Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness

Chiappori, Pierre‐André; McCann, Robert J.; Nesheim, Lars

doi:10.1007/s00199-009-0455-z

Cited by 178 publications

(147 citation statements)

References 28 publications

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“…Speci cally, both here and in Jerez (2014), we adopt the linear programming approach used by Shapley (1955), Shapley and Shubik (1972), and Grestky, Zame (1992, 1999) to study frictionless matching models with transferable utility. (See also more recent work by Chiappori, McCann, and Nesheim (2010) and Dizdar (2015), among others). Speci cally, we show that constrained e cient allocations can be determined as solutions to a linear programming (LP) problem, whereas the hedonic wage function supporting these allocations and the associated expected payo s for workers and rms correspond to the solutions of the dual of that linear program.…”

Section: Introductionmentioning

confidence: 87%

Competitive search equilibrium with multidimensional heterogeneity and two-sided ex-ante investments

Jerez

2017

Journal of Economic Theory

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We analyze a competitive search environment where heterogeneous workers and firms make costly investments (e.g. in education and physical capital, respectively) before they enter the labor market. A key novelty with respect to existing work is that we allow for multidimensional heterogeneity on both sides of the market. Our environment features transferable utility and symmetric information. As in classical hedonic models, wages depend both on the job's and on the worker's match-relevant characteristics. Yet the presence of search frictions implies that (unlike in those models) markets do not clear. The hedonic wage function and probabilities of finding and filling different jobs are determined endogenously in a competitive search equilibrium. We show that constrained efficient allocations can be determined as optimal solutions to a linear programming problem, whereas the wage function supporting these allocations and associated expected payoffs for workers and firms correspond to the solutions of the `dual' of that linear program. We use this characterization to show that a competitive search equilibrium exist and is constrained efficient under very general conditions. Jerez (2014) makes a similar point in the context of a model where all the match-relevant characteristics of the traders are exogenous. Here we extend the analysis to allow for two-sided ex-ante investments which are potentially multidimensional. The fact that linear programming techniques have been used for the structural estimation of frictionless matching models suggests that our framework is potentially useful for empirical studies of labor markets and other hedonic markets (like that for housing) where search frictions are prevalent Journal of Economic Literature Classification Numbers: D50, D61, D83.

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Section: Introductionmentioning

confidence: 87%

Competitive search equilibrium with multidimensional heterogeneity and two-sided ex-ante investments

Jerez

2017

Journal of Economic Theory

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“…This direction has been explored by Ekeland ([Eke05, Eke10]), and later by Chiappori, McCann, and Nesheim ( [CMN10]). Figalli, Kim, and McCann have also shown that the problem becomes a convex screening problem, under a strengthening of the (A3w) condition, often known as "non-negative cross curvature" in the optimal transport literature (see [FKM11]).…”

Section: 2mentioning

confidence: 99%

Pointwise Estimates and Regularity in Geometric Optics and Other Generated Jacobian Equations

Guillen

Kitagawa

2017

Comm Pure Appl Math

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Abstract. The study of reflector surfaces in geometric optics necessitates the analysis of certain nonlinear equations of Monge-Ampère type known as generated Jacobian equations. This class of equations, whose general existence theory has been recently developed by Trudinger, goes beyond the framework of optimal transport. We obtain pointwise estimates for weak solutions of such equations under minimal structural and regularity assumptions, covering situations analogous to that of costs satisfying the A3-weak condition introduced by Ma, Trudinger and Wang in optimal transport. These estimates are used to develop a C 1,α regularity theory for weak solutions of Aleksandrov type. The results are new even for all known near-field reflector/refractor models, including the point source and parallel beam reflectors and are applicable to problems in other areas of geometry, such as the generalized Minkowski problem.

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“…We refer to [2], [3], [4], [6], [21], [22], [23] and the surveys and books [1], [13], [25] and [26]. It has many applications, for example in economics (matching problems), [5], [7], [8], [9], [10], [11], [20]. Closely related to this article is the case in which the involved measures are concentrated in a small strip around the boundary of a fixed domain.…”

Section: 2mentioning

confidence: 99%

Optimal Mass Transport in Thin Domains

Climent

Rossi

Volpe

2014

Advanced Nonlinear Studies

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Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness

Abstract: Hedonic price equilibrium, Matching, Optimal transportation, Spence-Mirrlees condition, Monge–Kantorovich, Twist condition, C62, C78, D50,

Cited by 178 publications

References 28 publications

Competitive search equilibrium with multidimensional heterogeneity and two-sided ex-ante investments

Competitive search equilibrium with multidimensional heterogeneity and two-sided ex-ante investments

Pointwise Estimates and Regularity in Geometric Optics and Other Generated Jacobian Equations

Optimal Mass Transport in Thin Domains

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