## Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1.5 hours / session

## Prerequisites

*14.381 Statistical Method in Economics* or permission of the instructor.

## Course Overview

The course will cover several key models as well as identification and estimation methods used in modern econometrics. We shall begin with exploring some leading models of econometrics, then seeing structures, then providing methods of identification, estimation, and inference. You will learn the modern ways of setting up problems and doing better estimation and inference than the current empirical practice. You will learn generalized method of moments, the method of M-estimators, as well more modern versions of these methods dealing with important issues such as weak identification or biases arising in high dimensions. You will also learn the bootstrap. At the end of the course, we shall also explore very high dimensional formulations, or "big data", where some penalization via lasso or ridge methods is necessary to say anything useful. You will get a lot of hands-on experience with using the methods on real data sets.

## Outline

- Review of regression and partialling out. Simultaneous inference
- Linear Structural Equations Models (SEM), Wright's IV Principle, linear GMM
- Nonlinear SEMs, Hansen's Euler Equations, nonlinear GMM
- Bootstrap and simulation. Inference using BS
- Binary choice models, distributional regression, and M-estimators
- Linear and non-linear panel models, basic principles
- GMM and M estimators in high dimensions. Bias correction
- Program evaluation and Treatment Effect Models (TEMs)
- Modern principles for estimation of high-dimensional models
- Post-selection and post-regularization inference in SEMs and TEMs

## Grading

You will have three options:

Do only homeworks. There will be N=7 of them. (The last assignment is to fill out the course evaluations, which will not be included for OCW users.) If you choose to have your problem sets determine your grade, we will count your best N–1 grades of your N problem sets. However, you must hand in all N problem sets. However please note that we will not grade assignments that get handed in after the solutions are posted. This is a low-risk, but a high effort way to get a good grade. If you hand-in all of homeworks you are guaranteed to earn a passing grade (this does take away the anxiety and allows you to focus on learning).

Do the final exam only. This is only recommended if you know the material or don't want to spend too much time on the homework. This entails potentially lower effort cost, albeit involves higher risk (you would not know what grade you are getting until the final is graded).

- Do both. Of course, if you are not doing well with homeworks, you can always take the exam.

## Homework Policy

In this class we have the following grading policy for problem sets:

- The very best solutions receive check++ (A+)
- Very good solutions receive check+ (A)
- Good solutions receive a check (A-/B+)
- Satisfactory solutions receive check- (B)
- Acceptable solutions receive check-- (B-), which is our lowest passing grade.

Conversions of scores from the check system to the letter grades occurs at the end of the semester, subject to graders’ decisions.

## Prizes

The best performing students in this class receive prizes at the end of the semester. These prizes may include a copy of:

van der Vaart, A.W.

*Asymptotic Statistics.*Cambridge University Press, 2000. ISBN: 0521784506.Pearl, Judea.

*Causality: Models, Reasoning, and Inference. 2nd Edition.*Cambridge University Press, 2009. ISBN: 052189560X.-
Imbens, Guido W., and Donald B. Rubin.
*Causal Inference for Statistics, Social and Biomedical Science: An Introduction.*Cambridge University Press, 2015. ISBN: 0521885884.

## Text

There is no particular text that we shall follow. For each theme, we will post readings. There is a free online version of Bruce Hanse's *Econometrics* text. Other nice texts include Wooldridge's grad text, *Econometric Analysis of Cross Section and Panel Data*, 2nd edition; Hayashi's *Econometrics*, and Cameron and Trivedi's *Microeconometrics*. I can't really say which one you should buy. We also highly recommend Van der Vaart's text called *Asymptotic Statistics* to those planning to specialize in econometrics.