# The meaning of percentage changes

##### Monthly Statistical Bulletin Feature Articles

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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