on optimal transport, part I
This intensive course, part of the ‘math+econ+code’ series, is focused on matching models and optimal transport methods, with various applications pertaining to labor markets, economics of marriage, industrial organization, matching platforms, networks, and international trade, from the crossed perspectives of theory, empirics and computation. It will introduce tools from economic theory, mathematics, econometrics and computing, on a needs basis, without any particular prerequisite other than the equivalent of a first year graduate sequence in econ or in applied math.
This first part focuses on predicting the equilibrium and the "direct optimal transport problem".
Because it aims at providing a bridge between theory and practice, the teaching format is somewhat unusual: each teaching “block” will be made of a mix of theory and coding (in Python), based on an empirical application related to the theory just seen. Students will have the opportunity to write their own code, which is expected to be operational at the end of each block. This course is therefore closer to cooking lessons than to traditional lectures.
The course will be taught over three consecutive days, October 26-27 2023, 230pm-6pm Paris time / 830am-12pm New York time.
The instructor is Alfred Galichon (professor of economics and of mathematics at NYU and principal investigator of the ERC-funded project 'equiprice' at Sciences Po).
Applications are now open: you can apply here
Lecture: an overview introduction to optimal transport
○ Two centuries of ideas across economics and mathematics
○ Optimization and equilibrium
○ Kantorovich duality
Coding session 2: semi-discrete optimal transport
○ Semi-Discrete Optimal Transport
○ Voronoi Tesselations
○ Aurenhammer's method
Coding session 1: optimal transport in the discrete case
○ Computation using a black-box solver
○ Transportation simplex
Coding session 3: optimal transport and entropic regularization
○ Entropic regularization
○ Microfoundations using random utilities
○ IPFP/Sinkhorn’s algorithm