# Summerschool 2017: Bayesian Econometrics (F)

### Course content

This course will provide an introduction to modern Bayesian methods in econometrics.

The first part of the course will present the fundamentals of the Bayesian approach, from the derivation of Bayes' theorem to its practical application to econometric models. It will introduce basic concepts such as prior, posterior and predictive distributions, before presenting essential tools based on simulation methods: Markov chain Monte Carlo methods, including the Gibbs sampler and the Metropolis-Hastings algorithm. Common econometric models students are already familiar with will be revisited from a Bayesian perspective (e.g., linear regression model, binary/discrete variable models).

The second part of the course will dive into more specific and technical topics. It will present some selected econometric models where Bayesian methods are particularly useful, such as latent variable models and random coefficient models (relying on data augmentation methods). It will also discuss some problems that can affect standard simulation methods (e.g., slow convergence, bad mixing), and explain how these problems can be successfully overcome using recent developments in statistics.

Bayesian methods can be applied to any field of economics. The examples and exercises offered during the course will be drawn from various topics, including micro- and macroeconometrics, and finance.

The main goal of this course is to provide students with practical skills to apply Bayesian methods to a specific problem. Therefore, it should be of particular interest for students planning on writing a Master's thesis or preparing for a PhD programme.

Education

MSc programme in Economics – elective course

The course is part of the MSc programme in Economics - Financial line symbolized by ‘F’.

Learning outcome

At the end of the summer school, students will:

Knowledge:

• Understand Bayes' theorem and how it can be applied in econometrics.
• Have a grasp of simulation methods, understand their principle and how they can be used to make inference.

Skills:

• Demonstrate an ability to select the most appropriate method for a given estimation problem.
• Be able to implement Markov chain Monte Carlo methods such as the Gibbs sampler and the Metropolis-Hastings algorithm, both theoretically (analytical derivation of the algorithm) and practically (programming).
• Demonstrate technical skills in writing code to implement Bayesian methods. Be able to develop a computer program with the R programming language or use publicly available packages to carry out their own empirical analysis.

Competencies:

• Be able to conduct a full Bayesian analysis: (1) formulate an economic model, (2) organize prior knowledge and ”beliefs” about the model (prior), (3) use relevant data to express the observed information in the model (likelihood), (4) use Bayes' theorem to update beliefs (posterior), (5) derive an appropriate algorithm to compute the posterior distribution, (6) write code to implement the algorithm, (7) interpret the results and criticize the model.

The summer school will combine formal lectures with exercise classes and computer
tutorials.

Since Bayesian approaches rely on simulation methods, the course will have a
computational component. Students will be trained to develop algorithms and to code them
using the R programming language.

Students will be asked to prepare exercises and computer tutorials in groups. To this end,
student groups (about three students each) will be formed at the beginning of the summer
school.

Lynch, Scott M. (2007). Introduction to Applied Bayesian Statistics and Estimation for Social Scientists. Springer. ISBN 978-0-387-71264-2.

Lancaster, Tony (2004). An Introduction to Modern Bayesian Econometrics. Blackwell Publishing. ISBN 978-1-405-11720-3.

Recent research articles on selected topics will be introduced and studied during the course. They will be made available on the course website.

Bsc. of Economics or equivalent.
It is strongly recommended that a course in econometrics (Econometrics II or similar) has
been followed prior to attending this summer school. The student should feel comfortable
with basic elements of probability (marginal, conditional and joint distribution of random
variables, law of large numbers, central limit theorem, likelihood principle, etc) and with
standard econometric methods (maximum likelihood estimation, method of moments, etc).
A reading list will be provided to prepare appropriately, should these requirements not be
completely fulfilled before the start of the summer school.

The R programming language will be introduced and used in this course. This
programming language is not a prerequisite, but it is required that the students have some
programming experience. Students will be allowed to use a different language (like
Matlab), but examples and support will only be provided in R.

Schedule:
46 hours divided between lectures, exercises classes and computer tutorials.

Monday to Friday: 9am–12pm and 1pm–3pm, except Wednesdays afternoon (free for
group work).

Lectures in the morning, exercises/computer tutorials in the afternoon (subject to
changes).

Timetable and venue:
To see the time and location of the lectures press the link seen under "Se skema" in the left side of the page or

https:/​/​skema.ku.dk/​ku1617/​uk/​module.htm
Then
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-B5-5F17; [Name of course]”
-Select Report Type: “List – Week Days”
-Select Period: “Forår/Spring – Weeks 4-29”
Press: “ View Timetable”

ECTS
7,5 ECTS
Type of assessment
Written assignment, 7 days
take-home exam. The exam is given in English and must be answered in English. The exam should be answered individually.
Aid
All aids allowed
Marking scale
Censorship form
External censorship
100 % censurship
##### Criteria for exam assessment

Students are assessed on the extent to which they master the learning outcome for the course.

To receive the top grade, the student must be able to demonstrate in an excellent manner that he or she has acquired and can make use of the knowledge, skills and competencies listed in the learning outcomes.

Single subject courses (day)

• Category
• Hours
• Lectures
• 46
• Preparation
• 112
• Exam
• 48
• English
• 206