# Graduate Course Offerings

This course is part of the microeconomics sequence offered to students in the Economics PhD program. It covers the basic concepts at the foundation of modern microeconomic theory. The two courses in this sequence (ECON 5005 and ECON 5006) rely heavily on calculus and other mathematical tools. ECON 5005 focuses on game theory, industrial organization and consumer theory. The follow-up course, ECON 5006, covers the topics of production theory and general equilibrium among others.

This is the second course in microeconomic theory at the graduate level. We continue to build rigorous formal models and study the behavior of producers, the role of markets in coordinating economic activities and the conditions required by those markets for an efficient allocation of resources. We will also deal with the classical theory of choice under uncertainty and discuss the chief role of financial markets.

The first part of the course uses a classical, market-clearing model to describe output, interest rates, employment, and the price level in the absence of economic growth. The latter part of the course has an introduction to the theory of economic growth as represented by the Solow model. After studying the Solow model other topics are pursued as time permits.

It is the second class in the graduate-level macroeconomics sequence. The first two topics are on tools (dynamics and expectations), and then useing those tools to study three important topics: real business cycle models (the role of technological shock), models with nominal rigidities (the role of money) and asset pricing (the relationship between asset prices and the macroeconomy). In addition to using the relevant chapters of the textbook, relevant journal articles are incorporated for each topic.

The purpose of this course is not to mold first year economics graduate students into mathematicians. Rather, it is to make students familiar with some of the basic elements of mathematics used in economics and econometrics. The main topics that will be covered are:

- Basic elements of set theory and real analysis.
- A short review of some elements of matrix algebra.
- Quadratic Forms.
- Concave, convex and quasi-concave functions.
- Optimization.
- Homogenous and Homothetic functions.
- A Fix point theorem and its uses.
- Separating and supporting hyperplanes.
- Upper and lower hemicontinuence correspondences.

This is the first of a two semester course sequence in **Empirical Research Methods in Economics** (ECON 5126 being the next one). It is a pre-requisite for other optional courses in Econometrics (ECON 6024, ECON 5945, ECON 5946). This course provides an introduction to Probability Theory and Statistical Inference with a view to lay the foundations and erect the overarching framework for empirical modeling in general, and economics and the social sciences in particular. This course differs from traditional courses in Probability and Statistics in several respects, including the following:

- It offers a seamless integration of probability and statistical inference with a view to elucidate the interplay between deduction and induction in learning from data.
- It develops frequentist modeling and inference from first principles by emphasizing the notion of a statistical model as the cornerstone of inductive inference.
- It places special emphasis on the appropriate selection and validation of the statistical model (its probabilistic assumptions) vis-a-vis the data before any inference is drawn, with a view to ensure its reliability and precision.
- It focuses primarily on skills and knowledge one needs to develop to be able to begin with a substantive question of interest, a carefully chosen data set, and proceed to establish trustworthy evidence for or against a hypothesis or a claim relating to the question of interest. These skills include understanding the statistical information conveyed by data plots, selecting appropriate statistical models as well as validating them vis-a-vis the data.
- It presents frequentist inference (estimation, testing and prediction) as well-grounded procedures whose optimality is assessed by their capacity to advance learning from data.
- It addresses several foundational issues, including the use and abuse of p-values, Neyman-Pearson testing and confidence intervals, that have bedeviled frequentist inference since the 1940s.
- It offers reasoned replies to several charges against frequentist inference.

This course constitutes the second module of the first-year PhD sequence in Economics or Agricultural and Applied Economics, following ECON/AAEC 5125. The 5125 module provided the statistical and probability-theoretic foundation for engaging in econometric research. This course addresses the interplay between economic theory, actual data, and statistical processes in addition to analyzing modeling assumptions, and to question and examine them as rigorously as possible.

Building on this foundation, the emphasis of this course lies primarily on the mathematical description and the computational implementation of econometric models.

The former requires proficiency in matrix algebra, an important objective of this course. The latter will introduce you to computational programming. You will build all of your models “from scratch”, and thus maintain full control over their components.

This course uses R as the chosen programming software. It is not only free, but also well supported by a worldwide community of experts and users. Numerous meetings and conferences in econometrics and statistics in recent years attest to its widespread adoption by the stats community, and its rapidly growing popularity amongst empirical economists.

Another aim of this course is to get you started on technical writing, of the kind you would use to produce a professional journal paper with mathematical and statistical content. You will be using LaTeX, via TeXnicCenter, another free and widely supported package. In essence, LaTeX is a programming approach to typesetting. If you’re already “TeXting,” great. If not, you have likely experienced at least some frustration with Word’s equation editor or Mathtype, and you will find the LaTeX technology an attractive alternative to these “canned” packages. I recently made the switch, and would never go back to conventional word processors for my technical writing.

Using LaTeX also promotes another advantage of R: Via R’s sub-module Sweave you will learn to create unified documents that include all of your (i) statistical programming code, (ii) mathematical equations, (iii) comments and discussion, and (iv) results in a single file. Welcome to the new age of technical writing!

To lower your startup costs getting a handle on these software packages, you will _nd detailed installation and configuration instructions on our course web site, given in the header above. Throughout the semester, I will post numerous examples of R, LaTeX, and Sweave files on the course website to facilitate your use of these packages.

In terms of econometric topics, we revisit some of the estimation methods you encountered in ECON/AAEC 5125, such as least-squares (LS) and maximum likelihood (ML), this time focusing on mathematical structure and computational implementation. In addition, we will cover extensions of the basic (“ordinary”) LS framework to incorporate more flexible model structures. Most notably, these extensions include instrumental variable (IV) approaches and generalized least squares (GLS).

We will also spend some time on perhaps the most popular analytical framework in applied micro-economics these days: the estimation of causal treatment effects. This topic builds naturally on Least Squares and MLE techniques, but introduces some new perspectives on causality and its “enemy” – endogeneity.

Last but not least, I would like to provide you with some exposure to Bayesian modeling, for the following reasons: (i) It provides several advantages over \classical” (or \frequentist”) methods in many situations, (ii) With the advent of enhanced computing power, it has enjoyed a strong resurgence amongst econometricians in recent years, (iiI) It is not covered – at least not in any technical detail – in any other mandatory ECON or AAEC course, and (sel_shly) (iv) It’s the approach I prefer for my own research.

This course is all about the analysis of “time-series” data. An ordinary econometrics course primarily focuses on the analysis of “cross-sectional data,” where (for example) we seek to explain the sample variation in earnings across a large number of individual households, all in a specific year. The analogous “time series” data would consist of aggregate household earnings, as observed monthly, say, over a period of a number of years. The econometric challenges of dealing with time-series data are quite different, for two reasons.

First, since the time series data are in time order, it is very likely that the regression model error for the current observation (period) is substantially correlated with recent model errors, violating one of the model assumptions crucial to deriving the usual inference results used to construct confidence intervals and hypothesis tests. This problem can usually be ignored with cross-sectional data, but it is typical – and often substantial – with economic time series data.

Second, the reason for making a time-series model usually involves a desire to forecast future values, which brings up an additional set of issues – and an entire tradition in the literature. This tradition is called “time series analysis,” and is extremely useful as area of study in its own right. It is also an analysis paradigm which is both sufficiently distinct from and sufficiently related to ordinary time-series econometrics analytics as to shed important light on how we should analyze economic time series data, even if we do not have forecasting in mind.

This class is for the economics major who has already taken an introductory course in econometrics.

The objective of this course is to help students develop a working knowledge of the theory and methods that are widely used for microeconometric analysis. Topics will include instrumental variables, basic panel data methods, simultaneous equation models, simulation methods, nonlinear estimators, generalized method of moments, discrete choice models, and selection models.

Prerequisites: AAEC/ECON 5125-5126, or by the permission of the professor. Most importantly, students must be comfortable with a first-year Ph.D. level treatment of matrix algebra, probability theory, and the multivariate linear regression model. Experience with statistical software and programming is useful, but not required.

As a methodological field within the discipline, experimental economics develops laboratory experimental techniques (similar in spirit to those found in the ‘hard sciences’) in the pursuit of two broad ends: to empirically evaluate existing assumptions and theories of economic behavior and to ‘wind tunnel’ test new assumptions, theories and policies. In this course, we will learn how to marry theory with the experimental economists’ laboratory, how to interpret the results of experiments, how to advance economic thinking using experimental results and how this tool applies equally to individual, group, ‘micro’ and ‘macro’ behavior.

This course will be an introduction to graduate level research in philosophy of inductive statistical inference and probabilistic methods of evidence (a branch of formal epistemology). We explore philosophical problems of confirmation and induction, the philosophy and history of frequentist and Bayesian approaches, and key foundational controversies surrounding tools of statistical data analytics, modeling and hypothesis testing in the natural and social sciences, and in evidence-based policy.

Game theory deals with strategic interaction and provides the formal framework to describe and analyze situations with conflicting interests, as well as situations with both common and conflicting interests. The course is meant for graduate students who are familiar with optimization techniques and basic calculus. Having taken an introductory class on game theory is much useful (though not required). Proof of applicability is provided by means of examples and real life cases relating to industrial organization, contract theory, auctions and voting.

Varies Depending on Semester

The classes will consist primarily of discussions of the significance of the ideas developed in the text. Students will generally be responsible for satisfying themselves that the mathematical assertions in the text are true, unless they ask for discussion of specific points. Grades will be based half on class assignments and half on an open-book take-home exam.

Topics covered: The origin of and rationale for government, positive and normative analysis of redistribution, positive analysis of majority rule alternatives to the plurality rule, mobility as voting, the logic of federalism, two-party competition, multi-party systems, why do people vote?, rent-seeking, theories of bureaucracy, theories of legislative behavior, advantages and disadvantages of dictatorship, theories of social justice.

This course reviews selected topics in economic development at the graduate level. Main topics covered are growth theory, dualistic models, economics of the family, inequality, and policy evaluation. The criteria for picking these topics from the much larger set of the development economics literature are centrality to the development process, relevance to the current literature, and my own research interests. Lack of time does not permit a more comprehensive treatment of the economics of development. In particular, macroeconomic issues for open economies are not covered.

This course is motivated by questions and data on individual employment and human capital accumulation behaviors over the life time. The main objective is to study quantitative methods for analyzing these decisions in dynamic and stochastic environments. Students focus on empirical econometric studies that have been developed during the last 15 years. Previous covered topics: wage structural and inequality, labor market selection, compensating wage differentials and hedonic wage function, labor supply, human capital and returns to education, topics in family economics.

The classes will consist primarily of discussions of the significance of the ideas developed in the text. Students will generally be responsible for satisfying themselves that the mathematical assertions in the text are true, unless they ask for discussion of specific points. Grades will be based half on class assignments and half on an open-book take-home exam.

Topics covered: The origin of government, principles for evaluating government action and the legitimacy of government, public goods and their efficient production, identifying preferences for public goods, local public goods, externalities, cost-benefit analysis, the incidence of taxation, the excess burden of taxation, the theory of debt finance, the theory of optimal taxation, inflation as a tax, redistribution through taxation, tax evasion.

The goal of this course is to provide a graduate-level introduction to Industrial Organization (IO). We will be surveying a variety of topics within the field, including but not limited to static models of firm competition, firm entry, dynamic models of agent and firm behavior, product differentiation, production function estimation and auctions. We will also revisit some econometric techniques that are most useful in this field. It will start the process of preparing economics Ph.D. students to conduct thesis research in the area, though the tools and techniques covered can also be of interest to doctoral students in other fields. The course covers both theoretical models and empirical studies.

This course is designed to be an in-depth examination of the modern econometric approaches currently employed to study dynamic relationships and to model the differences (or heterogeneity) among subjects. It is an advanced econometrics course suitable for graduate students with an applied orientation. The content will include both theory derivations and practical applications.

Prerequisites: AAEC/ECON 5125, 5126 and 5946, or by the permission of the professor. Most importantly, students must be comfortable with a first-year Ph.D. level treatment of matrix algebra, probability theory, and the linear and nonlinear models. Experience with statistical software and programming is useful, but not required.

This is a course intended for Ph.D. students interested in conducting research in applied microeconomics, including I.O., Labor, Environmental, etc. The main goal of this course is to provide students with a set of tools so that they can begin to write their own original research in applied microeconomics. Special attention will be paid to the most recent research in these areas so that students are exposed to papers on the research frontier. In the course, we will discuss the estimation and applications of several broad classes of models:

- Modeling demand system in differentiated product markets
- Imperfect competition under product differentiation
- Entry and market structure: Identification and estimation of static discrete games
- Industry dynamics I: Dynamic imperfect competition with exogenous number of firms
- Industry dynamics II: Dynamic imperfect competition with endogenous number of firms
- Information asymmetry and contracts (optional)

The empirical techniques emphasized in this course are centered on the structural estimation of strategic interactions. Due to the instructor’s own research interests, many of the examples and applications are drawn from I.O. However, these techniques can be readily applied to other fields, such as finance (especially market microstructure), labor, marketing, and environmental economics.

The only prerequisite for this course is ECON5125, or an equivalent statistics course. The additional background in statistics/econometrics will be covered during the course.

__Motivation__: This recent global financial crises raised numerous questions pertaining

to economics as a scientific discipline, and, in particular, the soundness of its empirical underpinnings. How do we acquire knowledge about economic phenomena?

How do we distinguish between well-grounded knowledge and idle speculation stemming from strong personal beliefs? How do we distinguish between ‘good’ theories and ‘bad’ theories? What is the role of the data in testing the adequacy of theories or hypotheses?

A major part of the problem lies with the way we educate economists in using the data to provide evidence for a hypothesis or a theory. This is where this course becomes relevant. We can and should do better!

__Primary objective of this course__: To redress the balance between two different perspectives on empirical modeling and teach the students practical skills on how we can do better in learning from data about economic phenomena of interest.

(a) Traditional textbook econometrics. A list of regression-type models, together with a menu of different estimation procedures (OLS, GLS, IV, GMM, kclass, LIML, FIML, etc.), that can be implemented using certain software packages (STATA, EViews, Minitab, etc.). The primary emphasis is placed on learning how to derive the relevant estimators and tests associated with different models. No wonder some students have a hard time distinguishing between the statistical and the matrix theoretic aspects of the linear regression model. This list of models and estimators leaves the practitioner none the wiser as to ‘how’ and ‘when’ to apply them to real data.

All a practitioner can do is ‘try out the different models and estimation procedures’ using several data sets, hoping that occasionally a computer output will enable them to ‘tell a story’. However, this story-telling sheds no real light on economic phenomena because the reported empirical ‘evidence’ is usually totally untrustworthy. The computer output pertaining to parameter estimates, their standard errors, the t-ratios, F-statistics, R2, etc., is often statistically meaningless primarily because this ‘evidence’ was produced by ignoring certain key foundational issues like (i) validating the invoked statistical and substantive premises vis-à-vis the data, or (ii) bridging the gap between theory and data, and inference results and economic phenomena of interest.

(b) An alternative framework for empirical modeling. The ECON6614 course is designed to:

(i) Review in some detail what is currently being taught as textbook econometrics for all types of data, time series, cross-section and panel data,

(ii) Bring out the limitations and the most serious weaknesses of these traditional tools, and

(iii) Propose a more appropriate modeling framework where one can see WHEN and HOW these traditional techniques can be properly applied in practice with a view to learn from data about economic phenomena of interest.

The focus of the course is on the proper application of the various techniques that give rise to reliable inferences and trustworthy evidence. That requires one to address several key foundational problems in statistical modeling and inference. The course aims to teach the nitty-gritty of what it takes to begin with:

(i) a substantive question of interest,

(ii) choose an appropriate data set, and

(iii) proceed to use statistical procedures to shed light on the question of interest, placing the emphasis on detecting, eliminating or sidestepping potential errors that could derail any learning from data. This includes separating the statistical from the substantive model, validating the statistical model, bridging the gap between theory and data, as well as confronting theories to data to appraise their empirical validity.

In a nutshell, the primary objective of this course to provide a fresh look at the empirical foundations of economics with a view to improve the reliability and precision of statistical inference. Emphasis throughout the course will be placed on the effectiveness of different ways to ‘learn from data’ at the level of a practitioner.

Throughout the semester, various speakers from academia and the professional world will come and give talks on different topics. Students from first year to fourth year must be enrolled and maintain a seminar attendance rate above 50%.

Research credits to work on dissertation.