Columbia Transportation Day

Transportation Day: Monday 25 June 2007

Columbia University, 1027 International Affairs Building
Under the auspices of the National Science Foundation Award SES-0532398

List of Participants

Administrative Support provided by Kevin Findlan
For more information, contact Marc Henry. To download the program, click here.

Conference Description

Introduction:

Since Gaspard Monge formulated the problem of finding an optimal transportation plan for piles of soil in his 1781 "Mémoire sur les déblais et remblais", the problem of transporting a given distribution of mass from one location to another distribution of mass in a different location, while minimizing a certain cost of transportation, has become a major field of study in mathematics and operations research. That it also provides a powerful and versatile tool for a wide range of economic applications is now becoming apparent. Mass transportation duality is useful in formulating the problem of existence, uniqueness and purity of equilibrium in hedonic models. It lies at the heart of improvements of estimates of monotone functions (such as cumulative distribution and quantile functions), and of the problem of testing economic model specification, to name only a few applications.

This conference brings together researchers at the forefront of developments of these economic applications. Its main goals are to increase their awareness of each other's work, to identify the most important unexplored problems and pave the way for collaborations. It is also intended to become the first of a long series of annual meetings in rotating venues.

Abstract of the Conference proceedings:

The conference is opened by Pierre-André Chiappori (Columbia) who, after thanking all participants, insists on the flexible and informal nature of the presentations, aimed at maximizing the opportunity for discussion.

He then introduces the first speaker, Lars Nesheim (University College London). In his presentation of joint work with Robert McCann (University of Toronto) and Pierre-André Chiappori, he shows how mass transportation duality allows for the formulation of conditions for existence and uniqueness of equilibrium in hedonic models. He also shows how to derive conditions under which one buyer is matched to exactly one seller (so that no randomization is involved), and an equivalence between hedonic and matching models. [presentation]

Guillaume Carlier (Université Paris Dauphine) then shows, in a presentation of joint work with Ivar Ekeland (University of British Columbia and PIMS), that the application of mass transportation duality can be extended to hedonic models where the production of the differentiated good requires  a team of producers. This extension also applies to the study of optimal group matchings, when group members belong to disjoint populations. [presentation]

The discussion then moves to an econometric application of mass transportation. In his presentation of joint work with Ivan Fernadez-Val (Boston University) and Alfred Galichon (Columbia and École polytechnique), Victor Chernozhukov (Massachusetts Institute of Technology) shows that rearrangements of estimates of monotone functions provide systematic improvements of the latter estimates, and derives asymptotic results for the improved estimates. [presentation]

Jay Sethuraman (Columbia) then gives a description of the Hungarian method, at the core of efficient algorithms to compute optimal transportation plans.

After lunch, Marc Henry (Columbia) shows in his presentation of joint work with Alfred Galichon that the question of correct specification of an economic model has an optimal mass transportation formulation, which is particularly useful when testing incomplete specifications (economic models with multiple equilibria or censored observables). [presentation]

Alfred Galichon gives insights into a broad program of application of mass transportation to a probabilistic version of the central limit theorem in higher dimension, and illustrates it with joint work with Victor Chernozhukov on empirical Wasserstein distances and joint work with Marc Henry on inference in partially identified economic models. [presentation]

The last presentation shows the application of a related mathematical programming tool, as Heleno Pioner (Chicago) shows how to identify a monopolistic model with differentiated products, some of whose quality dimension is unobserved. [presentation]

Finally, the conference is closed with a discussion led by Ivar Ekeland and Robert McCann. Ivar Ekeland insists on the need for more research on the identification of hedonic models, and the relation between pure equilibria with unobserved consumer heterogeneity and mixed equilibria without unobserved characteristics. Robert McCann insists on the potential for insights provided by geometric interpretations of mass transportation problems, especially in the problem of higher-dimensional rearrangements and in the relation between the Spense-Mirlees condition for purity and a curvature based on transportation cost.

In his closing remarks, Pierre-André Chiappori remarks how strikingly different the uses of the duality principle are in micro-economics and in econometrics. In the former, duality corresponds essentially to market decentralization, whereas in econometrics, it serves as a bridge between strong (probabilistic) representations and distributional representations.