Could an Active Monetary Policy Create a Liquidity Trap?

John Taylor's seminal 1993 paper illustrated how US monetary policy could be described by an interest rate feedback rule, whereby the short-term interest rate is set as an increasing function of both inflation and output. An extensive literature has since developed that explores the efficiency and dynamic properties of such feedback rules, with particular attention being paid to their supposedly stabilizing properties. The central policy recommendation that has emerged from this literature is that monetary authorities should conduct an 'active' monetary policy, in the sense that they should increase the nominal interest rate by more than one-for-one when the inflation rate increases. These active interest rate feedback rules have come to be known as Taylor rules and, given the amount of controversy that usually surrounds macroeconomic policy, the degree of consensus that has emerged regarding their desirability is remarkable.

Subsequent empirical studies have confirmed that Taylor rules are not specific to the US: for the past two decades, the central banks of Japan, France and the UK all seem to have followed an active monetary policy rule. In fact, even the Bundesbank, which consistantly emphasised its adherence to monetary targets, was shown to follow a simple Taylor rule. All of this would seem to imply that actual monetary policy has been contributing to macroeconomic stability. But are Taylor rules always stabilizing? A Discussion Paper by Jess Benhabib, Stephanie Schmitt-Grohé and Martin Uribe suggests not.

Using the same theoretical framework as the previous literature, the authors demonstrate that for both flexible- and sticky-price models and for simulations of calibrated economies, an active monetary policy will generally lead to indeterminacy and multiple equilibria. Central banks that follow such a policy around a given inflation target may well lead the economy into a deflationary spiral similar to the one observed in Japan and, as some have argued, Europe. The reason for this multiplicity of equilibria stems from one simple fact: the impossibility of negative nominal interest rates.

The above box formalises a simple Taylor rule. Specifically, an active monetary policy (i.e. a > 1) can be defined as one that aggressively fights inflation by raising(lowering) the nominal interest rate by more than the increase(decrease) in inflation. This is generally thought to stabilize the real side of the economy by ensuring the uniqueness of the equilibrium. A passive monetary policy (i.e. a < 1), defined as one that underreacts to inflation by raising(lowering) the nominal interest rate by less than the increase(decrease) in inflation, is generally thought to destabilize the economy by giving rise to expectation-driven fluctuations. By constraining the nominal interest rate to be non-negative, the authors are able to illustrate that if there exists a steady state with an active monetary policy then there must also exist another steady state with a passive monetary policy.

To intuitively illustrate the source of multiplicity, consider a simplified monetary policy rule whereby the monetary authority sets the nominal rate as a non-decreasing function of inflation: R=R(p), where R denotes the nominal interest rate and p denotes the rate of inflation. Combining this rule with the Fischer equation, R = r + p, where r is the real interest rate, yields the steady-state Fischer equation R(p) = r + p. Suppose that there exists a steady state with active monetary policy, that is a value of p that solves the steady-state Fischer equation and satisfies R’(p)>1. If the policy rule respects the zero bound on nominal rates, then there must also exist another steady state in which monetary policy is passive, that is a steady state in which R’(p)<1.

The graph above demonstrates the existence of multiple solutions to the steady-state Fischer equation and establishes the possibility of at least two steady-state equilibria: one, an active equilibrium (i.e. R’(p*)>1) at the inflation target (i.e. p*); the other, a passive equilibrium (i.e. R’(pL)>1) at a level of inflation below the inflation target (i.e. pL) that is possibly negative and a nominal interest rate close to zero. It immediately follows from this that a central bank cannot have a globally active monetary policy, in that for inflation rates sufficiently below the inflation target, the bank can no longer respond to declines in inflation by cutting the nominal interest rate by more than the observed fall in inflation.

Previous authors have limited their analysis to the local stability properties of interest rate feedback rules in which inflation is constrained to remain forever near the central bank's long-run inflation target. One of the justifications for such a strategy is the implicit assumption that all inflation paths which move far enough away from the inflation target are explosive and will therefore not be able to be supported as equilibrium outcomes. Benhabib et al demonstrate that the zero bound on nominal rates implies that paths for the inflation rate in which inflation moves further and further below the inflation target do not become explosive and can indeed be supported as equilibrium outcomes.

Of course, it does not necessarily follow that active monetary policy rules are destabilizing solely because they give rise to multiple steady-state equilibria. Observed inflation dynamics are quite smooth, giving little support to a model in which movements in inflation are due to jumps from one steady state to another. The authors argue, however, that Taylor rules are destabilizing because the multiplicity of steady-state equilibria that they induce opens the door to a much larger class of equilibria. Specifically, the paper illustrates, through both flexible- and sticky-price models, that in general there exists an infinite number of equilibrium trajectories originating in the vicinity of the active steady state that converge either to the passive steady state (via a saddle connection) or to a stable limit cycle around the active steady state.

Simulations of calibrated versions of the sticky-price model indicate that saddle connections from the active steady state to the passive one exist for empirically plausible parameterizations and are indeed the most typical pattern as they are robust to a wide variety of parameter values. This type of equilibrium is of particular interest as it sheds light on the precise way in which economies may fall into liquidity traps. Interestingly, owing to the nature of the saddle connection that links the active steady state to the passive one, an economy may seem to be fluctuating around the inflation target when in actual fact it is spiralling down towards a liquidity trap. Hence, the recent rise in Euroland inflation, to a figure above the ECB's 2% inflation ceiling, is not inconsistent with the theory of an economy moving towards a liquidity trap.

Recent work on liquidity traps by Paul Krugman has also focused on the zero bound on nominal interest rates. An additional element in Krugman's model of the liquidity trap (that has received some criticism) is the assumption of negative equilibrium real interest rates. By contrast, in Benhabib et al's model liquidity traps arise even when the real interest rate is positive. They emerge as a consequence of the central bank's commitment to an active monetary policy rule, which in combination with the zero bound on nominal rates, prevents the monetary authority from credibly threatening to follow an inflationary policy at near zero interest rates.