Applied Welfare Analysis for Discrete Choice with Interval-Data on Income

50 Pages Posted: 23 Apr 2018 Last revised: 2 Apr 2019

See all articles by Ying-Ying Lee

Ying-Ying Lee

University of California, Irvine - Department of Economics

Debopam Bhattacharya

University of Cambridge

Date Written: January 1, 2019


This paper concerns empirical measurement of Hicksian consumer welfare under interval-reported income. Bhattacharya (2015, 2018a) has shown that for discrete choice, welfare distributions resulting from a hypothetical price-change can be expressed as closed-form transformations of choice probabilities. However, when income is interval-reported, as is the case in many surveys, the choice probabilities, and hence welfare distributions are not point-identified. We derive bounds on average welfare in such scenarios under the assumption of a normal good. A finding of independent interest is a set of Slutsky-like shape restrictions which are linear in average demand, unlike those for continuous choice. A parametric specification of choice probabilities facilitates imposition of these Slutsky conditions, and leads to computationally simple inference for the partially identified features of welfare. In particular, the estimand is shown to be directionally differentiable, so that recently developed bootstrap methods can be applied for inference. Under mis-specification, our results provide a "best parametric approximation" to demand and welfare. These methods can be used for inference in more general settings where a class of set-identified functions satisfy linear inequality restrictions, and one wishes to conduct inference on functionals thereof. We illustrate our theoretical results using a simulation exercise based on a real dataset where actual income is observed. We artificially introduce interval-censoring of income, calculate bounds for the average welfare effects of a price-subsidy using our methods, and find that they perform favorably in comparison with estimates obtained using actual income.

Keywords: Binary Choice, Equivalent Variation, Interval-Data, Slutsky Restriction, Set Identified Function, Inference on Functionals, Directional Differentiability

JEL Classification: C14, C25, C25

Suggested Citation

Lee, Ying-Ying and Bhattacharya, Debopam, Applied Welfare Analysis for Discrete Choice with Interval-Data on Income (January 1, 2019). Available at SSRN: or

Ying-Ying Lee (Contact Author)

University of California, Irvine - Department of Economics ( email )

3151 Social Science Plaza
Irvine, CA 92697-5100
United States

Debopam Bhattacharya

University of Cambridge ( email )

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

Register to save articles to
your library


Paper statistics

Abstract Views
PlumX Metrics