# The Cointegrated VAR Approach: Methodology and Applications – University of Copenhagen

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# The Cointegrated VAR Approach: Methodology and Applications

• Course name: The Cointegrated VAR Approach: Methodology and Applications
• Offered: 6th August - 26th August 2012
• ECTS: 10
• Chronology: Master
• Teacher: Prof. Katarina Juselius, katarina.juselius@econ.ku.dk (KJ) , Prof. Søren Johansen, soren.johansen@econ.ku.dk (SJ), PhD Peter Sullivan (PS)
• Teaching assistants: Mark Klemp (MK) og Andreas Hetland (AH)
• Time and place: 9:00-13:00 in CSS 5-0-28 (Building 5, Ground floor, Room 28), 13:00-21:00 in CSS 5.0.34 (Building 5, Ground floor, Rooms 34, 40

Academic Aim 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.

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) Identification and estimation of structural econometric models and common trends models. (iv) Introduction to processes integrated of order 2.

Syllabus Main textbook: [1] Juselius, K. (2007): The Cointegrated VAR Model: Methodology and Applications, Oxford University Press. Additional Material: [2] Johansen, S. (1996): Likelihood Based Inference in Cointegrated Vector Autoregressive Models, Oxford University Press. [3] 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.

Language: English. Prerequisites: Students should know the principle of maximum likelihood estimation and understand the dynamic linear model corresponding to Quantitative Methods 3 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.

Teaching and Work Forms: Lectures, exercises, and individual project work under guidance. Formal Requirements: None. Examination: 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. It should pay to address difficult and

### Scholarship

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.