Masterclass

Optimal Transport and Applications to Econometrics

Speaker

Alfred Galichon (New York University)

Date & Time

From: 3 June 2024
Until: 4 June 2024

Type

Masterclass

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) (Click here for presentation)
S2. Computational optimal transport (1h30) (Click here for presentation)
https://www.math-econ-code.org/optimal-assignment

Part II OT and matching models (3h)
S3. Matching with Transferable Utility and random utility (1h30) (Click here for presentation)
https://www.math-econ-code.org/regularized-optimal-transport

S4. Estimation of matching models (1h30) (Click here for presentation)
https://www.math-econ-code.org/matching-estimation

Part III OT and quantiles (2h)
S5. 1D optimal transport and quantiles (1h) (Click here for presentation)
https://www.math-econ-code.org/one-dimensional-assignment
S5. Connection with quantile regression (1h) (Click here for presentation)
https://www.math-econ-code.org/quantile-regression

Schedule

Day 1:

10:30-11:00: Registration

Part I Introduction

11:00-12:30: S1. Monge-Kantorovich duality

12:30-13:30: Lunch

13:30-15:00: S2. Computational optimal transport

15:00-15.30: Coffee break

Part II OT and matching models

15:30-17:30: S3. Matching with Transferable Utility and random utility

Day 2:

9:30-11:00: S4. Estimation of matching models

11:00-11:30: Coffee break

Part III OT and quantiles

11.30-12:30: S5. 1D optimal transport and quantiles

12:30-13:30: Lunch

13:30-14:30: S5. Connection with quantile regression