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A, B, C’s, (and D’s) for understanding VARs

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  • Jesús Fernández-Villaverde
  • Juan F. Rubio-Ramirez
  • Thomas J. Sargent

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. An associated state space system (A, K, C, S) determines a vector autoregression (VAR) for observables available to an econometrician. We review circumstances in which the impulse response of the VAR resembles the impulse response associated with the economic model. We give four examples that illustrate a simple condition for checking whether the mapping from VAR shocks to economic shocks is invertible. The condition applies when there are equal numbers of VAR and economic shocks.

Suggested Citation

  • Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez & Thomas J. Sargent, 2005. "A, B, C’s, (and D’s) for understanding VARs," FRB Atlanta Working Paper 2005-09, Federal Reserve Bank of Atlanta.
    • Handle: RePEc:fip:fedawp:2005-09
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    1. Greenwood, Jeremy & Hercowitz, Zvi, 1991. "The Allocation of Capital and Time over the Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 99(6), pages 1188-1214, December.
    2. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Thomas J. Sargent & Mark W. Watson, 2007. "ABCs (and Ds) of Understanding VARs," American Economic Review, American Economic Association, vol. 97(3), pages 1021-1026, June.
    3. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(1), pages 147-180.
    4. 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 1166-1187, December.
    5. 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.
    6. 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.
    7. Lippi, Marco & Reichlin, Lucrezia, 1994. "VAR analysis, nonfundamental representations, blaschke matrices," Journal of Econometrics, Elsevier, vol. 63(1), pages 307-325, July.
    8. Anderson, Evan W. & McGrattan, Ellen R. & Hansen, Lars Peter & Sargent, Thomas J., 1996. "Mechanics of forming and estimating dynamic linear economies," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 4, pages 171-252, Elsevier.
    9. Harald Uhlig, 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper / Institute for Empirical Macroeconomics 101, Federal Reserve Bank of Minneapolis.
    10. David Berger & Ricardo J. Caballero & Eduardo Engel, 2003. "Missing Aggregate Dynamics: On the Slow Convergence of Lumpy Adjustment Models," NBER Working Papers 9898, National Bureau of Economic Research, Inc.
    11. 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.
    12. Rosen, Sherwin & Murphy, Kevin M & Scheinkman, Jose A, 1994. "Cattle Cycles," Journal of Political Economy, University of Chicago Press, vol. 102(3), pages 468-492, June.
    13. Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2007. "Assessing Structural VARs," NBER Chapters, in: NBER Macroeconomics Annual 2006, Volume 21, pages 1-106, National Bureau of Economic Research, Inc.
    14. V. V. Chari & Patrick J. Kehoe & Ellen R. McGrattan, 2004. "A Critique of Structural VARs Using Real Business Cycle Theory," Levine's Bibliography 122247000000000518, UCLA Department of Economics.
    15. Barro, Robert J, 1979. "On the Determination of the Public Debt," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 940-971, October.
    16. Christopher J. Erceg & Luca Guerrieri & Christopher Gust, 2005. "Can Long-Run Restrictions Identify Technology Shocks?," Journal of the European Economic Association, MIT Press, vol. 3(6), pages 1237-1278, December.
    17. Chari, V.V. & Kehoe, Patrick J. & McGrattan, Ellen R., 2008. "Are structural VARs with long-run restrictions useful in developing business cycle theory?," Journal of Monetary Economics, Elsevier, vol. 55(8), pages 1337-1352, November.
    18. David Berger & Ricardo J. Caballero & Eduardo Engel, 2003. "Missing Aggregate Dynamics: On the Slow Convergence of Lumpy Adjustment Models," NBER Working Papers 9898, National Bureau of Economic Research, Inc.
    19. 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.
    20. Sims, Christopher A. & Zha, Tao, 2006. "Does Monetary Policy Generate Recessions?," Macroeconomic Dynamics, Cambridge University Press, vol. 10(2), pages 231-272, April.
    21. Uhlig, H.F.H.V.S., 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper 1995-97, Tilburg University, Center for Economic Research.
    22. 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.
    23. Topel, Robert H & Rosen, Sherwin, 1988. "Housing Investment in the United States," Journal of Political Economy, University of Chicago Press, vol. 96(4), pages 718-740, August.
    24. Jaewoo Ryoo & Sherwin Rosen, 2004. "The Engineering Labor Market," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages 110-140, February.
    25. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979.
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    JEL classification:

    • E0 - Macroeconomics and Monetary Economics - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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