We compare distributions of body mass index (BMI) categories among genders in France, the United States, and the United Kingdom on the basis of efficiency and inequality considerations. The new normative criteria that we propose are well suited to the ordinal nature of this variable. Our empirical results, which are supported by robust statistical inference, are twofold. First, BMI categories for the two genders are better distributed in France than in the UK, and in the UK than in the US. Second, BMI categories happen to be more equally distributed among men than among women in all three countries.
We establish an equivalence between three criteria for comparing distributions of an ordinal variable taking finitely many values. The first criterion is the possibility of going from one distribution to the other by a finite sequence of increments and/or Hammond transfers. The latter transfers are like the Pigou–Dalton ones, but without the requirement that the amount transferred be fixed. The second criterion is the unanimity of all comparisons of the distributions performed by a class of additively separable social evaluation functions. The third criterion is a new statistical test based on a weighted recursion of the cumulative distribution. We also identify an exact test for the possibility of going from one distribution to another by a finite sequence of Hammond transfers only. An illustration of the usefulness of our approach for evaluating distributions of self-reported happiness level is also provided.
What would be the analogue of the Lorenz quasi-ordering when the variable of interest is continuous and of a purely ordinal nature? We argue that it is possible to derive such a criterion by substituting for the Pigou-Dalton transfer used in the standard inequality literature what we refer to as a Hammond progressive transfer. According to this criterion, one distribution of utilities is considered to be less unequal than another if it is judged better by both the lexicographic extensions of the maximin and the minimax, henceforth referred to as the leximin and the antileximax, respectively. If one imposes in addition that an increase in someone’s utility makes the society better off, then one is left with the leximin, while the requirement that society welfare increases as the result of a decrease of one person’s utility gives the antileximax criterion. Incidentally, the paper provides an alternative and simple characterisation of the leximin principle widely used in the social choice and welfare literature.
The widely used Oaxaca decomposition applies to linear models. Extending it to commonly used nonlinear models such as duration models is not straightforward. This paper shows that the original decomposition that uses a linear model can also be obtained by an application of the mean value theorem. By extension, this basis provides a means of obtaining a decomposition formula which applies to nonlinear models which are continuous functions. The detailed decomposition of the explained component is expressed in terms of what are usually referred to as marginal effects. Explicit formulae are provided for the decomposition of some nonlinear models commonly used in applied econometrics including binary choice, duration and Box-Cox models.