The Observational Equivalence of Natural and Unnatural Rate Theories of Macroeconomics

Abstract

The usual proof that Friedman's simple k-percent growth rule for the money supply is suboptimal comes from mechanically manipulating a reduced-form equation. Those manipulations, in general, show that pursuing a rule with feedback from current economic conditions to the money supply is better than following Friedman's advice. To be valid, the proof requires that, as written in one particular way, the reduced-form equation will remain unaltered when the monetary authority departs from the old "rule" used during the estimation period and follows a new one. Here I point out that there are always alternative ways of writing the reduced form, one being observationally equivalent with the other, so that each is equally valid in the estimation period. If one assumes that the first form is invariant when the policy rule is changed, the proof of the superiority of rules with feedback over Friedman's rule goes through. But if one assumes that it is the reduced form as written in the second way that remains unchanged, the proof that Friedman is wrong does not obtain-instead, the implication is that Friedman's rule does as well as any other deterministic feedback rule and better than a stochastic rule. Therefore, estimates of reduced forms alone will not permit one to settle the difference between Friedman and advocates of rules with feedback. Given any set of reduced-form estimates, there is an invariance assumption that will permit a member of either camp to make his point. In effect, then, this paper poses the question: Does the view that Friedman's k-percent feedback rule is as good as any other deterministic feedback rule place any restrictions on reduced forms? The answer is no. This is distressing since, for a given sampling interval and estimation period, the reduced-form estimates summarize everything that the data can ever tell