2.3 The Central Bank
Following the current practice of central banks in developed economies, it is customary to
assume that setting the nominal interest rate is the main instrument of monetary policy
and, hence, this is modelled by some form of interest rate rule. Nominal and real interest
rates are related by the Fischer equation
where the nominal interest rate Rn,t , set at the beginning of period t, is a policy variable,
typically given in the literature by a simple Taylor-type rule:
Et[1 + Rt+1] = Et
1 + Rn,t
π t +1
(29)
logμ +R )=ρ logμ + )+θo μ π ) (30)
As mentioned in the introduction, that is not necessarily the case of the RBI. In fact,
we will model monetary policy in a more general way by formulating a Calvo-type forward-
backward interest rate rule as in Levine et al. (2007) and Gabriel et al. (2009). This is
defined by
∕∣I RnΛ 1 1 + Rn,t-ɪʌ zjl θ t , 1 φ t ∕21x
'4π⅛ ) = ρ 1 + Rn + θ θ logΘ +φ Φ tMPst (31)
where eMPS,t is a monetary policy shock and
log Φt = log Πt + τ log Φt-1 (32)
φEt[log Θt +ɪ] = log Θt — (1 — φ) log(Πt) (33)
The Calvo rule can be interpreted as a feedback from expected inflation (the θ log Θt
term) and past inflation (the φ log φφ term) that continues at any one period with proba-
bilities φ and τ, switching off with probabilities 1 — φ and 1 — τ. The probability of the rule
lasting for h periods is (1 — φ)φh, hence the mean forecast horizon is (1 — φ) ∑∞=1 hφh =
φ/(1 — φ). With φ = 0.5, for example, we would have a Taylor rule with one period lead
in inflation (h = 1). Similarly, τ can be interpreted as the degree of backward-lookingness
of the monetary authority.
This rule can also be seen as a special case of a Taylor-type rule that targets h-step-ahead
(back) expected rates of inflation and past inflation rates (with h = 1, 2, ..., ∞)
it = pit-ɪ + θ о ∏t + θ ɪ Et ∏t+ɪ + θ 2 Et∏t+2 + ... + γ ɪ ∏t-ɪ + γ2 ∏t-2 + ■■■, (34)
albeit one that imposes a specific structure on the θi,s and γi,s (i.e., a weighted average of fu-
ture and past variables with geometrically declining weights).6 This has an intuitive appeal
6it and πt correspond to log ( 1j+¾t,* ) and log ( ∏∏-¢, to simplify notation.