Robust Real Rate Rules

The paper proposes and analyzes real rate rules — monetary policy rules of the form i_t = r_t + φπ_t (φ > 1), where r_t is the current-period real interest rate observed via TIPS yields or inflation swap markets. The central analytical result is that combining this rule with the Fisher equation i_t = r_t + E_t[π_{t+1}] immediately yields E_t[π_{t+1}] = φπ_t, whose unique non-explosive solution is π_t = 0 for all t. This proof uses only the Fisher equation — not the aggregate Euler equation — making the determinacy result robust to household heterogeneity, hand-to-mouth consumers, non-rational household or firm expectations, active fiscal policy, missing transversality conditions, and any specification of intertemporal or nominal-real links. The Fisher equation itself requires only two deep-pocketed, fully-informed, rational agents to arbitrage between nominal and real bonds — a much weaker assumption than aggregate Euler equation rationality. Under the real rate rule, inflation is decoupled from the Phillips curve: causation runs monetary policy → inflation, then inflation → output gap, not the reverse; the Phillips curve determines the output gap residually given already-determined inflation. In a three-equation New Keynesian model with a mark-up shock ζ_t and cost-push shock ω_t, the output gap satisfies x_t = −(ζ_t/(κ(φ − ρ_ζ))) − (ω_t/κ), where the Euler equation plays no role in inflation determination. The rule is globally stable under learning via a contraction argument using Gautschi’s inequality: even if financial market participants hold incorrect prior beliefs, the learning process converges to the target inflation. With a time-varying inflation target π*_t, the modified rule i_t = r_t + φ(π_t − π*_t) implements any target path determinately — π_t = π*_t for all t, including optimal Ramsey paths — making real rate rules observationally equivalent to any other monetary policy specification. The Taylor principle (φ_π > 1) is neither necessary nor sufficient for determinacy in richer models (Bilbiie 2008 TANK; Leeper-Leith 2016 FTPL); the real rate rule achieves determinacy without invoking Euler equation structure. An additional result: with long-maturity government debt, a stable inflation equilibrium always exists under the real rate rule regardless of whether fiscal policy is active or passive — the fiscal theory of the price level fails to produce unique outcomes in this setting.

Tom D. Holden | Macro Paper Warehouse

Robust Real Rate Rules