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:
Introduction to central concepts: vector autoregressive
processes, error-correction models, non-stationary processes and
Representation of cointegrated processes.
Estimation and testing in the cointegrated VAR
Identification and estimation of structural econometric models
and common trends models.
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 to
critically assess empirical analyses of macroeconomic time series.
The overall goal is that the students - after having completed the
course - should be able to: - Formulate a vector autoregressive
(VAR) model for a given set of data and test whether it is a
congruent representation of the information in the data. -
Formulate the hypotheses of unit roots and cointegration as
restrictions on the VAR model. Test for the cointegration rank of
the VAR model. - Explain the role of constants, trend terms, and
dummy variables in the cointegrated 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. -
Analyze whether the VAR model has constant parameters. - Explain
when a structure is exact-, under- or overidentified. - Impose
identifying restrictions on the long-run and short-run structure of
the model - Impose identifying restrictions on the common trends of
the model and perform a structural VAR analysis. - Understand the
basics of the cointegration model for variables integrated of order
two and perform a nominal-to-real transformation. - Apply the
cointegration theory to a real problem and interpret the results at
the background of available theories.
Syllabus Main textbook:  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.  Juselius, K. and R. MacDonald
(2000): International Parity Relationships between Germany and the
United States: A Joint Modelling Approach. Department of Economics,
University of Copenhagen, Working paper 00-10.
This is a very compressed
and, therefore, demanding course. Previous experience shows that
unless students are prepared to read through the syllabus before
the course starts, it is hard to adopt the very demanding material
during the three weeks of the course. The pace is very fast with
lectures and exercises from nine in the morning to four in the
evening after which the work on the individual project continues
until nine in the evening. Students should know the principle of
maximum likelihood estimation and understand the dynamic linear
model corresponding to Econometrics C at the Economics Department
at the University of Copenhagen (link to course description). In
addition, a fairly good knowledge of macroeconomics at least
corresponding to the basic course in macroeconomics is recommended.
After completing this course it will NOT be possible to take the
course Advanced Macroeconometrics since the content of these two
courses are similar.
Lectures, exercises, and
individual project work under guidance. A standard day starts with
3.5 hrs of lectures: first a mathematical/statistical discussion of
the topic followed by a discussion of how to apply it to the data.
After lunch there are 2 hrs of exercises in class followed by work
on an individual problem. Thus, each day the student has to learn
new mathematical/statistical theory, its applicability to real
problems, the computer program and how to use it to answer
realistic and, therefore, difficult questions of economic
The Institute of New
Economic Thinking www.ineteconomics.org has granted 10 scholarships
of 4000$ each to cover tuition fee and other expenses associated
with participation in the Cointegrated VAR Approach. Priority is
given to students of less privileged background. To be selected for
a scholarship the applicant needs to document (1) excellence in
graduate/postgraduate studies, in particular in more demanding
subjects such as econometrics, statistics, mathematics and
economics and (2) her/his economic background, for example monthly
allowances, parental support, etc.
Passing the course requires a successful completion of the
empirical project that is chosen and approved by the teachers at
the start of the course. The grade is based on the quality relative
to the difficulty of the analysis. A more demanding analysis will
get a higher grade than a less demanding even when the former is
less perfect than the latter. Finally it needs to be emphasized
that the student should be prepared to work extremely hard during
the three weeks of the summer school (and before) as it is
otherwise hard to pass the exam (unless the student is
mathematically very talented).
All aids allowed
7-point grading scale
100 % censorship
Will be updated before the start of the semester
Same as ordinary. But if only a few students have registered
for the re-exam, the exam might change to an oral exams with a
synopsis to be handed in. This means that the examination date also
Criteria for exam assesment
The Student must in a satisfactory way demonstrate that he/she
has mastered the learning outcome of the course.