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A, B, C’s (And D’s) For Understanding VARS

Author

Listed:
  • Jesus Fernandez-Villaverde

    (Department of Economics, University of Pennsylvania)

  • Juan F. Rubio-Ramirez

    (Federal Reserve Bank of Atlanta)

  • Thomas J. Sargent

    (New York University and Hoover Institution)

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, Sigma) determines a vector autoregression for observables available to an econometrician. We review circumstances under 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

  • Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez & Thomas J. Sargent, 2005. "A, B, C’s (And D’s) For Understanding VARS," PIER Working Paper Archive 05-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    • Handle: RePEc:pen:papers:05-018
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    More about this item

    Keywords

    VARs ; Invertibility; Estimation of Dynamic Equilibrium Models; economic shocks; innovations;
    All these keywords.

    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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    1. Advanced Monetary Theory and Policy (ECON 447)

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