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  - elective course with research module (PhD students must contact the study administration and the lecturer in order to write the research assignment)


The course is an admission requirement for the 5+3 PhD Programme in Economics 


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.

During the semester mandatory assignments must be handed in and not later than the given deadline.

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

Basic knowledge of time series econometrics, autoregressive processes, theory for likelihood estimation and hypothesis testing and unit root testing from Econometrics II at the Bachelor of Economics, University of Copenhagen.

It is recommended that participants have followed the Online MATLAB Course for Students of Economics prior to the course start: https:/​/​​courses/​25988/​pages/​online-matlab-course-for-students-of-economics

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.

lectures every week from week 36 to 50 (except week 42).

Update: June 3rd 11:30: The Thusday lectures have been changed to 15-17 o'clock in the even weeks.

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 please press the link under "Se skema" (See schedule) 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-E19; [Name of course]””
-Select Report Type: “List – Weekdays”
-Select Period: “Efterår/Autumn – Weeks 31-5”
Press: “ View Timetable”

7,5 ECTS
Type of assessment
Written assignment, 48 hours
individual take-home exam.
The exam assignment is given in English and must be answered in English. It is not allowed to collaborate on the assignment with anyone.
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
The exam may be choosed for external censorship by random check.
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 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.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 42
  • Preparation
  • 116
  • Exam
  • 48
  • English
  • 206