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

Course content

The aim of the course is to provide students with a working knowledge of important econometric methods widely used in macroeconomics, financial economics and international finance. In addition, students will develop programing skills in MATLAB, 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. Grading will be based on an individual take-home exam.


The course covers topics in time series analysis with an emphasis on applications in macroeconomics and international finance. The aim of the course is to provide students with a working knowledge of structural vector autoregressive (VAR) models. Substantial emphasis will be placed on the development of programming skills in MATLAB which is a matrix algebra program.


The course will be divided into four parts. The first part will provide an introduction to MATLAB including data handling, running programs and the basics of programming. 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. 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. 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’.


Learning outcome

The aim of this course is to provide the students with a theoretical and practical knowledge of structural vector autoregressive models within stationary and non-stationary frameworks. After completion of the course, students should be able to carry out the analysis of economic data using structural VAR models, assessing the empirical results, use the approach to identify the model given the data generating process and be able to program the chosen method in MATLAB.


  • The distinction between stationary and nonstationary VAR models.
  • The estimation, interpretation and identification of structural VAR models.
  • Be able to distinguish and assess alternative approaches to identify structural VARs.
  • Inference in structural VARs.
  • How to evaluate and compare empirical results from other approaches (DSGE models) with structural VARs.
  • MATLAB user interface and programming. 



  • Specify and estimate structural VAR models.
  • Formulate economic hypotheses used as restrictions when identifying structural VARs including cointegration restrictions. 
  • Estimate structural VAR models applying different types of identification and assess whether the model is exact-, under- or over-identified. 
  • Apply structural VARs to the analysis of macroeconomic and Analyze the VAR model for variables integrated of order two and perform a nominal-to-real transformation.
  • Use MATLAB to analyze new data sets using pre-programmed modules and program new procedures.   



After completion, the students should have competencies to apply the obtained knowledge and skills to analyses of new data sets. In particular to:

  • 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.
  • Able to 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 and journal articles

No previous knowledge of MATLAB is assumed.

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.

BSc in Economics or similar.
Basic knowledge of time series econometrics, autoregressive processes, theory for likelihood estimation and hypothesis testing and unit root testing from Econometrics II at the BA of Economics.

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

The overall schema for the Master can be seen at https:/​/​​polit_ba/​undervisning/​Lektionsplan-E18/​skemaer/​Sider/​default.aspx

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.

Will be available not later than of May

7,5 ECTS
Type of assessment
Written assignment, 48
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
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