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6440.0 - A Guide to the Consumer Price Index: 16th Series, 2011  
Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 26/10/2011   
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USING THE CPI


CPI movements over the past 60 years
Graph: Graph shows CPI percentage change from 1948 to 2011


INTERPRETING INDEX NUMBERS

Why use index numbers?

3.1 Deriving useful price measures for single, specific items such as Granny Smith apples is a relatively straightforward exercise. An estimate of the average price per kilogram in each period is sufficient for all applications. Price change between any two periods would simply be calculated by direct reference to the respective average prices.

3.2 However, if the requirement is for a price measure that covers a number of diverse items, the calculation of a 'true' average price is both complicated and of little real meaning. For example, consider the problem of calculating and interpreting an average price for two commodities as diverse as apples and motor vehicles. Because of this, price measures such as the CPI are typically presented in index number form.


Description of a price index

3.3 Price indexes provide a convenient and consistent way of presenting price information that overcomes problems associated with averaging across diverse items. The index number for a particular period represents the average price in that period relative to the average price in some base period for which, by convention, the average price has been set to equal 100.0.

3.4 A price index number on its own has little meaning. For example, the CPI All groups index number of 179.4 in the September quarter 2011 says nothing more than the average price in the September quarter 2011 was 79.4% higher than the average price in the base year 1989–90 (when the index was set to 100.0). The value of index numbers stems from the fact that index numbers for any two periods can be used to directly calculate price change between the two periods.


Percentage change is different to a change in index points

3.5 Movements in indexes from one period to any other period can be expressed either as changes in index points or as percentage changes. The following example illustrates these calculations for the All groups CPI (weighted average of the eight capital cities) between the September quarter 2010 and the September quarter 2011. The same procedure is applicable for any two periods.

Index number
September quarter 2011
179.4
less September Quarter 2010
173.3
Change in index points
6.1
Percentage change
6.1/173.3 x 100 = 3.5%



Movements in the CPI best measured using percentage changes

3.6 For most applications, movements in price indexes are best calculated and presented in terms of percentage change. Percentage change allows comparisons in movements that are independent of the level of the index. For example, a change of 2 index points when the index number is 120 is equivalent to a percentage change of 1.7%, but if the index number was 80 a change of 2 index points would be equivalent to a percentage change of 2.5% – a significantly different rate of price change. Only when evaluating change from the base period of the index will the points change be numerically identical to the percentage change.


Percentage changes are not additive

3.7 The percentage change between any two periods must be calculated, as in the example above, by direct reference to the index numbers for the two periods. Adding the individual quarterly percentage changes will not result in the correct measure of longer–term percentage change. That is, the percentage change between say the June quarter one year and the June quarter of the following year typically will not equal the sum of the four quarterly percentage changes. The error becomes more noticeable the longer the period covered and the greater the rate of change in the index. This can readily be verified by starting with an index of 100 and increasing it by 10% (multiplying by 1.1) each period. After four periods, the index will equal 146.4 delivering an annual percentage change of 46.4%, not the 40% given by adding the four quarterly changes of 10%.


Calculating index numbers for periods longer than quarters

3.8 Although the CPI is compiled and published as a series of quarterly index numbers, its use is not restricted to the measurement of price change between particular quarters. Because a quarterly index number can be interpreted as representing the average price during the quarter, index numbers for periods spanning more than one quarter can be calculated as the simple (arithmetic) average of the relevant quarterly indexes. For example, an index number for the year 2010 would be calculated as the arithmetic average of the index numbers for the March, June, September and December quarters of 2010.

Index number
March quarter 2010
171.0
June quarter 2010
172.1
September quarter 2010
173.3
December quarter 2010
174.0
Divided by
4.0
equals CPI Index 2010
172.6

This characteristic of index numbers is particularly useful. It allows for comparison of average prices in one year (calendar or financial) with those in any other year. It also enables prices in say the current quarter to be compared with the average prevailing in some prior year.


ANALYSING THE CPI

3.9 The quarterly change in the All groups CPI represents the weighted average price change of all the items included in the CPI. While publication of index numbers and percentage changes for components of the CPI are useful in their own right, these data are often not sufficient to enable important contributors to overall price change to be reliably identified. What is required is some measure that encapsulates both an item’s price change and its relative importance in the index.


Points contribution and points contribution change

3.10 If the All groups index number is thought of as being derived as the weighted average of indexes for all its component items, the index number for a component multiplied by its weight to the All groups index results in what is called its ‘points contribution’. It follows that the change in a component item’s points contribution from one period to the next provides a direct measure of the contribution to the change in the All groups index resulting from the change in that component’s price.

3.11 Information on points contribution and points contribution change (or points change) is of immense value when analysing sources of price change and for answering ‘what if’ type questions. Consider the following data extracted from the September quarter 2011 CPI publication:

Index number
Percentage change
Points contribution
Points change
Item
June qtr 2011
Sept qtr 2011
June qtr 2011
Sept qtr 2011
All groups
178.3
179.4
0.6
178.3
179.4
1.1
Electricity
248.4
267.7
7.8
3.55
3.83
0.28


Using points contributions

3.12 Using only the index numbers themselves, the most that can be said is that between the June and September quarters 2011, the price of Electricity increased by more than the overall CPI (by 7.8% compared with an increase in the All groups of 0.6%). The additional information on points contribution and points change can be used to:

a) Calculate the effective weight for Electricity in the June and the September quarters (given by the points contribution for Electricity divided by the All groups index). For the June quarter, the weight is calculated as 3.55/178.3 x 100 = 2.0% and for the September quarter is 3.83/179.4 x 100 = 2.1%. Although the underlying quantities are held fixed, the effective weight in expenditure terms has increased due to the price of Electricity increasing by more than the prices of all other items in the CPI basket (on average).

b) Calculate the percentage increase that would have been observed in the CPI if all prices other than those for Electricity had remained unchanged (given by the points change for Electricity divided by the All groups index number in the previous period). For the September quarter 2011 this is calculated as 0.28/178.3 x 100 = 0.16%. In other words, a 7.8% increase in Electricity prices in September quarter 2011 would have resulted in an increase in the overall CPI of 0.2%.

c) Calculate the average percentage change in all other items excluding Electricity (given by subtracting the points contribution for Electricity from the All groups index in both quarters and then calculating the percentage change between the resulting numbers which represents the points contribution of the ‘other’ items). For the above example, the numbers for All groups excluding Electricity are: June quarter 2011, 178.3–3.55 = 174.8; September quarter 2011, 179.4–3.83 = 175.6; and the percentage change (175.6–174.8)/174.8 x 100 = 0.5%. In other words, prices of all items other than Electricity increased by 0.5% on average between the June and September quarters 2011.

d) Estimate the effect on the All groups CPI of a forecast change in the prices of one of the items (given by applying the forecast percentage change to the item's points contribution and expressing the result as a percentage of the All groups index number). For example, if the price of Electricity was forecast to increase by 25% in the December quarter 2011, then the points change for Electricity would be 3.83 x 0.25 = 1.0, which would deliver an increase in the All groups index of 1.0/179.4 x 100 = 0.6% . In other words, a 25% increase in the Electricity price in the December quarter 2011 would have the effect of increasing the CPI by 0.6%. Another way commonly used to express this impact is ‘Electricity’ would contribute 0.6 percentage points to the change in the CPI.


ABS rounding conventions

3.13 To ensure consistency in the data produced from the CPI, it is necessary for the ABS to adopt a set of consistent rounding conventions or rules for the calculation and presentation of data. The conventions strike a balance between maximising the usefulness of the data for analytical purposes and retaining a sense of the underlying precision of the estimates. These conventions need to be taken into account when using CPI data for analytical or other special purposes.

3.14 Index numbers are always published to a reference base of 100.0. Index numbers and percentage changes are always published to one decimal place, with the percentage changes being calculated from the rounded index numbers. Points contributions are published to two decimal places, with points contributions change being calculated from the rounded points contributions. Index numbers for periods longer than a single quarter (e.g. for financial years) are calculated as the simple arithmetic average of the relevant rounded quarterly index numbers.


SOME EXAMPLES OF USING THE CPI

The following questions and answers illustrate the uses that can be made of the CPI. For more information about which index to use in contracts see 'Use of Price Indexes in Contracts' at
http://www.abs.gov.au/websitedbs/c311215.nsf/web/Inflation+and+Price+Indexes.


CPI can be used to compare money values over time

3.15 Question 1: What would $200 in 2005 be worth in the September quarter 2011?

3.16 Response 1: This question is best interpreted as asking ‘How much would need to be spent in the September quarter 2011 to purchase what could be purchased in 2005 for $200?’ As no specific commodity is mentioned, what is required is a measure comparing the general level of prices in the September quarter 2011 with the general level of prices in the calendar year 2005. The All groups CPI would be an appropriate choice.

3.17 Because CPI index numbers are not published for calendar years, two steps are required to answer this question. The first is to derive an index for the calendar year 2005. The second is to multiply the initial dollar amount by the ratio of the index for September quarter 2011 to the index for 2005.

3.18 The index for the calendar year 2005 is obtained as the simple arithmetic average of the quarterly indexes for March (147.5), June (148.4), September (149.8) and December (150.6) 2005 giving 149.1 rounded to one decimal place. The index for the September quarter 2011 is 179.4.
The answer is then given by:

$200 x 179.4/149.1 = $240.64


Forecasting impact of price changes on the CPI

3.19 Question 2: What would be the impact of a 10% increase in vegetable prices on the All groups CPI in the December quarter 2011?

3.20 Response 2: Two pieces of information are required to answer this question; the All groups index number for the September quarter 2011 (179.4), and the September quarter 2011 points contribution for Vegetables (2.33).

3.21 An increase in vegetable prices of 10% would increase vegetables points contribution by 2.33 x 10/100 = 0.23 index points which would result in an All groups index number of 179.6 for the December quarter 2011, an increase of 0.2%.


Indexes used should be representative of specific items

3.22 Question 3: How does the CPI reflect changes in electricity prices?

3.23 Response 3: The All groups CPI measures price change for all goods and services. In Table 4 of Consumer Price Index, Australia (cat. no. 6401.0) there is a range of component indexes by capital city which can be used. The example below sets out the price change for electricity compared to the All groups CPI over the last 10 years. This shows that the price of electricity has increased faster than the headline number.

All groups CPI index number
Electricity index number
September quarter 2001
134.2
133.8
September quarter 2010
173.3
237.9
September quarter 2011
179.4
267.7
Percentage change – 1 year ago
(179.4 – 173.3)/173.3 x 100
= 3.5%
(267.7 – 237.9)/237.9 x 100
= 12.5%
Percentage change – 10 years ago
(179.4 – 134.2)/134.2 x 100
= 33.7%
(267.7 – 133.8)/133.8 x 100
= 100.1%

Price indexes can be used to estimate changes in volumes

3.24 Question 4: Household Expenditure Survey data show that average weekly expenditure per household on Food and non–alcoholic beverages increased from $158.58 in 2003–04 to $216.40 in 2009–10 (i.e. an increase of 36.5%). Does this mean that households, on average, purchased 36.5% more Food and non–alcoholic beverages in 2009–10 than they did in 2003–04?

3.25 Response 4: This is an example of one of the most valuable uses that can be made of price indexes. Often the only viable method of collecting and presenting information about economic activity is in the form of expenditure or income in monetary units (e.g. dollars). While monetary aggregates are useful in their own right, economists and other analysts are frequently concerned with questions related to volumes, for example, whether more goods and services have been produced in one period compared with another period. Comparing monetary aggregates alone is not sufficient for this purpose as dollar values can change from one period to another due to either changes in quantities or changes in prices (most often a combination).

3.26 To illustrate this, consider a simple example of expenditure on oranges in two periods. The product of the quantity and the price gives the expenditure in any period. Suppose that in the first period 10 oranges were purchased at a price of $1.00 each and in the second period 15 oranges were purchased at a price of $1.50 each. Expenditure in period one would be $10.00 and in period two $22.50. Expenditure has increased by 125%, yet the volume (number of oranges) has only increased by 50% with the difference being accounted for by a price increase of 50%. In this example all the price and quantity data are known, so volumes can be compared directly. Similarly, if prices and expenditures are known, quantities can be derived.

3.27 But what if the actual prices and quantities are not known? If expenditures are known and a price index for oranges is available, the index numbers for the two periods can be used as if they were prices to adjust the expenditure for one period to remove the effect of price change. If the price index for oranges was equal to 100.0 in the first period, the index for the second period would equal 150.0. Dividing expenditure in the second period by the index number for the second period and multiplying this result by the index number for the first period provides an estimate of the expenditure that would have been observed in the second period had the prices remained as they were in the first period. This can easily be demonstrated by reference to the oranges example:

$22.50/150.0 x 100.0 = $15.00 = 15 x $1.00

3.28 So, without ever knowing the actual volumes (quantities) in the two periods, the adjusted second period expenditure ($15.00), can be compared with the expenditure in the first period ($10.00) to derive a measure of the proportional change in volumes $15/$10 = 1.50, which equals the ratio obtained directly from the comparison of the known quantities.

3.29 We now return to the question on expenditure on Food and non–alcoholic beverages recorded in the HES in 2003–04 and 2009–10. As the HES data relates to the average expenditure of Australian households, the ideal price index would be one that covers the retail prices of Food and non–alcoholic beverages for Australia as a whole. The price index which comes closest to meeting this ideal is the index for the Food and non–alcoholic beverages of the CPI for the weighted average of the eight capital cities. The Food and non–alcoholic beverages index number for 2003–04 is (149.3+152.0+154.7+153.3)/4 = 152.3 and for 2009–10 it is (186.6+189.9+191.3+190.7)/4 = 189.6. Using these index numbers, recorded expenditure in 2009–10 ($216.40) can be adjusted to 2003–04 prices as follows:

$216.40/189.6 x 152.3 = $173.82

Food and non–alcoholic beverages
2003–04
2009–10
HES expenditure
$158.58
$216.40
Food and non–alcoholic beverages price index number
152.3
189.6
revalued 2009–10 quantities at 2003–04 prices
$158.58
$173.83
Volume change ($173.83 – $158.58)/$158.58 x 100
9.6%


3.30 The revalued 2009–10 quantities at 2003–04 prices of $173.82 can then be compared to the expenditure recorded in 2003–04 ($158.58) to deliver an estimate of the change in volumes. This indicates a volume increase of 9.6% between 2003–04 and 2009–10. Over the same period food prices increased (189.6 – 152.3)/152.3 x100 = 24.5% and total expenditure (($216.40 – $158.58)/$158.58 x 100) increased 36.5%,

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