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ABCs (and Ds) of Understanding VARs

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Author Info
Jesús Fernández-Villaverde
Juan F. Rubio-Ramírez
Thomas J. Sargent
Mark W. Watson

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Abstract

The dynamics of a linear (or linearized) dynamic stochastic economic model can be expressed in terms of matrices (A, B, C, D) that define a state space system for a vector of observables. An associated state space system (A,ˆB,C,ˆD) determines a vector autoregression for those same observables. We present a simple condition for checking when these two state space systems match up and when they do not when there are equal numbers of economic and VAR shocks. We illustrate our condition with a permanent income example. (JEL C32, E32)

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File URL: http://hdl.handle.net/10.1257/aer.97.3.1021
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File URL: http://www.aeaweb.org/articles/article_detail.php?journal=AER&volume=97&issue=3&article=24&issue_date=June2007
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Article provided by American Economic Association in its journal American Economic Review.

Volume (Year): 97 (2007)
Issue (Month): 3 (June)
Pages: 1021-1026
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Handle: RePEc:aea:aecrev:v:97:y:2007:i:3:p:1021-1026

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  1. Advanced Monetary Theory and Policy (ECON 447)
References listed on IDEAS
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  2. Benhabib, Jess & Rogerson, Richard & Wright, Randall, 1991. "Homework in Macroeconomics: Household Production and Aggregate Fluctuations," Journal of Political Economy, University of Chicago Press, vol. 99(6), pages 1166-87, December. [Downloadable!] (restricted)
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  3. Barro, Robert J, 1979. "On the Determination of the Public Debt," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 940-71, October. [Downloadable!] (restricted)
  4. V. V. Chari & Patrick J. Kehoe & Ellen R. McGrattan, 2005. "A critique of structural VARs using real business cycle theory," Working Papers 631, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  5. V. V. Chari & Patrick J. Kehoe & Ellen R. McGrattan, 2007. "Are structural VARs with long-run restrictions useful in developing business cycle theory?," Staff Report 364, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  6. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez & Thomas J. Sargent, 2005. "A,B,C's (and D's)'s for Understanding VARS," Levine's Bibliography 172782000000000096, UCLA Department of Economics. [Downloadable!]
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  7. Christopher Erceg & Luca Guerrieri & Christopher Gust, 2004. "Can long-run restrictions identify technology shocks?," International Finance Discussion Papers 792, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
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  8. Hansen, Lars Peter & Sargent, Thomas J., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May. [Downloadable!] (restricted)
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  9. Rosen, Sherwin & Murphy, Kevin M & Scheinkman, Jose A, 1994. "Cattle Cycles," Journal of Political Economy, University of Chicago Press, vol. 102(3), pages 468-92, June. [Downloadable!] (restricted)
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  10. Harald Uhlig, 1998. "A Toolkit for Analysing Nonlinear Dynamic Stochastic Models Easily," QM&RBC Codes 123, Quantitative Macroeconomics & Real Business Cycles. [Downloadable!]
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  11. Jordi Gali, 1999. "Technology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations?," American Economic Review, American Economic Association, vol. 89(1), pages 249-271, March. [Downloadable!] (restricted)
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  12. Ricardo J. Caballero & Eduardo Engel, 2003. "Adjustment is Much Slower than You Think," NBER Working Papers 9898, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  13. Erceg, Christopher J. & Henderson, Dale W. & Levin, Andrew T., 2000. "Optimal monetary policy with staggered wage and price contracts," Journal of Monetary Economics, Elsevier, vol. 46(2), pages 281-313, October. [Downloadable!] (restricted)
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  14. Christiano, Lawrence J, 1990. "Linear-Quadratic Approximation and Value-Function Iteration: A Comparison," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 99-113, January.
  15. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules And Macroeconomic Stability: Evidence And Some Theory," The Quarterly Journal of Economics, MIT Press, vol. 115(1), pages 147-180, February. [Downloadable!] (restricted)
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  16. Topel, Robert H & Rosen, Sherwin, 1988. "Housing Investment in the United States," Journal of Political Economy, University of Chicago Press, vol. 96(4), pages 718-40, August. [Downloadable!] (restricted)
  17. Jaewoo Ryoo & Sherwin Rosen, 2004. "The Engineering Labor Market," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages S110-S140, February. [Downloadable!] (restricted)
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  19. Lippi, Marco & Reichlin, Lucrezia, 1994. "VAR analysis, nonfundamental representations, blaschke matrices," Journal of Econometrics, Elsevier, vol. 63(1), pages 307-325, July. [Downloadable!] (restricted)
  20. Lucas, Robert E, Jr & Stokey, Nancy L, 1987. "Money and Interest in a Cash-in-Advance Economy," Econometrica, Econometric Society, vol. 55(3), pages 491-513, May. [Downloadable!] (restricted)
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  21. Lars Peter Hansen & Ellen R. McGrattan & Thomas J. Sargent, 1994. "Mechanics of forming and estimating dynamic linear economies," Staff Report 182, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  22. Christopher A. Sims & Tao A. Zha, 1998. "Does monetary policy generate recessions?," Working Paper 98-12, Federal Reserve Bank of Atlanta. [Downloadable!]
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