The meaning of percentage changes
Many of the time series statistics presented in Monthly Economic and
Social Indicators include tables and graphs of annual, quarterly and
monthly percentage changes.
Examples of tables include the ANZ Job Advertisements Series, Consumer
Price Index and Dwelling Approvals. Annual percentage changes are graphed
for such statistics as Average Weekly Earnings, Gross Domestic Product
and Turnover of Retail Establishments.
How are these figures calculated? What do they mean? And how can they
be used to better interpret economic and social activity in Australia?
Calculating percentage changes
The percentage change between two values in a time series is calculated
by finding the difference between those two values then dividing that
difference by the starting value and multiplying by 100.
For example the number of dwelling units approved in Australia in May
1997 was 12 263 and in May 1998 was 13 256. The annual percentage
change is thus
(13256 - 12263) / 12263 x 100 = 8.1%
It is crucial to note that percentage changes are always relative to
a starting value. Thus a series which increases from a starting value
of 100 to a final value of 200 has increased by 100% thus
(200 - 100) / 100 x 100 = 100.0%
If this series then declines from 200 to 100 again this percentage change
is relative to the new starting value of 200 and is thus equal to -50%
not -100% as could be imagined. Thus
(100 - 200) / 200 x 100 = -50.0%
Significance of percentage changes
Because they only use the information from two time periods percentage
changes can show only the growth rate between the two periods concerned.
Percentage changes are positive-greater than zero-when the series of
numbers is growing. Large positive changes show that the series is growing
rapidly or strongly. Small positive changes show that the series is growing
steadily or weakly.
Percentage changes are negative-less than zero-when the series of numbers
is declining. Large negative changes show that the series is declining
rapidly or strongly. Small negative changes show that the series is declining
steadily or weakly.
Figure 1 shows average annual percentage change in dwelling approvals
in the period since June 1993. It shows that in December 1997 dwelling
approvals were growing at 21.8%. This means that in December 1997 building
approvals increased strongly over the corresponding month in the year
before. Similarly in October 1995 dwelling approvals were changing at
-36.4%. This means that in October 1995 building approvals had declined
strongly compared to the previous October.
Changes in percentage changes
A percentage changes series that is positive and getting bigger implies
that the actual series is growing at a faster rate as time passes, ie
the actual series is accelerating and economic activity is picking up.
A percentage changes series that is positive and getting smaller implies
that although the main series is growing it is growing at a slower rate
as time passes.
A percentage changes series that is negative and becoming more negative
implies that the main series is declining at a greater rate as time passes.
A percentage changes series that is negative and becoming less negative
implies that although the actual series is declining it is declining at
a slower rate as time passes.
For dwelling approvals shown in Figure 2, in the period from November
1994 building approvals were declining and declining at an ever increasing
rate. That decline slowed from October 1995. From that time building approvals
were still declining but at a slower rate as the time approached the end
of 1996. From October 1996 building approvals have been increasing relatively
strongly but that increase has not been consistent.
Further information
Further information can be obtained by contacting a member of the Statistics
Group, Information and Research Services, Department of the Parliamentary
Library.
This feature was prepared by Greg Baker.
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