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)
S2. Computational optimal transport (1h30)
https://www.math-econ-code.org/optimal-assignment
Part II OT and matching models (3h)
S3. Matching with Transferable Utility and random utility (1h30)
https://www.math-econ-code.org/regularized-optimal-transport
S4. Estimation of matching models (1h30)
https://www.math-econ-code.org/matching-estimation
Part III OT and quantiles (2h)
S5. 1D optimal transport and quantiles (1h)
https://www.math-econ-code.org/one-dimensional-assignment
S5. Connection with quantile regression (1h)
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