THE ECONOMETRICS OF MACROECONOMIC MODELLING
Four groups of interest rate rules
The rules we consider are of the type
RSt = ш RSt_i + (1 — шr )(n* + RR*) + Шп (fit+в — n*)
+ шу (A4 Vt+K — 3*y) + Wealzreal, t + ^openzopen, t?
where RSt denotes the short-term nominal interest rate, RR* is the equilibrium real interest rate, fit+e is a model-based forecast of inflation (i. e. A4pu) в periods ahead, n* is the inflation target for A4put, A4yt+K is a model-based forecast of output growth к periods ahead, gy is the target output growth rate, zrealt denote real-time variables and zopen t denotes open economy variables (typically the real exchange rate). When the target horizons в and к are set to zero, the rules are based on contemporary values of output and inflation. In Section 10.3.4 the optimality of the different rules are evaluated in terms of welfare losses based on minimising the loss function
£(A) = V Ы+AV [A4Vt],
where V[•] denotes the unconditional variance and n is the inflation measure, in our case A4put. A large number of possible variations over this theme obtains by combining different rules and loss functions, cf. the survey in Taylor (1999).[105] The interest rate rules we consider are specified in Table 10.1 and they fall
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Table 10.1 Interest rate rules used in the counterfactual simulations, as defined in equation (10.1)
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into four categories. The first category has two members: (1) a variant of the standard Taylor rule for a closed economy (‘flexible’ rule) where interest rates respond to inflation and output (FLX in the table), and (2) a strict inflation targeting rule where all weight is put on inflation (ST). The next class of rules introduces interest rate smoothing (‘smoothing’ rule), where we also include the lagged interest rate (SM), and the third category contains an ‘open economy’ rule, in which the interest rate responds to the real exchange rate, vrt (RX). Similar rules have previously been used in, for example, Ball (1999) and Batini et al. (2001). The fourth category includes real-time variables, where we use unemployment (UR), wage growth (WF), and credit growth (CR) as alternative indicators for the state of the real economy. The motivation for using realtime variables is well known. As discussed in the introduction, the output gap is vulnerable to severe measurement problems, partly due to a lack of consensus about how to measure potential output, motivating our choice of output growth, following Walsh (2003). However, another source of uncertainty is data revisions. In practice, statistical revisions of output would also render output growth subject to this source of uncertainty, so using output growth rates does not necessarily remove the measurement problem in real time. The alternative ‘real-time’ interest rate rules use variables, observed with greater timeliness, which are less vulnerable to later data revisions.
The first lines of Table 10.1 contain the different variables (x, say), their associated target parameters (h*) and the assumptions about the target
parameter’s trigger values. Each rule correspond to a line in Table 10.1 and the weights attached to the different variables are shown in the columns.[106] In Table 10.1 gw and gcr are the target growth rates for wages and credit.
All the interest rate rules considered can be written as a special case of equation (10.1). The first line in equation (10.1) defines the standard FLX and SM rules. The second line defines the rule which responds directly to the real exchange rate (rule RX). And finally, in line three, we include the different ‘real-time’ variables which are potential candidates to replace output growth in the interest rate rule—registered unemployment (UR), annual wage growth (WF), or annual credit growth (CR)—cf. Table 10.1.
RSt = ^RSt_i + (1 - Ur)(n* + RR*) + Un(Apput - n*) + uy(Apgt - g*y)
+ uVr (vrt - vr*)
+ Uu(ut - u*) + uw(Apwt - g*w) +Ucr(A4crt - g*„) (10.1)
In order to facilitate the comparison between the different interest rate rules we maintain the weights on inflation (un = 1.5) and output growth (uy = 0.5) in all rules where applicable in Table 10.1. Note that these values alone define the interest rate rule denoted FLX. Hence, the FLX rule serves as a benchmark for comparison with all other rules in Table 10.1.
