This paper explores the theoretical implications of different policy rules and discre-tionary policy under varying parameters in the New Keynesian model. With the comparison of short-run gains from discretion over rule-based policy and long-run
26Here, LDIS ≥ LOP for ρ = 0 with any combination of parameters, and increasing ρ only aggravates this situation.
27For a completely myopic private sector, i.e. βP S = 0, the optimal timeless rule causes a loss equivalent to the one under discretion because equations (2.6) and (2.23) are identical forβP S= 0.
Hence, there is no equivalent to Proposition 2.2 for OP.
28An analytical proof of this result could be given as follows: Since limβP S→0LOP =LDIS and
dLOP
dβ <0 for 0< β≤1, while dLdβDIS = 0,LOP < LDIS for 0< β≤1. But dLdβOP is too complex to allow an analytical determination of sign³
dLOP
dβ
´ .
29Recall also the discussion of the influence ofβ and ωin sections 2.3.2 and 2.3.3.
−0.05
0
0.05
−0.05 0
0.05
−0.2
−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
u0
y−1
RL
Figure 2.11: RLc = LLOP
DIS depending on y−1 and u0.
losses from discretion, we have provided a framework in which to think about the impact of different parameters on monetary policy rules versus discretion. This framework allows intuitive economic explanations of the effects at work.
Already Blake (2001), Jensen and McCallum (2002) and Jensen (2003) provide evidence that a policy rule following the timeless perspective can cause larger losses than purely discretionary modes of monetary policy making in special circumstances.
But none of these contributions considers an economic explanation for this rather unfamiliar result let alone analyses the relevant parameters as rigorously as this chapter.
What recommendations for economic policy making can be derived? Most im-portantly, the timeless perspective in its standard formulation is not optimal for all economies at all times. In particular, if an economy is characterised by rigid prices, a low discount factor, a high preference for output stabilisation or a sufficiently large deviation from its steady state, it should prefer discretionary monetary policy over the timeless perspective. The critical parameter values obtained in this chapter suggest that – for a number of empirically reasonable combinations of parameters – the long-run losses from discretion may be less relevant than previously thought.
In an overall laudatory review of Woodford (2003), Walsh (2005) argues that Woodford’s book ‘will be widely recognized as the definitive treatise on the new Keynesian approach to monetary policy.’ He critisises the book, however, for its lack of an analysis of the potential short-run costs of adopting the timeless perspec-tive rule. Walsh (2005) sees these short-run costs arising from incomplete credibility
of the central bank. Our analysis has completely abstracted from such credibility effects and still found potentially significant short-run costs from the timeless per-spective. Obviously, if the private sector does not fully believe in the monetary authority’s commitment, the losses from sticking to a rule relative to discretionary policy are even greater than in the model used in this chapter. One way to incorpo-rate such issues is to assume that the private sector has to learn the monetary policy rule. Evans and Honkapohja (2001) provide a convenient framework to analyse this question in more detail.
Appendix
2.A Derivation of L
T PThe unconditional loss for the timeless perspective, equation (2.21), can be derived in several steps. The MSV solution (2.16) and (2.17) depends on two state variables, yt−1 and ut. From the conjectured solution in (2.15), we have
E[yt2] =φ221E[yt−12 ] +φ222E[u2t] + 2φ21φ22E[yt−1ut]. (2.29) E[yt−1ut] can be calculated from (2.15) with ut =ρut−1+² as
E[yt−1ut] = E[(φ21yt−2+φ22(ρut−2+²t−1))(ρut−1 +²t)]
= E[φ21ρ yt−2ut−1
| {z }
=E[yt−1ut]
+φ22(ρ2ut−1ut−2
| {z }
=ρσu2
+ρ ut−1²t−1
| {z }
=σ2
)] + 3·0, (2.30)
since the white noise shock²t is uncorrelated with anything from the past. Solving forE[yt−1ut] withσu2 = 1−ρ1 2 σ2 gives
E[yt−1ut] = φ22ρ
1−φ21ρ · 1
1−ρ2 σ2. (2.31)
Plugging this into (2.29), using E[yt2] = E[y2t−1] = E[y2] and φ21, φ22 from the MSV solution (2.17) leaves
E[y2] = 1 1−φ221
µ
φ222+2φ21φ222ρ 1−φ21ρ
¶ 1 1−ρ2 σ2
= α2(1 +δρ)
ω2(1−δ2)(1−δρ)[γ−β(δ+ρ)]2 · 1
1−ρ2 σ2. (2.32) From the conjectured solution in (2.14), we have
E[π2t] = φ211E[yt−12 ] +φ212E[u2t] + 2φ11φ12E[yt−1ut]. (2.33) Combining this with the previous results and the MSV solution (2.16) results in
E[π2] = 2(1−ρ)
(1 +δ)(1−δρ)[γ−β(δ+ρ)]2 · 1
1−ρ2 σ2. (2.34) Hence, LT P as the weighted sum of E[π2] and E[y2] is given by
LT P = 2ω(1−δ)(1−ρ) +α2(1 +δρ)
ω(1−δ2)(1−δρ)[γ−β(δ+ρ)]2 · 1
1−ρ2 σ2. (2.35)
2.B Influence of parameters on RL f
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−0.06
−0.05
−0.04
−0.03
−0.02
−0.01 0
RL
Value of β
Figure 2.12: Variation of discount factor β, OP vs. DIS.
0 2 4 6 8 10 12
−0.06
−0.05
−0.04
−0.03
−0.02
−0.01 0
RL
Value of ω
Figure 2.13: Variation of weight on the output gap ω, OP vs. DIS.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−0.2
−0.15
−0.1
−0.05 0
RL
Value of ζ
Figure 2.14: Variation of degree of price rigidity ζ, OP vs. DIS.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−0.8
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1 0
RL
Value of ρ
Figure 2.15: Variation of degree of serial correlation ρ in the benchmark model, OP vs. DIS.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−0.02
−0.018
−0.016
−0.014
−0.012
−0.01
−0.008
−0.006
−0.004
−0.002 0
RL
Value of ρ
Figure 2.16: Variation of degree of serial correlation ρ with ω = 10, OP vs. DIS.
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Using Taylor rules to understand ECB monetary policy ∗
Abstract
Over the last decade, the simple instrument policy rule developed by Taylor (1993) has become a popular tool for evaluating monetary policy of central banks. As an extensive empirical analysis of the ECB’s past behaviour still seems to be in its infancy, we estimate several instrument policy reaction functions for the ECB to shed some light on actual monetary policy in the euro area under the presidency of Wim Duisenberg and answer questions like whether the ECB has actually followed a stabilising or a destabilising rule so far.
Looking at contemporaneous Taylor rules, the presented evidence suggests that the ECB is accommodating changes in inflation and hence follows a destabilising policy. However, this impression seems to be largely due to the lack of a forward-looking perspective in such specifications. Either assuming rational expectations and using a forward-looking specification, or using expectations as derived from surveys result in Taylor rules which do imply a stabilising role of the ECB. The use of real-time industrial production data does not seem to play such a significant role as in the case of the US.
∗This chapter is based on joint work with Jan-Egbert Sturm and provides an extended and updated version of Sauer and Sturm (2007).
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