Determinacy and Indeterminacy in Monetary Policy Rules with Money

Does Friedman’s k-percent rule guarantee a unique equilibrium outcome? We show analytically the answer to this question is sensitive to the method of aggregation. Focusing on broad measures of money, we show that fixing the growth rate of the true monetary aggregate will generate a unique rational expectations equilibrium. Since the true monetary aggregate is parametric, we show this determinacy result extends to the non-parametric Divisia monetary aggregate growth rule. Interestingly, Friedman’s proposal to fix the growth rate of the broad simple-sum monetary aggregate is shown to result in indeterminacy stemming from this aggregate’s inaccuracy in tracking the true monetary aggregate. Determinacy regions of interest rate rules reacting to the growth rate of monetary aggregates are also discussed and a novel Taylor principle is shown to hold for such rules when the monetary aggregate is accurately measured. All of these results are presented in the framework of the canonical New-Keynesian model.