Advanced Macroeconomics: Structural Vector Autoregressive (VAR) Analysis (F)

Course content

The aim of this course is to provide the students with a theoretical and practical knowledge of structural vector autoregressive (VAR) models within stationary and non-stationary frameworks as well as important econometric methods widely used in macroeconomics, financial economics and international finance.


The course covers topics in time series analysis with an emphasis on applications in macroeconomics and international finance. Substantial emphasis will be placed on the development of programming skills in MATLAB which is a matrix algebra software used extensively among practitioners and researchers. It will be assumed that students have no previous knowledge of MATLAB. Problem sets, practical sessions and homework assignments will typically consist of running programs and the development of additional procedures programmed in MATLAB.


The course will be divided into four parts:

1. The first part will provide an introduction to MATLAB including data handling, running programs and the basics of programming.

2. The second part introduces the basic VAR model as well as the vector error correction (VEC) model. We discuss the fundamentals of VARs, including the Wold theorem, specification issues, prediction, Granger causality tests and non-stationarity.

3. In the third part we focus on structural VARs, that is the transformation of reduced form information into structural relationships. Topics include structural impulse response analysis, forecast error variance decompositions, historical decompositions, forecasts and counterfactual analysis. Four different approaches to identification will be discussed, identification using short-run restrictions, long-run restrictions, combinations of short- and long-run restrictions, the narrative approach and sign restrictions. These approaches will be illustrated with applications in macroeconomics and international finance. Inference in these models will also be discussed.

4. The fourth part focuses on the relationship between structural VARs and other macroeconomic models such as, for example, the DSGE model. We will assess structural VARs and compare to other approaches and discuss, among other things, policy evaluations using structural VARs and DSGE models and how these approaches can be combined. These issues will also be illustrated using empirical examples from the literature.


MSc programme in Economics – elective course

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


The PhD Programme in Economics at the Department of Economics:

  • The course is an elective course with research module. In order to register for the research module and to be able to write the research assignment, the PhD students must contact the study administration AND the lecturer.
  • The course is a part of the admission requirements for the 5+3 PhD Programme. Please consult the 5+3 PhD admission requirements.


The course is open to:

  • Exchange and Guest students from abroad
  • Credit students from Danish Universities
  • Open University students
Learning outcome

After completing the course the student is expected to be able to:



  • Identify and distinguish between stationary and nonstationary VAR models.
  • Estimate, interpretate and identificate the structural VAR models.
  • Distinguish and assess alternative approaches to identify structural VARs.
  • Inference in structural VARs.
  • Evaluate and compare empirical results from other approaches (DSGE models) with structural VARs.
  • Formulate economic hypotheses used as restrictions when identifying structural VARs including cointegration restrictions. 



  • Specify and estimate structural VAR models.
  • Estimate structural VAR models applying different types of identification and assess whether the model is exact-, under- or overidentified. 
  • Apply structural VARs to the analysis of macroeconomic
  • Analyze the VAR model for variables integrated of order two and perform a nominal-to-real transformation.
  • Analyze economic data using structural VAR models and assess the empirical results.
  • Use MATLAB to analyze new data sets using pre-programmed modules and program new procedures.   
  • Identify the model given the data generating process and to program the chosen method in MATLAB.



  • Independently formulate and analyze structural VARs for new economic problems.
  • Formulate hypotheses used to identify structural VARs derived from economic theory.
  • Apply economic theory to obtain an understanding of the mechanisms governing the dynamics of a certain data set.
  • Use and design new programs in MATLAB.

A combination of lectures and practical sessions/exercises.

  • Kilian, L., and H. Lütkepohl (2017), Structural Vector Autoregressive Analysis, Cambridge University Press
  • Journal articles

This course requires a good grasp of mathematics as well as economics corresponding to intermediate macroeconomics from a similar course as "Macroeconomics II" at the Bachelor of Economics, Copenhagen University.

It is strongly recommended that the course "Econometrics II" at the Studies of Economics, University of Copenhagen has been followed before taking "Advanced Macroeconomics Structural Vector Autoregressive Analysis". Or a equivalent course with time series econometrics, autoregressive processes, theory for likelihood estimation and hypothesis testing and unit root testing.

It is recommended, but not a prerequisite, that students follow the Matlab basics tutorial available on the course homepage in Absalon prior to the start of the course.

Practical sessions will be held in a lecture room, not in a computer lab. Participants must bring a laptop in order to follow these sessions. Participants should install the MATLAB software on their laptops for use during the practical sessions.

2 hours lectures one to two times a week from week 36 to 50 (except week 42).
2 hours exercise classes a week from week 36/37 to 50 (except week 42).

The overall schema for the Master can be seen at KUnet:
MSc in Economics => "Courses and teaching" => "Planning and overview" => "Your timetable"

Timetable and venue:
To see the time and location of lectures and exercises please press the link under "Timetable"/​"Se skema" at the right side of this page (E means Autumn).

You can find the similar information partly in English at
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-E22; [Name of course]””
-Select Report Type: “List – Weekdays”
-Select Period: “Efterår/Autumn”
Press: “ View Timetable”

Please be aware:
- The study administration allocates the students to the exercise classes according to the principles stated in the KUnet.
- If too many students have wished a specific class, students will be registered randomly at another class.
- It is not possible to change class after the second registration period has expired.
- If there is not enough registered students or available teachers, the exercise classes may be jointed.
- The student is not allowed to participate in an exercise class not registered.
- The teacher of the exercise class cannot correct assignments from other students than the registered students in the exercise class except with group work across the classes.
- All exercise classes are taught in English and it is expected that the students ask questions in English, so foreign students are included in the dialog.
- The schedule of the lectures and the exercise classes can change without the participants´ acceptance. If this occur, you can see the new schedule in your personal timetable at KUnet, in the app myUCPH and through the links in the right side of this course description and at the link above.
- It is the students´s own responsibility continuously throughout the study to stay informed about their study, their teaching, their schedule, their exams etc. through the curriculum of the study programme, the study pages at KUnet, student messages, the course description, the Digital Exam portal, Absalon, the personal schema at KUnet and myUCPH app etc.



The students receive individual written feedback at the mandatory assignments.

The lecturer gives collective oral feedback in the lectures.  

7,5 ECTS
Type of assessment
Written assignment, 48 hours
Type of assessment details
Individual take-home exam.
The exam assignment is given in English and must be answered in English.
The students are not allowed to communicate about the given problem-set or collaborate on the assignment with anyone. If done so, it will be regarded as cheating.
Exam registration requirements

To qualify for the exam the student must no later than the given deadlines during the course:

  • hand in and have approved two mandatory assignments.


The assignments typically consist of programming exercises in MATLAB and replication of empirical analysis in journal articles or in the textbook discussed during the lectures. They may be prepared in groups of up to three students but must be handed in individually. Everyone is responsible for writing their own code.


All aids allowed at the written exams.


Use of AI tools is permitted. You must explain how you have used the tools. When text is solely or mainly generated by an AI tool, the tool used must be quoted as a source.

Marking scale
7-point grading scale
Censorship form
No external censorship
for the written exam.

The oral re-examination may be with external assessment.
Exam period

Exam information:

More information is available in Digital Exam from the middle of the semester.

More information about examination, rules, aids etc. at Master (UK) and Master (DK).


Reexam is a 20 min. oral exam without preparation time.

Reexam information:

More information is available in Digital Exam in February. 


More information: Master (UK) and Master (DK).

Criteria for exam assessment

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


In order to obtain the top grade "12", 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.


For this course, in particular, the student should be able to independently analyze new data sets using the tools and theories covered in the course. This includes construction of structural VAR models (both stationary and non-stationary models) for the data and a discussion and testing of the underlying assumptions including determination of the cointegration properties. Formulation and test of relevant hypotheses on the cointegrating relations and the short-term adjustment. Interpretation of impulse response functions and variance decompositions.


In order to obtain the grade “02”, the student must in a satisfactory way be able to demonstrate a minimal acceptable level of  the knowledge, skills and competencies listed in the learning outcomes.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 42
  • Class Instruction
  • 28
  • Preparation
  • 88
  • Exam
  • 48
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 semester

- Go to 'Signup' for information about registration and enrollment.

Information about admission and tuition fee:  Master and Exchange Programme, credit students and guest students (Open University)

and venue:
- For teaching: Go to 'Remarks'.
- For exam and re-sits: Go to 'Exam'.
Department of Economics, Study Council
Contracting department
  • Department of Economics
Contracting faculty
  • Faculty of Social Sciences
Course Coordinator
  • Michael Bergman   (15-516d676c656970324669766b7165724469677372326f7932686f)

See 'Course Coordinators'

Teacher of excercise classes:
Exercise class 1:
Exercise class 2:

Please read "Remarks" regarding the schedule of the teaching.

Saved on the 17-05-2024

Are you BA- or KA-student?

Are you bachelor- or kandidat-student, then find the course in the course catalog for students:

Courseinformation of students