NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

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

Jesus Fernandez-Villaverde, Juan Rubio-Ramirez, Thomas J. Sargent

NBER Technical Working Paper No. 308
Issued in June 2005
NBER Program(s):   TWP

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.

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Document Object Identifier (DOI): 10.3386/t0308

Published: Jesús Fernández-Villaverde, Juan F. Rubio-Ramírez, Thomas J. Sargent, and Mark W. Watson, 2007. "ABCs (and Ds) of Understanding VARs," American Economic Review, vol. 97(3), pages 1021-1026.

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