# Evaluation of monetary. policy rules

We now relax the assumption of an exogenous interest rate in order to focus on monetary policy rules. We evaluate the performance of different types of reaction functions or interest rate rules using the small econometric model we developed, in Chapter 9. In addition to the standard efficiency measures, we look at the mean, deviations from targets, which may be of particular interest to policy makers. Specifically, we introduce the root mean squared target error (RMSTE), which is an analogue to the well known root mean squared forecast error. Throughout we assume that the monetary policy rules aim at stabilising inflation around an inflation target and that the monetary authorities also put some weight on stabilising unemployment, output, and interest rates. Finally we conduct simulation experiments where we vary the weights in the interest rate rules as well as the weights of other variables in the loss function of a policy maker. The results are summarised by estimating response surfaces on the basis of the whole range of weights considered, in the simulations.

Taking full account of inflation targeting entails that we supplement our model description of the economy with a monetary rule in terms of an interest rate reaction function for the central bank. The monetary rule can be forecast-based or focused on contemporary values of the target variables in the reaction function. We have chosen to analyse the latter alternative, although our discussion below is related to Levin et al. (2003), who consider (optimised) forecast-based interest rate rules which they derive for several different models assuming that the preference function of the central bank depends on the variances of inflation and the output gap.

In this chapter, we evaluate a different, and also wider, set of interest rate rules, using the model of Chapter 9.[101] First, the choice of preference function of Levin et al. (2003) reflects what seems to be a consensus view, namely that inflation and output gap stabilisation are the main monetary policy objectives of a central bank. While we do not dispute the relevance of this view, there are several arguments for looking at output growth rather than the output gap. In addition to the inherent possibility of measurement error in the output gap, as emphasised by Orphanides (2003), there are also theoretical reasons why output growth might be a sensible objective. Walsh (2003) argues that changes in the output gap—growth in demand relative to growth in potential output— can lead to better outcomes of monetary policy than using the output gap. He demonstrates that such a ‘speed limit policy’ can induce inertia that dominates monetary policy based on inflation targeting and the output gap—except when inflation expectations are primarily backward-looking.[102] A policy rule with output growth and inflation is therefore used as a baseline. Second, rules based on different criteria are considered: those include criteria like simplicity, smoothness or gradualism, and fresh information, which all are considered to be important by policy makers. Finally, we also follow the common practice of central banks to adopt inflation measures that captures underlying inflation rather than the headline consumer price index (CPI) inflation.[103]

More specifically, the interest rate rules we evaluate are based on

• output growth and inflation—as a baseline

• interest rate smoothing

• open economy information: exchange rates

• real-time information on the state of the economy: unemployment, wage

growth, and credit growth.[104]

The third item is particularly relevant to the small open economy—and that perspective has not previously been emphasised either in the theoretical or the empirical literature.

The different interest rules are presented in Section 10.2. Section 10.3 gives an overview of the basis of three different sets of evaluation criteria. We evaluate the rules along the dimensions fit, relative losses, and optimality, all derived from the counterfactual simulations. The fit is evaluated on standard efficiency measures as well as using a new measure called root mean squared target errors (RMSTEs), which takes into account both the bias (i. e. the average deviation from target) and the variability of selected report variables, such as alternative measures of inflation (e. g. headline CPI inflation, underlying inflation), and output growth etc. Relative losses summarise the performance of any given rule relative to a benchmark rule as we vary the monetary authorities’ weight on output variability and interest rate variability. Finally, in Section 10.3.4 we trace out optimal rules using an estimated response surface based on counterfactual simulations over a grid range of weights in the instrument rule and with varying parameters in the loss function.

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