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# Explanatory Notes - Growth rates

OVERVIEW

Growth rates measure the rate of increase/decrease in a series from one period to the next.  The growth rate is calculated by dividing the ‘change’ or ‘flow’ for each period (i.e. month or quarter) (see definitions of ‘Changes’) by the level in the previous period.  Longer period growth rates are calculated by concatenating the one‑month rates, (rather than dividing the flow for these longer periods by the opening level) to avoid distortions where there are breaks in the series, see ‘Revisions’.

GROWTH RATE FORMULAE

Each of the following examples are for June 2006 M4 as shown in Tables A2.1.1 and A2.2.1 of Monetary and Financial Statistics.  The figures shown in the three, six and twelve-month growth rate examples are rounded but calculations are performed on un-rounded data.

One-month growth rate (in per cent):

For example June 2006 M4 (sa) (data shown in Tables A2.1.1 and A2.2.1):

Y =  =  1.5%

Three-month (annualised) growth rate:

where

For example June 2006 M4 (sa) (data shown in Tables A2.1.1 and A2.2.1):

((1.015*1.007*1.013)4-1)*100 = 14.6%

Six-month (annualised) growth rate:

For example June 2006 M4 (sa) (data shown in tables A2.1.1 and A2.2.1):

((1.015*1.007*1.013*1.010*1.011*1.007)2-1)*100 = 13.1%

Twelve-month growth rate:

For example June 2006 M4 (sa) (data shown in Tables A2.1.1 and A2.2.1):

((1.015*1.007*1.013*1.010*1.011*1.007*1.012*1.012*1.012*1.015-1.001*1.014)-1)*100 = 13.5%

Quarterly growth rates

In April 2007 the Bank changed the method it uses to compute quarterly growth rates. Where the underlying data are only available quarterly (say if they are collected on returns which are only reported quarterly), the method is as described above. So for instance, the four-quarter growth rate of lending to agriculture and fishing in table C1.3 is calculated as

where the  are the last four one-quarter growth rates.

However, where there are monthly and quarterly versions of the same series (say if the data are collected on monthly returns, but there is interest in both monthly and quarterly growth rates, and both are published), the quarterly growth rate is defined in terms of the monthly to ensure consistency between the two. In particular, the one-quarter growth rate of such series is defined to be exactly the same as the three-month growth rate of the monthly series, and the four-quarter growth rate is defined to be exactly the same as the twelve-month growth rate of the same series. This means that for any underlying series (say M4) there is a single annual growth rate, and this is unaffected by whether the data are presented in monthly or in quarterly form.

FURTHER INFORMATION