Why not consider that being absolutely poor is worse than being only relatively poor?
Forthcoming in Journal of Public Economics
The properties of income poverty measures based on absolute poverty lines have been extensively studied in the model of Sen (1976). In contrast, poverty measures based on relativist poverty lines have never been rigorously studied. This issue is not merely theoretical: mainstream relativist measures are increasingly used in spite of their counterintuitive behavior. Importantly, these measures deny a minimal priority to individuals in deep poverty. This paper proposes a non-trivial extension of Sen’s model designed for the study of relativist measures. This extension relies on the introduction of an ethical ordering, a form of other-regarding preferences inspired from the Behavioral literature. The two major results are (I) the characterization of a family of additive poverty indices generalizing the result of Foster and Shorrocks (1991) and (II) the characterization of an index guaranteeing a minimal priority to individuals in deep poverty (Decerf, 2017). The latter result constitutes the first ever characterization of a relativist measure.
In constrained school choice mechanisms, students can only rank a subset of the schools they could potentially access. We characterize dominant and undominated strategies in the constrained Boston (BOS) and deferred acceptance (DA) mechanisms. Using our characterization of dominant strategies we show that in constrained DA, the single tie-breaking rule outperforms the multiple tie-breaking rule in terms of both manipulability and stability. We also show that DA is less manipulable than constrained BOS in the sense of Arribillaga and Massó (2015). Using our characterizations of undominated strategies, we derive advice for the students and show that more strategies can be excluded on the basis of dominance in constrained DA than in constrained BOS.
Riedel and Sass (2013) study complete information normal form games in which ambiguity averse players use ambiguous randomization strategies, in addition to pure and mixed strategies. The solution concept they propose, the Ellsberg equilibrium, is a coarsening of the classical Nash equilibrium. We provide a foundation of the new equilibrium concept in the spirit of Harsanyi. We prove an extension of the Purification Theorem for 2×2 normal form games. Our result implies that any Ellsberg equilibrium of such game is the limit case of a mixed strategy equilibrium in a disturbed version of the game for which payoffs are ambiguously disturbed.
Evolution of income poverty under unequal growth: Settling the dispute between absolutists and relativists.
(with Mery Ferrando)
We study the impact on income poverty of unequal growth experienced in the US over 1989-2013 using a new measure of poverty. This measure accounts for both the relative and absolute aspects of income poverty. It depends on a key normative parameter that defines how much weight is given to each of these two aspects. The preferred parameter value for an absolutist moral observer lies at one extreme of the parameter range, whereas that of a relativist observer lies at the other extreme. Under unequal growth, absolutists often disagree with relativists. The former typically consider that poverty decreases and the latter that poverty increases. We first develop simple theoretical conditions under which the poverty judgments obtained with our measure are fully robust to the choice of its normative parameter. For non-robust cases, we derive a simple formula returning the threshold parameter value at which the judgment is reversed. We then apply our measure to study the evolution of poverty in the US over the recent period of unequal growth. Interestingly, poverty judgments are largely robust to the choice of the normative parameter.
In Europe poverty is usually measured with the at-risk-of-poverty indicator which defines the poverty threshold as 60 per cent of national median income. With this indicator, poverty seems to be lower in some ‘poor’ EU countries than in some of the richest EU Member States. Also, when the median income changes quickly, the evolution of poverty as shown by the indicator can be counterintuitive, for instance resulting in stagnation or even a decrease in poverty when median incomes fall and living conditions of the poor deteriorate. In this article we propose a new poverty indicator, the Poverty Gap Ratio with priority to the pan-European poor (PGR-PAN) which is not subject to these limitations. On the basis of EU-SILC data we show that our indicator results in results that are in better agreement with intuitive notions about poverty within the EU and captures more adequately changes as well as cross-national differences in living standards.
We introduce a new criterion to compare the properties of mechanisms when the solution concept used induces multiple solutions. Our criterion generalizes previous approaches in the literature. We use our criterion to compare the stability of constrained versions of the Boston (BOS) and deferred acceptance (DA) school choice mechanisms in which students can only rank a subset of the schools they could potentially access. When students play a Nash equilibrium, we show that there is a stability cost to increasing the number of schools students can rank in DA. On the other hand, when students only play undominated strategies, increasing the number of schools students can rank increases stability. We find similar results for BOS. We also compare BOS and DA. Whatever the number of schools students can rank, we find that BOS is more stable than DA in Nash equilibrium, but less stable in undominated strategies.
WORK IN PROGRESS:
Fair inheritance taxation (with François Maniquet)
Poverty measurement and the mortality paradox (with J.M. Baland, G. Cassan, C. Guirkinger and Y. Luo)