# Methods of Econometrics

## News

19.09.2023:

In the winter term the course Methods of Econometrics will take place in person.

The overall grade of this course consists of a midterm, presentation of homeworks during the tutorials and a final exam.

For empirical work the statistical programming language R is used. There will be an introduction to R during this course. For all students who like to deepen their knowledge in R beyond this course, a separate tutorial Programming with R is offered.

## COURSE DESCRIPTION

The course introduces students to the fundamental methods in econometric analysis and the relevant tools from linear algebra, probability theory and mathematical statistics that are relevant for a profound understanding of econometric methods. The mathematical foundations are taught jointly with the courses Advanced Microeconomics and Dynamic Macroeconomics during the first two weeks of the lecture period. In Methods of Econometrics it is discussed what econometric models are and which properties of estimators are desirable as well as how statistical tests are constructed. Statistical tests are needed for checking (economic) hypothesis, for selecting appropriate econometric models as well as for analyzing whether the requirements of a selected econometric estimator are not violated.  Estimation methods include (ordinary) least-squares estimation (OLS) of multiple (dynamic) linear regression models and (feasible) generalized least-squares estimators (GLS, FGLS) for data exhibiting (conditional) heteroskedasticity. Statistical tests cover t-tests and F-tests as well as bootstrap tests. Finally, important concepts for modeling time series data are covered including moving-average models and stationary as well as non-stationary autoregressive models. Students will apply the methods covered in their homework by working through theoretical and practical examples, the latter with the software R. They will present their results during the tutorial. At the end of this course, students will be able to conduct typical econometric investigations in economics, judge the quality of empirical studies and successfully study advanced econometric methods.

## COURSE OUTLINE

### Math Camp

• Linear algebra (vectors, vector spaces, Euklidian space, matrix algebra)
• Foundations of probability theory (random numbers, distribution and density functions, moments, conditional probabilities and moments)
• Important probability distributions (standard normal distribution, multivariate normal distribution chi squared distribution, F distribution, t distribution)
• Toos for asymptotic analysis (convergence of sequences of random numbers (in probability, almost surely, in distribution), Slutzky's theorem, continuous mapping theorem)

## Main course

• Foundations of statistical tests for testing single and joint hypotheses: exact tests and their relevant assumptions and non-exact tests such as asymptotic tests and bootstrap tests including their relevant assumptions
• Structural and reduced form econometric models
• The multiple and dynamic linear regression model
• The ordinary least-squares (OLS) estimator including its geometric and statistical properties and some generalizations (GLS, FGLS)
• Model selection and model diagnostics
• Models for time series data (stochastic processes, moving-average processes, autoregressive processes)
• Autocorrelation- and heteroskedasticity-robust standard errors
• Use of R for empirical examples and Monte-Carlo simulations

## LITERATURE

Davidson, R. und MacKinnon, J.G. (2004). Econometric Theory and Methods. Oxford University Press.
Corrections since publication

Further Literature

see handout of the course.

## SOFTWARE

For the course the free software R will be used.

## AUDIENCE / QUALIFICATION

Methods of Econometrics is a compulsory course for master students in economics.

For students that have not attended any introductory course in econometrics during their studies yet, it is highly recommended to attend the course Einführung in die Ökonometrie (in German) prior to the course Methoden der Ökonometrie.

The overall grade of this course consists of a midterm, presentation of homeworks during the tutorials and a final exam. Details are contained in the module catalogue (in German) or the GRIPS page of the course.

The English course material for Methods of Econometrics will be made available on the GRIPS page of the course as the course proceeds.

Some course material in German can be found on the German page of the course.

## Schedule for the math camp (Weeks 1 and 2)

 1. Lecture Wednesday 10:15 - 11:45 H 26 Rolf Tschernig 25.10.2023 2. Lecture Thursday 08:30 - 10:00 H 26 Rolf Tschernig 26.10.2023 3. Lecture Thursday 10:15 - 11:45 H 26 Rolf Tschernig 26.10.2023 4. Lecture Thursday 14:15 - 15:45 H 26 Rolf Tschernig 26.10.2023 5. Lecture Friday 10:15 - 11:45 H 26 Rolf Tschernig 27.10.2023 1. Tutorial Friday 08:30 - 10:00 H 26 Dominik Ammon 27.10.2023 2. Tutorial Monday 08:30 - 10:00 H 26 Dominik Ammon 30.10.2023 3. Tutorial Monday 10:15 - 11:45 H 26 Dominik Ammon 30.10.2023

## Schedule for main part (Week 3)

 Lectures Tuesday 14:15 - 15:45 H 26 Rolf Tschernig 31.10.2023 Thursday 16:00 - 17:30 H 26 Rolf Tschernig 02.11.2023 Tutorial (Gr. 1 and Gr. 2) Thursday 14:15 - 15:45 H 26 Dominik Ammon 02.11.2023

## Schedule for main part (Weeks 4 to 15)

 Lectures Wednesday 08:30 - 10:00 H 26 Rolf Tschernig 08.11.2023 onwards Wednesday 10:15 - 11:45 H 26 Rolf Tschernig 08.11.2023 onwards Tutorial (Gr. 1) Thursday 14:15 - 15:45 H 26 Dominik Ammon 09.11.2023 onwards Tutorial (Gr. 2) Thursday 16:00 - 17:30 H 26 Dominik Ammon 09.11.2023 onwards

For an overview of all mandatory modules, see current schedule as PDF