# Statistics and Econometrics 1 (ECO-CO-STATS1)

## ECO-CO-STATS1

 Department ECO Course category ECO Compulsory courses Course type Course Academic year 2021-2022 Term BLOCK 1 Credits 1 (EUI Economics Department) Professors Prof. Andrea ICHINO Prof. Andrea Ichino Contact Simonsen, Sarah Sessions

### Purpose

Regression analysis
Andrea  Ichino ([email protected])

The main goal of this Core course is to give an introduction to the basic tools that an econometrician  needs: the most popular estimation methods; inference and hypothesis testing; asymptotics; simple and multiple regression; instrumental variables.
In addition to the lectures there will be five exercise classes. Examples and applications will be used to illustrate the theoretical content of the course.

Topics

Topic 1
Introduction:  what is econometrics about; the tool-box of economet- rics; the econometrics  sequence at the EUI; Content of this course. Estimation : Estimators and estimates; the Method of maximum Like- lihood; the Method of Moments.
Larsen and Marx, chapter 5. Casella and Berger, chapter 7 . Lecture notes.

Topic 2
Estimation: Finite sample properties of estimators; Unbiasedness, Ef- ficiency,, Sufficiency, Minimum variance estimators; The Cramer-Rao Lower Bound, Invariance.
Larsen and Marx, chapter 5. Casella and Berger, chapter 7 and chapter
5. Lecture notes.

Topic 3
Estimation:  Asymptotic properties of estimators; Asymptotic Unbi- asedness, Asymptotic Efficiency, Consistency; Asymptotic Normality Basic asymptotics: concepts of convergence;  Law of Large Numbers; Central Limit theorem; Continuous Mapping Theorem, Slutzky Theo- rem and Delta Method.
Larsen and Marx, chapter 5. Casella and Berger, chapter 7 and chapter
5. Lecture notes.

Topic 4
Simple regression :  The Conditional Expectation Function; The Pop- ulation Regression Function; The Sample Regression Function; OLS,

Method of Moments and Maximum Likelihood estimation of a regres- sion; Algebraic and geometric properties of the OLS-MM estimators.
Angrist and Pischke chapter 1, 2 and 3.  Wooldridge part 1.  Lecture notes.

Topic 5
Simple regression:  Goodness of fit and the R-Squared; Statistical Prop- erties of the OLS-MM estimator; The Gauss-Markov Theorem’.
Angrist and Pischke chapter 1, 2 and 3.  Wooldridge part 1.  Lecture notes.

Topic 6
Simple regression:  Causality and Regression.

Angrist and Pischke chapter 1, 2 and 3. Lecture notes.

Topic 7
Multiple regression:   The Conditional Independence Assumption; In- terpretation of the partial  Multiple  Regression Coefficient; Multiple Regression in matrix notation; Omitted variable bias and inclusion of irrelevant regressors.
Angrist and Pischke chapter 1, 2 and 3.  Wooldridge part 1.  Lecture notes.

Topic 8
Multiple regression:  The Gauss-Markov Theorem and Multiple Regres- sion; “Partialling  out” and the interpretation of coefficients; Good and bad habits concerning control variables;
Angrist and Pischke chapter 1, 2 and 3.  Wooldridge part 1.  Lecture notes.

Topic 9
Inference and Hypothesis testing: what is a statistical test and how it is constructed; The decision rule; Type I and type II errors; Power of a test.
Larsen and Marx, chapters 6 and 9.  Casella and Berger, chapter 8. Lecture notes.

Topic 10
Inference and Hypothesis testing: finite sample and asymptotic tests in the context of a regression model.

Larsen and Marx, chapters 6 and 9.  Casella and Berger, chapter 8. Lecture notes

Topic 11
Instrumental Variable estimation: .

Woolridge (2009); Angrist and Pischke (2013). Lecture notes

Exercise classes:  Jandarova Nurfatima

There will be 5 exercise classes.

Teaching material

Richard J. Larsen and Morris L. Marx. An introduction to mathemat- ical statistics and its applications. Prentice Hall, Fifth Edition, 2012.

George Casella and Roger L. Berger. Statistical Inference. Thomson, Second Edition, 2002.

Jeffrey Wooldridge, Introductory Econometrics. A Modern Appproach.
South Western Cengage Learning,  2009

Joshua Angrist and Jorn-Steffen Pischke. Mostly Harmless Economet- rics. An Empiricist’s Companion. Princeton University Press, 2013.

Lecture notes by the instructor.

There will be two separate class room exams for Core 1A and Core 1B, but a single final grade based on:

seven problem sets (two for Core 1A and five for Core 1B) that will count for 20% of the final grade;

the exam for Core 1A will count for 20% of the final grade;

the exam for Core 1B will count for 60% of the final grade.

### Description

see under goals

Page last updated on 21 September 2018