Since the seminal work by Gale and Shapley (1962) and Shapley and Shubik (1971), matching theory has developed and matured to a point where matching theorists could guide designs of medical match (Roth and Peranson, 1999) and other entry-level labor markets (Roth, 2002), school choice (Abdulkadiroglu and Sonmez, 2003), course allocation (Sonmez and Unver, 2010; Budish and Cantillon, 2012), and organ donation (Roth, Sonmez, and Unver, 2004, 2005, 2007), among others.
A first goal of this programme is to give an overview of the basic theoretical results and their applications. In the process, the professors will show that with the discovery of new applications, new challenges had to be addressed and these gave rise to the introduction of new models. They will present these most recent theoretical frameworks that are at the frontier of this research field.
Finally, the literature has been spurred by increasingly available administrative data, especially from settings that use formalized placement mechanisms. Detailed knowledge of the assignment rules combined with microdata provide a unique window into evaluating theory through structural estimation. The programme will also present the most recent techniques in econometrics of matching.
- Theme I: Two-sided matching theory and application to school choice, Olivier Tercieux
- Theme II: Empirics of school choice, Atila Abdulkadiroglu
- Theme III: Matching theory with transfers: optimal transport and economic applications, Alfred Galichon
Two-sided matching theory and application to school choice - Olivier Tercieux
This course will provide all the basics of matching theory, in particular, those necessary to investigate the most recent applications (student assignment, kidney exchange….). A special focus will be put on school choice both in terms of theory and first empirical analysis. The most recent theoretical models including « large markets models » will be presented.
- Basics of two sided matching theory
- Application to school choice
- Models of large markets
- Abdulkadiroglu A. and T. Sonmez (2003) « School Choice: A Mechanism Design Approach, » American Economic Review, 93, 729–747.
- Azevedo, E. and J. Leshno (2016): “A Supply and Demand Framework for Two-sided
Matching Markets,”Journal of Political Economy, 124, 1235-1268
- Che, Y-K. and O. Tercieux (2019) “Efficiency and Stability in Large Matching Markets,” Journal of Political Economy 127, 2301-2342.
- Roth A. and M. Sotomayor (1990) « Two Sided Matching, » Econometric Society Monographs; Cambridge University Press, Cambridge
Empirics of school choice - Atila Abdulkadiroglu
This course will extend on the literature by providing further theoretical analysis of student assignment, laying down a foundational framework for research design with data from centralized matching markets, and empirical analysis of matching markets via estimating structural models. The course will provide an overview of empirical results obtained using these models and discuss some open questions.
- Further theoretical analysis of student assignment
- Foundational framework for research design with data from centralized markets
- Empirical analysis of matching markets via demand estimation
- Abdulkadiroglu, A., N. Agarwal, and P. Pathak (2017) “The Welfare Effects of Coordinated Assignment: Evidence From the NYC HS Match” American Economic Review, 107, 3635-89
- Abdulkadiroglu, A., J. Angrist, Y. Narita and P. Pathak (2017) “Research Design Meets Market Design: Using Centralized Assignment for Impact Evaluation”, Econometrica, 85, 1373-1432
- Abdulkadiroglu, A., Y-K. Che and Y. Yasuda (2015) “Expanding “Choice” in School Choice”, American Economic Journal: Microeconomics, 7, 1-42
Matching theory with transfers: optimal transport and economic applications - Alfred Galichon
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.
- Introduction to optimal transport
- Multinomial choice
- Matching models with transfers
- A. Galichon (2016). Optimal Transport Methods in Economics. Princeton University Press
- Choo, E., and A. Siow (2006): “Who Marries Whom and Why,” Journal of Political
Economy, 114, 175–201
- Shapley, L. and M. Shubik (1971) « The assignment game, » International Journal of Game Theory, 1, 111–130
Contents - The Design of Market Places