Short course

Optimal transport and economic applications

PSE summer school, June 22-26, 2020

Content

This short course is focused on optimal transport theory and matching models and their applications to economics, in various fields such as labor markets, economics of marriage, industrial organization, matching platforms, networks, and international trade. It will provide the crossed perspectives of theory, empirics and computation. A particular emphasis will be given on computation (R and Python). This course is partly based on Galichon’s 2016 monograph, Optimal Transport Methods in Economics. Princeton University Press.

Schedule

Wednesday, June 24, 9am-12:30pm
Thursday, June 25, 9am-12:30pm
Friday, June 26, 9am-11am

Course material

The lecture slides will be available before each lecture.

References

These lectures will be based on my text:
Galichon, A. (2016). Optimal transport methods in economics. Princeton.

Other references include:
∙ For mathematical foundations:
– [OTON] C. Villani, Optimal Transport: Old and New, AMS, 2008.
– [OTAM] F. Santambrogio, Optimal Transport for Applied Mathematicians, Birkhäuser, 2015.
∙ For an introduction with a fluid mechanics point of view:
– [TOT] C. Villani, Topics in Optimal Transportation, AMS, 2003.
∙ With a computational focus:
– [NOT] G. Peyré, M. Cuturi (2018). Numerical optimal transport, Arxiv.
∙ With a family economics focus:
– [MWT] P.-A. Chiappori. Matching with Transfers: The Economics of Love and Marriage, Princeton, 2017.

Outline

• intro to optimal transport (3h)
• multinomial choice (3h)
• matching models (3h)

Lecture series

Optimal transport methods in economics: an introduction

UCLA, April 16 and 20, 2018

Content

These lectures will provide an introduction to optimal transport and its applications in economics.

Schedule

Monday, April 16, 2018, 9am-11am
Friday, April 20, 2018, 9am-11am

Course material

The lecture slides are available before each lecture from the following github repository.

References

These lectures will be based on my text:
Galichon, A. (2016). Optimal transport methods in economics. Princeton.

Other references include:
∙ For mathematical foundations:
– [OTON] C. Villani, Optimal Transport: Old and New, AMS, 2008.
– [OTAM] F. Santambrogio, Optimal Transport for Applied Mathematicians, Birkhäuser, 2015.
∙ For an introduction with a fluid mechanics point of view:
– [TOT] C. Villani, Topics in Optimal Transportation, AMS, 2003.
∙ With a computational focus:
– [NOT] G. Peyré, M. Cuturi (2018). Numerical optimal transport, Arxiv.
∙ With a family economics focus:
– [MWT] P.-A. Chiappori. Matching with Transfers: The Economics of Love and Marriage, Princeton, 2017.

Outline

L1. The labor market as an optimal transport problem: efficiency and equilibrium
L2. Multivariate quantile methods using optimal transport

Mini-course

Matching models with general transfers

Summer school “Optimal transport and economics,” Hausdorff Center, Bonn, July 23-27, 2018 (4h30)

Content

These lectures will deal with optimal and equilibrium transport, and applications to matching models in economics.
In order to introduce the Monge-Kantorovich theorem of optimal transport theory in lecture 1, we consider a stylized assignment problem. Assume that a central planner (say, a plant manager) needs to assign workers to machines in order to maximize total output. Workers vary by their individual characteristics, and machines come in various sorts, where the set of characteristics of workers and firms may be either discrete or continuous. The output of a worker assigned to a machine depends on both the worker’s and the machine’s characteristics, so some workers may be better with some machines, and worse with some others. The central planner’s problem, which is the optimal transport problem, consists of assigning workers to machines in a way such that the total output is maximized. It will predict the equilibrium wages and the assignment of workers to machine.
Lecture 2 will introduce additional heterogeneity in preferences, so that the surplus of a match is the sum of a deterministic and a random term. We shall show that this leads to a regularized optimal transport problem, with an additional regularization term which is an entropy in the case when random utility belong in the logit specification, but can be characterized much more generally as a generalized entropy beyond that case. We will discuss implications for identification, comparative statics and the estimation of these models. This model can be used to estimate the structural parameters of the matching market, i.e. workers’ productivity and job amenity.
In lecture 3, we shall discuss a far-reaching extension of this setting called equilibrium transport. The classical theory of optimal transport relies on the assumption that the utilities should be quasi linear in payments, that is, everybody has a valuation expressed in the same monetary unit, which can be transferred without losses. That assumption is, of course, very strong as various nonlinearities may arise in practice, from taxes for example. Removing this strong assumption requires moving beyond optimal transport theory, to “Equilibrium transport theory”, which is strongly connected with the theory of “prescribed Jacobians equations”. We will see that this is the right framework to unify collective models of the households with matching models, and we provide a key technical tool to handle these, the distance-to-frontier (DTF) function, and we will study in detail a regularized version of this problem.

Schedule

L1: Monday 11am-12:30pm
L2: Monday 2pm-3:30pm
L3: Wednesday 9am-10:30am

Course material

The lecture slides will be available before each lecture on the following github repository.

References

Galichon, A. (2016). Optimal transport methods in economics. Princeton.

Outline

L1. The labor market as an optimal transport problem: Monge-Kantorovich duality
L2. Introducing unobserved heterogeneity among agents: regularized optimal transport
L3. Introducing taxes: equilibrium transport

Lecture series

Economic applications of optimal transport

Lake Como School of Advanced Studies from May 7-11, 2018 (6h)

Course material

The lecture slides will be available before each lecture on this Github link.

Description of the Course

These lectures will deal with economic applications of optimal transport.

References

Galichon, A. (2016). Optimal transport methods in economics. Princeton.

Schedule:
Monday 5/7, 2:30pm-4:30pm
Tuesday 5/8, 11am-12:30pm
Thursday 5/20, 9am-10:30am
Thursday 5/20, 11am-12:30pm

Outline:
1. Multinomial choice models and their inversion (1h30)
Based on:
– Chiong, Galichon, Shum (2016). Duality in dynamic discrete choice models. Quantitative Economics.
– Bonnet, Galichon, Shum (2017). Yogurts choose consumers? Identification of Random Utility Models via Two-Sided Matching. Preprint.

2. Separable matching models with heterogeneity (1h30)
Based on:
– Galichon, Salanié (2010) Matching with Trade-offs: Revealed Preferences over Competing Characteristics. Technical report.
– Galichon, Salanié (2017) Cupid’s Invisible Hand: Social Surplus and Identification in Matching Models. Preprint.

3. Affinity estimation: a framework for statistical inference in matching models (1h30)
Based on:
– Dupuy, Galichon (2014) Personality traits and the marriage market. Journal of Political Economy.
– Dupuy, Galichon, Shum (2017) Estimating matching affinity matrix under low-rank constraints. Preprint.

4. Equilibrium transport: incorporating taxes in matching models (1h30)
Based on:
– Galichon, Kominers, Weber (2017) Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility. Preprint.
– Dupuy, Galichon, Jaffe, Kominers (2017) Taxation in matching markets. Preprint.

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.

References

These lectures will be based on my monograph, Optimal Transport Methods in Economics, Princeton, 2016.

Schedule

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

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.

References

TBA.

Schedule:
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

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.

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.