Econometrics, Quantitative Economics, Data Science

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Short course

Optimal Transport Methods in Economics

Toulouse School of Economics, Fall 2017 (15h)

Course material

The lecture slides will be available before each lecture.

Description of the Course

These lectures will introduce the theory of optimal transport, and various applications to economics and finance.



Monday, Oct 9, 3:30pm–6:30pm
Monday, Oct 16, 3:30pm–6:30pm
Monday, Nov 6, 3:30pm–6:30pm
Monday, Nov 13, 3:30pm–6:30pm
Monday, Nov 20, 3:30pm–6:30pm


Older Lecture series

(Recent and upcoming lecture series can be found here.)


Older Talks

(Recent and upcoming talks can be found here.)

  • July 10, 2014, Economics seminar, EIEF, Rome
  • June 19, 2014, Conference in honor of Ivar Ekeland’s 70th birthday, Université Paris Dauphine
  • June 16-29, 2014, Guest Lectures on the Econometrics of Matching Markets, Toulouse School of Economics
  • June 5, 2014, Workshop on Econometrics Methods, Sciences Po
  • June 4, 2014, Economics seminar, Aalto University, Helsinki
  • May 19, 2014, NERA / STICERD Industrial Organization seminar, London School of Economics
  • April 10, 2014, Malinvaud Seminar, CREST, Paris
  • March 17, 2014, Roy Seminar, Paris
  • March 4, 2014, EPFL, Lausanne
  • February 14, 2014, Séminaire Léon Brillouin, IRCAM, Paris. Video here.
  • November 22, 2013, Research seminar, Austrian Central Bank, Wien
  • October 19, 2013, Harvard-MIT econometrics seminar
  • September 13, 2013, lunch seminar, Sciences Po Department of Economics


  • June 11, 2013, workshop “Advances in Mechanism Design”, Paris School of Economics
  • June 6, 2013, workshop on Economic Theory, University of Manchester
  • June 5, 2013,  Finance & Stochastics seminar, Imperial College London
  • May 16, 2013, Econometrics and Statistics Seminar, Ecares, Université Libre de Bruxelles
  • May 10, 2013,  joint Econometrics-Family economics workshop, University of Chicago
  • April 26, 2013, Econometrics Seminar, Università della Svizzera italiana, Lugano
  • April 22-26, 2013, Workshop “Partial Identification”, Oberwolfach
  • April 8, 2013, Lunch seminar, Economics Department, Ecole Polytechnique
  • March 5, 2013, brown bag seminar, CalTech
  • February 19, 2013, Conference in honor of Rose-Anne Dana, Dauphine
  • December 14, 2012, Groupe de Travail Humaniste, Université Pierre-et-Marie-Curie, Paris
  • November 26-30, 2012, Workshop “Frontiers in Quantile Regression”, Oberwolfach
  • November 22, 2012, Econometrics seminar, Universite de Montreal
  • November 12, 2012, Econometrics seminar, Queen Mary University, London
  • November 5, 2012, Economics Research Seminar, ETH, Zurich


  • June 21, 2012, “OTtO” workshop, Orsay
  • June 8, 2012, FiME workshop, IHP, Paris
  • May 21-25, 2012, Guest lecture, French Statistical Society, Brussels
  • May 16, 2012, Economics Seminar, Stanford GSB
  • May 4, 2012, Economics Seminar, SciencesPo, Paris
  • May 2, 2012, Economics Seminar, Paris School of Economics
  • April 11, 2012, Economics Seminar, HEC, Paris
  • March 29, 2012, Econometrics Seminar, Columbia University
  • March 15, 2012, Malinvaud Seminar, CREST, Paris
  • March 5, 2012, Economics Seminar, Queen Mary University, London
  • March 2, 2012, Economics Seminar, University of Alicante
  • December 14, 2011, Econometrics and Statistics seminar, Tilburg University
  • December 7, 2011, ESRC Seminar on testability in game theory, Warwick
  • November 25, 2011, Plenary speaker, Conference on Optimization & Practices in Industry, Clamart


  • June 7, 2011, Finance seminar, Imperial College, London
  • May 20, 2011, Econometrics seminar, DEFI, Université de la Méditerranée
  • May 9, 2011, Séminaire Parisien d’Optimisation, Institut Henri Poincare
  • March 2, 2011, Econometrics colloquium, Columbia University
  • Feb 21, 2011, Economic Theory Seminar, Columbia University
  • Jan 8, 2011, Econometric Society Winter Meeting, Denver
  • Dec 13, 2010, 2nd meeting of the French Econometrics Society, Paris
  • Nov 30, 2010, Econometrics seminar, Cemmap, University College London
  • Nov 25, 2010, Workshop “Recent Advances in Revelealed Preferences,” Universite Paris-Dauphine, Paris
  • Oct 27, 2010, Economics department, University of British Columbia, Vancouver
  • Sept 24, 2010, Conference “Partial Identification and Revealed Preferences,” Montreal
  • Sept 1, 2010 Conference OKASE, Toulouse School of Economics
  • Aug 19, 2010, Econometric Society World Congress, Shanghai


  • June 2, 2010, Econometrics workshop, UCLA
  • May 19, 2010, Econometrics seminar, UC Riverside
  • May 18, 2010, Econometrics seminar, UC San Diego
  • May 13, 2010, Labor Economics and Econometrics seminar, Northwestern University
  • May 12, 2010, Econometrics workshop, University of Chicago, Economics Department
  • May 5, 2010, Stochastic Analysis Seminar, Institut Henri Poincaré
  • April 27, 2010, Economic Theory seminar, Vanderbilt University
  • April 15, 2010, Econometrics and Statistics seminar, University of Chicago Booth School of Business
  • April 7, Econometrics and applied microeconomics seminar, CalTech
  • March 16, 2010, Conference “Large portfolio, Concentration and Granularity,” Paris
  • March 8, 2010, Econometrics seminar, Paris School of Economics
  • Feb 4, 2010, Econometrics seminar, Columbia University
  • Jan, 4, 2010, North American Winter meeting of the Econometric Society, Atlanta
  • Dec 17, 2009, Stochastics seminar, University of Freiburg
  • Dec 4, 2009, Bachelier Seminar, Paris
  • Oct 13, 2009, Economic Theory seminar, Toulouse School of Economics


  • July 7, 2009, “Optimization, Transport and Equilibrium” workshop, Paris
  • June 3, 2009, North American Summer Meeting of the Econometric Society, Boston
  • April 20, 2009, Risk Seminar, Department of Statistics, Columbia University
  • March 20, 2009, 2nd International Financial Research Forum, Europlace Institute of Finance, Paris
  • Feb 28, 2009, conference “New Economics of the Family”, Milton Friedman Institute, the University of Chicago
  • Jan 16, 2009, IHPST, Paris
  • Nov 32, 2008, Statistics seminar, LUISS, Rome
  • Oct 24, 2008, Cireq conference on Inference with Incomplete Models, Montreal
  • Oct 17, 2009, Workshop on dynamic and multivariate measures, IHP, Paris
  • Oct 6, 2008, Collegio Carlo Alberto, Torino


  • Jul 18, 2008, “Optimization, Transport and Equilibrium” workshop, University of British Columbia, Vancouver
  • June 26, 2008, “Risk, Decision and Uncertainty” conference, Oxford
  • June 12, 2008, Workshop “Nonsmooth Inference, Analysis and Dependence,” Goteborg
  • June 12, 2008, Finance seminar, Toulouse School of Economics
  • May 22, 2008, Finance seminar, Universite de Geneve
  • May 20, 2008, Workshop on New Directions in Quantitative Finance, Paris
  • May 16, 2008, Bachelier Seminar, Paris
  • March 28, 2008, Conference “Inference in Partially Identified Models and Applications,” UCL, London
  • Jan 5, 2008, North American Winter meeting of the Econometric Society, New Orleans
  • Nov 29, 2007, Malinvaud seminar, CREST, Paris
  • Nov 9, 2007, Workshop “Model Validation, Predictive Ability and Model Risk,” Banque de France, Paris
  • June 25, 2007, “Optimization, Transport and Equilibrium” workshop, Columbia University
  • May 22, 2007, Econometrics Seminar, Northwestern University
  • April 27, 2007, PhD Defense, Harvard University



Past Classes

(Current classes can be found here.)
“Matching Markets: Theory and Applications”. PhD course, Sciences Po, Spring 2014.
“Decision under risk”. Master (M2) Finance and Strategy and Financial Regulation and Risk Management, Sciences Po, Winter 2013.
“Matching Markets: Theory and Applications”. PhD course, Sciences Po, Spring 2013.
“Economics of the Firm”. Undergraduate course, Ecole Polytechnique, Winter 2011.
“Theoretical and Empirical Aspects of Matching Markets”. PhD Course, Columbia University, Winter 2011.
“Business statistics,” MBA course, Chicago University, Booth School of Business, Winter 2010.
“Corporate and Financial Strategy”. Master (M1) course, Ecole Polytechnique, 2007-2011.
“Asset Pricing and Economics of Uncertainty”. Master (M1) course, Ecole Polytechnique, 2007-2010.

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Best of my (scientific) bookshelf

Without any logical order or any explanation of my picks, here is a selection of my very favorite books:

  • Villani, C. (2003). Topics in Optimal Transportation. AMS.
  • Vohra, R. (2011). Mechanism design. A linear programming approach. Cambridge.
  • Vohra, R. (2004). Advanced Mathematical Economics. Routledge.
  • Frankel, T. (2012). The geometry of physics. An introduction. Cambridge.
  • Gale, D. (1960). The theory of linear economic models. Chicago.
  • Burkard, R. Dell’Amico, M., Martello, S. (2012) Assignment Problems. SIAM.
  • Henry-Labordere, P. (2008). Analysis, Geometry, and Modeling in Finance: Advanced methods in option pricing. Chapman & Hall.
  • Roth, A. and Sotomayor, M. (1990). Two-sided matching. A Study in Game-Theoretic Modeling and Analysis. Cambridge.
  • Border, K. (1989). Fixed Point Theorems with Applications to Economics and Game Theory. Cambridge.
  • Krishna, V. (2010). Auction Theory. Second edition. Elsevier.
  • Hiriart-Urruty, J.-B., and Claude Lemaréchal, C. (2004). Fundamentals of Convex Analysis. Springer.
  • Aubin, J.-P., and Ekeland, I. (2006). Applied nonlinear analysis. Dover.
  • Grady, L., and Polimeni, J. (2010). Discrete Calculus: Applied Analysis on Graphs for Computational Science. Springer.
  • Bertsekas, D. (1998). Network Optimization: Continuous and Discrete Models (Optimization, Computation, and Control). Athena Scientific.
  • Bobzin, H. (2008). Principles of Network Economics. Springer.
  • Rheinboldt, W. (1987). Methods for Solving Systems of Nonlinear Equations. SIAM.
  • Bhatia, R. (2011). Matrix Analysis. Springer.
  • Horn, R. and Johnson, C. (1994). Topics in Matrix Analysis. Cambridge.


DS-GA 3001

Introduction to Causal Inference for Data Scientists

NYU, Center for Data Sciences, NYU Spring 2017

Course information

Instructor: Alfred Galichon (NYU FAS Economics and CIMS Mathematics).
Section leader: Yifei Sun (NYU CIMS Mathematics).

Lecture: Thursday 4:55pm – 6:35pm
Lab: Thursday 6:45pm – 7:35pm

Location (lecture and lab): 60 Fifth Avenue, Room 110.


ECON-GA 1802.001 and MATH.GA 2840.02

Matching Models And Their Applications.

NYU, Economics Department and Courant Institute, PhD Course Spring 2017

Course information

Instructor: Alfred Galichon.

Class meets on Mondays 9am-10:50am in WWH 102.

Assessment: A short paper (12 pages or more), to be discussed with the instructor. The paper will bear some connections, in a broad sense, with the topics of the course. Many papers are considered acceptable: original research paper, survey paper, report on numerical experiments, replication of existing empirical results… are all acceptable.

The first part of the course will be based on my text:
[OTME] A. Galichon (2016). Optimal Transport Methods in Economics, Princeton University Press.
The second part will be based on lecture notes distributed in class.

Other textbooks used for reference (although not required) are:
[TSM] A. Roth and M. Sotomayor. Two-Sided Matching A study in Game-Theoretic Modeling and Analysis, Monographs of the Econometrics Society, 1990.
[DCMS] K. Train. Discrete Choice Methods with Simulation. 2nd Edition. Cambridge University Press, 2009.
[TOT] C. Villani, Topics in Optimal transportation, AMS, 2003.

Course material

The lecture notes will be available here before each lecture.

Description of the Course

This course provides the mathematical and computational tools needed for an operational knowledge of discrete choice models, and matching models. A number of economic applications of these concepts will be discussed.
The first part of the course will introduce basic results around optimal transport theory: the Monge-Kantorovich duality, the optimal assignment problem, basic results in linear programming, and convex analysis. Those concepts will serve as building blocks in the sequel.
The second part will cover discrete choice models, from the classical theory to more recent advances. The classical generalized extreme value (GEV) specification will be recalled, as well as maximum likelihood estimation in the parametric case. Comparative statics results will be derived using tools from convex analysis, and nonparametric identification will be worked out using optimal transport theory. Simulations methods will be covered. A computationally intensive application will be demonstrated.
The third part will be devoted to matching models with stochastic utility, starting with the transferable utility (TU) case which is then generalized to imperfectly transferable utility (ITU) including non-transferable utility (NTU). Equilibrium computation in the general case will be worked out using techniques from general equilibrium. The more specific, but empirically relevant logit case, will be efficiently addressed using more the specific techniques of alternated projections. Various algorithms will be described and compared in practice. Moment matching estimation and maximum likelihood estimation will be worked out and compared. Several applications, to collective models of family economics, and to labor markets with taxes, will be described.

Organization of the Course

Part I: An introduction to Optimal Transport theory

L1. Monge-Kantorovich duality

  • Primal and dual formulations
  • The Monge-Kantorovich theorem
  • Equilibrium and Optimality

Reference: [TOT], Ch. 1; [OTME] ch. 2

L2. The optimal assignment problem

  • Linear programming duality
  • Purity, Stability
  • Computation

Reference: [OTME], ch. 3, [TSM], Ch 8.
Complements: Shapley & Shubik (1972).

L3. The Becker model

  • Copulas and comonotonicity
  • Positive Assortative Matching
  • The Wage Equation

Reference: [OTME], ch. 4. [TOT], Ch. 2.2

L4. Convex conjugacy

  • Basics of convex analysis: Convex conjugates, Subdifferential, Fenchel-Young inequality
  • Brenier’s theorem

Reference: [OTME], ch. 6. [TOT], ch. 2.1.


Part II: Discrete Choice models

L5. The logit model and its extensions

  • The Logit model and its parametric estimation
  • The Generalized Extreme Value (GEV) model
  • The Daly-Zachary-Williams theorem

Reference: [DCMS], ch. 2-4, Anderson, de Palma & Thisse, Ch. 3, Carlier (2010).

L6. Identification of discrete choice models

  • Reformulation as an Optimal Transport problem
  • Consequences on the structure of the identifed set
  • The Random Scalar Coefficient Model
  • Incorporating peer effects

Reference: Hotz and Miller (1993), Chiong et al. (2014), Galichon and Salanie (2015).

L7. Simulation methods

  • Simulation methods for parametric estimation
  • Probit and the GHK simulator
  • Simulation methods for nonparametric estimation

Reference: [DCMS], ch. 5 and 9, Chiong et al. (2014).


Part III: Matching models

L8. Models with transferable utility

  • The TU-logit model of Choo and Siow
  • Beyond Logit: general heterogeneity
  • Simulation methods
  • Moment matching estimation; Maximum Likelihood Estimation

Reference: Choo and Siow (2006), Galichon and Salanie (2015).

L9. Estimation of complementarity

  • Index models
  • Affinity matrix estimation
  • Application: marital preference estimation

Reference: Chiappori, Oreffice and Quintana-Domeque (2012), Dupuy and Galichon (2014).

L10. Models with imperfectly transferable utility

  • Equilibrium: Existence and Uniqueness
  • The ITU-logit model
  • Computation
  • Maximum Likelihood Estimation

Reference: Galichon, Kominers and Weber (2015).

L11. Models with non-transferable utility

  • Models with no idiosyncratic utility shocks
  • Models with idiosyncratic utility shocks

Reference: Dagsvik (2000), Menzel (2015), Galichon and Hsieh (2015).

L12. Hedonic models

  • Hedonic Equilibrium: definition and existence
  • Estimation

Chiappori, McCann & Nesheim (2010), Ekeland, Heckman & Nesheim (2004), Dupuy, Galichon & Henry (2014).


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. (2010). Lecture notes on “Optimal Transportation and Economic Applications.”.
Chiong, K, Galichon, A., Shum, M. “Duality in dynamic discrete choice models.”
Quantitative Economics, forthcoming.
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.
Pierre-André Chiappori, Sonia Oreffice and Climent Quintana-Domeque, C. (2012). “Fatter Attraction: Anthropometric and Socioeconomic Matching on the Marriage Market,”
Journal of Political Economy 120, No. 4, pp. 659-695.
Dagsvik, J. (2000) “Aggregation in matching markets,”
International Economic Review 41, 27-57.
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.
• Galichon, A. (2016). Optimal Transport Methods in Economics, Princeton University Press.
• Galichon, A., Hsieh, Y.-W. (2015). “Love and Chance: Equilibrium and Identification in a Large NTU matching markets with stochastic choice”.
• Galichon, A., Kominers, S., and Weber, S. (2015). Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility.
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.
Hotz, V.J. and Miller, R.A. (1993). “Conditional Choice Probabilities and the Estimation of Dynamic Models”.
Review of Economic Studies 60, No. 3 , pp. 497-529.
Koopmans, T. C. (1949), “Optimum utilization of the transportation system”. Econometrica.
Menzel, K. (2015). Large Matching Markets as Two-Sided Demand Systems. Econometrica 83 (3), pages 897–941.
• 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.
• Train, K. (2009).
Discrete Choice Methods with Simulation. Cambridge University Press.
• Villani, C. (2003).
Topics in Optimal transportation. Lecture Notes in Mathematics, AMS.
• Vohra, R. (2011).
Mechanism Design. A Linear Programming Approach. Cambridge University Press.


CORE lectures

Optimal Transport And Economic Applications: Modelling and Estimation

CORE Louvain-la-Neuve, June, 2016 (9h)

Course material

The lecture slides will be available before each lecture.

Description of the Course

These lectures will introduce the theory of optimal transport, and applications to discrete choice analysis and to the estimation of matching markets. The basics of optimal transport are recalled. A compact presentation of additive demand models and matching models with transferable utility is given. The second part of the course deals with the statistical estimation of these models and presents empirical applications.



Monday June 6, 2016: Monge-Kantorovich theory
04:00 p.m.-5:30 p.m. Monge-Kantorovich duality; the optimal
assignment problem

Tuesday June 7, 2016: Models of choice and matching
11:00 a.m.-12:30 p.m. Optimal transport and convex analysis
02:00 p.m.-03:30 p.m. Models of choice
04:00 p.m.-05:30 p.m. Matching models with transferable utility

Wednesday June 8, 2016: Estimation of matching models and empirical applications
09:00 a.m.-10:30 a.m. Estimation of matching surplus
11:00 a.m.-12:30 p.m. Matching function equilibria: theory and estimation