Non-parametric well-being comparisons

Abstract

We study the problem of making interpersonal well-being comparisons when individuals have heterogeneous -possibly incomplete -preferences. We present a robust -also incompletecriterion for well-being comparisons that states that one individual is better off than another one if the intersection between the extended upper contour set of the better off individual and the extended lower contour set of the worse off individual is empty. We implement the criterion in the consumption-health space using an online survey with 2,260 respondents in the United States to investigate how incomplete the resulting interpersonal well-being comparison is. To chart the contour sets of the respondents, we propose a new "adaptive bisectional dichotomous choice" (ABDC) procedure that is based on a limited number of dichotomous choices and some mild nonparametric assumptions on the preferences. While the ABDC procedure does not reject that the preferences of a large majority of the respondents satisfy these non-parametric assumptions, it has sufficient power to reject several standard parametric assumptions such as linearity or Cobb-Douglas preferences for an overwhelming number of respondents. Finally, we find that about one fifth of all pairs of respondents can be ranked in a robust way with the proposed criterion. A more complete version of the criterion is able to rank more than half of the pairs.