Working papers

Abstract We provide an axiomatic characterization of a family of criteria for comparing distributions of individuals into categories. The characterized family consists in all rankings that compare distributions based on the expectation of the pairwise dissimilarities between categories for some numerical valuation of these dissimilarities. In the context of biological diversity measurement, such criteria are sometimes referred to as Rao (1982) quadratic entropy. Beside the ordinal characterization of the family of all these criteria that produce quasiconcave rankings of distributions, this paper also singles out with an additional axiom the specific member of this family that considers all distinct categories to be equally dissimilar. This criterion turns out to be the ranking of distributions induced by the comparison of their Herfindahl (1950)-Hirschman (1945)-Simpson (1949) index.
Keywords Axioms, Herfindahl-Hirschman-Simpson, Rao Quadratic Entropy, Mixture Symmetry, Quasi-Concavity, Diversity
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Abstract This article examines gender differences in early childhood capability deprivation in Algeria, Morocco, Syria, and Yemen. Using nationally representative surveys from the Pan Arab Project for Family Health, we estimate deprivation among children aged 0-4 in three latent dimensions: nutrition, sanitation, and access to information. The empirical strategy combines a capability-deprivation framework with multi-group structural equation modelling, measurement-invariance tests, and multidimensional aggregation. The results show that gendered deprivation is neither uniform nor always to the disadvantage of girls. Female children are more likely to be capability deprived on aggregate in Algeria, Morocco, and Yemen, while male children appear more deprived in Syria. Gender disparities also vary across dimensions: boys are more likely to be nutrition-deprived in Morocco and Syria, while girls are more likely to be sanitation-deprived in Algeria and Morocco and information-deprived in Morocco and Yemen. Rural residence and low household-head education are generally associated with weaker achievements in nutrition, sanitation, and information. The findings contribute to applied research on child poverty measurement and gender inequality by showing that gendered capability deprivation is observable before school age and is patterned by household and public-service conditions.
Keywords Early childhood deprivation, Gender inequality, Structural equation modelling, Multidimensional poverty, MENA, Capability approach
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Abstract An agent, Sleeping Beauty, in a game with self-locating uncertainty (i.e. one play of the game visits the same information set multiple times, as in the paradox of the absentminded driver) must select a behavioural strategy that is self-ratifying: a best-response to the belief that her other instances do likewise. When there are multiple such fixed points, the standard treatment of Aumann et al. (1997) assumes that all instances of the agent can simply coordinate. I drop this assumption (supposing that Sleeping Beauty 'lose her magic psychic powers' ), and study said agent iteratively reasoning her way to an equilibrium selection instead. Which strategy other instances select can be seen as ambiguous, so I model Beauty's choice via a response function that encodes her response to ambiguity, and a procedure that describes in what manner she iterates the application of this response function. I consider two response functions, 'Bayesian' and EU-maximin, and two procedures, replacement and accumulation, and characterise in which cases the iterative reasoning converges. For either response function, accumulation always converges, but replacement does so if and only if there are no cycles of length weakly greater than two on a particular finite functional digraph I call the support digraph.
Keywords Sleeping Beauty Problem, Imperfect Recall, Self-Locating Uncertainty, Decision Instability, Ambiguity, Absent-Minded Driver
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Abstract This paper studies the comparison of multidimensional ordinal distributions when outcome profiles are only partially ordered. Such settings arise naturally in inequality analysis whenever well-being is described by several ordinal attributes and some profile comparisons cannot be resolved without introducing additional value judgments about the relative importance of dimensions. To address this problem, the paper introduces a rank-membership representation based on the admissible linear extensions of the underlying partial order. Each profile is thereby associated with a probability distribution over ranks, which in turn yields completion-averaged rank frequencies and multidimensional Hammond coordinates. The paper shows that these coordinates coincide with the uniform average of the corresponding one-dimensional Hammond coordinates across admissible completions. We define a coordinate-wise multidimensional Hammond dominance criterion and establish its relation to unanimous completion-wise Hammond dominance. We also introduce a graded refinement based on the proportion of coordinates at which one distribution weakly dominates another and derives its basic transitivity structure. The proposed framework provides a way to extend rank-sensitive inequality comparisons to multidimensional ordinal settings with incomplete comparability, while making explicit the informational trade-off implied by averaging across admissible completions.
Keywords Ordinal data, Partial Orderings, Dominance criteria, Rank-Sensitive Comparisons, Multidimensional Inequality
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Abstract The World Bank's "Doing Business" (DB) report ranked nearly 190 countries on their private-sector business climate from 2003 to 2020, grading countries primarily on de jure regulatory performance. Using panel data for 2010–2014 and 2016–2019, we test whether DB scores are associated with or predictive of private investment flows, measured by both Foreign Direct Investment (FDI) and Gross Fixed Capital Formation (GFCF). Across pooled OLS, two-way fixed-effects, and Jordà local projection specifications, we find no robust relationship between DB score improvements and either investment measure. DB's apparent cross-sectional relevance for GFCF dissolves once institutional fragility is controlled for, revealing the index as a proxy for stability rather than a measure of regulatory quality. Capital account openness is the dominant within-country predictor of domestic investment intensity, a dimension entirely absent from DB's framework. A synthetic index of our construction, combining institutional stability, capital account openness, and trade integration consistently outperforms DB in cross-sectional horse races. These findings carry direct implications for Business-Ready (B-Ready), DB's successor due in late 2026, whose continued reliance on de jure scoring risks reproducing the same structural limitations and ultimately fail to capture the conditions firms actually face.
Keywords Business-Ready, Doing business, De jure regulation, Gross Fixed Capital Formation, Foreign direct investment, World Bank
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Abstract We study the effects of macroprudential policies on income and wealth inequality across 18 Eurozone countries over the period 2000–2024. We focus on the financially constrained Wealthy Hand-to-Mouth households for whom the regulation changes are likely to be consequential. We present insights from a stylised two-economy incomplete-markets model where the heterogeneity in household portfolio composition shapes the effects on inequalities of borrower-based regulation. Using panel regressions and local projections, we test empirically the model's predictions that macroprudential policies matter for inequalities and their effects differ depending on the concentration of housing or pension assets in the Wealthy Hand-to-Mouth households' illiquid portfolios. The empirical findings underscore that in housing dominant economies, the reduction of the LTV ratio improves wealth inequalities in the short term through a collateral-leverage mechanism, whereas it persistently widens wealth disparities in pension-dominant economies through credit exclusion effects.
Keywords Loan-to-value regulation, Macroprudential policy, Eurozone, Local projections, Wealthy hand-to-mouth, Heterogeneity, Portfolio, Wealth inequalities
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Abstract Standard models of international trade treat factor endowments as exogenous and stable. This paper argues that biological invasions induced by trade itself erode productive endowments, generating a feedback loop from comparative advantage to invasive species pressure and back. We call this mechanism the biological endowment curse : the very endowment that confers comparative advantage in agriculture raises the exposure to invasion, which in turn degrades the endowment. This dynamic cost of trade has been largely absent from the received theory of comparative advantage. We formalise this idea in two steps. First, in a single-country model with Cobb-Douglas endowment dynamics, we establish the existence and global stability of a long-run equilibrium and show that the equilibrium healthy endowment decreases with import pressure and with ecological fragility. Second, in a two-country discrete-time game, we derive closed-form expressions for the Markov Perfect Nash equilibrium and the cooperative solution. Both countries under-invest in biosecurity at Nash, and the under-investment gap is larger for countries with stronger regeneration capacity and greater commercial interdependence. We then characterise the optimal international agreement, modelled as a Nash equilibrium in trigger strategies. A key structural result is that the incentive compatibility constraint reduces to a purely parametric condition, independent of the current state of endowments. When the pure trigger fails, trade linkage can restore viability. Finally, policy implications are discussed.
Keywords Sanitary and Phytosanitary SPS agreements, Biosecurity, Levhari-Mirman, Differential game, Biological endowment curse, Comparative advantage, Factor endowments, Invasive species
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Abstract We study an n-country pollution linear-quadratic differential game in which countries differ in their sensitivity to environmental damages while contributing to a common pollution stock. Such heterogeneity implies that countries value environmental quality differently and disagree on the desirable long-run environmental outcome. Consistently with the rising literature on carbon dioxide removal (CDR), we also allow for (optimal) negative emissions. We characterize the unique linear Markov-perfect (MPE) equilibrium and compare it to a centralized benchmark that maximizes aggregate welfare. We show that the inefficient steady-state pollution level at the MPE depends systematically on the distribution of damage sensitivities: intriguingly, holding average damages constant, more evenly distributed damages lead to more long-run pollution. Optimal negative emissions arise when the distribution of damage sensitives is asymmetric enough. We next show, among others, that while polarized damages reduce equilibrium pollution, they do generate distributional tensions. We therefore suggest a mechanism combining Pigouvian taxation with lump-sum transfers that can found an International Environment Agreement redistributing gains and implementing the first-best allocation despite divergent incentives.
Keywords Differential games, Asymmetric players, International Envionmental agreements, Transboundary pollution
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Abstract Urban low-emission zones (LEZs) are increasingly used to reduce transportrelated air pollution, yet little is known about their long-run general equilibrium effects on the urban spatial structure and their implications in term of pollution exposure. To explore this question, we develop a quantitative spatial equilibrium model with endogenous commuting, transport mode choice and air pollution generated by transport, housing and firms activity. Pollution dispersion is described by an advection-diffusion equation accounting for atmospheric diffusion, deposition, and wind. We apply the model to the Grand Paris Low-Emission Zone and evaluate a long-run counterfactual in which internal combustion engine vehicles are banned from commuting within or through the regulated area. The results show that the policy substantially reduces car use and transport-related emissions. However, endogenous relocation by workers and firms partly offsets environmental gains by shifting economic activity and commuting flows toward more car-dependent peripheral areas, while simultaneously attenuating welfare losses. As a result, partial-equilibrium approaches that abstract from spatial reorganization tend to overestimate both the environmental benefits and welfare costs of the LEZ policy.
Keywords General equilibrium effects, Low-emission zones, Air pollution, Transport policies, Quantitative spatial equilibrium
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Abstract We develop a unified dynamic game-theoretic theory of institutional change that delivers three common equilibrium outcomes as limiting cases: Lipsetian transition to democracy, transition through popular revolution, and permanent autocracy. An impulse-control framework captures both the citizens’ revolutionary option and the elites’ strategic choice of voluntary democratisation, with human capital as the unique endogenousstate and resource windfalls as an exogenous contributor to production and exports. The framework allows us to (1) characterise a reformation frontier, a state-feedbacklocus of minimal concessions that keeps the regime marginally stable as human capital evolves, and (2) identify conditions under which voluntary handover strictly dominates revolution or the status quo, providing a formal stopping rule for elites. We then confront the most distinctive part of the theory, the reformation-frontier mechanism, with data on a panel of 223 autocratic spells between 1970 and 2024. Two empirical signatures of the mechanism are present in the data: the within-spell adjustment of concessions saturates as human capital accumulates, and a cluster of long-lived high-polyarchy autocracies persists on the back of rent revenues. The joint configuration is consistent with our theoryand inconsistent with thin modernisation, rentier-curse, and state-capacity alternatives.
Keywords Dynamic games, Reformation frontier, Redistribution, Education, Political transition
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Abstract This paper studies whether large swings in global crude oil prices reflect observable fundamentals alone or also embody forward-looking speculative dynamics. We develop a stylised asset-pricing model in which fundamentalists and sentimentdriven speculators coexist, which motivates a two-component equilibrium price: a backward-looking fundamental part and a forward-looking speculative part. Longmemory in the dividend process further motivates the use of fractional filtering. The theoretical model motivates our empirical specification: we combine fractional filtering with a mixed causal-noncausal autoregressive model to distinguish persistent movements from expectation-driven price dynamics in the oil prices, allowing speculative pressures to be two-sided and generate both upward bubble-like episodes and downward crash-like dislocations. We find that, even conditional on a rich set of oil-market, macro-financial, and geopolitical determinants, crude oil prices retain a forward-looking component. The results suggest that major oil-price fluctuations are shaped not only by fundamentals, but also by expectation-driven forces that amplify boom-bust dynamics.
Keywords Overpricing, Crashes, Noncausal models, Long-memory, Oil prices
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Abstract I study games with self-locating uncertainty in which an agent at a single information set is uncertain of his position evenwithina given information set of a given play of the game. In such games, there is an analogy to be drawn with Newcomb’s problem: in bothsettings, locally rational (thirder) reasoning and globally optimal (planning) reasoning can prescribe different strategies. I call this aNewcomb tension, and present a representation theorem: a Bayesian with commitment power and an uncommitted agent holding incorrect ‘one-boxer’ beliefs are behaviourally equivalent. In the single-agent case, randomisation always resolves the tension but in multi-agent games, in which planning and interim social weights diverge under some conditions, a multi-agent Newcomb tension can survive this randomisation resolution with an asymmetric awakening structure across agents. I consider the implications of this for the duplicating Sleeping Beauty problem, and a duplicating variant of the absent-minded driver.
Keywords Sleeping Beauty Problem, Newcomb’s Problem, Self-Locating/Indexical Uncertainty, Imperfect Recall, Absent-Minded Driver
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Abstract I study games with self-locating uncertainty in which an agent at a single information set is uncertain of his position evenwithina given information set of a given play of the game. In such games, there is an analogy to be drawn with Newcomb’s problem: in bothsettings, locally rational (thirder) reasoning and globally optimal (planning) reasoning can prescribe different strategies. I call this aNewcomb tension, and present a representation theorem: a Bayesian with commitment power and an uncommitted agent holding incorrect ‘one-boxer’ beliefs are behaviourally equivalent. In the single-agent case, randomisation always resolves the tension but in multi-agent games, in which planning and interim social weights diverge under some conditions, a multi-agent Newcomb tension can survive this randomisation resolution with an asymmetric awakening structure across agents. I consider the implications of this for the duplicating Sleeping Beauty problem, and a duplicating variant of the absent-minded driver.
Keywords Sleeping Beauty Problem, Newcomb’s Problem, Self-Locating/Indexical Uncertainty, Imperfect Recall, Absent-Minded Driver
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Abstract This paper proposes a dynamic model in which natural disasters affect the accumulation of private wealth, public spending, and output in an economy that is intended to capture salient features of developing countries. The central object of the analysis is the stationary distribution of key macroeconomic variables that emerges in the presence of recurrent, stochastic disasters. Within this framework, we derive analytic characterizations of the stationary distributions of private wealth, government spending, and GDP, and study how their shapes and tails depend on both disaster risk and institutional parameters. Natural disasters affect the economy via two channels. First, the effects on production are transmitted through a demand channel by altering the consumption-savings trade-off of households and thus the proportion of capital that can be invested in capital accumulation. Second, natural disaster shocks also activate a supply channel: they destroy capital and alter the way in which public spending influences total factor productivity. The stationary distributions of capital stock and public expenditure exhibit unusual characteristics such as Pareto laws and upper Gamma distributions. Our stylized model describes key mechanisms in developing countries and allows us to investigate the factors that enhance economic resilience to shocks, as well as those that may render their effects persistent.
Keywords Stochastic growth, Public spending, Developing countries, Natural disasters
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Abstract This paper is devoted to developing the alternating minimization algorithm for problems of structured nonconvex optimization proposed by Attouch, Bolt´e, Redont, and Soubeyran in 2010. Our main result provides significant improvements of the convergence rate of the algorithm, especially under the low exponent PolyakLojasiewicz-Kurdyka condition when we establish either finite termination of this algorithm or its superlinear convergence rate instead of the previously known linear convergence. We also investigate the PLK exponent calculus and discuss applications to noncooperative games and behavioralscience.
Keywords Polyak- Lojasiewicz-Kurdyka conditions, Convergence rates, Noncooperative games, Alternating minimization algorithm, Nonsmooth optimization
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Abstract We study the problem of maximizing Rényi entropy of order $2$ (equivalently, minimizing the index of coincidence) over the set of joint distributions with prescribed marginals. A closed-form optimizer is known under a feasibility condition on the marginals; we show that this condition is highly restrictive. We then provide an explicit construction of an optimal coupling for arbitrary marginals. Our approach characterizes the optimizer's structure and yields an iterative algorithm that terminates in finite time, returning an exact solution after at most $p-1$ updates, where $p$ is the number of rows.
Keywords Entropy maximization, Index of coincidence minimization, Coupling, Marginal constraints
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Abstract Using field data from an insurtech firm and a survey experiment, this paper studies health belief formation within couples. We document a strong gender asymmetry: Women increase critical illness insurance purchases for their husbands after negative health signals of COVID-19, hospital visits, and unhealthy lifestyles but do not adjust coverage for themselves, while men do not respond to either. Experimental evidence reveals pervasive health overconfidence and shows that women update on husbands’ negative health information but not their own, whereas men update neither. The findings highlight gendered belief updating and the importance of household decision-makers in financial choices.
Keywords Health overconfidence, Motivated beliefs, Gender differences, Insurance
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Abstract This paper studies whether expanding women’s decision-making authority within marriage affects female labor supply and girls’ human capital investment. We exploit a major reform of French marital law in 1966, which reallocated control over labor and financial decisions from husbands to wives while leaving divorce institutions unchanged. Using census and family survey data, we implement two complementary empirical strategies. First, exploiting the discontinuity in access to the new marital regime by date of marriage, we show that women married under the new regime are 7 percentage points more likely to be employed more than thirty years later, after childrearing constraints have largely passed. Second, using cohort- and gender-based exposure to the reform, we find that girls who are at key educational decision ages when the reform is announced complete more schooling and are 13 percent more likely to obtain a baccalauréat or a higher-education degree. These education gains translate into higher employment rates and access to higher-skilled occupations in adulthood.
Keywords Gender, Education, Labor supply, Marriage law, Intra-household decision making
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Abstract A subset of economic agents in a society is aware of the existence of an economic opportunity, and compete to exploit the opportunity. We study incentives to communicate about the existence of this economic opportunity when the exploitation of the opportunity by the winner generates externalities to other agents. We characterize the equilibria of the communication game and identify conditions under which more externalities generate more communication.
Keywords Opportunity, Strategic Communication, Externalities
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Abstract We study the almost sure convergence of the occupation measure of evolution models where mutation rates decrease over time. We show that if the mutation parameter vanishes at a controlled rate, then the empirical occupation measure converges almost surely to a specific invariant distribution of a limiting Markov chain. Our results are obtained through the analysis of a larger class of time-inhomogeneous Markov chains with finite states pace, where the control on the mutation parameter is explained by the energy barrier of the limit process. Additionally, we derive an explicit L1 convergence rate, explained through the tree-optimality gap, that may be of independent interest.
Keywords Evolution models, Inhomogeneous Markov chain, Occupation measure, Energy barrier
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