# Publications

The citizen candidate models of democracy assume that politicians have their own preferences that are not fully revealed at the time of elections. We study the optimal delegation problem which arises between the median voter (the writer of the constitution) and the (future) incumbent politician under the assumption that not only the state of the world but also the politician's type (preferred policy) are the policy-maker's private information. We show that it is optimal to tie the hands of the politician by imposing both a policy floor and a policy cap and delegating him/her the policy choice only in between the cap and the floor. The delegation interval is shown to be the smaller the greater is the uncertainty about the politician's type. These results are also applicable to settings outside the specific problem that our model addresses.

Information provision is a relatively recent but steadily growing environmental policy tool. Its emergency and topicality are due to the current escalation of ecological threats. Meanwhile, its high complexity and flexibility require a comprehensive approach to its design, which has to be tailored for specific characteristics of production process, market structure, and regulatory goals. This work proposes such an approach and builds a framework based on a three-level mathematical program extending well-known two-level Stackelberg game by introducing one more economic agent and one extra level of this sequential game. This study provides simple and very intuitive algorithms to compute optimal multi-tier information provision policies, both mandatory and voluntary. The paper urges for the wide implementation of such efficient environmental policy design tools.

The purpose of this paper is twofold. First, we examine convergence properties of an inexact proximal point method with a quasi distance as a regularization term in order to find a critical point (in the sense of Toland) of a DC function (difference of two convex functions). Global convergence of the sequence and some convergence rates are obtained with additional assumptions. Second, as an application and its inspiration, we study in a dynamic setting, the very important and difficult problem of the limit of the firm and the time it takes to reach it (maturation time), when increasing returns matter in the short run. Both the formalization of the critical size of the firm in term of a recent variational rationality approach of human dynamics and the speed of convergence results are new in Behavioral Sciences.

We study optimal contracts in a regulator–agent setting with joint production, altruistic and selfish agents, limited liability, and uneasy outcome measurement. Such a setting represents sectors of activities such as education and healthcare provision. The agents and the regulator jointly produce an outcome for which they all care to some extent that is varying from agent to agent. Some agents, the altruistic ones, care more than the regulator does while others, the selfish agents, care less. Moral hazard is present due to both the agent's effort and the joint outcome that are not contractible. Adverse selection is present too since the regulator cannot a priori distinguish between altruistic and selfish agents. Contracts consist of a simple transfer from the regulator to the agents together with the regulator's input in the joint production. We show that, under the conditions of our setting and when we face both moral hazard and adverse selection, the regulator maximizes welfare with a menu of contracts, which specify higher transfers for the altruistic agents and higher regulator's inputs for the selfish agents.

Central properties of geometric quantiles have been well-established in the recent statistical literature. In this study, we try to get a grasp of how extreme geometric quantiles behave. Their asymp-totics are provided, both in direction and magnitude, under suitable moment conditions, when the norm of the associated index vector tends to one. Some intriguing properties are highlighted: in particular, it appears that if a random vector has a finite covariance matrix, then the magnitude of its extreme geometric quantiles grows at a fixed rate. We take profit of these results by defining a parametric estimator of extreme geometric quantiles of such a random vector. The consistency and asymptotic normality of the estimator are established, and contrasted with what can be obtained for univariate quantiles. Our results are illustrated on both simulated and real data sets. As a conclusion, we deduce from our observations some warnings which we believe should be known by practitioners who would like to use such a notion of multivariate quantile to detect outliers or analyze extremes of a random vector.

The promotion system for French academic economists provides an interesting environment to examine the promotion gap between men and women. Promotions occur through national competitions for which we have information both on candidates and on those eligible to be candidates. Thus, we can examine the two stages of the process: application and success. Women are less likely to seek promotion, and this accounts for up to 76 percent of the promotion gap. Being a woman also reduces the probability of promotion conditional on applying, although the gender difference is not statistically significant. Our results highlight the importance of the decision to apply.

This paper concerns applications of variational analysis to some local aspects of behavioral science modeling by developing an effective variational rationality approach to these and related issues. Our main attention is paid to local stationary traps, which reflect such local equilibrium and the like positions in behavioral science models that are not worthwhile to quit. We establish constructive linear optimistic evaluations of local stationary traps by using generalized differential tools of variational analysis that involve subgradients and normals for nonsmooth and nonconvex objects as well as variational and extremal principles.

In this paper, we propose a new variance reduction method for quantile regressions with endogeneity problems, for alpha-mixing or m-dependent covariates and error terms. First, we derive the asymptotic distribution of two-stage quantile estimators based on the fitted-value approach under very general conditions. Second, we exhibit an inconsistency transmission property derived from the asymptotic representation of our estimator. Third, using a reformulation of the dependent variable, we improve the efficiency of the two-stage quantile estimators by exploiting a tradeoff between an inconsistency confined to the intercept estimator and a reduction of the variance of the slope estimator. Monte Carlo simulation results show the fine performance of our approach. In particular, by combining quantile regressions with first-stage trimmed least-squares estimators, we obtain more accurate slope estimates than 2SLS, 2SLAD and other estimators for a broad set of distributions. Finally, we apply our method to food demand equations in Egypt.

We study the determination of public tuition fees through majority voting in a vertical differentiation model where agents' returns on educational investment differ and public and private universities coexist and compete in tuition fees. The private university offers higher educational quality than its competitor, incurring higher unit cost per trained student. The tuition fee for the state university is fixed by majority voting while that for the private follows from profit maximization. Then agents choose to train at the public university or the private one or to remain uneducated. The tax per head adjusts in order to balance the state budget. Because there is a private alternative, preferences for education are not single-peaked and no single-crossing condition holds. An equilibrium is shown to exist, which is one of three types: high tuition fee (the “ends” are a majority), low tuition fee (the “middle” is a majority), or mixed (votes tie). The cost structure determines which equilibrium obtains. The equilibrium tuition is either greater (majority at the ends) or smaller (majority at the middle) than the optimal one.

We provide with an optimal growth spatio-temporal setting with capital accumulation and diffusion across space in order to study the link between economic growth triggered by capital spatio-temporal dynamics and agglomeration across space. We choose the simplest production function generating growth endogenously, the AK technology but in sharp contrast to the related literature which considers homogeneous space, we derive optimal location outcomes for any given space distributions for technology (through the productivity parameter A) and population. Beside the mathematical tour de force, we ultimately show that agglomeration may show up in our optimal growth with linear technology, its exact shape depending on the interaction of two main effects, a population dilution effect versus a technology space discrepancy effect.