The Taylor Rule and Optimal Monetary Policy

Questions & answers

Q1. What question does the paper set out to answer, and in what kind of model?

Whether Taylor’s (1993) proposed interest-rate feedback rule “resembles the sort of policy that economic theory would recommend,” evaluated in “a simple, but widely used, optimizing model of the monetary transmission mechanism, which allows one to reach clear conclusions about economic welfare” (Section 1, p. 1). The paper is explicit that it seeks “broad, qualitative features” likely to be “robust to a variety of precise model specifications” rather than claiming the simple Taylor rule is literally optimal in any one model (Section 1, p. 1).

Q2. What is the “Taylor principle,” and where does the paper’s own determinacy result come from?

“A feedback rule satisfies the Taylor principle if it implies that in the event of a sustained increase in the inflation rate by k percent, the nominal interest rate will eventually be raised by more than k percent” (Section 2, p. 3). In the paper’s neo-Wicksellian model, this corresponds exactly to the formal determinacy condition φ_π + [(1−β)/κ]φ_y > 1 for the feedback rule i_t = i*_t + φ_π(π_t − π*) + φ_y(y_t − y^n_t − x*), and “the coefficient values associated with the classic Taylor rule (φ_π = 1.5, φ_y = 0.5) necessarily satisfy the criterion, regardless of the size of β and κ” (Section 2, p. 3). The same condition, generalized to allow for interest-rate inertia (a lagged-rate term with coefficient ρ), becomes φ_π + [(1−β)/κ]φ_y > 1 − ρ, “once again correspond[ing] precisely to the Taylor principle” (Section 2, p. 4).

Q3. Why doesn’t the Sargent-Wallace indeterminacy critique of interest-rate rules apply to the Taylor rule?

Because Sargent and Wallace’s (1975) classic result assumes a rule that fixes an exogenous path for the nominal interest rate, whereas the Taylor rule specifies feedback from an endogenous state variable (inflation and the output gap), and “determinacy is instead possible in the case of feedback” of this kind (Section 2, p. 2, citing McCallum 1981). The paper further notes that Bullard and Mitra (2000a,b) show the same condition (2.5)/(2.7) that ensures rational-expectations determinacy also ensures “expectational stability” – convergence of adaptive learning dynamics to the rational-expectations equilibrium – so that “there is no intrinsic unsuitability of an interest-rate rule as an approach to inflation control,” provided it satisfies the Taylor principle (Section 2, p. 4).

Q4. Does the Wicksellian “cumulative process” critique of interest-rate pegs undermine the Taylor rule?

No – that critique, in which a rise in expected inflation lowers the perceived real rate, stimulates demand, and drives inflation higher in a self-fulfilling spiral, “once again… implicitly assumes an exogenous target path for the nominal interest rate,” while “the sort of feedback from inflation and the output gap called for by the Taylor rule is exactly what is needed to damp such an inflationary spiral” (Section 2, p. 3-4).

Q5. What welfare-theoretic justification does the paper give for the Taylor rule’s stabilization goals?

A second-order Taylor-series approximation to the expected utility of a representative household yields a period loss function of the form L_t = π_t² + λ(y_t − y^n_t − x)², so that inflation and output-gap stabilization “have a sound theoretical basis” (Section 3, p. 5-6).* The intuition traced through the model: because relative-price dispersion from staggered price-setting is (under Calvo pricing) proportional to squared inflation, and dispersion is itself a source of deadweight loss, “a goal of inflation stabilization may be justified” quite generally, alongside stabilizing the output gap relative to the natural (not simply trend) rate of output (Section 3, p. 5-6).

Q6. What two qualifications does the paper attach to this welfare-theoretic justification of the Taylor rule?

First, that the welfare-theoretic optimal long-run inflation rate is zero, not Taylor’s two percent, “as this is the rate that minimizes relative-price distortions associated with imperfect synchronization of price changes” – though monetary frictions and the zero lower bound can push the true optimum slightly positive, “but still much less than one percent per annum” (Section 3, p. 6). Second, that the “output gap” that should be stabilized is the gap between actual output and the natural rate of output – not, as in Taylor’s own comparisons, output relative to a simple exponential trend – and the paper cites Sbordone’s finding that a more theoretically grounded proxy, real unit labor cost, is actually negatively correlated (-.35) with detrended real GDP over her sample, so “the use of such measures in a Taylor rule would make a significant difference in practice” (Section 3, p. 7-9).

Q7. What is the paper’s central critique of the Taylor rule’s specific formulation, and what does optimal policy require instead?

That achieving full stabilization of inflation and the output gap requires the rule’s intercept term to move one-for-one with the time-varying Wicksellian natural rate of interest, r^n_t = σ⁻¹[g_t + E_t(y^n_{t+1} − y^n_t)], whereas “Taylor (1993) assumes… a constant intercept term, equal to the sum of ’the central bank’s estimate of the equilibrium real rate of interest’ and the inflation target” – fixed at two percent even though “the natural rate should vary over time in response to many types of real disturbances” (Section 4, p. 11-13). “Failure to adjust the intercept i*_t in the policy rule to track variation in the natural rate of interest will result in fluctuations in inflation and the output gap, for any finite values of the coefficients φ_π and φ_y – just as in the classic analysis of Wicksell (1898)” (Section 4, p. 12-13). The paper argues a rule with a time-varying, natural-rate-tracking intercept and modest feedback coefficients (like Taylor’s own) is particularly robust because the natural rate and the optimal targets (zero inflation, zero output gap) can be derived independently of the precise degree or form of price stickiness assumed (Section 4, p. 13).

Q8. Why might full inflation and output-gap stabilization not actually be optimal in practice?

Because several real-world considerations break the clean case for complete stabilization: inefficient variation in the natural rate of output (creating a gap between the natural rate and the welfare-relevant efficient rate), the zero lower bound on nominal rates (making “incomplete inflation stabilization… typically… preferable to complete stabilization around a higher rate”), and a distaste for the interest-rate volatility that literal full stabilization could require (Section 4, p. 13-14). In these cases the relevant loss function acquires an explicit interest-rate-volatility term, L_t = π_t² + λ_y(y_t − y^n_t − x*)² + λ_i(i_t − i*)², and optimal policy no longer fully stabilizes inflation, though the paper notes this more complex optimum can still be achieved via a rule of the same feedback form, with a more elaborate history-dependent intercept (Section 4, p. 14, citing Woodford 1999b and Giannoni 2000).