Rational Vector Error Correction Models

Sharon Kozicki - Federal Reserve Bank of Kansas City and Peter A. Tinsley - Federal Reserve Board

Vector error correction models are reduced form time series models that are commonly used to empirically analyze the dynamic behavior of a set of I(1) variables. Despite their general lack of structure, these models are intuitively attractive to macroeconomists because they explicitly recognize long-run equilibrium relationships among variables in the system. This paper provides an economic justification for the use of these time series models. In particular, the paper shows how the dynamic behavior of a system in which rational agents optimize subject to convex adjustment costs can be characterized as a vector error correction model with cross-coefficient and cross-equation restrictions. The closed form analytic solution, which we call a rational vector error correction model, is derived using two companion systems, a lead companion system that solves for the forward anticipations required by instrument adjustment costs and a lag companion forecast system associated with projections of agent forecasts on lagged information.

The paper outlines how the general approach can be used to address two classes of common multivariate economic problems. The first class includes problems in which an optimizing representative agent is faced with multiple decision instruments, such as multiple factors of production. The second class includes problems with multiple optimizing agents and general equilibrium interactions between agents.

The paper also shows how the restrictions imposed in rational vector error correction models provide economic insight into a number of related time series technologies commonly used in empirical economic analyses. Three issues explored in detail include: (1) the structural interpretation of appropriately defined error correction terms as deviations of decision variables from optimal behavior in the absence of adjustment costs; (2) the relationship between some popular econometric definitions of trends and the behavior of Euler equation forcing terms; (3) the relationship between the generalized adjustment costs that constrain agent decisions and the lag order of vector error correction models.

Scheduled for Session 1.1 Computation And Econometrics - I