New techniques for estimation of rational expectation models and Volcker deflation

Multivariate autoregressive moving average models are used to form the “reduced forms” of Muth's rational expectation models. One implication of the modern macroeconomic theory is that economic agents' expectations should change in the presence of major policy changes. This paper proposes a simple method for directly comparing the formulation of expectations, and illustrates it by considering the impact of a recent policy change in the US under Paul Volcker of the Federal Reserve Bank. Many new interpretations are based on transfer functions, “gain” calculations, Green's function matrices from solutions of difference equations, and complex conjugate roots to measure cyclical phenomena. Furthermore, the traditional distributed lag models are criticized for arbitrarily assuming that the gain is unity. We provide an equation for minimum mean squared error regulation, and indicate the role played by rational two-step ahead speculations made by economic agents, along with changes therein emanating from the policy change.