John H. Boyd, III and Michael Dotsey
Monetary economists have recently begun a serious study of money supply rules that allow the Fed to adjustably peg the nominal interest rate under rational expectations. These rules vary from procedures that produce stationary nominal magnitudes to those that generate nonstationarities in nominal variables. Our paper investigates the determinacy properties of three representative interest rate rules.
We use Blanchard and Kahn's solution technique as a starting point. It doesn't directly apply, so we first modify their procedure. We then narrow the range of solutions by considering the ARMA solutions of Evans and Honkapohja and the global minimum state variable solution of McCallum. We then examine these solutions in light of the expectational stability notions employed by DeCanio, Bray and Evans.
Two of the three classes of rules yield a unique admissible solution. The exclusion of bubbles usually rules out the general ARMA solutions present in Evans and Honkapohja and leads to unique solutions via a saddlepoint property. Nonetheless, the nonstationary money supply rules we examine do not generally yield a well determined system over all parameter values. We employ the global minimum state variable methodology of McCallum and Evans' expectational stability in an effort to insure uniqueness. Although these methods are usually in agreement, one of the nonstationary rules yields a global minimum state variable solution that is expectationally unstable when the central bank is sensitive to interest rate deviations. Moreover, under these conditions, an alternative (non-global) minimum state variable solution is expectationally stable, casting doubt on the applicability of McCallum's global procedure in this context.