Optimal Transport Methods in Economics

Princeton University Press, 2016

This text provides an introduction to the theory of optimal transport, with a focus on applications to microeconomics and econometrics. It intends to cover the basic results in optimal transport, in connection with linear programming, network flow problems, convex analysis, and computational geometry. Several applications to various fields in economic analysis (econometrics, family economics, labor economics and contract theory) are provided.
The book is available on Amazon.com here.
The book webpage on the publisher’s site is here.
The code examples and solution programs to the exercises are implemented in R and are available here.
An erratum can be found here here

Short Course

Matching Models: Theory and Estimation

CEMFI, Madrid, July, 2015 (6h)

Course time and location

July 6, 7, and 8, 2015. Time and location TBA.

Course material

Available here.

Description of the Course

TBA.

References

TBA.

14.386 (first half)

Optimal Transport Methods in Economics

MIT, Economics Department, Spring 2015 (14h)

Course information

Instructor: Alfred Galichon

Schedule and location: Tuesdays, 4pm-6pm until Spring Break. Classes will meet February 3, 10, 17, 24, and March 3, 10, 17. Location: E17-128.

Validation: Paper to be discussed with instructor.

Course material

Available before each lecture.

Description of the Course

This course is an introduction to the theory of Optimal Transportation, with a focus on applications to Economic Modeling and Econometrics. The basic results in Optimal Transportation will be covered, as well as its relations to linear programming, network flow problems, convex analysis, and computational geometry. Several applications to various fields (econometrics, family economics and labor economics) will be given: discrete choice models, identification and estimation of matching markets with Transferable Utility, and of hedonic models.

Recommended (though not required) text: C. Villani, Topics in Optimal transportation, AMS, 2003.

Organization of the Course

L1. Monge-Kantorovich theory. Application: optimal assignments
Reference: Villani, Ch. 1.1; Roth & Sotomayor, Ch 8. Complements: Shapley & Shubik (1972).

L2. Univariate case. Application: Becker’s model of matching
Reference: Villani 2.2; Lorentz (1953); Becker (1973). Complement: Chernozhukov, Galichon, & Fernandez-Val (2010).

L3. Power diagrams. Application: Characteristics-based demand
Reference: Aurenhammer (1987); Anderson, de Palma & Thisse, Ch. 4. Complements: Feenstra & Levinsohn (1995); Fryer & Holden (2011).

L4. Quadratic surplus. Application: principal-agent problems
Reference: Villani, 2.1, Carlier (2011), Ch. 3.2.

L5. Convex duality. Application: discrete choice models
Reference: Anderson, de Palma & Thisse, Ch. 3, Carlier (2010), Ch. 3.2; Galichon & Salanié (2014).

L6. Network flow problems. Application: econometrics of hedonic models
Reference: Vohra (2011), Ch. 3; Chiappori, McCann & Nesheim (2011); Dupuy, Galichon & Henry (2014). Complements: Villani, Ch. 5 and Ch. 8; Koopmans (1949); Ekeland, Heckman and Nesheim (2004); Heckman, Matzkin & Nesheim (2010).

L7. Schrodinger systems. Application: econometrics of matching
Reference: Choo & Siow (2006); Dupuy & Galichon (2014).

Bibliography

• Anderson, de Palma, and Thisse (1992). Discrete Choice Theory of Product Differentiation. MIT Press.
• Aurenhammer, F. (1987). “Power diagrams: properties, algorithms and applications,” SIAM Journal on Computing.
• Becker, G. (1973). “A theory of marriage, part I,” Journal of Political Economy.
• Carlier, G. (2001). “A general existence result for the principal-agent problem with adverse selection,” Journal of Mathematical Economics.
• Carlier, G. (2010). Lecture notes on “Optimal Transportation and Economic Applications.”.
• Chernozhukov, V., Galichon, A., & Fernandez-Val, I. (2010). “Quantile and probability curves without crossing,” Econometrica.
• Choo, E., and Siow, A. (2006). “Who Marries Whom and Why,” Journal of Political Economy.
• Chiappori, P.-A., McCann, R., and Nesheim, L. (2010). “Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness,” Economic Theory.
• Dupuy, A., and Galichon, A. (2014). “Personality traits and the marriage market,” Journal of Political Economy.
• Dupuy, A., Galichon, A. and Henry, M. (2014). “Entropy Methods for Identifying Hedonic Models,” Mathematics and Financial Economics.
• Ekeland, I., J. Heckman, and L. Nesheim (2004): “Identification and estimation of hedonic models,” Journal of Political Economy.
• Feenstra, R., and Levinsohn, J. (1995). “Estimating Markups and Market Conduct with Multidimensional Product Attributes”. Review of Economic Studies.
• Fryer, R. and Holden, R. (2011). “Measuring the Compactness of Political Districting Plans.” Journal of Law and Economics.
• Galichon, A., and Salanié, B. (2014). “Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models”. Working paper.
• Heckman, J., R. Matzkin, and L. Nesheim (2010). “Nonparametric identification and estimation of nonadditive hedonic models,” Econometrica.
• Koopmans, T. C. (1949), “Optimum utilization of the transportation system”. Econometrica.
• Lorentz, G. (1953), “An inequality for rearrangements”. American Mathematical Monthly.
• Roth, A., and Sotomayor, M. (1990). Two-Sided Matching A study in Game-Theoretic Modeling and Analysis.
• Shapley, L. and Shubik, M. (1972) “The assignment game I: the core”. International Journal of Game Theory.
• Villani, C. (2003). Topics in Optimal transportation. Lecture Notes in Mathematics, AMS.
• Vohra, R. (2011). Mechanism Design. A Linear Programming Approach. Cambridge University Press.

Mini-course

Estimation of Matching Models

Toulouse School of Economics, June, 2014 (6h)

Course material

Available here.

Description of the Course

These lecture aims at providing an empirical framework for matching models with heterogeneity in tastes and general transfer technologies. They are organized in two parts:
1. Generalized Entropy of Choice and Capacity-constrained Discrete Choice. We first revisit the literature on random utility models by emphasizing the role of a proper generalization of the notion of entropy, defined using Legendre transforms. The duality between the selection model and the assignment model follows, as well as the duality between the equilibrium characterization problem and the identification problem.
2. Equilibrium characterization and identification in matching models. The previous theory is then applied to characterize equilibrium and provide identification in matching models with imperfectly transferable utility (ITU), including as special cases both the transferable utility (TU) and nontransferable utility (NTU) models.

References

Chiong, K., Galichon, A., and M. Shum, “Duality in dynamic discrete choice models”
Galichon, A., “DARUM: Deferred Acceptance for Random Utility Models”.
Galichon, A., S. D. Kominers and S. Weber, “Costly Concessions: Estimating the Unintended Consequences of Policy Intervention in Matching Markets”
Galichon, A. and B. Salanié, “Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models”

Mini-course

Estimation of Matching Models With and Without Transferable Utility

Fields Institute, September 17, 2014 (4h)

Course material

Available here.

Description of the Course

This lecture aims at providing an empirical framework for matching models with heterogeneity in tastes and general transfer technologies. It is organized in two parts:
1. Generalized Entropy of Choice and Capacity-constrained Discrete Choice. We first revisit the literature on random utility models by emphasizing the role of a proper generalization of the notion of entropy, defined using Legendre transforms. The duality between the selection model and the assignment model follows, as well as the duality between the equilibrium characterization problem and the identification problem.
2. Equilibrium characterization and identification in matching models. The previous theory is then applied to characterize equilibrium and provide identification in matching models with imperfectly transferable utility (ITU), including as special cases both the transferable utility (TU) and nontransferable utility (NTU) models.

References

Bonnet, O., Galichon, A., and M. Shum, “Yoghurt chooses man: estimating nonadditive discrete choice models”
Chiong, K., Galichon, A., and M. Shum, “Duality in dynamic discrete choice models”
Galichon, A., “DARUM: Deferred Acceptance for Random Utility Models”.
Galichon, A., S. D. Kominers and S. Weber, “Costly Concessions: Estimating the Unintended Consequences of Policy Intervention in Matching Markets”
Galichon, A. and B. Salanié, “Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models”

Master Class

Linear Programming: Theory and Economic Applications

Sciences Po Summer 2014 (8h)

Course material

Available here.

Description of the Course

The course will focus on linear programming and its economic applications. The main concepts (feasibility, duality, complementary slackness) will be introduced. Algorithms and softwares will be discussed. Various applications will be proposed: optimal assignments, flows on networks, Walrasian equilibrium, discrete choice theory.

Day 1. (4h)
General introduction.
Fundamentals 1: Basic concepts and duality.
Application 1: Optimal assignments.
Application 2: Network flows.

Day 2. (4h)
Fundamentals 2. Computation: algorithms and softwares..
Application 3: Walrasian equilibrium.
Application 4: Discrete choice theory.

KECD 2175 – Seminar

Matching markets: theory and applications

Sciences Po, M2 Economics and Public Policy, PhD track Spring 2014 (24h)

Course information

Instructor: Alfred Galichon

Schedule: Mondays, 8am-10am, starting January 20, 2013. Classes will meet Jan 20, 27, Feb 3, 10, 17, Mar 3, 10, 17, 24, 31, and Apr 7 and 14.

Location: D501 – 199 bld Saint-Germain.

Validation: A test will be organized during last class.

Course material

Please email.

Description of the Course

The course will focus on the economic theory and the econometrics of matching and complementarities. It is intended to give the attendees an overview of the basic theory of matching with Transferable Utility, its testable implications, as well as its application to various fields such as labor economics, family economics, international trade and industrial organization. A particular emphasis is put on the empirical aspects and identification issues, and numerical methods will also be discussed. This course will not cover matching models without money and the Gale and Shapley algorithm (and applications such as the school choice problem, kidney exchanges) which will be covered in Sidartha Gordon’s Microeconomics 3 course.

Part I. Theory (9h)

1. Optimal matching and stability (9h). General introduction. Shapley-Shubik, welfare theorems. Network flows (time permitting). Optimization: theory and numerical methods.

Part II. Applications (15h)

2. The economics of the marriage market (5h). The Becker model. Choo and Siow’s model.

3. The economics of the labor market (5h). The Sattinger-Rosen “hedonic” approach. Rosen’s theory of superstars. CEO compensation.

4. International trade (5h). The Roy model. Ricardian models and Gravity revisited.

KFIN 2655A – 16243

Decision under Risk

Sciences Po, M2, Finance and Strategy and M2, Financial Regulation and Risk Management
Winter 2013 (24h)

Course material

The course material is available here.

The institutional web page of the course is here.

Final exam’s grade statistics:

Course information

Teaching assistant is Odran Bonnet. Email: odran.bonnet@sciencespo.fr

Schedule: Tuesdays, 8am-10am, starting September 3, 2013.

Location: Albert Sorel – Leroy-Beaulieu (27, St Guillaume – 3^ème étage, escalier des amphis).

Validation: Midterm (3h) and Final exam (3h).

Description of the course

This course is intended to give the students an overview on how the main concepts from Economics are used to deal with financial risks. It will put together many of the financial concepts seen across the master in a coherent framework, and will demonstrate how they are used in practice to make decisions facing risk. Risk is considered from three point of views: households, firms and the state.

First, individual decisions of households facing risk (insurance, investment, saving) are explored using Markowitz and Sharpe’s portfolio theory, with its implications for the asset management industry (L2). The notion of market for risk is presented in Arrow and Debreu’s equilibrium framework, with an application to prediction markets (L3). The limits of the mainframe theory are presented based on recent developments from behavioral finance and from macroeconomics (L4).

Second, the point of view of the firm is taken. What drives exchanges of risk? Are firms risk averse? The question is examined in the light of the Modigliani and Miller paradigm, and its consequences for financial disintermediation (L5). Economic theory suggests individual incentives within firms are a key aspect of the risk-taking behavior of the latter; applications to CEO compensation and capital structure are explored (L6). The conditions for risk to be traded efficiently are not always met; the concept of “market failures” is investigated, in particular moral hazard and adverse selection, which threaten the existence of some markets (L7).

Third, the point of view of the state is discussed. What is the rationale for the state to interfere with individual risk decisions? First, paternalism: agents may not take optimal decision for themselves. We shall discuss the welfare state and alternative models (L8). Second, externalities: risk taking behavior by financial institutions may have negative consequences for other market participants. We shall explore the essence of systemic regulation and its main tools (L9). We shall discuss financial bubbles and crisis, and investigate the case  for policy intervention (L10).

Two lectures will conclude the course. A case study will draw lessons from the past crisis in terms of risk management (L11). The last lecture will open up perspectives, especially in terms of careers opportunities (L12).

KECD 2175 – Seminar

Matching markets: theory and applications

Sciences Po, M2 Economics and Public Policy, PhD track
Spring 2013 (24h)

Please note: this is the webpage of a previous year. To go to the current year’s course webpage, please visit

http://alfredgalichon.com/courses/.

Lecture slides

The lecture slides  will be distributed in class or emailed upon request. A syllabus is available here.

Lecture 1 (1/23/2013): Introduction.
Lecture 2 (1/30): The optimal assignment problem.
Lecture 3 (2/6): Stability and the core. Optimal transportation.
Lecture 4 (2/13): Optimal transportation (continued). Assortative mating.
Lecture 5 (2/20): Transportation on networks.
Lecture 6 (2/27): The theory of hedonic models (1).
No lecture 3/6 (holidays).
Lecture 7 (3/13): The theory of hedonic models (2).
Lecture 8 (3/20): The econometrics of hedonic models (1).
Lecture 9 (3/27): The econometrics of hedonic models (2)
Lecture 10 (4/10): The econometrics of matching models: handout.
Lecture 11 (4/16): Search and friction in matching: handout.
Lecture 12 (4/17): Final exam. Perspectives: handout.

Course information

Schedule: Wednesdays, 8am-10am, starting January 23, 2013.

Location: Room H S2, 28 rue des Saints-Pères.

Validation: A test will be organized during last class.

Description of the course

The course will focus on the economic theory and the econometrics of matching  from a number of points of view. It is intended to give an overview of the basic theory of matching with transferable utility, its testable  implications, as well as its application to various fields such as hedonic models, labor economics, family economics, and to a lesser extent some other topics such as geographical economics and industrial organization. A particular emphasis is put on the empirical aspects and identification issues, and numerical methods will also be discussed.

The institutional web page of the course is here.

Available slides:

• Ivar Ekeland
• Chloe Jimenez
• Pierre-Noel Giraud
• Jean-Michel Lasry
• Pascal Mossay
• Walter Scachermayer