Avoiding Liquidity Traps

Questions & answers

Q1. What two simplifications does the paper argue are common to prior work praising Taylor rules, and why do they matter?

Prior studies (Levin-Wieland-Williams, Rotemberg-Woodford, Leeper, Bernanke-Woodford, Clarida-Galí-Gertler among them) “restrict attention to local dynamics, or small fluctuations, around a target level of inflation” and “do not take into account the fact that nominal interest rates are bounded below by zero” (Section I, p. 536-537). The paper argues “these two simplifications have serious consequences for aggregate stability” once relaxed, since the zero bound interacts with the global shape of the interest-rate feedback rule in a way local analysis cannot see.

Q2. Why does a Taylor rule necessarily create a second, unintended steady state?

Because the interest-rate rule R(π) is increasing and bounded below by zero, while the steady-state Fisher equation requires R = r + π, the two relationships must intersect a second time beyond the intended active-policy target (π, R(π))** (Section I, p. 537-538, Fig. 1). “The presence of a zero bound on nominal interest rates and the assumption that the interest rate rule is increasing in inflation necessarily imply the existence of a second inflation rate, π_L, at which the feedback rule and the Fisher equation intersect. At this second intersection, inflation is low and possibly negative, the nominal interest rate is low and possibly zero, and monetary policy is passive” (Section I, p. 537-538).

Q3. What is the paper’s claim about the character of this second steady state, and why does that matter more than its mere existence?

The unintended steady state is locally indeterminate, and more importantly, gives rise to equilibrium paths that start arbitrarily close to the intended target and drift gradually toward the trap: “equilibria exist in which inflation, interest rates, and aggregate activity fluctuate in response to nonfundamental revisions in expectations. More important, the second steady state gives rise to equilibrium trajectories along which inflation and the nominal interest rate start arbitrarily close to the intended targets… and converge gradually” (Section I, p. 538). The authors emphasize this is not merely a theoretical curiosity near an obscure equilibrium far from the target – it is a self-fulfilling deflationary path reachable from arbitrarily near the central bank’s intended equilibrium, and once under way, “monetary policy becomes ineffective in bringing about the government’s goals regarding the stability of output and prices” (Section I, p. 538).

Q4. What is the paper’s fiscal remedy, and through what economic channel does it work?

Replacing a Ricardian fiscal rule with one in which the sensitivity of government revenue to total liabilities, a(π), rises with inflation and satisfies a(π) > 0 but a(π_L) < 0, so that the government’s transversality condition holds along the intended constant-inflation path but fails along any path converging to the trap (Section V.A, eqs. 18-22, p. 547-549).* “Under the proposed inflation-sensitive revenue schedule, the government manages to fend off the unintended low-inflation equilibrium by threatening to implement a fiscal stimulus package consisting of a severe increase in the consolidated deficit should the inflation rate become sufficiently low” (p. 549). The authors are explicit the mechanism is not the traditional Keynesian multiplier but “more akin to Pigou’s argument on the implausibility of liquidity traps”: in a closed economy, a tax cut raises household after-tax wealth, creating excess demand for goods that, with fixed aggregate supply, must raise the price level to restore equilibrium (Section V.A, p. 549).

Q5. Is switching to a money-growth-rate target, as often proposed for Japan, a reliable fix on its own?

No – the paper shows its effectiveness depends entirely on the accompanying fiscal regime: under a Ricardian fiscal rule, “switching from an interest rate feedback rule to a money growth rate rule as the nominal interest rate gets close to zero will not eliminate self-fulfilling deflations” (Section VI.A, p. 550-551, attributing this specific finding to Woodford 1999). The paper illustrates with paired examples that the same monetary regime switch can succeed or fail to rule out the deflationary trap depending on the fiscal policy in place alongside it, concluding “the effectiveness of such an alternative will in general depend on the accompanying fiscal regime” (Section VI, p. 550-551).

Q6. Are these liquidity-trap and remedy results specific to the paper’s flexible-price, continuous-time setup?

The authors argue no on both counts. Citing their own companion work, they note “Taylor rules also engender liquidity traps in environments with sluggish price adjustment,” where the trap additionally indeterminates the level of aggregate demand, and the same transversality-condition-based fiscal and monetary remedies remain effective “because… the violation of this long-run restriction depends on the asymptotic behavior of the endogenous variables of the model, which is independent of short-run nominal price rigidities” (Section VII, p. 559). Similarly, they note a discrete-time cash-in-advance analysis (Schmitt-Grohé and Uribe 2000) produces “an unintended liquidity trap” of identical character, so the continuous-time assumption is not doing essential work either (Section VII, p. 559).

Q7. What alternative failure mode of Taylor rules does the paper flag as beyond the scope of its proposed remedies?

Chaotic dynamics identified in companion work (Benhabib et al. 2000): even when monetary policy follows the Taylor principle, the economy can fluctuate chaotically in “a potentially large neighborhood around the equilibrium intended by the central bank” without ever falling into the permanent low-inflation trap analyzed in this paper (Section VII, p. 559-560). Because the fiscal and monetary remedies developed here work by making a permanent slide to a lower inflation level fiscally or monetarily unsustainable, “the specific policies described in this paper may not be successful in eliminating these chaotic equilibria since they rely on the convergence of inflation to a permanently lower level” (Section VII, p. 560).

Q8. What does the paper conclude about proposals to use negative interest rates (Gesell taxes) to avoid liquidity traps?

That a Gesell tax on money holdings does not eliminate liquidity traps at all – it merely relocates the effective lower bound below zero, since “what is important for the possibility of falling into a liquidity trap is the combination of a Taylor-type interest rate rule with the existence of some lower bound on nominal interest rates. Whether this bound is positive, zero, or negative is immaterial” (Section VII, p. 560). Because a liquidity trap in the paper’s sense is a state where the opportunity cost of holding money is driven to zero, and a Gesell tax simply shifts the bond rate at which that opportunity cost hits zero, the underlying mechanism the paper identifies survives such a policy unchanged.