The Perils of Taylor Rules
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
Textbook advice says a central bank that raises rates more than one-for-one with inflation (a Taylor rule) keeps the economy stable. This 2001 paper shows a hidden catch: because interest rates cannot go below zero, any such rule also creates a second, low-inflation "liquidity trap" equilibrium, and the economy can drift there from near the target equilibrium along a slow, smooth path that looks like ordinary stable fluctuations until it is too late. Simulations suggest this is not a rare edge case but a common risk for economies with aggressively enforced inflation targets -- a cautionary result for central banks like Japan's, and arguably the United States'.
What this paper finds — and why it matters
Benhabib, Schmitt-Grohe, and Uribe show that active interest-rate feedback (“Taylor”) rules – which raise the nominal rate more than one-for-one with inflation and are conventionally recommended as stabilizing – carry a global instability risk that purely local (linearized) analysis misses: because the nominal interest rate cannot go negative, any continuous, non-decreasing Taylor rule that supports an “active” steady state (where policy responds more than one-for-one to inflation) must also admit a second, “passive” steady state consistent with a liquidity trap (near-zero nominal rate, possibly negative inflation). The paper’s central result is that this multiplicity of steady states opens the door to infinitely many equilibrium trajectories originating arbitrarily close to the locally-unique active steady state that nonetheless converge either to the passive, liquidity-trap steady state (a “saddle connection”) or to a stable limit cycle around the active steady state, even when the active steady state is itself locally determinate. Along these global equilibria, inflation can fluctuate for long periods near the active-policy target, so an econometrician estimating the policy rule’s slope from such data could easily conclude the economy displays ordinary stationary fluctuations around the inflation target even while it is, in fact, spiraling toward a liquidity trap. Simulations of calibrated sticky-price models show saddle connections from the active to the passive steady state are not a knife-edge curiosity but the typical, parameter-robust outcome, leading the authors to suggest that central banks committed to an actively enforced inflation target may be more prone to sliding into a deflationary liquidity trap than central banks following a globally passive policy such as an interest- or exchange-rate peg.
Summary of a classic paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Questions & answers
Q1. What is the basic mechanism that generates a second steady state whenever an “active” Taylor rule steady state exists?
Combining a simplified interest-rate feedback rule R(π) (nominal rate as a non-decreasing function of inflation) with the steady-state Fisher equation R(π) = r + π, the paper shows that if there is a value of π at which policy is active (R′(π) > 1) and the feedback rule is continuous and respects the zero lower bound (R(π) ≥ 0 for all π), then there must exist another solution to the same equation at which policy is passive (R′(π) < 1). This is a purely graphical/algebraic consequence of the rule’s shape relative to the 45-degree line implied by the Fisher equation and does not depend on whether prices are flexible or sticky, or on the particular way money enters the model (utility function, production function, or cash-in-advance).
Q2. Why isn’t the mere existence of two steady states enough to call Taylor rules “destabilizing,” and what is the paper’s stronger claim?
The authors note that two steady-state equilibria existing is not by itself alarming, since in the data inflation moves smoothly rather than jumping discretely between steady states, and it would be implausible for policymakers to switch discretely between active and passive policy stances. Their actual claim is stronger: the presence of the second (passive) steady state opens up a much larger class of bounded, non-explosive equilibrium paths originating near the active steady state – including a continuum converging to the passive steady state along a saddle connection, or to a stable limit cycle around the active steady state – that would not exist, and could not be ruled out by any amount of further theorizing about the active steady state alone, if the zero lower bound and the second steady state were ignored.
Q3. How does local (linearized) analysis around the active steady state differ from what the paper’s global analysis reveals?
Linearizing the equilibrium conditions around the active steady state, the authors confirm the familiar local-determinacy result – under plausible assumptions (e.g., consumption and real balances not strongly Edgeworth-complementary), the active steady state is the unique bounded equilibrium in a small neighborhood of itself – but show this local conclusion is “misplaced” as a global statement, since trajectories starting arbitrarily close to the active steady state but moving away from it in one direction can still remain globally bounded by converging to the passive steady state or to a limit cycle rather than exploding.
Q4. What do the paper’s global/numerical results say about which type of equilibrium is typical, and under what conditions does a limit cycle instead of a saddle connection arise?
Simulating calibrated sticky-price versions of the model, the authors find that saddle-connection equilibria – trajectories running from the vicinity of the active steady state to the passive, liquidity-trap steady state – exist for empirically plausible parameterizations and are robust to substantial parameter perturbation, making them, in the authors’ assessment, the most typical pattern rather than a special case. The existence of a stable limit cycle instead of a saddle connection is shown (via a bifurcation/normal-form analysis around the active steady state, following Kuznetsov’s results on Hopf-type bifurcations) to depend on the sign of a specific coefficient (denoted s) determined by the structural parameters of the economy, in particular the curvature of preferences in the non-separable-preferences case.
Q5. Why might an econometrician be misled about which kind of equilibrium the economy is actually on?
Along a saddle-connection equilibrium, the paper notes that inflation fluctuates for a long period of time in the vicinity of the steady state associated with active monetary policy before eventually diverging toward the passive steady state, so a researcher estimating the slope of the interest-rate feedback rule from such a sample could well conclude the economy is exhibiting ordinary stationary fluctuations around the active inflation target, even though the economy is, along its true equilibrium path, gradually spiraling down into a liquidity trap.
Q6. What policy comparison does the paper draw between actively-targeting and globally-passive central banks?
The authors suggest that central banks that maintain an actively enforced monetary policy stance near a given inflation target are, by this analysis, more likely to lead their economies into a deflationary spiral – citing Japan’s experience, and suggesting the United States may be similarly exposed – than central banks that instead maintain a globally passive monetary stance, such as an interest-rate or exchange-rate peg, which by construction does not generate the active/passive steady-state multiplicity the paper’s result relies on.
Q7. How does this paper relate to the authors’ own earlier work, and in what way does it go further?
The paper builds on the authors’ earlier finding (Benhabib, Schmitt-Grohe, and Uribe, “Monetary Policy and Multiple Equilibria,” 1998/2001) that active monetary feedback policies can produce local indeterminacy under a range of standard model specifications (sticky prices, Taylor rules with leads/lags, Ricardian and non-Ricardian fiscal regimes); this paper’s contribution is to go beyond local multiplicity and show that active policy generically generates global multiplicity and instability – including liquidity-trap convergence – “in the simplest and most innocuous monetary models, using the simplest and most standard assumptions.”
Key terms in this paper
Definitions below follow the paper's own usage.
- Active versus passive monetary policy (in the Taylor-rule sense)
- a policy is "active" at a steady-state inflation rate if the interest-rate feedback rule's slope there exceeds one (R′(π) > 1, a more-than-one-for-one response to inflation) and "passive" if the slope is less than one; the paper's central finding is that the zero lower bound on nominal rates forces any continuous, non-decreasing feedback rule supporting an active steady state to also admit a passive one.
- Saddle connection
- an equilibrium trajectory that begins arbitrarily close to the (locally determinate) active steady state and converges over time to the passive, liquidity-trap steady state; the paper's simulations find such trajectories exist for plausible calibrations and are robust across a wide range of parameters, making them, in the authors' view, the typical way an actively-targeting economy could slide into a liquidity trap.
- Liquidity trap (passive steady state)
- in this paper, the second steady-state equilibrium implied by combining the Fisher equation with a zero-lower-bound-respecting interest-rate rule, characterized by a near-zero nominal interest rate and, typically, negative or low inflation -- the destination of the saddle-connection equilibria the paper identifies as a realistic risk of active interest-rate targeting.
- Stable limit cycle around the active steady state
- an alternative class of bounded global equilibrium, distinct from the saddle connection, in which inflation and other variables orbit persistently around the active steady state rather than converging to it or to the passive steady state; the paper shows its existence depends on the sign of a bifurcation coefficient tied to the economy's structural (preference) parameters.