| FEDERAL RESERVE BANK OF ATLANTA (2005) | |||||||||||||||
Abstract | |||||||||||||||
| 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,Σ) 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. KEY WORDS: Vector autoregression, economic shocks, innovations, invertibility. “(Likelihood Principle) The information brought by an observation x about [a parameter] θ is entirely contained in the likelihood function. ” The Bayesian Choice, by Christian P. Robert, p. 15. 1 “... with a specific parameterization of preferences the theory would place many restrictions on the behavior of endogenous variables. But these predictions do not take the form of locating blocks of zeros in a VAR description of these variables. ” Money and Interest in a Cash-in-Advance Economy, Robert E. Lucas, Jr., and Nancy L. Stokey, p. 512. 2 We thank James Nason and Mark Watson for very insightful criticisms of an earlier draft. | |||||||||||||||
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