Economics

An exposition of those parts of mathematics necessary to equip the graduate student in economics with modern techniques of analysis and empirical investigation. (This is a service course.)

First term of a two-term sequence in microeconomic theory. Topics include consumer and producer theory, choice under uncertainty, and an introduction to game theory.

Second term of a two-term sequence in microeconomic theory. Topics include static and intertemporal general equilibrium theory, public goods and externalities, auctions, mechanism design, bargaining, repeated games, social choice, and implementation.

This course is the first term of a two-term sequence in macroeconomics. Topics include consumption, saving, and investment; real interest rates and asset prices; long-term economic growth; money and inflation; and econometric methods for macroeconomics.

This course is the second term of a two-term sequence in macroeconomics. Topics include classical and Keynesian theories of cyclical fluctuations; the determination of employment and real wages; credit markets and financial stability; and stabilization policy.

Students develop a research question and present results in class, supervised by two faculty members. Each student presents three times: on the research question and motivation; literature review and data or modeling plan, and on the final proposal. By the end of the term, students must submit a plan for research, which must be approved by the supervising faculty members.

Students carry out research on a topic and present results in class, supervised by two faculty members. Classmates will provide feedback and suggestions for improvement. Course culminates in a written draft. ECO 506 (Directed Research I) in the fall is a prerequisite.

Topics vary from year to year reflecting, among other things, current developments and the instructor's interests. General areas covered include experimental design and methodology, analysis of experimental data, as well as specific topics of experimental investigation, such as social learning, public goods, auctions, and collective action.

Topics vary from year to year reflecting, among other things, current developments and the instructor's interests. Topics covered in past years have included expected and nonexpected utility theory, intertemporal general equilibrium theory, evolutionary game theory, dynamic games, contract theory, theory of organizations, and bounded rationality.

Topics vary from year to year. See 511.

Concepts and methods of time series analysis and their applications to economics. Time series models to be studied include simultaneous stochastic equations and VAR, ARIMA, and state-space models. Methods to analyze trends, second-moment properties via the auto covariance function and the spectral density function and methods of estimation and hypothesis testing and of model selection are presented. Kalman filter and applications as well as unit roots, cointegration, ARCH, and structural breaks models are also studied.

Course provides a broad treatment of game theory and its applications, particularly in economics. Coverage includes topics such as common knowledge and rationality, refinements of the Nash equilibrium, auctions, bargaining, mechanism design, dynamic games, and reputation. This follows up on the introduction to game theory provided in the microeconomic sequence.

The construction, estimation, and testing of econometric models as a process, from theory to model formulation to estimation and testing and back again to theory. Bridging the gap between theory and applied work. A series of topics in macroeconomic time series and microeconomic cross-sectional analysis that include consumption at the household and aggregate level, commodity prices, and nonparametric and parametric estimation.

A first-year course in the first-year econometrics sequence, it is divided into two parts. The first gives students the necessary background in probability theory and statistics. Topics include definitions and axioms of probability, moments, some univariate distributions, the multivariate normal distribution, sampling distributions, introduction to asymptotic theory, estimation and testing. The second introduces the linear regression model and develops associated tools. Properties of the ordinary least squares estimator will be studied in detail and a number of tests developed.

This course begins with extensions of the linear model in several directions: (1) predetermined but not exogenous regressors; (2) heteroskedasticity and serial correlation; (3) classical GLS; (4) instrumental variables and generalized method of moments estimators. Applications include simultaneous equation models, VAR's and panel data. Estimation and inference in nonlinear models are discussed. Applications include nonlinear least squares, discrete dependent variables (probit, logit, etc.), problems of censoring, truncation and sample selection, and models for duration data.

Economics 519 is half of the second-year sequence in econometrics methodology (Economics 513 is the other). The course covers nonlinear statistical models for the analysis of cross-sectional and panel data. It is intended both for students specializing in econometric theory and for students interested in applying statistical methods to statistical data. Approximately half of the course is devoted to development of the large-sample theory for nonlinear estimation procedures, while the other half concentrates on application of the methods to econometric models for discrete and limited dependent variables.

Focused on analytical models of political institutions, this course is organized around canonical models and their applications. These include voting models, menu auctions, models of reputation, and cheap talk games. These models are used to explain patterns of participation in elections, institutions of congress, lobbying, payments to special interest groups, and other observed phenomena.

Topics vary from year to year, reflecting current developments and the instructor's interests. Topics covered in the past years have included methods of numerical analysis and econometric testing of equilibrium business cycle models, the role of monetary and fiscal policy in inflation determination, the nature of optimal monetary policy, and dynamic games and time consistency in macroeconomic policy formation, central banking, and theories of price stickiness.

A continuation of Economics 521. Topics vary from year to year.

A microeconomic examination of the role of government in the economy. Topics include the theory and measurement of excess burden, optimal tax theory, the analysis of tax incidence, and an examination of the effects of taxation on behavior.

The course examines the collective-decision mechanisms through which government policy is formulated, with an emphasis both on theoretical models of social choice and positive studies of governmental decision making. Additional topics include social insurance and the study of intergovernmental fiscal relations, with attention given to the division of functions among levels of government and basic issues in state and local finance.

Asset pricing in competitive markets where traders have homogeneous information as well as empirical tests of asset-pricing models and associated "anomalies" are also surveyed. Measures of riskiness and risk aversion; atemporal asset-pricing models; dynamic portfolio choice; option pricing; and the term structure of interest rates, corporate investment and financing decisions, and taxation are studied.

Theories and empirical evidence regarding financial markets and institutions that focus on asymmetric information, transaction costs, or both; and rational expectation models of asset pricing under asymmetric information, dynamic models of market making, portfolio manager performance evaluation, principal-agent models of firm managerial structure, takeover bids, capital structure, and regulation of financial markets are studied.

Advanced asset pricing and corporate finance including a selection from: models of financial crises and bubbles; interaction between finance and macroeconomics, derivative pricing in incomplete markets; tests of asset pricing models and associated anomalies; models of investor behavior; financial econometrics, including tests of asset pricing models and methods for high frequency data. Pre-requisites: ECO 525 and 526 (526 may be taken concurrently).

The course covers research topics that require the use of dynamic macroeconomic models with heterogeneous agents (households, firms, financial intermediaries, etc.). The methodological emphasis is both (a) on the coherent construction of the models and (b) on their parameterization and numerical solution. ECO 504 is a prerequisite.