KECD 2195

Advanced topics in microeconometrics: Matching Models and their Applications

Sciences Po, Economics Department, PhD Course Spring 2018

Course information

Instructor: Alfred Galichon.

Schedule: Mondays, 8am-10am, starting January 29, 2016.

Class meets: Jan 29, Feb 5,12,19, Mar 5(+),12,19(+),26, Apr 9,16,23,30.

Location: 28 SP, H103.

Course material: Available on this github repository.

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

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
Available after each lecture on the class webpage at url http://alfredgalichon.com/microeconometrics2018s.
Description of the Course
This course provides the mathematical and computational tools needed for an operational knowledge of discrete choice models, matching models, and network flow models. A number of economic applications of these concepts will be discussed.
The first part of the course will introduce basic results around Optimal Transportation 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. Simulation 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 or Iterative Fitting. 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.
Time permitting, the fourth and last part will provide an introduction to problems on networks. The basic tools to describe the topology on a network will be described: discrete differential operators, diffusions on networks, shortest paths on networks. The Optimal Transport problem on networks will be formulated, along with its extension to stochastic utility.

Textbooks
The first part of the course will be based on my textbook:
• [OTME] Optimal Transport Methods in Economics (Princeton University Press, in press), a draft of which is available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2699381.
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] Train, K.. Discrete Choice Methods with Simulation. 2nd Edition. Cambridge University Press, 2009.
• [TOT] C. Villani, Topics in Optimal transportation, AMS, 2003.
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: [OTME] chapters 1 and 2.
Complements: [TOT], chapter 1.
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).

Part IV: Network models
L12. Optimal flow problems
• Basic concepts
• Min-cost flow problem
• Incorporating Stochastic Utility
Reference: [OTME], ch. 8. Koopmans (1949).
L13. Equilibrium flow problems
• Traffic equilibrium with congestion
• The Equilibrium Flow Problem.
Reference: Carlier (2010).
L14. Hedonic models
• Hedonic Equilibrium: definition and existence
• Estimation
Chiappori, McCann & Nesheim (2010), Ekeland, Heckman & Nesheim (2004), Dupuy, Galichon & Henry (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. (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 for Economics. Princeton University Press, in 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.

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).

Schedule:
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.

Texts:
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 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).

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. (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.

ECON.GA 3002.09 and MATH.GA 2840.03

Matching Models And Their Applications

NYU, Economics Department and Courant Institute, PhD Course Spring 2016

Course information

Instructor: Alfred Galichon.

Schedule: Mondays, 9am-10:50am, starting January 25, 2016.

Class meets Jan 25, Feb 1, 8, 22, 29, March 7, 21, 28, April 4, 11, 18, 25, May 2, 9.
** OPTIONAL LECTURE ON MAY 16, 9AM-11AM IN WWH 1302. **

Location: Courant Institute (Warren Weaver Hall, 251 Mercer) #201.

Validation: 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.

Texts: The first part of the course will be based on my text:
[OTME] A. Galichon. Optimal Transport Methods in Economics (Princeton University Press, in press), a draft of which is available here.
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 before each lecture.

Description of the Course

This course provides the mathematical and computational tools needed for an operational knowledge of discrete choice models, matching models, and network flow models. A number of economic applications of these concepts will be discussed.
The first part of the course will introduce basic results around Optimal Transportation 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 or Iterative Fitting. 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.
The fourth and last part will provide an introduction to problems on networks. The basic tools to describe the topology on a network will be described: discrete differential operators, diffusions on networks, shortest paths on networks. The Optimal Transport problem on networks will be formulated, along with its extension to stochastic utility.

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).

Part IV: Network models

L12. Optimal flow problems

• Basic concepts
• Min-cost flow problem
• Incorporating Stochastic Utility

Reference: [OTME], ch. 8. Koopmans (1949).

L13. Equilibrium flow problems

• Traffic equilibrium with congestion
• The Equilibrium Flow Problem.

Reference: Carlier (2010).

L14. Hedonic models

• Hedonic Equilibrium: definition and existence
• Estimation

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

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.

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.

Columbia University G6232, Spring 2011

Course information

Lecturer: Alfred Galichon,
Office: SIPA building, Rm 1113. Please schedule appointment by email.
Time and Location: Tu 11am-12:50pm, location 1027 International Affairs Building.
Course starts Feb 1.
Texts: No text is required. A worthwhile reading is Roth and Sotomayor, Two-Sided Matching A study in Game-Theoretic Modeling and Analysis, Cambridge.
Grading: Students taking this course for credit should write a paper relevant to an aspect of the course, to be dicussed with the instructor. This course will be graded on a pass/fail basis.

Description of the Course

The course will focus on the economic theory of matching both from a theoretical and empirical point of views. It is intended to give the attendees an overview of the fundamental theory of the optimal assignment problem, as well as its application to various fields such as labor, family and transportation economics. A particular emphasis is put on the empirical aspects and identification issues, and the main matching algorithms will also be discussed. The last part of the course tries to make a link with matching games with nontransferable (or partially transferable) utility and attempts to provide a unified treatment.

A syllabus can be found here.

The lecture notes can be found here.

Course outline

Part I. Matching with Transferable Utility (TU) Feb 1,8,15. 11am-1pm.
General introduction to matching. Optimal matching and duality. Optimal transportation theory.

Part II. Empirical issues in TU models. Feb 22, March 1, 8, 15. 11am-1pm.
Identification and estimation issues. Computational issues. Economics of the family. Hedonic models.

Part III. Matching with Non-transferable Utility (NTU) March 22, 29, April 5, 12, 19. 11am-1pm.
The stable marriage problem and the Gale-Shapley procedure. The kidney problem. Linking TU and NTU models. Empirical issues in NTU matching. Incorporating frictions and search. Matching with contracts.

There will be two make-up classes which are informal “crash courses” on more technical aspects of the subject. Attendance is encouraged, but not necessary for following the rest of the course.
Feb 8, 9–11am. Crash course on convex analysis and linear programming.
Feb 22, 9-11am. Crash course on algorithms and computational issues.