GALICHON Alfred

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Structural estimation of demand models in differentiated product markets plays an important role in economics. It allows us to better understand consumer choices and, among other things, to measure the effects of a company merger, the introduction of a new product on the market or a new regulation. The traditional approach is to specify a utility model, typically an additive random utility model, calculate its demands and invert them to obtain inverse demand equations that will serve as a basis for estimation. However, in general, these inverse demands do not have an analytical form. Estimation therefore requires numerical inversion and the use of nonlinear estimation procedures, which can be difficult and time consuming.This thesis takes a different approach, developing new inverse demand models that are consistent with a heterogeneous consumer utility model. This approach allows for more flexible capture of substitutions between products through simple linear regressions based on data including market shares, prices and product characteristics. The first chapter of this thesis develops the inverse product differentiation logit (IPDL) model, which generalizes nested logit models, allowing for flexible capture of substitutions between products, including complementarity. It shows that the IPDL model belongs to a class of inverse demand models, called generalized inverse logit (GIL), which includes a large majority of additive random utility models that have been used for demand estimation purposes. The second chapter develops the flexible inverse logit (FIL) model, a GIL model that uses a flexible nesting structure with one nest for each pair of products. It shows that the FIL model, projected into the product characteristic space, yields price elasticities that depend directly on product characteristics and, using Monte Carlo simulations, is able to reproduce those of the "flexible" logit model with random coefficients. The third chapter studies the microfoundation of the GIL model. It shows that the restrictions that the GIL model imposes on the inverse demand function are necessary and sufficient conditions for consistency with a model of heterogeneous consumers maximizing their utility function, known as the perturbed utility model (PUM). He also shows that any GIL model generates a demand function that satisfies a slight variant of the Daly-Zachary conditions, which allows the combination of substitutability and complementarity in demand.

This article presents a set of tools for the modeling of a spatial allocation problem in a large geographic market and gives examples of applications. In our settings, the market is described by a network that maps the cost of travel between each pair of adjacent locations. Two types of agents are located at the nodes of this network. The buyers choose the most competitive sellers depending on their prices and the cost to reach them. Their utility is assumed additive in both these quantities. Each seller, taking as given other sellers prices, sets her own price to have a demand equal to the one we observed. We give a linear programming formulation for the equilibrium conditions. After formally introducing our model we apply it on two examples: prices offered by petrol stations and quality of services provided by maternity wards. These examples illustrate the applicability of our model to aggregate demand, rank prices and estimate cost structure over the network. We insist on the possibility of applications to large scale data sets using modern linear programming solvers such as Gurobi. In addition to this paper we released a R toolbox to implement our results and an online tutorial (http://optimalnetwork.github.io) .

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This thesis examines the themes of matching, inequality and the impact of technological change on the labor market. In particular, it addresses questions about matching between employees and firms and how this influences inequality in the labor market, both within the entire population, as well as between demographic and skill groups. It also examines how technological change affects the labor market conditions faced by workers and firms. These issues are addressed over three chapters. The first chapter, entitled "Multidimensional Heterogeneity and Matching in a Frictional Labor Market - An Application to Polarization" discusses the matching of workers to firms along multidimensional characteristics and quantifies the impact of technological change on the matching, wage, and employment patterns of different demographic groups. I construct a directed search model with multidimensional heterogeneity and estimate the model on U.S. data. I find that production complementarities between cognitive and interpersonal skills and tasks have increased, compared to those between manual skills and tasks. This shift in production technology explains much of the wage and job polarization in the United States. Moreover, although it does not control for gender differences, the model can explain a substantial fraction of the narrowing of gender gaps in wages and jobs. Co-authored with Nicolo Dalvit and Aseem Patel, the second chapter, "Intra-firm Hierarchies and Gender Disparity," examines the ranking of women in hierarchies within firms. It uses French administrative data and examines the impact of wage and employment gaps across hierarchies over time. In addition, by exploiting a corporate board quota policy in France, it assesses the impact of increased female leadership on wages and employment outcomes within firms. We find that hierarchies matter in gender wage and employment gaps. Gender wage and employment gaps increase with each level of corporate hierarchy, although these gaps narrow more over time at higher levels. Moreover, improving female leadership has different impacts across hierarchies. While a higher proportion of female board members reduces the gender pay gap at the top of the hierarchy, it does not have such an impact at the bottom. Instead, it increases the proportion of women in the lower levels working part-time, at the expense of full-time employment. The opposite is true for women in the upper levels. The third chapter, "Labor Shortages and Labor Market Adjustments: An Island Theory," co-authored with Riccardo Zago, discusses the impact of labor shortages and whether they lead to wage and salary adjustments. Using unique data on vacancies reported by firms to be difficult to fill, we document the impact of shortages across regions, industries, and occupational groups. We find that shortages lead only to wage and employment adjustments in non-routine occupations, but not in routine occupations. We show how the secular decline in routine occupations, caused by technological change, can explain the persistence of shortages in this sector and its inability to adjust.

This thesis is composed of four chapters that focus on different aspects of real estate markets. The first chapter considers real estate as a financial investment. We analyze the influence of real estate on households' portfolio choices and more precisely on the share of risky assets held. We distinguish between the effect of net housing wealth and the effect of housing debt and obtain two effects of opposite signs. The second chapter analyzes real estate as a durable good and seeks to explain its price formation on the basis of its own characteristics as well as those of its environment. The third chapter evaluates the impact of an increase in transfer taxes that took place between 2014 and 2016 in France on real estate volumes and prices. The effect of this reform was a decrease in transaction volumes only in the least tense areas, suggesting a very strong inelasticity of demand in tense markets. Moreover, the increase in the tax was entirely borne by the buyer, regardless of the degree of market tension. The fourth chapter is an analysis of the effects of the Zones Franches Urbaines (localized subsidy program) on real estate prices. The empirical results suggest that the implementation of these zones has had an inflationary effect on commercial real estate and to a lesser extent on residential real estate. Moreover, this inflationary effect is driven by zones with low real estate supply elasticity.

This thesis addresses several questions related to the economics of education and the economics of teams. In the first chapter, based on a collaboration with Laurent Rossignol, we focus on school guidance. We highlight the existence of orientation biases in the French educational system: the orientation of students does not depend only on their academic performance but also on their gender and social background. Our main contribution is to distinguish the impact of students' aspirations from the impact of teachers' ratings and recommendations on these orientation biases. The second chapter, co-authored with Antoine Chapsal, aims to understand some of the incentives and psychological effects associated with teamwork, using data on squash team championships. We show that players value participating in the success of their team, which partly explains why incentives to exert effort are stronger in collective contexts than in individual contexts. The third chapter, stemming from initial work with Rodrigo Lopez-Kolkovsky, aims to develop an estimation procedure to measure individual team productivity, using data on European soccer. We then confront this measure with the market value of players and show that Black players are discriminated against in the market.

This thesis deals with the formation of couples in the marriage market, and proposes as a guideline to focus on the issue of inequalities, both inter- and intra-household. The first chapter examines the role of marital preferences in the rise of income inequality between households. Edoardo Ciscato and I use US data to measure the impact of changing marital preferences on inter-household income inequality. Using structural methods, we show that if marital preferences had not changed since 1971, the Gini coefficient today would be 6% lower. In Chapter 2, I introduce the idea of bringing together the literature on matching models and that on collective models. For this purpose, Alfred Galichon, Scott Kominers and I have worked on a matching model with imperfectly transferable utility. We prove the existence and uniqueness of equilibrium in this framework. In addition, we construct two algorithms for determining the equilibrium. We show how the model can be estimated by maximum likelihood and propose an illustration. In the last chapter, I focus on resource sharing within couples. The idea is that collective models are inseparable from the marriage market, in the sense that the sharing of bargaining power is endogenous to the determination of an equilibrium in the marriage market. I discuss in depth the connection between collective models and matching models. In particular, I characterize the classes of collective models that can be integrated with the imperfectly transferable utility (ITU) matching model developed earlier. I propose a general method to estimate these models. Finally, I propose to illustrate my results on data extracted from the US PSID, and to estimate a model with private consumption, leisure and domestic work.

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We characterize solutions for two-sided matching, both in the transferable- and in the nontransferable-utility frameworks, using a cardinal formulation. Our approach makes the comparison of the matching models with and without transfers particularly transparent. We introduce the concept of a no-trade stable matching to study the role of transfers in matching. A no-trade stable matching is one in which the availability of transfers does not affect the outcome.

We propose new concepts of statistical depth, multivariate quantiles, vector quantiles and ranks, ranks and signs, based on canonical transportation maps between a distribution of interest on Rd and a reference distribution on the d-dimensional unit ball. The new depth concept, called Monge–Kantorovich depth, specializes to halfspace depth for d = 1 and in the case of spherical distributions, but for more general distributions, differs from the latter in the ability for its contours to account for non-convex features of the distribution of interest. We propose empirical counterparts to the population versions of those Monge–Kantorovich depth contours, quantiles, ranks, signs and vector quantiles and ranks, and show their consistency by establishing a uniform convergence property for empirical (forward and reverse) transport maps, which is the main theoretical result of this paper.

Optimal Transport Methods in Economics is the first textbook on the subject written especially for students and researchers in economics. Optimal transport theory is used widely to solve problems in mathematics and some areas of the sciences, but it can also be used to understand a range of problems in applied economics, such as the matching between job seekers and jobs, the determinants of real estate prices, and the formation of matrimonial unions. This is the first text to develop clear applications of optimal transport to economic modeling, statistics, and econometrics. It covers the basic results of the theory as well as their relations to linear programming, network flow problems, convex analysis, and computational geometry. Emphasizing computational methods, it also includes programming examples that provide details on implementation. Applications include discrete choice models, models of differential demand, and quantile-based statistical estimation methods, as well as asset pricing models.Authoritative and accessible, Optimal Transport Methods in Economics also features numerous exercises throughout that help you develop your mathematical agility, deepen your computational skills, and strengthen your economic intuition.The first introduction to the subject written especially for economists. Includes programming examples. Features numerous exercises throughout. Ideal for students and researchers alike.

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This is the first text to develop clear applications of optimal transport to economic modeling, statistics, and econometrics. It covers the basic results of the theory as well as their relations to linear programming, network flow problems, convex analysis, and computational geometry. Emphasizing computational methods, it also includes programming examples that provide details on implementation. Applications include discrete choice models, models of differential demand, and quantile-based statistical estimation methods, as well as asset pricing models.

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In this thesis, our goal is to give a general numerical framework to approximate the solutions of optimal transport (OT) problems. The general idea is to introduce an entropy regularization of the initial problem. The regularized problem corresponds to minimize a relative entropy with respect to a given reference measure. Indeed, this is equivalent to finding the projection of a coupling with respect to the Kullback-Leibler divergence. This allows us to use the Bregman/Dykstra algorithm and to solve several variational problems related to TO. We are particularly interested in the solution of multi-marginal optimal transport (MMOT) problems that arise in the context of fluid dynamics (incompressible Euler equations à la Brenier) and quantum physics (the density functional theory). In these cases, we show that entropy regularization plays a more important role than simple numerical stabilization. Moreover, we give results concerning the existence of optimal transports (e.g. fractal transports) for the TOMM problem.

n this paper, we extend Gary Becker's empirical analysis of the marriage market to same-sex couples. Beckers's theory rationalizes the well-known phenomenon of homogamy among heterosexual couples: individuals mate with their likes because many characteristics, such as education, consumption behaviour, desire to nurture children, religion, etc., exhibit strong complementarities in the household production function. However, because of asymmetries in the distributions of male and female characteristics, men and women may need to marry "up" or "down" according to the relative shortage of their characteristics among the populations of men and women. Yet, among homosexual couples, this limit does not exist as partners are drawn from the same population, and thus the theory of assortative mating would boldly predict that individuals will choose a partner with nearly identical characteristics. Empirical evidence suggests a very different picture: a robust stylized fact is that the correlation of characteristics is in fact weaker among the homosexual couples. In this paper, we build an equilibrium model of the same-sex marriage market which allows for straightforward identification of the gains to marriage. We estimate the model with 2008-2012 ACS data on California and show that positive assortative mating is weaker for homosexuals than for heterosexuals with respect to age and race. Yet, contrarily to previous empirical findings, our results suggest that postitive assortative mating with respect to education is stronger on the same-sex marriage market. As regards labor market outcomes, such as hourly wages and working hours, we find that the process of specialization within the household mainly applies to heterosexual couples.

In this paper we relate the Equilibrium Assignment Problem (EAP), which is underlying in several economics models, to a system of nonlinear equations that we call the “nonlinear Bernstein-Schrodinger system”, which is well-known in the linear case, but whose nonlinear extension does not seem to have been studied. We apply this connection to derive an existence result for the EAP, and an efficient computational method.

In this paper we relate the Equilibrium Assignment Problem (EAP), which is underlying in several economics models, to a system of nonlinear equations that we call the “nonlinear Bernstein-Schrödinger system”, which is well-known in the linear case, but whose nonlinear extension does not seem to have been studied. We apply this connection to derive an existence result for the EAP, and an efficient computational method.

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We propose a notion of conditional vector quantile function and a vector quantile regression. A conditional vector quantile function (CVQF) of a random vector Y, taking values in ℝd given covariates Z=z, taking values in ℝk, is a map u↦QY∣Z(u,z), which is monotone, in the sense of being a gradient of a convex function, and such that given that vector U follows a reference non-atomic distribution FU, for instance uniform distribution on a unit cube in ℝd, the random vector QY∣Z(U,z) has the distribution of Y conditional on Z=z. Moreover, we have a strong representation, Y=QY∣Z(U,Z) almost surely, for some version of U. The vector quantile regression (VQR) is a linear model for CVQF of Y given Z. Under correct specification, the notion produces strong representation, Y=β(U)⊤f(Z), for f(Z) denoting a known set of transformations of Z, where u↦β(u)⊤f(Z) is a monotone map, the gradient of a convex function, and the quantile regression coefficients u↦β(u) have the interpretations analogous to that of the standard scalar quantile regression. As f(Z) becomes a richer class of transformations of Z, the model becomes nonparametric, as in series modelling. A key property of VQR is the embedding of the classical Monge-Kantorovich's optimal transportation problem at its core as a special case. In the classical case, where Y is scalar, VQR reduces to a version of the classical QR, and CVQF reduces to the scalar conditional quantile function. Several applications to diverse problems such as multiple Engel curve estimation, and measurement of financial risk, are considered.

Given a convex bounded domain Ω in Rd and an integer N≥2, we associate to any jointly N-monotone (N−1)-tuplet (u1,u2,.,uN−1) of vector fields from into Rd, a Hamiltonian H on Rd×Rd.×Rd, that is concave in the first variable, jointly convex in the last (N−1) variables such that for almost all , \hbox{(u1(x),u2(x),.,uN−1(x))=∇2,.,NH(x,x,.,x). Moreover, H is N-sub-antisymmetric, meaning that ∑i=0N−1H(σi(x))≤0 for all x=(x1,.,xN)∈ΩN, σ being the cyclic permutation on Rd defined by σ(x1,x2,.,xN)=(x2,x3,.,xN,x1). Furthermore, H is N% -antisymmetric in a sense to be defined below. This can be seen as an extension of a theorem of E. Krauss, which associates to any monotone operator, a concave-convex antisymmetric saddle function. We also give various variational characterizations of vector fields that are almost everywhere N-monotone, showing that they are dual to the class of measure preserving N-involutions on Ω.

This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the cross-covariance matrices, we also generalize the notion of positive upper dependence. We then propose a means to quantify the strength of the dependence between two given multivariate series and to increase this strength while preserving the marginal distributions. This allows for the design of stress-tests of the dependence between two sets of financial variables that can be useful in portfolio management or derivatives pricing.

This paper contributes to the literature on hedonic models in two ways. First, it makes use of Queyranne’s reformulation of a hedonic model in the discrete case as a network flow problem in order to provide a proof of existence and integrality of a hedonic equilibrium and efficient computation of hedonic prices. Second, elaborating on entropic methods developed in Galichon and Salanié (Cupid’s invisible hand: social surplus and identification in matching models. Working Paper, 2014), this paper proposes a new identification strategy for hedonic models in a single market. This methodology allows one to introduce heterogeneities in both consumers’ and producers’ attributes and to recover producers’ profits and consumers’ utilities based on the observation of production and consumption patterns and the set of hedonic prices.

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This paper provides closed-form formulas for a multidimensional two-sided matching problem with transferable utility and heterogeneity in tastes. When the matching surplus is quadratic, the marginal distributions of the characteristics are normal, and when the heterogeneity in tastes is of the continuous logit type, as in Choo and Siow (2006), we show that the optimal matching distribution is also jointly normal and can be computed in closed form from the model primitives. Conversely, the quadratic surplus function can be identified from the optimal matching distribution, also in closed-form. The analytical formulas make it computationally easy to solve problems with even a very large number of matches and allow for quantitative predictions about the evolution of the solution as the technology and the characteristics of the matching populations change.

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We propose a methodology for constructing confidence regions with partially identified models of general form. The region is obtained by inverting a test of internal consistency of the econometric structure. We develop a dilation bootstrap methodology to deal with sampling uncertainty without reference to the hypothesized economic structure. It requires bootstrapping the quantile process for univariate data and a novel generalization of the latter to higher dimensions. Once the dilation is chosen to control the confidence level, the unknown true distribution of the observed data can be replaced by the known empirical distribution and confidence regions can then be obtained as in Galichon and Henry (2011) and Beresteanu, Molchanov and Molinari (2011).

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We propose a method to estimate differentiated costs of equity for electricity generation technologies. We provide evidence that there is a substantial difference in their cost of equity. This method is based on a regression between available information on electric utilities equity return and their electricity generation asset portfolio. Our first main finding is that there is a statistically significant risk premium for nuclear technology. This point is in line with the most recent studies using a higher discount rate for nuclear technology compared to coal fired plants. But, in contrast with these studies, we find that the value of the risk premium is on the order of 1% above the systematic risk of a coal-fired plant, which is considerably lower than their recommended value of 3%. The robustness of this result is tested for the structural breaks that may have been induced by the August, 2008 financial crisis and the Daishi-Fukushima accident of March, 2011. Our second finding deals with renewable energies. Despite the existence of subsidies through feed-in tariffs which would make them look like safe investments, they present a high level of systematic risk. A possible explanation for this important excess return is the fact that they are dependent on subsidies for their development and thus, bear a larger systematic exposure than can be seen on short term time series data.

Almost invariably, economic models postulate that agents behave according to some type of maximizing behavior. This is true even of models in behavioral economics, though agents in those settings may be unsophisticated in some way or have preferences that depart from classical assumptions (.).

We provide a geometric formulation of the problem of identification of the matching surplus function and we show how the estimation problem can be solved by the introduction of a generalized entropy function over the set of matchings.

This paper exhibits a duality between the theory of revealed preference of Afriat and the housing allocation problem of Shapley and Scarf. In particular, it is shown that Afriat's theorem can be interpreted as a second welfare theorem in the housing problem. Using this duality, the revealed preference problem is connected to an optimal assignment problem, and a geometrical characterization of the rationalizability of experiment data is given. This allows in turn to give new indices of rationalizability of the data and to define weaker notions of rationalizability, in the spirit of Afriat's efficiency index.

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This paper illustrates the link between partial identification in econometric models and Jaffray's decision criteria in non-probabilized uncertainty through the universe of the choice of the optimal level of toxic emissions in a lake shared by two municipalities.

This thesis deals with two aspects of dependence between financial assets. The first part concerns the dependence between random vectors. The first chapter consists in a comparison of algorithms computing the optimal transport application for the quadratic cost between two probabilities on R^n, possibly continuous. These algorithms allow to compute couplings with an extreme dependence property, called maximum correlation coupling, which appear naturally in the definition of multivariate risk measures. The second chapter proposes a definition of the extreme dependence between random vectors based on the notion of covariogram. The extreme couplings are characterized as couplings of maximum correlation with linear modification of one of the multivariate marginals. A numerical method to compute these couplings is provided, and applications to dependence stress-testing for portfolio allocation and valuation of European options on several underlyings are detailed. The last part describes the spatial dependence between two Markovian diffusions, coupled using a correlation function depending on the state of the two diffusions. A forward integrated Kolmogorov PDE links the family of spatial copulas of the diffusion to the correlation function. We then study the problem of the spatial dependence attainable by two Brownian motions, and our results show that some classical copulas are not able to describe the stationary dependence between coupled Brownian motions.

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