In our central forecast, interest rates are assumed to evolve in line with financial market expectations. For alternative economic scenarios which involve different paths for the output gap and inflation, it is useful to specify rules for the way monetary policy is set and for how output and employment will respond. In this box, we set out the rules that governed those relationships in the scenarios we analysed in the March 2011 Economic and fiscal outlook: a persistent inflation scenario and a weak euro scenario.

In our central forecast, interest rates are assumed to evolve as financial markets expect. These expectations are calculated from forward curves published on the Bank of England’s website and are derived from a number of financial market instruments.a In the November 2010 Outlook, the economic scenarios we presented featured broadly unchanged output gap and inflation projections relative to the central forecast. However, for the scenarios we present here, it is useful to specify simple rules for the way monetary policy is set and for how output and employment respond. To this end, we use three very simple rules: the Taylor rule, a simple aggregate demand relation and Okun’s law.

In its simplest form, the Taylor rule relates the interest rate to a natural nominal interest rate, the current deviation of the rate of Consumer Prices Index (CPI) inflation from target and the output gap.b Here we use the original coefficients from Taylor’s 1993 study and decompose the nominal rate into inflation and the real natural rate:

it = ir* + πt + 0.5(πt – π*) + 0.5(yt – yt*)

Where it is the policy rate at time t, ir* is the real natural interest rate, πt is the rate of CPI inflation, π* is the inflation target, yt is the level of output and is the yt* estimated potential level of output. The difference between the level of output and potential output is known as the output gap.

We take differences of this rule relative to the central forecast to arrive at marginal responses to deviations from the central forecast. It is assumed that the inflation target and the real natural interest rate are the same in both the scenario and the central forecast – superscript s denotes a variable relates to the scenario.

its – it = 1.5(πts – πt) + 0.5[(yts – yts*)-(yt – yt*)]

This expression indicates that if inflation is one percentage point higher under an alternative scenario, the Bank will set interest rates 1.5 percentage points higher than in the central forecast – a coefficient above unity ensures that the Bank returns inflation to target. If the output gap is 1 percentage point wider than in the central forecast, the Bank will set interest rates 0.5 percentage points lower under an alternative scenario.

Output responses to monetary policy are assumed consistent with a very simple aggregate demand equation:

yt = yt-1 – βi (it – πt – ir*)

The variables have the same interpretation as above and the β coefficient represents the sensitivity of output to deviations of the real interest rate from the real natural rate.

Again, taking differences relative to the central forecast:

yts – yt = (yt-1s – yt-1) + βi[(it – πt) – (its– πts)]

This expression indicates that the difference in output between the scenario and the central forecast is a function of the real interest rate differential in the current period and the output differential in the preceding period.

The beta coefficient gives the sensitivity of output to real interest rates. We assume a one percentage point increase in interest rates takes around 6 months to have its maximum impact on output of around -0.3 percentage points.

The output gap is assumed to have an effect on unemployment consistent with Okun’s law.c Unemployment in the scenario rises by around half a per cent for a one percentage point wider output gap relative to the central forecast.