2.4 The central bank reaction function
Taylor (1993) observed that the conduct of monetary policy can be well-captured by a simple rule relating interest rates to inflation and the output gap. Following Taylor's paper there began a concerted academic effort to assess this class of policy rules and their implications for optimal monetary policy. However, some form of Taylor's original rule, which is entirely backward-looking, remains the default specification for the behaviour of the central bank in many economic models.
The IS and Phillips relations described above operate with a lag. That is to say, it takes time for interest rates to affect the output gap and, in turn, for inflation to respond to the output gap. The lag structure embodied in these equations means that monetary policy should be conducted with a view to the future. Therefore, given the involvement of the central bank in forecasting the economy and the lags associated with the conduct of policy, I specify a forward-looking form of the Taylor rule which is consistent with the other equations in the model - the Bank's expectations are assumed to be model-consistent.
As well as being a reasonable empirical description of the conduct of monetary policy, Svensson (1997) and others have shown that the Taylor class of rules can also be derived from the inflation targeting central bank's optimisation problem. Simply allowing for the lag structure associated with the monetary transmission mechanism gives a forward-looking Taylor rule of the form,
(2.23)
where it is Bank Rate, 
is the equilibrium nominal rate of interest, 
is the output gap forecast at the relevant time horizon and 
is the forecast deviation of inflation from target.[14],[15]
Unlike the IS and Phillips relations, I do not include an exchange rate term in the specification of the Taylor rule. In this model, the central bank responds to movements in the exchange rate only indirectly, via its effect on output and domestically-generated inflation. This is consistent with both New Zealand's Policy Targets Agreement and the Taylor (2001) finding that the inclusion of exchange rates does little to improve the stabilisation of output and inflation and is possibly detrimental.
A substantial literature also exists on the observed inertia of interest rate setting by central banks around the world, see for example Goodfriend (1991). In what follows, I adopt the same approach as Clarida, Gali & Gertler (1999), which is to assume the presence of a policy rate smoothing parameter in the central bank's reaction function. They suggest this smoothing arises from a desire to avoid the credibility costs associated with large policy reversals, a desire to minimise disruption to capital markets and the time it takes build a consensus to support a policy change.[16]
Later discussions have identified ways in which interest rate smoothing might be optimal for a central bank in the presence of parameter uncertainty. Svensson (1999), for example, shows that parameter uncertainty for an inflation-targeting central bank dampens the policy response, confirming what Brainard (1967) first described. Soderstrom (2002) extends this analysis to a dual-mandate central bank with output in its loss function. He finds that uncertainty over inflation dynamics tends to heighten the response to inflation deviations (in case expectations become unanchored) but uncertainty over output dynamics encourages caution.
Regardless of the precise motive, the inclusion of central banks' smoothing of policy rates in their reaction functions significantly improves the fit with the data. Equation 2.24 captures interest rate inertia as in Clarida et al (1999),
(2.24)
where it is the interest rate set, ψ is the smoothing parameter, 
is the interest rate implied by the reaction function (absent smoothing) and it-1 is the interest rate set in the preceding period.
Substituting the generalised Taylor rule in to equation 2.21 as the term gives the central bank reaction function with policy rate smoothing equation 2.25,
(2.25)
I choose a forecast horizon of 6 months for the output gap and a year and a half for inflation, consistent with conventional wisdom over the transmission mechanism of monetary policy. Linearising equation 2.25 around the steady-state interest rate and inflation target gives the 'nominal interest rate gap' equation,
(2.26)
Notes
- [14]The specification is slightly different from the original Taylor rule but consistent with Nelson and Nikolov (2002).
- [15]I use effective bank rate in place of actual bank rate to account for the effects of credit spreads and unconventional monetary policy on lending rates to the wider economy. I discuss this in more detail from section 2.5.
- [16]In a rational expectations context, Woodford (2003) also shows that it can be optimal for a central bank to move the current policy rate less in response to demand and inflation shocks if, at the same time, the changes are characterised by a high level of persistence. This way, agents in the economy expect interest rates to be lower for longer once they have been cut, in turn lowering longer-term interest rates as well as short rates.
