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A, B, C's (and D)'s for Understanding VARs

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  • Jesus Fernandez-Villaverde
  • Juan 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,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 Rubio-Ramirez & Thomas J. Sargent, 2005. "A, B, C's (and D)'s for Understanding VARs," NBER Technical Working Papers 0308, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0308
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    More about this item

    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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