# optimaltransport-2015S

## 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 here.

Examples in R are here.

### 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.