Courses

Credits: 0  

Description

This course prepares for the Master of Science in Economics. Prerequisites are knowledge of Calculus and Multivariable Calculus. Beginning with a review of univariate differential calculus and optimization, the discussion moves to the basics of linear algebra, multivariate differential calculus, and tools related to the constrained optimization of functions, the core concepts of this course. Additional topics will be covered including duality, fixed-point theorems, implicit function theorem, and envelope theorems. While this course is not a study of pure mathematics, several results will be presented with rigorous proofs. For each of the topics covered, economics applications will be introduced and solved in class. 

Learning Outcomes

• Introduction to abstract mathematical concepts and thinking.
• Command of multivariable calculus.
• Ability to state and solve static constrained optimization problems.
• Ability to perform advanced linear algebra operations.
• Understanding the notion of equilibrium.
• Capacity to acquire mathematical concepts from studying the textbook.
  

Teaching Methodologies:

This is a lecture-based course. In recitations, students will solve exercises on the board under the guidance of the teaching assistant.

Credits: 4

Description

The goal of this course is to develop a detailed theoretical understanding of the linear regression model, which forms the cornerstone in Econometrics and an in-depth understanding of which is key for subsequent econometric studies as well as applications. The course will also introduce advanced econometric methods for cross-sectional and time-series data, such as the Maximum Likelihood and Generalized Method of Moments for univariate linear and nonlinear econometric models.

Learning Outcomes

• Assess suitability of econometric methods.
• Derive estimators and their statistical properties.
• Read and criticize empirical research papers.
• Implement estimators and hypothesis tests using data and various statistical software, such as STATA and R.R.

Teaching Methodologies

This is a lecture-based course. In recitations, students will solve exercises on the board under the guidance of the teaching assistant.

Credits: 4

Description

After taking this class, students should be familiar with the main techniques used in modern empirical microeconomics. They should understand the theory behind these methods, as well as threats to the validity of these methods. They should finally be able to implement these methods.

This class will cover the theory and implementation issues for situations where the assumptions of the classical linear model do not hold — see the reading list below for examples of such situations. Examples where appropriate will be taken from development economics, experimental economics, health economics, labor economics, and public finance.

We will use matrix algebra wherever possible. 

Learning Outcomes

• Assess the suitability of econometric methods.
  
• Learn about many econometric techniques and how to use them in STATA.
• Read about and criticize econometric practice in applied work.
  

Teaching Methodologies

Classes will consist of lectures on the application of econometric theory to real-world cases where we need to move from the standard linear model. While our emphasis is on applied work this will not be a cookbook course. Indeed, we will aim to prepare students to later tackle some different versions of the econometric model than considered in the textbook 

Credits: 4

Description

This course serves as a graduate level introduction to some fundamental questions in macroeconomics. We first theoretically and empirically study determinants of economic growth before proceeding to some major determinants of goods and labor supply and demand. We discuss fiscal and monetary policy issues as well as economic growth applying the methods and techniques used for the analysis of dynamic optimization problems using functional equations: dynamic programming. 

Learning Outcomes

• Analyze models and determinants of economic growth.
  
• State and solve dynamic decision problems of households and firms.
  
• Under guidance, replicate and extend fundamental models.
  

Teaching Methodologies:

This is a lecture-based course. In recitations, students will solve exercises on the board under the guidance of the teaching assistant.

The class requires substantial computational work but assumes no prior programming knowledge. Several exercises will involve the writing of basic computer code.

Credits:  4

Description

This course counts towards the Master of Science in Economics. This course follows the Math Camp that the students take prior to the beginning of the Master’s program. It trains the student to think rigorously and systematically at a level of high abstraction. The course is not meant primarily to serve other courses; it is designed to introduce advanced but standard mathematics that are both instructive in its own sake, and relevant for economic analysis.
This Mathematics 1 course introduces the fundamental elements of Set Theory, Linear Algebra, Topology, Convex Analysis and Differential Calculus that are needed to understand in depth, and practice at a high level of sophistication, a main pillar of economic analysis: Optimization.

Learning Outcomes

• Introduction to abstract mathematical concepts and thinking
  
• Command of basic mathematical spaces and operations
  
• Ability to state and solve dynamic optimization problems
  
• Ability to perform advanced linear algebra operations
  

Teaching Methodologies

This is a lecture-based course. In recitations, students will solve exercises on the board under the guidance of the teaching assistant. Active discussion of the concepts is strongly encouraged.

Credits:  4

Description

The course provides an introductory treatment of statistics including the relevant prerequisites of probability theory. The course takes an abstract, formal point of view and centers on the explanation of the underlying concepts behind statistical inference. At the end of the course the students understand the mechanisms underlying statistical inference. They are able to properly interpret the outcomes of a test. Moreover, the students possess the tools necessary in order to design and execute tests on their own scientific hypotheses. Additionally the level of the course is set such that the students acquire the relevant skills in order to be able to cope with scientific literature in the econometrics community.  

Learning Outcomes

• Know how to apply concepts of probability to analyze statistical estimators and tests.
• Can code simple routines to simulate concepts covered in class.
• Analyze steps of implementing code, plan time to design program, code, debug, and document.

Teaching Methodologies

This is a lecture-based course. In recitations, students will solve exercises on the board under the guidance of the teaching assistant.

Credits:  4

Description

This course provides an introduction to microeconomic theory designed to meet the needs of students in an economics PhD program. The course provides a rigorous overview of the main topics of microeconomic analysis including consumer theory, producer theory, game theory, general equilibrium, and information economics.

Students should be comfortable with multivariable calculus, linear algebra, and basic real analysis as covered in Math Camp.

Learning Outcomes

• State, interpret, and critically evaluate economic assumptions about individual behavior and economic institutions.
• State and solve decision problems for individuals and firms, and equilibrium problems for groups.
• Under guidance, replicate and extend existing models.
• Select and implement appropriate solution approaches to economic models.

Teaching Methodologies

This is a lecture-based course. In recitations, students will solve exercises on the board under the guidance of the teaching assistant.

Credits: 4

Description

The final project is a hands-on course designed to guide students on how to conduct economic research and prepare a research thesis or policy proposal. An important aspect of the course is to provide a forum to discuss project progress and provide each other with feedback. The course has three parts covering a number of topics. The first part is a practical guide for using statistical software such as STATA to master handling and visualizing data, using standard statistical methods, and making inferences. This component will utilize numerous labs, and also covers topics on how to
write a research thesis or policy report by formulating a research question and hypothesis, searching for related literature, preparing a literature review, citing literature, structuring a document, and presenting findings. The second part involves a replication exercise of a published economics/finance paper. The last part of the course requires students to extend on the replicated paper in a significant direction. Extensions can take numerous forms: for example, testing the validity of results in another country/firm context, using an alternative methodology, or highlighting potential heterogeneities in the existing results. The course also allows students to work on a topic of their interest under the supervision of faculty members from the Social Science division.

Expanded Course Description

Each project is unique. However, there are some general guidelines which you should try to satisfy:

1. Introduction. The final project should start with a polished and detailed introduction. The introduction should provide the context for your project (broad topic), should give a clear statement of your research question and motivate why the research question is of interest, formalize your research hypothesis, briefly explain the methodology you use to answer your research question, and discuss why the research methodology is appropriate for you to address your research question and hypothesis.
   
2. Relate literature. The project should provide a discussion of existing literature related to your research topic. Focus on the most relevant papers especially the replicated work. Summarize the papers very briefly, and focus on how your project extends on existing work.
   
3. Methodology. The project should have a separate section where you discuss in greater detail the research methodology you employ, and why it is appropriate to address the research question.
   

Analysis. The analysis will differ greatly across projects. As a rough guide, you should discuss in detail your data sources, provide clear and insightful summary statistics, and show and interpret your results.

At the end of the course, you will present your work. You will have approximately 30 minutes for presentation, and 10 additional minutes for Q&A. You should use the presentation to introduce people to your project: 

1. Start by providing some context (broad topic);
   
2. Clearly  articulate your specific  research question, and motivate why the research question is interesting;
   
3. Discuss how your projects is related to existing literature;
   
4. Briefly discuss hypothesis;
   
5. Briefly discuss your research methodology and why it is appropriate to address your research question and test your hypothesis;
   
6. Present your data and methodology using summary statistics;
   
7. Present your results clearly;
   
8. Conclude by indicating the take-away messages from your work.

Presentations will be graded based on:

• Organization and time management,
• Presentation style and clarity
• Content, and
  
• Interaction with the audience.
  

You will get one-on-one feedback on your presentation.

Credits: 4

Description

The aim of the course is to identify behavioral patterns that cannot be easily explained with standard economic models. This is done in a constructive manner. That means students will test the predictions of standard economic theories based on observational data from laboratory experiments, field experiments, and naturally occurring phenomena and learn about alternative theories that fare better in describing the behavioral patterns that they identify. Equipped with this knowledge, students will learn how to use behavioral theories to design public policy interventions and perfect business processes. The course is divided into four main themes: individual decision making, fairness and social norms, strategic interactions, and applications. In the first part, students study the rationality of preferences, a decision under uncertainty, and intertemporal choice. The second part reviews departures from self-regarding maximizing behavior and presents various models of other-regarding behavior that apply to settings where social norms and peer comparisons matter. In the third part, students tackle behavior in situations where strategic reasoning is central, such as the provision of public goods, the coordination of production, bargaining, and trading in financial markets. Finally, students turn to policy and institutional design for applications of behavioral insights.

Learning Outcomes

• Identify the shortcomings of the discounted model of expected utility in explaining behavior and explain how alternative models of individual decision-making overcome them.
  
• Explain how models of other-regarding preferences, such as models of guilt aversion and reciprocity, help us understand behavior in strategic interactions.
  
• Identify the components of proper experimental design in the social sciences and critically evaluate experimental studies.
  
• Apply insights from behavioral economic theories to design and communicate policies that further organizational and societal goals.
  

Teaching Methodologies

This course relies on a combination of lectures, in class discussions, recitation sessions, and participation in economic experiments. 

• Lectures are used to impart the foundational models in behavioral economics and present evidence of their support.
• The merits of these models will be discussed at length during in class discussions in which students are expected to actively participate.
  
• In recitations sessions, students will solve exercises based on the models seen in class under the guidance of the TA.
  
• To gain hand-on experience with the behavioral mechanisms that are at play, students will participate in economic experiments that will be conducted during class time.

Credits: 4

Description

How can the economies of the world become richer? Fairer? More open to opportunity?

We will investigate economic growth, poverty, inequality, and the sources of social change. The course begins by reviewing the relationships between poverty, inequality, and economic growth. Attention then turns to the role of markets, with a focus on finance. Then we turn to interventions designed to improve education, address demographic change, reduce the burden of disease, and confront corruption.

Learning Outcomes

• Identify the shortcomings of the discounted model of expected utility in explaining behavior and explain how alternative models of individual decision-making overcome them.
  
• Explain how models of other-regarding preferences, such as models of guilt aversion and reciprocity, help us understand behavior in strategic interactions.
• Identify the components of proper experimental design in the social sciences and critically evaluate experimental studies.
  
• Apply insights from behavioral economic theories to design and communicate policies that further organizational and societal goals.
  

Credits: 4

Description

We find that the exposure of many economists to programming languages tends to be limited to mastering statistical packages, such as STATA and EViews, just well enough in order to perform simple tasks like running a basic regression. These skills, however, do not scale up in a straightforward manner to handle complex projects. This course is designed to help address this challenge. It is aimed at Masters' students who expect to do research in a field that requires modest to heavy use of computations. In other words, any field that either involves real-world data; or that does not generally lead to models with simple closed-form solutions. Students will be introduced to effective programming practices that will substantially reduce their time spent programming, make their programs more dependable, and their results reproducible without extra effort. The course draws extensively on some simple techniques that are the backbone of modern software development, which most economists are simply not aware of. It shows the usefulness of these techniques for a wide variety of economic and econometric applications by means of hands-on examples.

This course has two distinct but closely intertwined objectives:

1.    Providing students with the tools to make their computations reproducible.
2.    Enhancing students’ programming efficiency.

Next to your economics background, the will only assume that you have written smaller pieces of code before, like STATA .do-files or Matlab .m-files. Knowledge of a specific programming language is not required. In fact, this course will use Python as an instructional language. Why? Because it is (1) freely available for all operating systems, (2) has numerical abilities closely mirroring those of Matlab but is (3) much more versatile and (4) easily extended with languages such as Fortran or C, which dominate computationally intensive fields. It is not a course about Python — but the course will use it as an example to teach the core concepts you need. You will be able to apply them in other languages with little transfer. A fair share of this course is really about tool choice — pointing out which language is most appropriate for which problem; but it is more instructive to stick to one language for the course.

Learning Outcomes

• Apply effective programming practices that require modest to heavy use of computations.
  
• Effectively plan and execute a project.
  
• Solve economic problems by applying programming methods with the aim of reducing time spent programming.
  
• Write programs that are more dependable and their results reproducible without extra effort.

Teaching Methodologies

This is a lecture-based course, however, students are expected to bring their laptops to perform hands-on exercises during the lecture. There will also be a recitation/lab twice a week that will be even more hands-on covering some material discussed in the lectures, as well as providing new complementary material to the course.  Throughout the course, you shall also be provided with five problem sets covering the various topics we will be covering.

Credits: 4

Description

Macroeconomics 2 presents an overview of macroeconomics at the Master’s level. The main theories are introduced in as intuitive a way as possible, to pinpoint as rigorously as possible which ones withstand empirical scrutiny and why. This is not a theoretical course, but techniques are discussed that help think about labor, goods and financial markets in a unified manner, and that motivates key empirical questions. Special attention is being paid to data and what empirical research has taught us. The proposed structure leaves plenty of room for group discussions, particularly as regards more recent developments on both empirical and theoretical fronts. The course covers basic concepts of labor market equilibrium and labor market institutions, capital investment and technical progress: business cycles and volatility. Financial market frictions, the demand for goods, demand management and the Phillips curve debate will be addressed as well as the relevance of heterogeneity in macroeconomics. After extensive coverage of a closed economy, the course moves to an internationally open economy: terms of trade, currency adjustment, and capital flows.

Learning Outcomes

• Analyze economic data and put it into the context of economic theories.
  
• Formulate and model economic policies.
  
• Assess the impact of economic policies theoretically and empirically.  

Teaching Methodologies

This is a lecture-based course. In recitations, students will solve exercises on the board under the guidance of the TA.

Credit: 4

Description

The Mathematics 2 course continues Mathematics 1 by deepening abstract mathematical concepts and thinking in Analysis (drawing from Set Theory, Linear Algebra, Topology, Differential and Integral Calculus, Convex Analysis, Measure Theory, and Differential Topology) in lecture format with extensive room for proofs in class as well as in recitations.

This course trains the student to think rigorously and systematically at a level of high abstraction. It is designed to introduce advanced but standard mathematics that is both instructive in their own sake, and relevant for economic analysis.

The Mathematics 2 course covers the mathematics of the main pillar of economic analysis: Equilibrium. 

Learning Outcomes

•  A deepening in abstract mathematical concepts and thinking
  

Teaching Methodologies

This is a lecture based course. In recitations students will solve exercises on the board under the guidance of the TA. Active discussion of the concepts is strongly encouraged.

Credit: 4

Description

This course provides a PhD-level introduction to game theory and market design. Game theory is the study of strategic decision making. It is routinely used in economics, political science, and computer science in the theoretical analysis of decision making. The course covers the analysis of static and dynamic games of both complete and incomplete information. Game theory provides the theoretical foundation for the study of how institutions shape behavior which, in turn, determines economic, social, and political outcomes. It provides the conceptual tools necessary to undertake “economic engineering,” i.e., to design institutions that generate desirable outcomes. The second part of the course concerns the market design, focusing on the two most-widely studied types of applications: auction design and the design of “matching” markets (e.g., school choice, kidney exchange).

Learning Outcomes

•  Use game theory to model strategic interaction.
  
• Apply game-theoretic solution concepts to generate predictions of behavior and outcomes in strategic interactions.
  
• Evaluate how the rules by which resources are allocated (or decisions made) affect incentives, behavior, and outcomes.
  

Teaching Methodologies

This is a lecture-based course. In recitations, students will solve exercises on the board under the guidance of the TA.

Prerequisites: 

Description

Numerical Methods cover basic methods of numerical analysis such as numerical optimization, the solution of linear, and nonlinear equation systems, etc. Special attention will be given to numerical methods for dynamic optimization, which are essential for dynamic analysis in all fields of economics. The course will cover in detail the solution of dynamic stochastic equilibrium models, including heterogeneous agent models, as they are used in modern macroeconomics, both in academic work and in central banks.

The coursework will be done in Matlab, the language most widely used in economic applications. Introductions will be given to Python, a scripting language used in all fields of computing, and to Julia, a new high-performance computing language. The focus of the course is on the practical implementation of these methods. At the end of the course, participants are supposed to be able to replicate the results of recent papers in quantitative economics. The grade of the course will be based on a series of exercises and a final computational project.

Learning Outcomes

• Understanding and applying important techniques in programming and numerical analysis.
• Being able to write economic models in the form suitable for numerical analysis.
• Judging whether a model can be solved numerically with sufficient precision, and modifying it so that it can be solved.
• Executing a computational project from beginning to end.
  

Teaching Methodologies

This course is based on a combination of lectures, recitation sessions and programming exercises, which consists of small computational projects, and a final individual project. The lectures are used to teach numerical methods, to discuss the application of suitable numerical methods to economic models, and to illustrate practical techniques for reliable and efficient programming (profiling, debugging, etc.). Students are required to apply these techniques on a continuous basis, in a series of programming exercises given every week. The solution of these exercises will be discussed in recitations under the guidance of the TA. The final project