Advanced Macroeconometrics (F)

Course content

The focus of this course is on likelihood based analysis of the cointegrated VAR model with an emphasis on applicability, particularly in the field of macroeconomics and international finance. Cointegration analysis is a means to uncover, estimate and test stationary relations among non-stationary variables. The reason why this is interesting is that such stationary relations often can be interpreted as equilibrium relations between economic variables. Within the cointegrated VAR model it is possible to investigate dynamic interaction and feed-back effects, in particular how deviations from a steady-state relation affect the economic system. Furthermore, it is also possible to make inference on the common driving trends which have generated the non-stationarity of the data. The reason why this is interesting is that these common trends can be interpreted in terms of unanticipated shocks to the variables of the system. In short the cointegrated VAR model allows us to investigate the economic reality as a system of pulling forces (the equilibrium correction forces) and the pushing forces (the common stochastic trends). The course includes the topics:

(i) Introduction to central concepts: vector autoregressive processes, error-correction models, non-stationary processes and cointegration. (ii) Representation of cointegrated processes. (iii) Estimation and testing in the cointegrated VAR model. (iv) Introduction to processes integrated of order 2.


MSc programme in Economics – elective course

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

Learning outcome

The aim of this course is to provide the students with a profound theoretical and practical knowledge of the econometric analysis of non-stationary time-series using multivariate dynamic models. At the end of the course students should be able to perform cointegration analyses based on a given set of data and critically assess empirical analyses of macroeconomic time series.


  • The distinction between stationary and nonstationary variables.

  • The implication of unit roots in VAR models.

  • The pulling and pushing forces in the cointegrated VAR model, and the Granger representation theorem.

  • The role of constants, trend terms, and dummy variables in the cointegrated VAR model.

  • Hypothesis testing and identification in the cointegrated VAR model.

  • The asymptotic behavior of estimators and test statistics.

  • The cointegration model for variables integrated of order two. 


  • Specify and estimate VAR models.

  • Analyze whether the VAR model is well-specified and has constant parameters. 

  • Formulate the hypotheses of unit roots and cointegration as restrictions on the VAR model. Test for the cointegration rank of the VAR model. 

  • Estimate the parameters of the cointegrated VAR model using maximum likelihood. Interpret the results in terms of equilibrium relationships and driving common trends. 

  • Formulate and test hypotheses on the cointegrating relationships and the equilibrium adjustments.

  • Explain when a structure is exact-, under- or overidentified. 

  • Impose identifying restrictions on the long-run and short-run structure of the model. 

  • Analyze the VAR model for variables integrated of order two and perform a nominal-to-real transformation. 


After having completed the course, 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 VAR models for new economic problems.

  • Test for unit roots and cointegration.

  • Formulate hypotheses on the model inspired from economic theory.

  • Apply the theoretical results to obtain an understanding of the mechanisms governing the dynamics of a certain data set.

  • Use the theory and apply the model also in the case of processes integrated of order two.


Teaching is based on lectures and exercise classes.

Main textbooks: 
Juselius, K. (2007): The Cointegrated VAR Model: Methodology and Applications, Oxford University Press. 

Additional Material: 
Johansen, S. (1996): Likelihood Based Inference in Cointegrated Vector Autoregressive Models, Oxford University Press.

Basic knowledge of time series econometrics, autoregressive processes, theory for likmelihood estimation and hypothesis testing and unit root testing.

2 hours lectures 1 to 2 times a week from week 6 to 20 (except holidays).
2 hours exercise classes a week from week 6 to 20 (except holidays).

Timetable and venue:
The schedule for the semester spring 2018 will be available no later than 7th of November 2017

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.
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship
if chosen by the Head of Studies.
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.

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 VAR model for the data and a discussion and testing of the underlying assumptions. Determination of the cointegration properties. Formulation and test of relevant hypotheses on the cointegrating relations and the short-term adjustment. Be able to analyze models for data integrated of order two.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 42
  • Preparation
  • 112
  • Class Instruction
  • 28
  • Exam
  • 24
  • English
  • 206