ABCs (and Ds) of Understanding VARs

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 for a vector of observables. An associated state space system (A, ^ B,C, ^D) determines a vector autoregression for those same observables. W...

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Bibliographic Details
Published in:The American economic review 2007-06, Vol.97 (3), p.1021-1026
Main Authors: Fernández-Villaverde, Jesús, Rubio-Ramírez, Juan F., Sargent, Thomas J., Watson, Mark W.
Format: Article
Language:English
Subjects:
Approximation
Balanced budgets
Central banks
Consumer economics
Econometric models
Econometrics
Economic expectations
Economic information
Economic models
Economic shock
Economics
Eigenvalues
Equilibrium
Federal Reserve Bank
Macroeconomics
Mathematical vectors
Present value
Regression analysis
Stochastic models
Studies
Technological change
Vector autoregression
Vector-autoregressive models
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Summary: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 for a vector of observables. An associated state space system (A, ^ B,C, ^D) determines a vector autoregression for those same observables. We present a simple condition for checking when these two state space systems match up and when they do not when there are equal numbers of economic and VAR shocks. We illustrate our condition with a permanent income example. (JEL C32, E32)
ISSN:0002-8282
1944-7981
DOI:10.1257/aer.97.3.1021