PhD Course: Topics in advanced macroeconometrics I

Structural VAR models, 11–14 December 2006

4-day mini course

Lecturer: Hilde C. Bjørnland, Norwegian School of Management BI



  • Monday and Tuesday: University of Oslo (Room 1247, Eilert Sundt's building B).
  • Wednesday and Thursday: Norwegian School of Management BI (Room C2-095)



The course is credited with 5 ECTS in the PhD - program in economics at the University of Oslo.



Monday 11 December, 13:15–16

Tuesday 12 December, 9:15-12

Wednesday 13 December, 9:15–11

Thursday 14 December, 9:15–12, 13:15-16


Course description

Following the pioneering work by Sims, macroeconomists have become increasingly preoccupied with the analysis of sources of economic fluctuations. Structural vector autoregressive (VAR) models have made it possible to analyze the importance of various structural shocks, and are among the main tools used in applied macroeconomic modeling today. Structural VARs have also obtained an important position as tool for policy evaluation.


This course will provide a thorough assessment of structural VARs. The course will be divided into three parts. The first part will discuss the fundamentals of structural VARs, including the Wold theorem, specification issues and the use of impulse responses and variance decompositions as a way to summarize the information content of VARs. Some preliminaries will also be covered, including a brief introduction to advanced time series concepts, stochastic processes and basic asymptotic theory.


The second part deals with the issue of transforming the information content of reduced form dynamics into structural relationships. Identification using short run and long run restrictions on the covariance matrix will be discussed. Recent policy experiments using a variety of restrictions will be used as examples.


The third and final part covers sign restrictions and Bayesian vectorautoregression. Bayesian VAR was originally developed as a way to improve out of sample forecast, but are now used for a variety of purposes, including policy analysis. Sign restrictions provide an alternative way of identifying structural shocks when we have no a priori reasoning for using zero short (or long) run restrictions. More recently, sing restrictions have been used to bridge the gap between DSGE models and VARs.


Detailed plan - Structural VARs

·         Time series analysis

·         Identification problem in econometrics


a)      Time series analysis

·         Preliminaries

·         Covariance stationary vector process

·         Vector moving average (MA) representation

·         The Wold theorem


b)      VAR – specification, estimation and information content

·          Impulse response function

·         Forecast error variance decompositions

·         Historical decompositions


c)      Identification of structural VARs

·         Structural vs. behavioral models

·         Cholesky decomposition

·         SVAR and contemporaneous restrictions

·         Long-run restrictions


d)     Sign restrictions and Bayesian VAR

·         Bayesian inference

·         Priors for VARs

·         Sign restrictions


a)      Potential, limitations and controversies (puzzles) in the SVAR literature.

·         Controversies using long run restrictions

·         Monetary policy analysis – puzzles

·         Conclusions


Reading list - Structural VAR Models


Blanchard Olivier J. and Danny Quah (1989), “The dynamic effects of aggregate demand and supply disturbances”, American Economic Review, 79, 655-673.


Christiano, L.J., Eichenbaum M. and C.L. Evans, (1999) “Monetary Policy Shocks: What Have We Learned and to What End?” in John Taylor and Michael Woodford, eds. Handbook of Macroeconomics Elsevier Science Ltd.


Favero, Carlo A. (2001) “Applied Macroeconometrics, Oxford University Press.


Hamilton, James D. (1994) “Time Series Analysis”, Princeton University Press.


Lütkepohl, Helmut (1993) “Introduction to Multiple Time Series Analysis”, Spring Verlag.


Sims, Christopher A. (1980), “Macroeconomics and reality”, Econometrica, 48, 1-48.



Additional literature


Bernanke, B. and 1. Mihov (1998) “Measuring Monetary Policy,” Quarterly Journal of Economics, 113, 869-902.


Bjørnland, H.C. (2005), “Monetary Policy and Exchange Rate Interactions in a Small Open Economy,” Working Paper 2005/16, Norges Bank.


Bjørnland, H.C. (2006), “Monetary policy and exchange rate overshooting: Dornbusch was right after all”, Manuscript, University of Oslo.


Bjørnland, H.C. and K. Leitemo (2005), “Identifying the Interdependence between US Monetary Policy and the Stock Market,” Manuscript, University of Oslo.


Canova F. and G. De Nicoló (2002), “Monetary disturbances matter for business fluctuations in the G-7”, Journal of Monetary Economics, 49, 1131-1159.


Chari, V.V., Patrick Kehoe and Ellen McGrattan, 2005, “A Critique of Structural VARs Using Real Business Cycle Theory,” Federal Reserve Bank of Minneapolis Working Paper 631.


Christiano, L., Eichenbaum, M. and C.L. Evans (2005), “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy,” Journal of Political Economy 113, 1-45.


Christiano, Lawrence J, Eichenbaum, Martin and Robert Vigfusson, (2006), “Alternative Procedures for Estimating Vector Autoregressions Identified with Long-Run Restrictions”, Journal of the European Economic Association, 4, 475-483.


Christiano, Lawrence J, Eichenbaum, Martin and Robert Vigfusson, (2006), “Assessing Structural VARs,” National Bureau of Economic Research Working Paper no. 12353.


Marco Del Negro and Frank Schorfheide, (2004). “Priors from General Equilibrium Models for VARS,” International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, 45, 643-673.


Doan, Thomas, Robert Litterman, and Christopher Sims (1984): Forecasting and Conditional Projections Using Realistic Prior Distributions," Econometric Reviews, 3, 1-100.


Eichenbaum, M. and C. Evans (1995), “Some empirical evidence on the effects of shocks to monetary policy on exchange rates,” Quarterly Journal of Economics, 110, 975-1010.


Faust, Jon (1998), “The Robustness Of Identified VAR Conclusions About Money,” Carnegie-Rochester Conference Series on Public Policy, 49, 207-244.


Faust, Jon and Eric M. Leeper (1997) “When Do Long-Run Identifying Restrictions Give Reliable Results?” Journal of Business and Economic Statistics. 345 ? 353.


Faust, Jon and J.H. Rogers (2003), “Monetary policy's role in exchange rate behaviour”, Journal of Monetary Economics, 50, 1403-1424.


Fernandez-Villaverde, J., J.Rubio-Ramirez, and T. Sargent, (2005), “A, B, C’s (and D’s) for Understanding VAR’s,” National Bureau of Economic Research Technical Working Paper no. 308 and forthcoming, American Economic Review.


Gali, J.,(1992) “How Well Does the ISLM Model Fit Postwar U.S. Data?” Quarterly Journal of Economics, vol 107, no.2 (May 1992), 709-38.


Gali J. (1999), “Technology, employment, and the business cycle: do technology shocks explain aggregate fluctuations?”, American Economic Review, Vol 89, p 249-271.


Gali, Jordi and Pau Rabanal (2004), “Technology Shocks and Aggregate Fluctuations: How Well Does the RBC Model Fit Postwar U.S. Data?”


Kim, S. and N. Roubini (2000), “Exchange rate anomalies in the industrial countries: A solution with a structural VAR approach”, Journal of Monetary Economics, 45, 561-586.


Leeper, E., C. Sims, and T. Zha, (1996), “What Does Monetary Policy Do?,Brookings Papers on Economic Activity, 2, 1-78.


Rudebusch, G. (1998) “Do Measures of Monetary Policy in a VAR Make Sense?” International Economic Review 39, 943-48.


Scholl, A. and H. Uhlig (2005), “New Evidence on the Puzzles. Results from Agnostic Identification on Monetary Policy and Exchange Rates,” Mimeo Humboldt University.


Sims, C.A. (1992), “Interpreting the Macroeconomic Time Series Facts: The Effects of Monetary Policy,” European Economic Review, 36, 975-1011.


Sims, Christopher A. and Tao Zha (1998) “Bayesian Methods For Dynamic Multivariate Models,” International Economic Review, 39, 949-968.


Sims, Christopher A. and Tao Zha (1999) “Error Bands For Impulse Responses,” Econometrica, 67, 1113-1155.


Stock, James J. and Mark W. Watson (2001): Vector Autoregressions," Journal of Economic Perspectives, 15, 101-115.


Uhlig Harald. (2005), “What are the effects of Monetary Policy: Results from an Agnostic Identification Approach”, Journal of Monetary Economics, 52, 381-419.


Uhlig, Harald (1998) “The Robustness Of Identified VAR Conclusions About Money. A comment”, Carnegie-Rochester Conference Series on Public Policy, 49, 245-263.