Princeton University Press (to appear Spring 2026)
This text provides an overview of discrete choice models with in-depth coverage of the random utility model framework, logistic regressions, generalized linear models and applications to the gravity equation, empirical models of matching, hedonic models. The theory of multivariate extreme value is reviewed with applications to the nested logit model and other generalizations. The characteristics approach is covered as well as BLP demand estimation, and dynamic discrete choice methods. Equilibrium in models with non-transferable utility are discussed. The book features exercises and problem sets, and it includes a rich mathematical appendix, as well as extensive Python code examples.
The table of content and the book’s preface is available here.
Research retreat and mini-workshop held at the IASC Cargese, Corsica, France, April 21-26, 2025
Organizers: Alfred Galichon (New York University and Sciences Po) and Antoine Jacquet (Sciences Po)
Funded by the European Research Council grant ERC-CoG No. 866274 “EQUIPRICE”.
This event combines a research retreat and a mini-workshop both seeking to cross perspectives in the construction of a general framework for estimation of the “equilibrium flow problem”. The “equilibrium flow problem,” extends minimum cost flow problems in order to provide a unified network-based framework to analyze problems such as matching problems, multinomial choice problems, hedonic pricing problems, shortest path problems, dynamic programming problems, international trade flows. The equilibrium flow problem is a far-reaching extension of Optimal Transport, and thus, this project can be seen as an extension of the increasingly popular topic of “Inverse Optimal Transport”. We have been studying the mathematical properties of the problem, with questions such as existence of equilibrium prices, investigating possible uniqueness, and lattice structure, and special attention paid to the Nontransferable Utility (NTU) limit of the problem, which, in the bipartite case, provides the Gale and Shapley stable marriage problem. An inferential theory is build using maximum likelihood estimation and minimax-regret estimators. Model selection is incorporated to estimation procedures; more precisely, the proximal mapping operator will be inserted in between two iterative phases of these procedures. Several applications are developed, one to the gravity equation in international trade, one to hedonic models, one to matching models.
Investigators and speakers:
Guillaume Carlier (Dauphine)
Alfred Galichon (NYU and Sciences Po)
Pierre Jacob (ESSEC)
Antoine Jacquet (Sciences Po)
Jean-Bernard Lasserre (Toulouse School of Economics)
Guillaume Pouliot (University of Chicago)
Maxime Sylvestre (Dauphine)
Talks are accessible to the public (on zoom) but registration is mandatory by emailing antoine.jacquet@sciencespo.fr.
Monday April 21, 2025
Morning: arrival and welcome coffee
Afternoon: 230pm – 330pm: Opening session, “leveling the playing field: what are the main results we are after?” (led by Antoine Jacquet and Maxime Sylvestre) 330pm – 4pm: coffee break. 4pm – 6pm: group work session.
Tuesday April 22, 2025
Morning 930am – 1030am: Guillaume Carlier, TBA. 1030am – 11am: coffee break. 11am – 1230pm: group work session.
Afternoon 230pm – 330pm: Maxime Sylvestre, “Convergence of a hybrid scheme for the computation of weak inverse optimal transport”. 330pm – 4pm: coffee break. 4pm – 6pm: group work session.
Wednesday April 23, 2025
Morning 930am – 1030am: Jean-Bernard Lasserr.e, “Gaussian mixtures closest to a given measure via optimal transport”. 1030am – 11am: coffee break. 11am – 1230pm: group work session.
Afternoon: free time
Thursday April 24, 2025
Morning 930am – 1030am: Antoine Jacquet, “Computation of NTU aggregate equilibria with a finite-time Newton-Jacobi method.” 1030am – 11am: coffee break. 11am – 1230pm: group work session.
Afternoon 230pm – 330pm: Pierre Jacob, “Optimal transport and related problems in the field of Monte Carlo methods.” 330pm – 4pm: coffee break. 4pm – 6pm: group work session.
Friday April 25, 2025
Morning 1030am – 1030am: Alfred Galichon, “Some partial results on the inference in ITU matching models using LCP theory.” 1030am – 11am: coffee break. 11am – 1230pm: group work session.
Afternoon 230pm -330pm: Guillaume Pouliot, “Distributionally Robust Optimal Transport”. 330pm – 4pm: coffee break. 4pm – 6pm: group work session.
This course will revisit some classical topics in microeconometrics (such as random utility models, dynamic discrete choice, demand estimation, matching models, and bundle choice problems) though the lenses of advanced computational methods (large scale optimization and machine learning). An important part of the course is dedicated to gaining familiarity with computational libraries such as scikit-learn, pytorch, openAI gym, chatGPT, gurobi, and others.
Lectures are delivered under a mix of in-person and online format. The language used is Python. Students not familiar with Python should contact the instructor to be provided a crash course before the start of classes.
Part 1. Random utility models
Content: Poisson regression and logistic regression as generalized Linear Models, Lasso and Elastic Net, Min-Max Regret. Computation using Scikit-learn and TensorFlow.
Lectures:
L1
L2
L3
L4
References:
An Introduction to Statistical Learning with applications in Python with by James, Witten, Hastie, Tibshirani and Taylor
The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman.
Generalized Linear Models by McCullagh and Nelder.
These lectures will introduce the optimal transport (OT) toolbox, with two applications in econometrics. The first one will pertain to the estimation of matching models. We start by introducing the discrete OT problem and its entropic regularization, and inverse OT, as well as its estimation using generalized linear models. The second application will deal with quantile methods. The one-dimensional OT problem will be discussed as well as its connections with the notions of quantile and rank is then covered. Connection with quantile regression will be discussed and the ‘vector quantile regression’ problem will then be introduced.
Part I Introduction (3h) S1. Monge-Kantorovich duality (1h30)
This course will revisit some classical topics in microeconometrics (such as random utility models, dynamic discrete choice, demand estimation, matching models, and bundle choice problems) though the lenses of machine learning and state-of-the-art optimization methods. An important part of the course is dedicated to gaining familiarity with computational libraries such as scikit-learn, pytorch, openAI gym, chatGPT, gurobi, and others.
Lectures are delivered under a mix of in-person and online format. The language used is Python. Students not familiar with Python should contact the instructor to be provided a crash course before the start of classes.
Part 1. Random utility models meet Machine learning
Content: Poisson regression and logistic regression as generalized Linear Models, Lasso and Elastic Net, Min-Max Regret. Computation using Scikit-learn and TensorFlow.
Lectures:
L1: Tue 1/30, 1145am-145pm (19W4, 802 and zoom)
L2: Thu 2/1, 1pm-3pm (19W4, 802 and zoom)
L3: Tue 2/6, 1145am-145pm (zoom)
L4: Thu 2/15, 1pm-3pm (zoom)
References:
An Introduction to Statistical Learning with applications in Python with by James, Witten, Hastie, Tibshirani and Taylor
The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman.
Generalized Linear Models by McCullagh and Nelder.
Part 3. Characteristics models meet Deep Learning and Optimal Transport Content: Pure characteristics model, random coefficient logit model, Power diagrams, matching models. Simulation (Probit, GHK), stochastic GD. Computation using pyopt package, pyBLP, pyTorch.
Lectures:
L9: Tue 4/2, 1145am-145pm (zoom)
L10: Tue 4/9, 1145am-145pm (zoom)
L11: Tue 4/16, 1145am-145pm (19W4, 802 and zoom)
L12: Thu 4/18, 1pm-3pm (19W4, 802 and zoom)
References:
Deep Learning by Aaron Courville, Ian Goodfellow, and Yoshua Bengio.
Train, K. (2009). Discrete Choice Methods with Simulation.
Galichon, A. (2016). Optimal Transport Methods in Economics.
Organizers: Alfred Galichon (New York University and Sciences Po) and Larry Samuelson (Yale University)
Substitutability has found itself at the core of modern economic modeling for two reasons. First, it arises naturally in classes of models such as one-to-one matching, discrete choice, hedonic models, and many others. Second, it leads to successful numerical methods, such as the greedy algorithm in the discrete case, and the Jacobi algorithm related ones in the continuous case. Leading experts in the field will gather to make a link between discrete and continuous models and to explore recent theoretical developments and economic applications.
Two lectures on matching models for family economics
Invited lectures given at the University of Toronto, April 1 and April 8, 2022
Content
The first lecture will cover transferable utility (TU) matching models with logit heterogeneity following the seminal paper by Choo and Siow (JPE 2006), its extension and parametric estimation following Galichon and Salanié (Restud 2022).
The second lecture will discuss the interplay between models of matching and collective models as depicted in Browning and Chiappori’s (Cambridge, 2014) monograph, and how models of imperfectly transferable utility (ITU) and logit or more general heterogeneity are needed to address this new class of problems, as is done in Galichon, Kominers and Weber (JPE, 2019).
Schedule
April 1 and April 8, 10am-12pm Eastern time, online.
Course material
The lecture slides are available from the following github repository.
References
These lectures are based on:
[GS] Galichon and Salanie (2022). Cupids invisible hands: Social Surplus and Identification in Matching Models. Review of Economic Studies.
[GKW] Galichon, Kominers and Weber (2019). Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility (2019). Journal of Political Economy.
[MEC-OPTIM] Galichon (2022). `math+econ+code’ masterclass on optimal transport and economic applications. https://www.math-econ-code.org/mec-optim
[MEC-EQUIL] Galichon (2022). `math+econ+code’ masterclass on equilibrium transport and matching models in economics. https://www.math-econ-code.org/mec-equil
Outline
Lecture 1: Matching models with transferable utility:
Matching models as an optimization problem / regularized optimal transport / generalized linear models
Lecture 2: Matching models with imperfectly transferable / nontransferable utility:
Matching models as an equilibrium problem with substitutes
Gross substitutes, optimal transport and matching models
Optimal Transport Summer School, the University of Washington, Seattle, June 19-July 1, 2022
Content
Gross substitutes is a fundamental property in mathematics, economics and computation, almost as important as convexity. It is at the heart of optimal transport theory — although this is often underrecognized — and understanding the connection key to understanding the extension of optimal transport to other models of matching.
Schedule
TBD
Course material
The lecture slides are available before each lecture from the following github repository.
References
These lectures will be loosely based on my math+econ+code lectures:
A. Galichon, ‘math+econ+code’ masterclass on equilibrium transport and matching models in economics. June 2021. Available here.
Outline
Lecture 1. Introduction to gross substitutes
M-matrices and M-maps, nonlinear Perron-Froebenius theory, convergence of Jacobi algorithm. A toy hedonic model.
Lecture 2. Models of matching with transfers
Problem formulation, regularized and unregularized case. IPFP and its convergence. Existence and uniqueness of an equilibrium. Lattice structure.
Lecture 3. Models of matching without transfers
Gale and Shapley’s stable matchings. Adachi’s formulation. Kelso-Craford. Hatfield-Milgrom.
Who? participation to this math+econ+code event is open to the public upon request.
What? Kidney transplant problems provide a very interesting real-life examples of dynamic matching problems. A large academic literature exists on the topic, both in economics and in operations research. Because the problem is a difficult problem computationally speaking, a number of algorithms exist out there to try to approximate the best solution. This hackaton will put you in the shoes of the transplant agency: at each period, you will receive the state of your population, which is made of your existing population of patients, plus new patients and minus deceased ones (simulated by our platform). Your role will be write the algorithm that matches donors and receivers, given the constraints on the way transplants can be done (state of the patient, compatibility between donor and receiver, length of transplant chains, etc.)
Each player plays in parallel and is evaluated by a score, which will reflect the state of their population of patients. The game is played over a very large number of periods. The player with the highest final score has come up with the best algorithm and wins the hackaton.
What is required? In order to participate, you need to be familiar with Python programming. Your only input is the matching function that assigns donors to receivers — a function whose length can be less than a hundred lines but can be more depending on your design. All the interfacing is done by the platform.
