Econometrics, Quantitative Economics, Data Science

Archive for the ‘mec_optim’ Category

mec_optim_archive_2020-01

ECON-GA 3503

‘math+econ+code’ part one: optimal transport and economic applications

NYU, Courant Institute (Warren Weaver Hall, 251 Mercer) Rm 101, January 20-24, 2020 (30 hours)

Instructor: A. Galichon (NYU Econ+Math). Email: alfred.galichon@nyu.edu. TA: James Nesbit (NYU Econ). Email: jmn425@nyu.edu.

Description

This intensive course, part of the ‘math+econ+code’ series, is focused on models of demand, 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.
A particular emphasis will be given on HPC computation and parallel computing.
Because it aims at providing a bridge between theory and practice, the teaching format is somewhat unusual: each teaching “block” will be made of 50 minutes of theory followed by 1 hour of coding, based on an empirical application related to the theory just seen. Students are expected to write their own code, and we will ensure that it is operational at the end of each block. This course is therefore closer to cooking lessons than to traditional lectures.
The course is open to graduate students in the fields of economics and applied mathematics, but also in other quantitative disciplines. Students need to bring a laptop with them to the lectures. The knowledge of a particular programming language is not required; students are however expected to have some experience with programming. The language of the course will be Python.
The lecturer is Alfred Galichon (professor of economics and of mathematics at NYU). The TA is James Nesbit (graduate economics student at NYU). Pauline Corblet (graduate economics student at Sciences Po), Octavia Ghelfi and James Nesbit (graduate economics students at NYU) have helped prepare the course material. Support from NSF grant DMS-1716489 is acknowledged.

Suggested preparation readings (optional)

Alfred Galichon (2016). Optimal Transport Methods in Economics. Princeton University Press.

Course material

Available on github here.
Available on NYU’s HPC cluster here.

Course material from past editions available from this Github repository.

Practical information

• Schedule: Monday to Friday, 8:30am-12:30pm and 1:30pm-3:30pm. Location: NYU Courant Institute, Warren Weaver Hall, 251 Mercer St, Room 101.
• Credits: 2, assessed through a take-home exam or a short final paper, at the student’s option.
• A syllabus is available at http://alfredgalichon.com/mec_optim/.
• NYU Students need to register on Albert (code ECON-GA 3503). Students are advised to contact the instructor (alfred.galichon@nyu.edu) ahead of time.

Outline

• Monday: linear programming, dynamic programming, network flows
• Tuesday: optimal transport toolbox 1 (discrete, one-dimensional, semi-discrete cases)
• Wednesday: optimal transport toolbox 2 (continuous transport, convex analysis, entropic regularization)
• Thursday: static and dynamic multinomial choice
• Friday: statistical estimation of models of matching with transfers

Synopsis

SYNOPSIS
Part I: Tools
Day 1: linear programming (Monday)
Block 1. Basics of linear programming (morning 1st half)
• Theory: linear programming duality; complementary slackness; minimax formulation
• Coding: How to eat optimally? Dataset: Stigler’s original diet data (1945).
Block 2. Network flow problems (morning 2nd half)
• Theory: directed graphs and min-cost flow problem
• Coding: How to find the shortest path through a network? Dataset: Paris subway; New York City street network.
Block 3. Dynamic programming as linear programming (afternoon)
• Theory: Bellman’s equation; interpretation of duality; forward induction, backward induction
• Coding: When to repair mechanical engines? Dataset: Rust’s bus maintenance data (1994).

Day 2: optimal transport I (Tuesday)
Block 4. Discrete matching (morning 1st half)
• Theory: Shapley-Shubik duality; stability; decentralized equilibrium
• Coding: How to solve it? Dataset from Dupuy and Galichon (JPE 2014).
Block 5. Positive assortative matching (morning 2nd half)
• Theory: Becker’s model; compensating differentials; comonotonicity
• Coding: What is a CEO worth? Dataset: Gabaix-Landier’s (QJE 2008) CEO pay data.

Block 6. Hotelling’s characteristics model (afternoon)
• Theory: power diagrams, Aurenhammer’s method
• Coding: How to infer the unobservable quality of a car model? Dataset: Feenstra-Levinsohn (Restud 1994) car data.

Day 3: optimal transport II (Wednesday)
Block 7. Continuous multivariate matching (morning 1st half)
• Theory: Knott-Smith criterion; Brenier’s map; McCann’s theorem
• Applications: exercises.
Block 8. A short tutorial on convex analysis (morning 2nd half)
• Theory: convex duality; Fenchel’s inequality; subdifferentials and their inverses
• Application: exercises.
Block 9. Regularized optimal transport (afternoon)
• Theory: optimal transport with entropic regularization, and with other regularizations.
• Coding: coordinate descent and the IPFP algorithm.

Part II. Models
Day 4: models of static and dynamic multinomial choice (Thursday)
Block 10. Basics of static discrete choice (morning 1st half)
• Theory: Dary-Zachary-Williams theorem, generalized entropy of choice, the inversion theorem
• Coding: How to solve it? simulation methods; AR, SARS, and GHK. Dataset: Greene and Hensher (1997) data on choice of travel mode.
Block 11. Demand models, old and new (morning 2nd half)
• Theory: the GEV model; the random coefficient logit model and the pure characteristics models
• Coding: How to estimate demand for automobiles? Dataset: BLP.
Block 12. Dynamic discrete choice methods (afternoon)
• Theory: Rust’s model; estimation; normalization issues
• Coding: maintenance choice.

Day 5: empirical matching models, the quasilinear case (Friday)
Block 13. Separable models of matching (morning 1st half)
• Theory: matching with unobservable heterogeneity
• Coding: Did Roe vs. Wade decrease the value of marriage? Dataset: Choo and Siow (JPE 2006).
Block 14. The gravity equation (morning 2nd half)
• Theory: optimal transport and the gravity equation; generalized linear models and pseudo-Poisson maximum likelihood estimation
• Coding: How to forecast international trade flows? estimating the gravity equation based on WTO international trade data.
Block 15. High-dimensional matching models (afternoon)
• Theory: estimation of rank-constrained models
• Application: Does physical appearance have a price? matching on socioeconomic and anthropomorphic characteristics. Dataset: Chiappori, Oreffice and Quintana-Domeque’s (JPE 2012).

mec_optim_archive_2019_06

ECON-GA 3503

‘math+econ+code’ in Paris: A masterclass on optimal transport, choice and matching models

NYU Paris (57 bd St-Germain, 75005 Paris), June 17-21, 2019 (30 hours)

Instructor: A. Galichon (NYU Econ+Math). Email: alfred.galichon@nyu.edu.

** Note: Interested students must contact the instructor ahead of time.**

Description

This intensive course, part of the ‘math+econ+code’ series, is focused on models of demand, 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.
Because it aims at providing a bridge between theory and practice, the teaching format is somewhat unusual: each teaching “block” will be made of 50 minutes of theory followed by 1 hour of coding, based on an empirical application related to the theory just seen. Students are expected to write their own code, and we will ensure that it is operational at the end of each block. This course is therefore closer to cooking lessons than to traditional lectures.
The course is open to graduate students in the fields of economics and applied mathematics, but also in other quantitative disciplines. Students need to bring a laptop with them to the lectures. The knowledge of a particular programming language is not required; students are however expected to have some experience with programming. The course can be taken for credit or as a registered auditor.
The lecturer is Alfred Galichon (professor of economics and of mathematics at NYU). Pauline Corblet (graduate economics student at Sciences Po) and Octavia Ghelfi and James Nesbit (graduate economics students at NYU) have helped prepare the course material. The course is partly based on Galichon’s book, Optimal Transport Methods in Economics.

Support from NSF grant DMS-1716489 is acknowledged.

Course material

Available on Github here.

Practical information

• Schedule: Monday to Friday, 8am-12noon and 2pm-4pm. Location: NYU Paris, 57 boulevard Saint-Germain, 75005 Paris, Room TBA.
• Credits: 2, assessed through a take-home exam or a short final paper, at the student’s option.
• A syllabus is available at http://alfredgalichon.com/mec_optim/.
• NYU Students need to register on Albert (code ECON-GA 3503). Non-NYU student can be allowed to audit the course. All students need to contact the instructor (alfred.galichon@nyu.edu) ahead of time.

Outline

• Monday: linear programming, dynamic programming, network flows
• Tuesday: optimal transport toolbox 1 (discrete, one-dimensional, semi-discrete cases)
• Wednesday: optimal transport toolbox 2 (continuous transport, convex analysis, entropic regularization)
• Thursday: static and dynamic multinomial choice
• Friday: statistical estimation of models of matching with transfers

Synopsis

SYNOPSIS
Part I: Tools
Day 1: linear programming (Monday)
Block 1. Basics of linear programming (morning 1st half)
• Theory: linear programming duality; complementary slackness; minimax formulation
• Coding: How to eat optimally? Dataset: Stigler’s original diet data (1945).
Block 2. Network flow problems (morning 2nd half)
• Theory: directed graphs and min-cost flow problem
• Coding: How to find the shortest path through a network? Dataset: Paris subway; New York City street network.
Block 3. Dynamic programming as linear programming (afternoon)
• Theory: Bellman’s equation; interpretation of duality; forward induction, backward induction
• Coding: When to repair mechanical engines? Dataset: Rust’s bus maintenance data (1994).

Day 2: optimal transport I (Tuesday)
Block 4. Discrete matching (morning 1st half)
• Theory: Shapley-Shubik duality; stability; decentralized equilibrium
• Coding: How to solve it? Dataset from Dupuy and Galichon (JPE 2014).
Block 5. Positive assortative matching (morning 2nd half)
• Theory: Becker’s model; compensating differentials; comonotonicity
• Coding: What is a CEO worth? Dataset: Gabaix-Landier’s (QJE 2008) CEO pay data.

Block 6. Hotelling’s characteristics model (afternoon)
• Theory: power diagrams, Aurenhammer’s method
• Coding: How to infer the unobservable quality of a car model? Dataset: Feenstra-Levinsohn (Restud 1994) car data.

Day 3: optimal transport II (Wednesday)
Block 7. Continuous multivariate matching (morning 1st half)
• Theory: Knott-Smith criterion; Brenier’s map; McCann’s theorem
• Applications: exercises.
Block 8. A short tutorial on convex analysis (morning 2nd half)
• Theory: convex duality; Fenchel’s inequality; subdifferentials and their inverses
• Application: exercises.
Block 9. Regularized optimal transport (afternoon)
• Theory: optimal transport with entropic regularization, and with other regularizations.
• Coding: coordinate descent and the IPFP algorithm.

Part II. Models
Day 4: models of static and dynamic multinomial choice (Thursday)
Block 10. Basics of static discrete choice (morning 1st half)
• Theory: Dary-Zachary-Williams theorem, generalized entropy of choice, the inversion theorem
• Coding: How to solve it? simulation methods; AR, SARS, and GHK. Dataset: Greene and Hensher (1997) data on choice of travel mode.
Block 11. Demand models, old and new (morning 2nd half)
• Theory: the GEV model; the random coefficient logit model and the pure characteristics models
• Coding: How to estimate demand for automobiles? Dataset: BLP.
Block 12. Dynamic discrete choice methods (afternoon)
• Theory: Rust’s model; estimation; normalization issues
• Coding: maintenance choice.

Day 5: empirical matching models, the quasilinear case (Friday)
Block 13. Separable models of matching (morning 1st half)
• Theory: matching with unobservable heterogeneity
• Coding: Did Roe vs. Wade decrease the value of marriage? Dataset: Choo and Siow (JPE 2006).
Block 14. The gravity equation (morning 2nd half)
• Theory: optimal transport and the gravity equation; generalized linear models and pseudo-Poisson maximum likelihood estimation
• Coding: How to forecast international trade flows? estimating the gravity equation based on WTO international trade data.
Block 15. High-dimensional matching models (afternoon)
• Theory: estimation of rank-constrained models
• Application: Does physical appearance have a price? matching on socioeconomic and anthropomorphic characteristics. Dataset: Chiappori, Oreffice and Quintana-Domeque’s (JPE 2012).

mec_optim_archive_2019-01

ECON-GA 3503.1410

‘math+econ+code’ masterclass on optimization in economics: optimal transport, demand models and matching models

NYU Courant Institute, January 14-18, 2019 (30 hours)

Instructor: A. Galichon (NYU Econ+Math)

Description

This intensive course, part of the ‘math+econ+code’ series, is focused on models of demand, 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.
Because it aims at providing a bridge between theory and practice, the teaching format is somewhat unusual: each teaching “block” will be made of 50 minutes of theory followed by 1 hour of coding, based on an empirical application related to the theory just seen. Students are expected to write their own code, and we will ensure that it is operational at the end of each block. This course is therefore closer to cooking lessons than to traditional lectures.
The course, jointly offered by NYU Econ and the Courant Institute, is open to graduate students in the fields of economics and applied mathematics, but also in other quantitative disciplines. Students need to bring a laptop with them to the lectures. The knowledge of a particular programming language is not required; students are however expected to have some experience with programming. The course can be taken for credit or as a registered auditor.
The lecturer is Alfred Galichon (professor of economics and of mathematics at NYU). James Nesbit (graduate Economics student at NYU) helped prepare the course material. The course is partly based on Galichon’s book, Optimal Transport Methods in Economics.

Support from NSF grant DMS-1716489 is acknowledged.

Course material

Available on Github here.

Practical information

• Schedule: Mon 1/14 — Fri 1/18, 2019, 9am-1pm and 2pm-4pm. Location: WWH 101 in the Courant building (251 Mercer St)
• Credits: 2, assessed through a take-home exam or a short final paper, at the student’s option.
• A syllabus is available at http://alfredgalichon.com/matheconcode/.
• Students need to register on Albert (code ECON-GA 3503.1410). For more information please contact: galichon@cims.nyu.edu.

Outline

• Monday: linear programming, dynamic programming, network flows
• Tuesday: optimal transport toolbox
• Wednesday: convex analysis, nonlinear inverse problems, and multivariate quantiles
• Thursday: static and dynamic multinomial choice
• Friday: statistical estimation of models of matching with transfers

Synopsis

SYNOPSIS
Part I: Tools
Day 1: linear programming (Monday)
Block 1. Basics of linear programming (morning 1st half)
• Theory: linear programming duality; complementary slackness; minimax formulation
• Coding: How to eat optimally? Dataset: Stigler’s original diet data (1945).
Block 2. Network flow problems (morning 2nd half)
• Theory: directed graphs and min-cost flow problem
• Coding: How to find the shortest path through a network? Dataset: Paris subway; New York City street network.
Block 3. Dynamic programming as linear programming (afternoon)
• Theory: Bellman’s equation; interpretation of duality; forward induction, backward induction
• Coding: When to repair mechanical engines? Dataset: Rust’s bus maintenance data (1994).

Day 2: optimal transport I (Tuesday)
Block 4. Discrete matching (morning 1st half)
• Theory: Shapley-Shubik duality; stability; decentralized equilibrium
• Coding: How to solve it? Dataset from Dupuy and Galichon (JPE 2014).
Block 5. Positive assortative matching (morning 2nd half)
• Theory: Becker’s model; compensating differentials; comonotonicity
• Coding: What is a CEO worth? Dataset: Gabaix-Landier’s (QJE 2008) CEO pay data.

Block 6. Hotelling’s characteristics model (afternoon)
• Theory: power diagrams, Aurenhammer’s method
• Coding: How to infer the unobservable quality of a car model? Dataset: Feenstra-Levinsohn (Restud 1994) car data.

Day 3: optimal transport II (Wednesday)
Block 7. Continuous multivariate matching (morning 1st half)
• Theory: Knott-Smith criterion; Brenier’s map; McCann’s theorem
• Applications: exercises.
Block 8. A short tutorial on convex analysis (morning 2nd half)
• Theory: convex duality; Fenchel’s inequality; subdifferentials and their inverses
• Application: exercises.
Block 9. Regularized optimal transport (afternoon)
• Theory: optimal transport with entropic regularization, and with other regularizations.
• Coding: coordinate descent and the IPFP algorithm.

Part II. Models
Day 4: models of static and dynamic multinomial choice (Thursday)
Block 10. Basics of static discrete choice (morning 1st half)
• Theory: Dary-Zachary-Williams theorem, generalized entropy of choice, the inversion theorem
• Coding: How to solve it? simulation methods; AR, SARS, and GHK. Dataset: Greene and Hensher (1997) data on choice of travel mode.
Block 11. Demand models, old and new (morning 2nd half)
• Theory: the GEV model; the random coefficient logit model and the pure characteristics models
• Coding: How to estimate demand for automobiles? Dataset: BLP.
Block 12. Dynamic discrete choice methods (afternoon)
• Theory: Rust’s model; estimation; normalization issues
• Coding: maintenance choice.

Day 5: empirical matching models, the quasilinear case (Friday)
Block 13. Separable models of matching (morning 1st half)
• Theory: matching with unobservable heterogeneity
• Coding: Did Roe vs. Wade decrease the value of marriage? Dataset: Choo and Siow (JPE 2006).
Block 14. The gravity equation (morning 2nd half)
• Theory: optimal transport and the gravity equation; generalized linear models and pseudo-Poisson maximum likelihood estimation
• Coding: How to forecast international trade flows? estimating the gravity equation based on WTO international trade data.
Block 15. High-dimensional matching models (afternoon)
• Theory: estimation of rank-constrained models
• Application: Does physical appearance have a price? matching on socioeconomic and anthropomorphic characteristics. Dataset: Chiappori, Oreffice and Quintana-Domeque’s (JPE 2012).

mec_optim_archive_2018-01

ARCHIVE

Current version to be found here.

ECON-GA 3002.015 and MATH.GA 2840.002

‘math+econ+code’ masterclass on optimization in economics: optimal transport, demand models and matching models

NYU Courant Institute, January 15-20, 2018 (36 hours)

Instructors: A. Galichon (NYU Econ+Math), Keith O’Hara (NYU Econ) and Yifei Sun (NYU Math)

Description

This intensive course, part of the ‘math+econ+code’ series, is focused on models of demand, 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.
Because it aims at providing a bridge between theory and practice, the teaching format is somewhat unusual: each teaching “block” will be made of 50 minutes of theory followed by 1 hour of coding, based on an empirical application related to the theory just seen. Students are expected to write their own code, and the teaching staff will ensure that it is operational at the end of each block. This course is therefore closer to cooking lessons than to traditional lectures.
The course, jointly offered by NYU Econ and the Courant Institute, is open to graduate students in the fields of economics and applied mathematics, but also in other quantitative disciplines. Students need to bring a laptop with them to the lectures. The knowledge of a particular programming language is not required; students are however expected to have some experience with programming. The course can be taken for credit or as a registered auditor.
The teaching staff is Alfred Galichon (professor of economics and of mathematics at NYU), Keith O’hara (economics graduate student at NYU and R and C++ guru), and Yifei Sun (mathematics graduate student at NYU focusing on machine learning). They are authors of the TraME library (https://github.com/TraME-Project), a toolbox for inference and simulation of discrete choice and matching problems. The course is based on Galichon’s popular graduate classes previously taught at NYU, and on his recent book, Optimal Transport Methods in Economics.

Support from NSF grant DMS-1716489 is acknowledged.

Course material

Available on Github here.

Practical information

• Schedule: Mon 1/15 — Sat 1/20, 2018, 8am-12 noon and 1pm-3pm. Location: WWH 102 in the Courant building (251 Mercer St)
• Credits: 3, assessed through a take-home exam or a short final paper, at the student’s option.
• A syllabus is available at http://alfredgalichon.com/matheconcode/.
• Students need to register on Albert (MATH-GA 2840.002 or ECON-GA 3002.015). For more information please contact: galichon@cims.nyu.edu.

Outline

• Monday 1/15: linear programming, dynamic programming, network flows
• Tuesday 1/16: optimal transport toolbox
• Wednesday 1/17: convex analysis, nonlinear inverse problems, and multivariate quantiles
• Thursday 1/18: static and dynamic multinomial choice
• Friday 1/19: statistical estimation of models of matching with transfers
• Saturday 1/20: more general models of matching

Synopsis

SYNOPSIS
Part I: Tools
Day 1: linear programming (Monday Jan 15)
Block 1. Basics of linear programming (8am-9:50am)
• Theory: linear programming duality; complementary slackness; minimax formulation
• Coding: How to eat optimally? Dataset: Stigler’s original diet data (1945).
Block 2. Network flow problems (10:10am-noon)
• Theory: directed graphs and min-cost flow problem
• Coding: How to find the shortest path through a network? Dataset: Paris subway; New York City street network.
Block 3. Dynamic programming as linear programming (1pm-2:50pm)
• Theory: Bellman’s equation; interpretation of duality; forward induction, backward induction
• Coding: When to repair mechanical engines? Dataset: Rust’s bus maintenance data (1994).

Day 2: optimal transport I (Tuesday Jan 16)
Block 4. Discrete matching (8am-9:50am)
• Theory: Shapley-Shubik duality; stability; decentralized equilibrium
• Coding: How to solve it? Dataset from Dupuy and Galichon (JPE 2014).
Block 5. Positive assortative matching (10:10am-noon)
• Theory: Becker’s model; compensating differentials; comonotonicity
• Coding: What is a CEO worth? Dataset: Gabaix-Landier’s (QJE 2008) CEO pay data.

Block 6. Hotelling’s characteristics model (1pm-2:50pm)
• Theory: power diagrams, Aurenhammer’s method
• Coding: How to infer the unobservable quality of a car model? Dataset: Feenstra-Levinsohn (Restud 1994) car data.

Day 3: optimal transport II (Wednesday Jan 17)
Block 7. Continuous multivariate matching (8am-9:50am)
• Theory: Knott-Smith criterion; Brenier’s map; McCann’s theorem
• Coding: How to solve it? the iterated proportional fitting procedure (IPFP). Dataset from Dupuy and Galichon (JPE 2014).
Block 8. Convex analysis and nonlinear inverse problems (10:10am-noon)
• Theory: convex duality; Fenchel’s inequality; subdifferentials and their inverses
• Coding: How to optimize with big data? Proximal gradient algorithms; LASSO; stochastic gradient algorithms.
Block 9. Quantiles methods (1pm-2:50pm)
• Theory: Rosenblatt’s quantiles; vector quantiles; vector quantile regression
• Coding: How to predict demand? vector quantile regression. Dataset: Engel’s (1857) original food expenditure data.

Part II. Models
Day 4: models of static and dynamic multinomial choice (Thursday Jan 18)
Block 10. Basics of static discrete choice (8am-9:50am)
• Theory: Dary-Zachary-Williams theorem, generalized entropy of choice, the inversion theorem
• Coding: How to solve it? simulation methods; AR, SARS, and GHK. Dataset: Greene and Hensher (1997) data on choice of travel mode.
Block 11. Demand models, old and new (10:10am-noon)
• Theory: the GEV model; the random coefficient logit model and the pure characteristics models
• Coding: How to estimate demand for automobiles? Dataset: BLP.
Block 12. Dynamic discrete choice methods (1pm-2:50pm)
• Theory: Rust’s model; estimation; normalization issues
• Coding: career choice.

Day 5: empirical matching models, the quasilinear case (Friday Jan 19)
Block 13. Separable models of matching (8am-9:50am)
• Theory: matching with unobservable heterogeneity
• Coding: Did Roe vs. Wade decrease the value of marriage? Dataset: Choo and Siow (JPE 2006).
Block 14. The gravity equation (10:10am-noon)
• Theory: optimal transport and the gravity equation; generalized linear models and pseudo-Poisson maximum likelihood estimation
• Coding: How to forecast international trade flows? estimating the gravity equation based on WTO international trade data.
Block 15. High-dimensional matching models (1pm-2:50pm)
• Theory: estimation of rank-constrained models
• Application: Does physical appearance have a price? matching on socioeconomic and anthropomorphic characteristics. Dataset: Chiappori, Oreffice and Quintana-Domeque’s (JPE 2012).

Day 6: empirical matching models beyond quasilinearity (Saturday Jan 20)
Block 16. Matching with imperfectly transferable utility (8am-9:50am)
• Theory: Galois connections, distance-to-frontier function, nonlinear complementary slackness, equilibrium transport
• Application: How do taxes affect matching patterns and wages? Dataset: Football coach data from Dupuy, Galichon, Jaffe and Kominers (2017).
Block 17. Integrating matching models and collective models of intrahousehold bargaining (10:10am-noon)
• Theory: collective models, Pareto weights, sharing rule
• Application: Do people marry for consumption or companionship? Dataset: Galichon, Kominers and Weber (2017).
Block 18. Matching with nontransferable utility (1pm-2:50pm)
• Theory: the Dagsvik-Menzel model; nonprice rationing and the NTU-logit separable model
• Application: Revisiting Choo and Siow’s data.

mec_optim

‘math+econ+code’ masterclass on optimal transport and economic applications

Online, January 18-22, 2021 (30h)
Time: 8am-12pm US Eastern time / 2pm-6pm Central European time Monday-Friday, plus five special lectures

Instructor: Alfred Galichon, email: alfred.galichon@nyu.edu
TA: Jules Baudet, email: jules.baudet99@gmail.com

Description

This intensive course, part of the ‘math+econ+code’ series, is focused on models of demand, 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.
A particular emphasis will be given on cloud computation and parallel computing.
Because it aims at providing a bridge between theory and practice, the teaching format is somewhat unusual: each teaching “block” will be made of 50 minutes of theory followed by 1 hour of coding, based on an empirical application related to the theory just seen. Students are expected to write their own code, and we will ensure that it is operational at the end of each block. This course is therefore closer to cooking lessons than to traditional lectures.
The course is open to graduate students in the fields of economics and applied mathematics, but also in other quantitative disciplines. Students need to bring a laptop with them to the lectures. The knowledge of a particular programming language is not required; students are however expected to have some experience with programming. The language of the course will be Python.
The instructor is Alfred Galichon (professor of economics and of mathematics at NYU and affiliate professor at Sciences Po), and the TA is Jules Baudet (graduate student at ENS, EQUIPRICE team member). Pauline Corblet (graduate economics student at Sciences Po), Octavia Ghelfi and James Nesbit (graduate economics students at NYU) have helped prepare the course material over time. Current support from ERC CoG-866274 EQUIPRICE, and past support from NSF grant DMS-1716489 are acknowledged.

Suggested preparation readings (optional)

Alfred Galichon (2016). Optimal Transport Methods in Economics. Princeton University Press.

Course material

Available on github here.

Practical information

• Schedule: Monday to Friday, 8am-12pm US Eastern time / 2pm-6pm Central European time, plus four additional lectures to be scheduled. A zoom link will be provided.
• Credits: assessed through a take-home exam or a short final paper, at the student’s option. To be discussed with the instructor.
• A syllabus is available at http://alfredgalichon.com/mec_optim/.
• Students are advised to contact the instructor (alfred.galichon@nyu.edu) ahead of time.

Synopsis

Day 1

Block 1. Basics of linear programming

• Theory: linear programming duality; complementary slackness; minimax formulation
• Coding: How to eat optimally? Dataset: Stigler’s original diet data (1945).

Block 2. Network flow problems

• Theory: directed graphs and min-cost flow problem
• Coding: How to find the shortest path through a network? Dataset: Paris subway; New York City street network.

Day 2

Block 3. Dynamic programming as linear programming

• Theory: Bellman’s equation; interpretation of duality; forward induction, backward induction
• Coding: When to repair mechanical engines? Dataset: Rust’s bus maintenance data (1994).

Block 4. Optimal assignments

• Theory: Shapley-Shubik duality; stability; decentralized equilibrium.
• Coding: How to solve it? Dataset from Dupuy and Galichon (JPE 2014).

Day 3

Block 5. Entropy-regularized optimal transport

• Theory: IPFP algorithm; log-sum-exp trick
• Coding: How to infer the unobservable quality of a car model? Dataset: Feenstra-Levinsohn (Restud 1994) car data.

Block 6. Basics of static discrete choice

• Theory: The MEV model; Daly-Zachary-Williams theorem, generalized entropy of choice, the inversion theorem
• Coding: How to solve it? simulation methods; AR, SARS, and GHK. Dataset: Greene and Hensher (1997) data on choice of travel mode.

Day 4

Block 7. Hotelling’s characteristics model and its offsprings

• Theory: the random coefficient logit model and the pure characteristics models; power diagrams, Aurenhammer’s method
• Coding: How to estimate demand for automobiles? Dataset: BLP.

Block 8. Parametric discrete choice

• Theory: MLE, moment-matching estimator, minimax regret.
• Coding: Choice of travel mode.

Day 5

Block 9. Separable models of matching

• Theory: matching with unobservable heterogeneity.
• Coding: Did Roe vs. Wade decrease the “value of marriage”? Datasets: Choo and Siow (JPE 2006); Chiappori, Oreffice and Quintana-Domeque’s (JPE 2012); and Dupuy-Galichon (JPE 2014).

Block 10. The gravity equation

• Theory: optimal transport and the gravity equation; generalized linear models and pseudo-Poisson maximum likelihood estimation; model selection using LASSO
• Coding: Forecasting international trade flows: estimating the gravity equation based on WTO international trade data.

Special lectures

Special lecture 1 (Feb 5, 2pm-4pm Paris time): cloud computing

Guest speakers: Flavien Léger (Sciences Po) and James Nesbit (NYU).

Special lecture 2 (March 5, 2pm-4pm Paris time): estimation of dynamic discrete choice problems

Speaker: Alfred Galichon

• Theory: Rust’s model; estimation; normalization issues
• Coding: maintenance choice.

Special lecture 3 (April 9, 2pm-4pm Paris time): kidney exchange problems

• Theory: Roth et al.
• Coding: an interactive multi-player simulator

Special lecture 4 (April 30, 2pm-4pm Paris time): traffic congestion

• Theory: Wardrop equilibria; price of anarchy
• Coding: traffic data.

Special lecture 5 (May 7, 2pm-4pm Paris time): matrix games

• Theory: Nash equilibria; correlated equilibria; zero-sum games and LP formulation
• Coding: soccer data on penalty.