On a Test by K.D. West

Abstract

This paper derives a variance bounds test for a broad class of linear rational expectations models. According to this test, if observed data accord with the model, then a weighted sum of autocovariances of the covariance-stationary components of the endogenous state variables should be nonnegative. The new test reinterprets West’s (1986) variance bounds test and extends its applicability by not requiring observable exogenous state variables, covariance-stationary exogenous or endogenous state variables, or a zero initial value for the endogenous state variable. The paper also extends the new test’s application to nonlinear rational expectations models.

This is a substantially revised version of a paper that was originally circulated as Federal Reserve Bank of Minneapolis Research Department Staff Report 113 on February of 1988. Some of the results of this paper are also contained in an earlier paper of mine entitled “A Generalized Variance Bounds Test: Wim an Application to the Holt et al. Inventory Model” which is forthcoming in the Journal of Economic Dynamics and Control in 1994.