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

  • Jesús Fernández-Villaverde
  • Juan Francisco Rubio-Ramírez
  • Thomas Sargent

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.

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Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 2005-09.

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Date of creation: 2005
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Handle: RePEc:fip:fedawp:2005-09
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