This course is taught in four modules. Modules I and II are taught in the first term, and Modules III and IV are taught in the second term.
Module I – Mathematical Methods
This part of the course covers the basic concepts from real and convex analysis
and static optimization theory. Topics include basic set theory, topological ideas
in metric spaces, finite-dimensional linear spaces, convex analysis and static
optimization. The course is taught in the first 6-7 weeks of the Fall semester.
It meets for four hours a week with an additional hour for discussion of problems.
Module II – Classical Microtheory
This part of the course develops classical general equilibrium theory
with a finite number of agents and commodities: in addition to
welfare economics and the basic existence theorems, it also
includes the two-sector model of production, public goods, core allocations
and Nash equilibria of games in normal form. The course is taught in the
second 6-7 weeks of the Fall semester, and meets for four hours a week, with
an additional hour for discussion of problems.
Module III – Game Theory
This part of the course introduces the students to the main game theoretic
tools used in economics research. Topics include normal form games, extensive
form games with perfect information, Bayesian games, and extensive form
games with imperfect information. It is taught over a period of 7 weeks, four hours
per week, with another hour discussion of problems.
Module IV – Information, Incentives, and Mechanism Design
This part covers issues related to uncertainty and asymmetric information,
incentives and mechanism design. Topics include axiomatic expected utility
theory, moral hazard and incentive contracts, adverse selection under signaling
and screening equilibria, social choice and mechanism design theory. It is taught
over a period of 6 weeks, four hours per week, with another hour discussion of
Prerequisites: 180.301-302 or equivalent and Differential Calculus 110.106 or permission of instructor.
Instructor: Khan (Module II), Eraslan (Module III), Karni (Modules I and IV)
First term: a comprehensive treatment of macroeconomic theory, including static analysis of aggregate output employment, the rate of interest, and the price level; aggregative theory of investment, consumption, demand and supply of money; empirical work on aggregative relationships.
Second term: the macrodynamic theory of growth, cycles, unemployment and inflation, and selected subjects.
Prerequisites: 180.301-302 or permission of instructor.
Instructor: Maccini, Carroll
Topics of recent research in macroeconomics. Prof. Ball’s course covers nominal rigidities, dynamic-consistency theories of inflation, inflation inertia and the costs of disinflation, monetary policy, costs and benefits of price stability, benefits of output stabilization, alternative policy rules, measuring inflation, unemployment, efficiency-wage theories, the behavior of the NAIRU, macro in middle-income countries, high inflation and stabilization, currency crises. Prof. Carroll’s course analyzes implications of the buffer-stock and habit formation theories of consumption for comovement of aggregate variables and asset pricing. The models are applied to study the phenomena of declining U.S. saving rate, the dynamic relationship between saving rates and growth, and the equity premium puzzle.
Instructor: Ball, Carroll
The course is an attempt to provide a framework for discussing the techniques that are used in macroeconometric analysis. Generally the bias that it has is one of looking at these from the perspective of someone analysing macroeconomic data for policy analysis. Consequently, many of the applications considered are drawn from the type of research conducted in central banks and finance ministries. Its emphasis is therefore upon the issues raised by the analysis of time series of macro-economic data. Today there is an emerging literature that looks at micro-economic data as well as conducting cross-country studies. We will tend to ignore that material as the methods used in such research are essentially those of micro-econometrics, although sometimes with adjustments made to reflect the nature of macro-economic time series.
Instructor: Faust, Wright
The course offers a review of alternative approaches to decision making under risk and under uncertainty. Starting with the subjective expected utility model, the course surveys axiomatic models that depart from the independence axiom under risk and the sure thing principle under uncertainty, exploring the notion of ambiguity and ambiguity aversion. Departures from the completeness of beliefs and tastes is also discussed and the representations of incomplete preferences under risk and uncertainty are examined.
Prerequisites: 180.601 and 180.603 or permission of instructor.
This course traces the extent to which modern economic theory, particularly as it pertains to pure competition in market and non-market games under the rationality postulate, is grounded in the language of probability and measure theory. Special attention will be paid to the formal expression of ideas such as economic and numerical negligibility, on the one hand, and diffuseness and conditional independence of information, on the other. Towards this end, the course will develop rigorous formulations of basic ideas of (conceptual rather than computational) probability and apply them: first, to develop the fundamental theorems of welfare economics, including the core theorems; and second, to large anonymous and non-anonymous games as well as to finite-agent games with private information. The course will be self-contained from the technical point of view but will presuppose a level of mathematical maturity that ought typically to be achieved by taking courses such as 180.615 and 180.601.
This course is taught as Module I of 601-602 sequence. Please see the course description of 601-602.
This course has two modules.
Module I (taught by Khan):
This module concerns dynamic optimization in both continuous and discrete time. More specifically, it develops Pontryagin’s maximum principle and the Euler-Lagrange conditions in the calculus of variations, on the one hand, and the basic tools of deterministic dynamic programming, on the other. The course will be self-contained from the technical point of view but will presuppose a level of mathematical maturity that ought typically to be achieved by taking a course such as 180:615 and 180:601.
Module II (taught by Carroll)
This module is an introduction to computational methods for solving models from micro- and macroeconomics. The emphasis will be on dynamic models. Students will learn the rudiments of several programming languages so that they gain some understanding of which languages are best suited to which problems.
Instructor: Khan, Carroll
This is a second-year doctoral course in game theory. The objective is to make sure that (1) students who plan to pursue applied research learn game theoretic tools well enough to fully understand the game theoretic arguments in the papers they read, identify problematic modeling techniques, build and solve their own models; (2) students who plan to pursue theoretical research in game theory get exposed to active research topics. The topics covered varies. Sample topics include repeated games, bargaining, voting, cheap talk, market microstructure, global games and network theory.
A review of experience in less-developed countries (LDCs) since 1945, theories of development, economic planning in the LDC context, and models of the development process.
Prerequisites: 180.601, 180.603
This course teaches methods for using micro-data to recover structural parameters of microeconomic models. We cover static models, but focus largely on single-agent dynamic programming, including “full solution” methods and innovations that permit circumvention of daunting computational tasks. Additional topics will be partially based on students’ interests, but will likely include: general equilibrium models, static and dynamic games, matching models, unobserved heterogeneity, structural methods with experimental data and biased expectations. The goal is to teach students to use structural methods in their own research, so we will delve into the nuts and bolts of structural work, examining how researchers actually get from raw data to results. This includes: how the subsample for analysis is chosen, how the model is specified, how the programming problem is solved, which moments are generated, how these are matched to the analogous moments in the data and, importantly, how identification is established.
Mathematical models of economic behavior and the use of statistical methods for testing economic theories and estimating economic parameters. Subject matter will vary from year to year; statistical methods, such as linear regression, multivariate analysis, and identification, estimation and testing in simultaneous equation models, will be stressed.
Prerequisites: Statistics Inference(180.636), Microeconomic Theory (180.601), Mathematical Economics (180.614). People who wish to audit need the same prerequisites.
This course covers two broad topics, probability theory and statistical inference, as prerequisites for the subsequent econometric courses. For the first part, we introduce theories of measure and integration. For the second part, we discuss finite sample statistics, estimation, hypothesis testing, and asymptotic statistics. Examples are drawn from economics and econometrics. The course is limited to graduate students in economics.
Prerequisites: analysis and linear algebra.
This is an advanced graduate course on major econometric techniques and models that are used in empirical microeconomics. The first half of the course introduces econometric theories of nonlinear extremal estimation, nonparametric estimation, and semiparametric estimation. The second half of the course illustrates applications of these theories to limited dependent variable models, selection models, and endogenous treatment models with unobserved heterogeneity.
Prerequisites: Statistics Inference (180.636), Microeconomic Theory (180.601-602) and Econometrics (180.633)
In this course techniques that are used in applied research in microeconomics are introduced. Focus is on a particular class of models, namely discrete choice models. Well-known models in this class are the logit and probit models. Models that have better properties involve high-dimensional integrals, and this leads us to a discussion of simulation estimation. Finally, dynamic decision models for forward looking agents who face irreversible decisions are introduced. As an application some models in economic demograpy are considered.
Prerequisites: Statistics Inference (180.636), Microeconomic Theory (180.601-602) and Microeconometrics I (180.637). People who wish to audit need the same prerequisites.
The pure theory of trade. Theories of comparative advantage, factor price equalization, trade and welfare, tariffs, trade
and factor movements.
Prerequisites: Corequisites: 180.601, 180.603
A link between the balance of payments and asset accumulation/decumulation, microeconomics of international finance and open-economy macroeconomics. The section on open-economy macroeconomics covers approaches to balance-of -payments adjustments, theories of exchange rate determination and monetary, fiscal and exchange-market policies under fixed and flexible rate regimes.
Prerequisites: Corequisites: 180.601, 180.603
First term: theories of the allocation of time and supply of labor, human capital, demand for labor, market equilibrium, and income distribution. As time allows, other topics, such as unemployment, unions, and compensating differences will be discussed.
Second term: current topics in labor economics. The content will vary from year to year. Likely areas include nature vs. nurture in the determination of earnings, the function(s) of unions the question of the existence of dual labor markets, and internal markets with specific human capital.
Prerequisites: 180.601 Corequisite for 652: 180.633-634
This course is an introduction and guide to the most important issues in asset pricing. It begins with classic concepts such as the Capital Asset Pricing Model and the Arbitrage Pricing Theory and continues through continuous-time dynamic no-arbitrage models. It covers both basic theory and classic empirical research.
View course website
First term: This course covers methods in applied empirical Industrial Organization. The focus will be on the use of econometric analysis and data both for descriptive and measurement purposes, and to test the predictions of economic theories. The course will cover demand estimation, cost and production function estimation, and estimation of auction models.
Second term: The emphasis in this course is on empirical analysis of firm behavior. The first part of the course focuses on models of the internal organization of the firm. The second part considers empirical analysis of firm behavior in markets, with an emphasis on the “new industrial economics.”
Instructor: Balat, Krasnokutskaya