# AØKK08359U  Summerschool 2018: Bayesian Econometrics (F)

Volume 2017/2018
Education

MSc programme in Economics – elective course

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

Content

This course provides an introduction to modern Bayesian methods in econometrics.

The first part of the course presents the fundamentals of the Bayesian approach, from the derivation of Bayes' theorem to its practical application to econometric models. It introduces 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 dives into more specific and technical topics. It presents 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 also discusses some problems that can affect standard simulation methods (e.g., slow convergence, bad mixing), and explains 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 summer school will be drawn from various topics, including micro- and macro-econometrics, 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 to students planning on writing a Master's thesis or preparing for a PhD programme.

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.

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

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. Students 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.).
Should these requirements not be completely fulfilled before the start of the summer school, a reading list will be provided before the start of the summer to prepare appropriately.
The R programming language will be introduced and used in this course. This programming language is not a prerequisite, but it is required that 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. Tutorials will be provided before the start of the summer school so that students get a good grasp of the basic features of R.

It is recommended to bring a laptop, but it is not a prerequisite.
The summer school will combine formal lectures with exercise classes and computer tutorials.

Since Bayesian approaches rely on simulation methods, the course will have an important 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 (two to three students, depending on the total number of participants) will be formed at the beginning of the summer school.
Schedule:
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 classroom please press the link under "Se skema" (See schedule) at the right side of this page.

You can find the similar information partly in English at
https:/​/​skema.ku.dk/​ku1718/​uk/​module.htm
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-B5-5F18; [Name of course]””
-Select Report Type: List
-Select Period: “Forår/Spring – Week 5-30”
Press: “ View Timetable"

Venue will be available from April 2018.
Credit
7,5 ECTS
Type of assessment
Written assignment, 5 days
individual take-home exam. It is not allowed to collaborate on the assignment with anyone. The exam is given in English and must be answered in English.
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Exam registration requirements

Full participation at the summerschool is mandatory and the student must actively participate in all activities (lectures, exercises and computer tutorials, group work etc.).

Two mandatory assignments will have to be passed during the summer school to be allowed to sign up for the final exam.

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Aid
All aids allowed
Marking scale
Censorship form
No external censorship
The course can be selected for external assessment.
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Exam period

The exam takes place from August 15 at 10.00 AM to August 20 at 10.00 AM, 2018.

For enrolled students more information about examination, exam/re-sit, rules etc. is available at the student intranet for Examination (English) and student intranet for Examination (KA-Danish).

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Re-exam

The re-exam will take place in the exam period December 2018 - January 2019.

The exact day and time of the exam will be informed at the  student intranet for Summer schools and in the Self-Service at KUnet during Autumn 2018.

If only a few students have registered for the written re-exam, the reexam might change to an oral exam including the date, time and place for the exam, which will be informed  by the Examination Office.

More information about reexamination, rules, schedule etc. is available at the intranet for master students (UK) and master students (DK)

##### Criteria for exam assesment

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

To receive the top grade, the student must with no or only a few minor weaknesses be able to demonstrate an excellent performance displaying a high level of command of all aspects of the relevant material and can make use of the knowledge, skills and competencies listed in the learning outcomes.

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