MSc in Quantitative Economics

Module 1: July 11 - August 26

ECON-GA 4011 Math Methods I

The course begins with a quick review of basic methods of optimization theory, including necessary and sufficient conditions for optimality, the method of Lagrange multipliers and the Kuhn-Tucker conditions. These methods are required in the microeconomics and macroeconomics courses in the program. The course then develops the tools of real analysis and study conver- gent sequences, compact sets, continuous and differentiable functions, the Heine-Borel Theorem and the Weierstrass Theorem. Several applications are presented, including one-dimensional discrete dynamic systems and price adjustment models, and existence of optimal solutions in economic problems, The course then goes on to study convex and concave functions, derive the basic results for unconstrained optimization, and provide some applications to risk theory. Finally, the course investigates the basic properties of convex sets and cones, prove Caratheodory’s Theorem (on convex closures), and deduces some important results (such as Radon’s Lemma and Helly’s Intersection Theorem.

ECON-GA 4021 Data & Computation I

This course is a hands-on approach to the study of open-source computational and data management tools now available online. Workhorses will be Python and affiliated programs for efficient calculations and numpy and pandas for data managment. These tools are presented in ways designed to open doors for doing applied quantitative economics at the graduate level. The aim is to help students become literate in the open source ecology for doing machine learning with economic data and models at the graduate level. It is assumed that students are comfortable with linear algebra, multivariable calculus, and probability and statistics.

ECON-GA 4031 Microeconomics I

This course studies how market outcomes are determined by the decision-making of individual consumers and firms in the economy. The focus for most of the course will be on the decisions of each side of the market separately, taking as given a set of prices which fix terms of trade. On the consumption side of the market, rigorous models of consumer preferences will be used to microfound demand curves and describe notions of complementarity and substitutability between different goods. On the production side, descriptions of production technologies coupled with an assumption of profit-maximization by firms will be used to generate supply curves. Finally, demand and supply will be brought together to determine market allocations in conditions of perfect competition, monopolistic competition, and monopoly, with particular emphasis on the welfare implications of each environment.

ECON-GA 4041 Macroeconomics I

The first course in the macro sequence introduces the technical foundation for the study of macroeconomic models, introducing the theory and applications of dynamic programming. The first part of the course develops the technical tools on dynamic programing, including Bellman equations and the principle of optimality. On the second part, these tools are applied to the workhorse model of macroeconomics, the one sector growth model, covering its deterministic and stochastic versions. As another application of application of dynamic programming, the canonical labor search model is studied.

Venky Venkateswaran

 

Module 2: September 06 - October 21

ECON-GA 4012 Math Methods II

The second course goes deeper into convex analysis and optimization theory, and derives a number of core results such as the characterization of convex and quasiconvex functions, separating hyperpane theorems, Krein-Milman Theorem, the Kuhn-Tucker Theorem, and the Envelope Theorem. Optimization is required in the analysis of almost every economic model. Many economic applications are presented here, including some basic results in demand theory, Birkhoff’s Theorem on bistochastic matrices and its consequences for measurement of income inequality, linear regression analysis, duality in linear programming, and job matching models.

ECON-GA 4071 Econometrics I

This course introduces the core tools used for conducting empirical research in economics. The course will focus primarily on estimation and inference using linear regression and instrumental variables methods. Theory of estimation and inference will be developed rigorously. In addition, the course will cover important topics for empirical research, such as causal inference, random experiments, selection bias, and control variables. Practical issues will also be discussed, such as standard errors for dependent, heterogeneous, or clustered data, specification tests, and measurement error. Methods will be illustrated using numerous empirical applications across diverse fields of economics.

ECON-GA 4032 Microeconomics II

This course introduces the study of general equilibrium theory in economics. The approach adopted in the course aims at introducing the theory as the canonical theoretical structure for the study of market economies. Compet- itive equilibria are therefore studied as the main micro-foundation for macroeconomics and finance. The series of fundamental theorems which constitute the classic theory of general equilibrium, concerning existence, characterization, and welfare properties of competitive equilibria in frictionless economies, are introduced in their rigor, abstraction, and elegance. But the course will complement the classic theory with the modern analysis of financial market equilibria in dynamic economies with different kind of frictions, exposing students to fundamental conceptual notions like complete and incomplete markets, constrained inefficiency, moral hazard, adverse selection, bubbles. Topics will be enriched with applications of the concepts and results.

ECON-GA 4042 Macroeconomics II

This course studies competitive macro models and its applications to growth and fiscal policies. The complete markets model is studied with rigor, showing its equivalence with the sequential environment, its recursive representation and the welfare theorems. We discuss the implementation of fiscal policies, focusing on its normative recommendations. The overlapping generation model is introduced, with emphasis on its dynamic properties and the role of money and fiscal policy when agents have finite and overlapping lives.

Venky Venkateswaran

Module 3: October 31 - December 16

ECON-GA 4051 Game Theory I

This course provides a rigorous treatment of the basic models and solution concepts of non-cooperative game theory primarily in a symmetric information setting. It begins with normal form games and dominance arguments, mixed strategies, and the fundamental concept of Nash equilibrium. Next, the course discusses extensive form games, subgame perfect equilibrium, and other refinements of Nash equilibrium. Applications include models which are often used in applied economics, such as bargaining and repeated games. From a critical perspective, the course also compares Nash equilibrium with reasoning-based solution concepts: rationalizability, and level-k reasoning.

ECON-GA 4061 Applied Micro I

The first course in the applied micro sequence, covering the main statistical tools and questions in the field. The course emphasizes a hands-on approach, with analysis of primary data to replicate and extend existing research papers. It will implement and evaluate the core methods used in modern regression analysis for identifying causal effects: difference-in-differences, regression discontinuities and bunching, instrumental variables, and experiments. It will cover both iconic papers in the field (such as those which measure the causal effects of education on earnings, or uncover labor supply elasticities), as well as frontier research projects in a variety of subfields, including innovation, migration, economic development, and economic history.

ECON-GA 4072 Econometrics II

This course continues the econometrics sequence, turning to broader estimation paradigms and more advanced inference concepts. The course aims to give students a rigorous theoretical understanding along with a practical understanding of how to implement econometric methods. Topics include nonlinear estimation, maximum likelihood estimation, discrete choice models, generalized method of moments, bootstrapping, model selection, and panel data. Influential studies from labor economics and industrial organization will illustrate important concepts and methods.

ECON-GA 4043 Macroeconomics III

Macroeconomics III builds on the real macroeconomic phenomena studied in Macroeconomics II, and extends the analysis to monetary and financial considerations, with an emphasis on short-term business cycle fluctuations. Students are introduced to a variety of macroeconomic models used to study the role of money and monetary policy, financial intermediation and high frequency macroeconomic fluctuations. We start with the introduction of macro economic models with money, such as the classical models of money in the utility function and cash in advance. We also study search based models of liquidity, which are the core of the macroeconomic study of financial securities. High frequency fluctuations are analyzed in the context of the real business cycle model and the New Keynesian model, the workhorse model for the analysis of demand-driven recessions and of fiscal and monetary counter-cyclical policies. To understand the role of financial intermediation and its impact to the macroeconomy, we study models of financial frictions and the canonical banking model of Diamond-Dybvig.

Gian Luca Clementi

Module 4: January 02 - January 20

ECON-GA 4052 Game Theory II

This course builds on Game Theory 1 and continues the presentation of non-cooperative games, with an emphasis on asymmetric information: Bayesian games, Bayesian equilibrium and associated refinements. Key applications include auctions, global games, cheap talk, and reputation formation. The course introduces cooperative game theory. Basic cooperative solution concepts like the core, Nash bargaining solution and Shapley value are also introduced and connections with the non-cooperative perspective explored.

ECON-GA 4022 Data & Computation II

This course is the sequel to Data and Computation 1, and shall in the same spirit, brings students up to speed with modern tools to manage economic data at a graduate level. The course is centered on the Python/numpy ecosystem, and has five parts. A first part introduces topics such as replicability through containerization, high performance computing, and cloud computing. A second part covers regression and model selection. A third part covers computational market design. A fourth part covers network problems. A fifth part covers dynamic discrete choice problems.

Alfred Galichon

Module 5: January 25 - March 10

ECON-GA 4081 Applied Micro II

The course uses examples from the fields of labor, development, and public economics in order to illustrate econometric methods employed in model-based estimation, in which an explicit model of agents’ decisions is the basis for the estimation of policy-invariant parameters. These estimates can then be used to perform (numerical) comparative statics exercises and counterfactual policy experiments. In addition to discussing the substantive details of each of the papers that we consider, we will present details of the econometric procedures utilized. In particular, the courses discusses maximum likelihood estimation, nonlinear least squares, and the method of simulated moments.

ECON-GA 4081 Industrial Organization I*

This is the first part of a two course se- quence in Industrial Organization. The primary focus of the course will be empirical, though theoretical concepts will be introduced and reviewed as needed. The main fo- cus of this course is measuring markups and market power in a static setting. Topics include: estimation of supply and demand for homogenous and differentiated products; Economics of antitrust: merger evaluation and detection of collusion. Price Discrimina- tion; Production Function Estimation, Measures of Productivity.

ECON-GA 4091 Computational Dynamics*

The solution of state-of-the-art quantitative models in economics and finance often requires numerical implementation on a computer. In this course, we will explore a range of computational methods used to solve such quantitative dynamic problems: Local approximations of equilibria in mod- els for macro-policy analysis, global methods for approximating solutions to nonlinear decision problems, filtering techniques used in learning and estimation, discretization methods popular in financial economics, as well as neural network models used in data science. Students will implement each method using Python.

ECON-GA 4073 Econometrics III*

This course includes topics at the frontier of econo- metrics including machine learning and simulation-based methods. The course aims to provide students with a broad overview of new methodologies and their practical applica- tions in economics. Starting by surveying both classic and new methods for prediction, the course then elaborates on how to use them to help draw causal conclusions in spe- cific economic contexts. The course concludes with an introduction to simulation-based methods.

ECON-GA 4121 Research Practicum I

The research practicum course sequence brings students closer to the frontier of economics research. The goal is to introduce the student to cutting-edge research tailored to their specific interests. During the course, students have the opportunity to work closely with faculty on ongoing projects, or to critically evaluate the current research on a given topic. The course proceeds according to two tracks. Each student must choose one of the tracks for both research practicum courses. The tracks, which are referred to as “topical research” and “applied research” tracks. In the topical research track, the student chooses an economics discipline of their interest, narrowing the focus to a specific research topic. Under the guidance of a faculty supervisor, the student works to acquire deep knowledge of the topic, critically evaluating prior research on it and eventually drafting a research proposal. The student meets regularly with the supervising faculty (every 2 weeks, sometimes weekly), each time presenting a progress report. By the end of this track the student is expected to write a research proposal. In the applied research track, the student works directly under the guidance of a faculty supervisor on a specific research project. The list of available research projects is supplied by the various faculty associated with the Masters program. This track is similar to a research assistantship, with additional mentoring by the faculty member involved in the research. Each RA job posted by faculty members includes a description of the research project as well as the skill requirements from the student. By the end of this track the student presents a final report, with the overall description of the tasks performed during the research project as well as a summary of the project’s results.

Luis Cabral

Module 6: March 20 - May 17

ECON-GA 4044 Macroeconomics IV

This course extends the macro models developed in the earlier courses in the macro sequence, focusing on models that can be used to give quantitative answers to economic questions, such as asset pricing and its macro implications, unemployment and wealth inequality. The course provides a rigorous description of theses models and discuss its empirical implications.

ECON-GA 4082 Industrial Organization II*

This course builds the analytical and quantitative tools necessary to study the links between economics and finance, both in theory and in practice. It is based on the microeconomics of individual decision-making in a dynamic environment in which uncertainty and information about that uncertainty change over time. The course then adds the macroeconomics of how financial markets intermediate those decisions both across economic agents and across time. Each part of the course combines mathematics and economics: the analytical tools needed to think clearly about uncertainty, dynamic optimization, and equilibrium asset prices. In addition, the course combines this theory with the quantitative tools (measurement, statistics, and computational algorithms) that relate these concepts to real-world data. The analysis makes extensive use of flexible higher-level programming languages, such as Matlab and Python.

ECON-GA 4111 Financial Economics*

This is the second part of a two course sequence in Industrial Organization. It presumes you have completed the first part. The primary focus of the course will be empirical, though theoretical concepts will be introduced and reviewed as needed. This course extends the study of market power to settings with dynamic consumer behavior (durable goods, storable goods, switching costs, state dependence) and to settings with assymmetric information (such as auctions). We also study market power in the long run including endogenous entry and exit of firms, and in markets with vertical separation.

ECON-GA 4101 International Economics*

This course covers advanced topics in international trade and macroeconomics. The trade topics include fundamental models of trade flows and their quantitative implementation, the role of firms in international trade, and the welfare gains from international trade. The macro topics include business cycles in advanced and emerging economies, macroeconomic and financial crises, the determination of exchange rates, the special role of the dollar, currency unions, and sovereign debt and default. Each topic is motivated with empirical evidence and presents a relevant theoretical framework, which involves dynamic optimization, general equilibrium and strategic interaction.

ECON-GA 4122 Research Practicum II

The research practicum course sequence brings students closer to the frontier of economics research. The goal is to introduce the student to cutting-edge research tailored to their specific interests. During the course, students have the opportunity to work closely with faculty on ongoing projects, or to critically evaluate the current research on a given topic. The course proceeds according to two tracks. Each student must choose one of the tracks for both research practicum courses. The tracks, which are referred to as “topical research” and “applied research” tracks. In the topical research track, the student chooses an economics discipline of their interest, narrowing the focus to a specific research topic. Under the guidance of a faculty supervisor, the student works to acquire deep knowledge of the topic, critically evaluating prior research on it and eventually drafting a research proposal. The student meets regularly with the supervising faculty (every 2 weeks, sometimes weekly), each time presenting a progress report. By the end of this track the student is expected to write a research proposal. In the applied research track, the student works directly under the guidance of a faculty supervisor on a specific research project. The list of available research projects is supplied by the various faculty associated with the Masters program. This track is similar to a research assistantship, with additional mentoring by the faculty member involved in the research. Each RA job posted by faculty members includes a description of the research project as well as the skill requirements from the student. By the end of this track the student presents a final report, with the overall description of the tasks performed during the research project as well as a summary of the project’s results.

Pricila Maziero

*All courses are required except for specially marked courses (with an *) in Terms 5 and 6. A student must take two out of three courses marked ' * ' in each module, with the understanding that Industrial Organization II is only open to students who have taken Industrial Organization I.