There are a number of different conventions used in expressing growth rates in the economics and statistics literature, which typically vary according to data frequencies and the reference period over which growth is being measured. In the Economic Outlook text and tables, growth rates are carefully qualified in the text accordingly and are always expressed at annual rates, as defined below:
The rate of growth a variable Y for a given quarter q of year t, is calculated as the rate of growth between quarter, q and the previous quarter, expressed at an annual rate. Mathematically this can be expressed as:
(1) G[Yt,q ] = 100[(Yt,q/ Yt,q-1)4 - 1]
where Yt,q and Yt,q-1 represent the values of variable Y in quarters q and q-1 of year t.
The annual year-on-year growth rate of a variable for year t is calculated as the percentage change in annual values of the variable since the previous year, t-1. Mathematically the annual growth of variable Y for year t can therefore be expressed as :
(2) G[Yt] = 100*(Yt/Yt-1 - 1)
where Yt and Yt-1 represent the annual levels of variable Y in years t and t-1.
Note that formulae (1) and (2) necessarily imply that the year-on-year growth rate for year t is not the average of quarterly growth rates within year t, which gives no weight to growth prior to the first quarter of the year in question.
The fourth quarter year-on-year growth rate for year t, also shown in a number of Annex Tables, is calculated as the rate of growth between the fourth quarters of the current and previous years t and t-1. Mathematically the fourth quarter year-on-year growth of variable Y for year t can therefore be expressed as:
(3) G[Yt,4 ] = 100(Yt,4/Yt-1,4 - 1)
where Yt,4 and Yt-1,4 represent the values of variable Y in the 4th quarters of years t and t-1.