# Syllabus

## Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1 hour / session

## Description

The course introduces statistical theory to prepare students for the remainder of the econometrics sequence. The emphasis of the course is to understand the basic principles of statistical theory. A brief review of probability will be given; however, this material is assumed knowledge. The course also covers basic regression analysis. Topics covered include probability, random samples, asymptotic methods, point estimation, evaluation of estimators, Cramer-Rao theorem, hypothesis tests, Neyman Pearson lemma, Likelihood Ratio test, interval estimation, best linear predictor, best linear approximation, conditional expectation function, building functional forms, regression algebra, Gauss-Markov optimality, finite-sample inference, consistency, asymptotic normality, heteroscedasticity, and autocorrelation.

## Prerequisites

The prerequisites for this course include Calculus (18.02) and permission of the instructor.

## Course Requirements

Each week there are two lectures and a recitation.

The problem sets will be due roughly every two weeks. The answer key to the problems in Statistical Inference will be available. It is important to do problems and to try and solve those problems without having seen the answers.

## Texts

### Part 1

The text, which will be followed closely, is:

Casella, George, and Roger Berger. Statistical Inference. 2nd ed. Pacific Grove, CA: Thomson Learning, 2001. ISBN: 9780534243128.

This book covers all of the material in Part 1 and provides many problems for practice as well as excellent references.

### Part 2

Greene, William. Econometric Analysis. 5th ed. Upper Saddle River, NJ: Prentice-Hall, 2002. ISBN: 9780130661890.

Errors in the 5th edition may be found here.

You can also find the material in any standard text on regression.

ACTIVITIES PERCENTAGES
Problem sets 40% (15% in Part 1 and 25% in Part 2)
Midterm Part I 35%
Final exam 25%

## Recommended Citation

For any use or distribution of these materials, please cite as follows:

Victor Chernozhukov, course materials for 14.381 Statistical Method in Economics, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

## Course Outline

### Part I

A. Brief review of probability

B. Random samples and asymptotic methods

1. Sampling and sums of random variables
2. Laws of large numbers and central limit theorem

C. Statistical theory

1. Point estimation
2. Evaluation of estimators: Unbiasedness, sufficiency, consistency, and the Cramer-Rao theorem
3. Hypothesis tests, Neyman Pearson lemma, and Likelihood Ratio and related tests
4. Interval estimation

### Part II

D. Fundamentals of regression

1. Regression in economics
2. Best linear predictor
3. Best linear approximation
4. Conditional expectation function
5. Building functional forms

E. Regression in finite samples

1. Basic regression algebra
2. Gauss-markov optimality
3. Finite-sample inference under normality and non-normality

F. Regression in large samples

1. Consistency
2. Asymptotic normality
3. Heteroscedasticity
4. Autocorrelation

G. Special topics (if time permits.)