric Welfare Analysis for Discrete Choice

32 Pages Posted: 13 Jun 2015

Date Written: November 17, 2014


We consider empirical measurement of equivalent/compensating variation resulting from price-change of a discrete good using individual-level data, when there is unobserved heterogeneity in preferences. We show that for binary and unordered multinomial choice, the marginal distributions of EV/CV can be expressed as simple closed-form functionals of conditional choice-probabilities under essentially unrestricted preference-distributions. These results hold even when the distribution/dimension of unobserved heterogeneity are neither known nor identified and utilities are neither quasi-linear nor parametrically specified. The welfare distributions take simple forms which are easy to compute in applications. In particular, average EV for a price-rise equals the change in average Marshallian consumer-surplus and is smaller than average CV for a normal good. These nonparametric point-identification results fail for ordered choice if the unit-price is identical for all alternatives, thereby providing a connection to Hausman-Newey's (2014) partial identification results for the limiting case of continuous choice.

Keywords: Binary Choice, Multinomial Choice, Ordered Choice, Applied Welfare Analysis, Compensating Varation, Equivalent Variation, Unobserved Heterogeneity, Unrestricted Heterogeneity, Nonparametric Identification.

JEL Classification: C14, C25, D12, D61

Suggested Citation

Bhattacharya, Debopam, Nonparametric Welfare Analysis for Discrete Choice (November 17, 2014). Econometrica, Vol. 83, No. 2, March 2015. Available at SSRN: or

Debopam Bhattacharya (Contact Author)

University of Cambridge ( email )

Sidgwick Site
Austin Robinson Building
Cambridge, CB3 9DD
United Kingdom

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