A Guide to the Consumer Price Index: 17th Series

2.1 The 17th series Consumer Price Index (CPI), consistent with the 13th, 14th, 15th and 16th series, has been designed as a general measure of price inflation for the household sector as a whole. The CPI measures changes in the price of a fixed quantity of goods and services acquired by consumers in metropolitan private households.

2.2 The simplest way of thinking about the CPI is to imagine a basket of goods and services comprising items bought by Australian households. Now imagine the basket is purchased each quarter. As prices change from one quarter to the next, so too will the total price of the basket. The CPI is simply a measure of the changes in the price of this basket as the prices of items in it change.

2.3 The CPI measures price changes relating to the spending pattern of all metropolitan private households. This group is termed 'the CPI population group', and includes a wide variety of sub-groups such as wage and salary earners, the self-employed, self-funded retirees, age pensioners, and social welfare beneficiaries. The term 'metropolitan' means the six State capital cities, and the Territory capitals of Darwin and Canberra. The current series CPI population group represents about 65% of all Australian private households.

2.4 Ideally the CPI population group should encompass all Australian households, but this is not possible due to the substantial additional resources that would be required to collect prices outside the capital cities. ABS research has shown that, in general, price movements (as distinct from price levels) are similar across regions.

2.5 The price of the CPI basket in the index reference period is expressed as an index by assigning it a value of 100.0. The prices in other periods are expressed as percentages of the price in this period. For example, if the price of the basket had increased by 35% since the reference period, then the index would be 135.0; similarly, if the price had fallen by 5%, the index would stand at 95.0. The current index reference period for the CPI is 2011-2012.

2.6 It is important to remember that the CPI measures price movements (i.e. percentage changes) and not actual price levels (dollar amounts). For instance, the index for Breakfast cereals of 92.4 and the index for Bread of 96.1 in the December quarter 2017 does not mean that Bread is more expensive than Breakfast cereals. It simply means that the price of Bread has risen by more than the price of Breakfast cereals since the index reference period.

2.7 The CPI is frequently called a cost-of-living index, but it differs in important ways from a complete cost-of-living measure. Both the CPI and a cost-of-living index measure the changes in prices of goods and services that are purchased by households. The Australian CPI measures the changes in price of a fixed basket of goods and services whereas a cost-of-living index measures the change in the minimum expenditure needed to maintain a certain standard of living.

2.8 In practice, no statistical agencies compile true cost-of-living or purchasing power measures as it is too difficult to do. A cost-of-living index requires access to both price and current household consumption each period as well as an assessment of households' welfare which depends on a variety of physical and social factors that have no connection with prices. As the CPI is intended to measure the overall inflation in prices of goods and services acquired by Australian households, it is sometimes used as a proxy measure of cost-of-living or purchasing power.

2.9 As a single index cannot be expected to adequately fulfil all purposes, and in recognition of the widespread interest in the extent to which the impact of price change varies across different groups in the community, the ABS compiles and publishes the Analytical Living Cost Indexes (ALCIs) and the Pensioner and Beneficiary Living Cost Index (PBLCI), collectively known as the Selected Living Cost Indexes (SLCIs) (cat. no. 6467.0). These indexes are specifically designed to measure changes in living costs for selected population sub-groups and are particularly suited for assessing whether or not the disposable incomes of households have kept pace with price changes. The SLCIs are produced as a by-product of the CPI with the main conceptual difference being that the SLCIs are constructed on an outlays basis, and the CPI on an acquisitions basis.

2.10 The most notable difference between these indexes and the CPI is that the living cost indexes include interest charges but do not include new house purchases, while the CPI includes new house purchases but does not include interest charges. Households in the SLCIs have been categorised based on the principal source of household income, derived from the 2015-16 Household Expenditure Survey (HES). The four household types in scope of these indexes account for over 90% of Australian households. They are:

• employee households (i.e. those households whose principal source of income is from wages and salaries);
• age pensioner households (i.e. those households whose principal source of income is the age pension or veterans affairs pension);
• other government transfer recipient households (i.e. those households whose principal source of income is a government pension or benefit other than the age pension or veterans affairs pension); and
• self-funded retiree households (i.e. those households whose principal source of income is superannuation or property income and where the HES defined reference person is ‘retired’ (not in the labour force and over 55 years of age)).
   

2.11 The scope of the PBLCI is households whose principal source of income is from government pensions and benefits (i.e. age pensioner and other government transfer recipient households).

2.12 The CPI affects almost all Australians because of the many ways in which it is used. The two most common uses of the CPI are:

• as a macroeconomic indicator. The CPI, and other index series derived from CPI data, are used by the Government and economists to monitor and evaluate levels of inflation in the Australian economy. Inflation and inflationary expectations play a major role in determining various aspects of Government economic policy, and in the business and investment decisions of private firms and individuals.
• as a means of maintaining dollar values. The value of many types of fixed payments such as social welfare benefits can be reduced over time when prices rise. The CPI is often used to adjust these payments to counter the effects of inflation. This process is referred to as 'indexation'. Indexation arrangements are also often applied to such things as rental agreements, insurance cover and child support payments.
   

2.13 Although the CPI is the best known price index, it is but one of many produced by the ABS. Examples of other price indexes include:

• selected living cost indexes (SLCIs);
• producer price indexes (PPI);
• international trade price indexes (ITPI);
• wage price indexes (WPI);
• residential property price indexes (RPPI); and
• chained price indexes produced in conjunction with the Australian National Accounts.
   

2.14 Having determined that a price index is required for a particular application, it is important to carefully consider the range of available indexes and select the index which best meets the specific requirement. While the ABS can provide technical and statistical guidance, it does not provide advice on indexation practices and it cannot tell users which index they should use. These are matters for users to determine.

2.15 For a general description of the range of issues that should be taken into account by parties considering an indexation clause, see 'Use of Price Indexes in Contracts' at https://www.abs.gov.au/websitedbs/D3310114.nsf/home/Inflation+and+Price+Indexes+-+Use+of+Price+Indexes+in+Contracts

2.16 The composition of the CPI basket is based on the pattern of household expenditure in the 'weight reference period', which is 2015-16 for the 17th series CPI. Information on the spending habits of Australian households during 2015-16 was obtained from the Household Expenditure Survey (HES) conducted by the ABS, as well as from other data sources including National Accounts estimates. The HES results provide the starting point for selecting the basket of goods and services to be priced for the CPI.

2.17 For practical reasons, the basket cannot include every item bought by households but it does include the most significant items. It is not necessary to include all the items people buy since many related items are subject to similar price changes. The idea is to select representative items so that the index reflects price changes for a much wider range of goods and services than is actually priced. Examples of the types of items included in the CPI basket are shown in Appendix 2.

2.18 When determining what items are to be priced for the CPI basket, various factors are taken into consideration. Items:

• must be representative of purchases made by the CPI population group;
• must have prices which can be associated with an identifiable and specific commodity or service (e.g. a 420g can of baked beans, or adult general admission to a club football game); and
• are not excluded on the basis of moral or social judgements. For example, some people may regard the use of tobacco or alcohol as socially undesirable, but both are included in the CPI basket because they are significant items of household expenditure and their prices can be accurately measured.

2.19 Income-based taxes, however, are not included in the CPI because they cannot be clearly associated with the purchase or use of a specific good or service.

2.20 The total basket is divided into 11 major groups, each representing a specific set of commodities:

• Food and non-alcoholic beverages
• Alcohol and tobacco
• Clothing and footwear
• Housing
• Furnishings, household equipment and services
• Health
• Transport
• Communication
• Recreation and culture
• Education
• Insurance and financial services
   

2.21 These groups are divided in turn into 33 sub-groups, and the sub-groups into 87 expenditure classes. An expenditure class is a grouping of similar items, such as various types of motor vehicles. See Appendix 1 for a full list of groups, sub-groups and expenditure classes and the figure at 4.1 for an illustration of the CPI structure.

2.22 The overall (or All groups) CPI provides a measure of the average rate of price change. In calculating an average measure of this type it is necessary to recognise that some items are more important than others. Price changes for the more important items should have a greater influence on the average rate of price change than price changes for less important items. The relative importance of the goods and services in the CPI is determined by the relative household expenditure on each product. For example, how much more households spend on rent than automotive fuel on average.

2.23 Measures of expenditure on each of the CPI groups, sub-groups and expenditure classes were most recently updated with the introduction of the 17th series CPI in the December quarter 2017. The 2015-16 HES was the primary data source for updating the weights. However, some adjustments were made to HES data to account for known instances of underreporting (the most notable being for alcohol and tobacco), as well as scope, coverage and measurement differences. The adjusted HES data were then used to derive a ‘weight’ for each expenditure class.

2.24 The CPI weights reflect the relative expenditures of the CPI population group as a whole and not those of any particular type or size of household. The weights reflect average expenditure of households and not the expenditure of an 'average household'. The household average weekly expenditure and corresponding 17th series CPI relative weights for the CPI groups are shown in Appendix 1.

2.25 Although the weights are expressed in terms of expenditure shares, it is not the expenditure shares (where expenditure is given by the product of quantity and price) that are held constant (or fixed) from period to period. What are held constant are the quantities of products underpinning these expenditures such as the number of litres of petrol purchased each period on average by households. Weights are presented in expenditure terms because it is not possible to present quantity weights in a meaningful way, e.g. the quantity of health services. The relative expenditure shares of items will change over time in response to changes in relative prices.

2.26 While the implicit quantity weights are held constant at the expenditure class level, the weights of items within an expenditure class (e.g. different types of bread) can be varied between periodic reviews to reflect changed purchasing patterns. Any weight changes are introduced into the CPI in such a way as to not affect the level of the index.

2.27 The average household weekly expenditure and weights for the CPI expenditure classes have previously been updated at six-yearly intervals with the timing generally linked to the availability of HES data.

2.28 From the introduction of the 17th series CPI in the December quarter 2017, the expenditure class weights are now updated annually. The HES will continue to be used as the primary data source to re-weight the CPI in the years where it is available, currently six-yearly. In inter-HES years, the principal data source for updating the weights will be Household Final Consumption Expenditure (HFCE) data from the National Accounts. The December quarter 2018 will be the first instance where HFCE data is used as the principal data source for the CPI re-weight. For further information, refer to Information Paper: An Implementation Plan to Annually Re-weight the Australian CPI, 2017 (cat. no. 6401.0.60.005).

2.29 Several modes of collection are used by the ABS to obtain prices for the Australian CPI, including:

• personal visits;
• online and telephone collection; and
• administrative data, including scanner and transactions data.
   

2.30 Personal visits are made by trained and experienced ABS staff, who observe actual marked prices as well as discuss with the retailers matters such as discounts, special offers and volume-selling items on the day. ABS staff record this information on the spot using mobile devices. The regular personal visits also enable ABS staff to continually monitor market developments such as market shares or possible quality changes. This information is used in maintaining the representativeness of the samples and assessing quality change.

2.31 Online pricing represents a more cost effective mode of collection with lower respondent burden compared to pricing through personal visits. As a result, online price collection is increasingly being used as it is becoming more common for prices in store to match the prices listed online. Prices are also collected online where this is the predominant method consumers use to purchase a particular good or service, for example, domestic and international airfares.

2.32 The ABS is increasingly using web scrapers to collect online prices. Web scrapers automatically collect all items and prices on a retailer's website. As the process can be run as frequently as desired, data collected via web scraping represents a 500 fold increase in the number of prices collected compared with manual price collection.

2.33 The ABS is also utilising transactions data as a method of obtaining prices for use in the CPI. Transactions data is high in volume and contains detailed information about individual transactions including: date of purchase, quantities purchased, product descriptions, and value of products purchased.

2.34 Prices are collected in the kinds of retail outlets and other places where metropolitan households purchase goods and services. This involves collecting prices from many sources such as supermarkets, restaurants, department stores, schools and on-line websites.

2.35 From the December quarter 2017, the ABS has introduced a new method to make greater use of transactions data in the CPI. This new method, known as a multilateral index method, utilises a census of products available in big datasets. This has resulted in a significant increase on the number of price observations used to compile the CPI. For further information on this change, see Information Paper: An Implementation Plan to Maximise the Use of Transactions Data in the CPI (cat. no. 6401.0.60.004). In total, almost 900,000 separate price quotations are now being collected each quarter.

2.36 Although the CPI is compiled quarterly, the frequency of price collection varies. Prices of goods and services that are considered to be volatile (i.e. likely to change more than once during a quarter) are collected more frequently. In the case of transactions data, revenue and quantity data are collected on a weekly basis. A small number of items are priced only once a year, either because that is the known frequency that prices are reviewed (e.g. council property rates) or because of seasonal availability (e.g. football matches). The general approach is to price each item as frequently as is necessary to ensure that reliable measures of quarterly price change can be calculated.

2.37 The prices used in the CPI are those that any member of the public would have to pay to purchase the specified good or service. Any taxes levied on goods or services (such as the GST) are included in the CPI price. Similarly, prices are adjusted by any subsidy or assistance provided directly by the government (e.g. Child Care Benefit, Medicare). Sale prices, discount prices and 'specials' are reflected in the CPI so long as the items concerned are of normal quality (i.e. not damaged or shopsoiled), and are offered for sale in reasonable quantities. Any concessions available to particular groups of the population (such as age pensioners) are also taken into account where significant. Where an item is priced over the internet, any delivery or processing charges payable are included in the price.

2.38 To ensure that price movements are representative of the experiences of metropolitan households, the brands and varieties of the goods and services which are priced are generally those which sell in greatest volume.

2.39 In concept, quality embraces all the attributes of an item which consumers would consider before making a purchase. For example in the case of tinned tomato soup, it would include the volume or weight of the contents, as well as the concentration and flavor.

2.40 As the CPI aims to measure pure price change over time, identical or equivalent items should ideally be priced in successive periods. However, products do change; their components or ingredients may change resulting in an improvement or degradation in quality. As the characteristics of products are altered, the statisticians responsible for the price index attempt to separate the effects of a quality change from any underlying price changes so that the CPI measures 'pure' price change. A simple example of quality adjustment is shown in paragraphs 2.52 to 2.54.

2.41 The requirement to take account of changes in quality, to ensure that the index reflects only pure price change, often poses difficult measurement problems and in some cases is impossible in practice. For example, while it is easy to monitor changes in rail or bus ticket prices, it is difficult to attach a dollar value to changes in the quality (e.g. frequency or punctuality of the service).

2.42 Like any other long-standing and important statistical series, the CPI is reviewed periodically to ensure that it continues to meet community needs. Beginning with the introduction of the 17th series in December quarter 2017, the CPI is reviewed on an annual basis in December quarters.

2.43 An important objective of these reviews is to update item weights to reflect changes in the range of available goods and services and changes in household spending patterns. They also provide an opportunity to reassess the scope and coverage of the index and other methodological issues.

2.44 Following these reviews, the new CPI series is linked to the old to form a continuous series. This linking is carried out in such a way that the resulting continuous series reflects only pure price change and not differences in the cost of the old and new baskets.

2.45 The index reference period for the CPI is also updated, but at less frequent intervals. Changes in index reference periods have no effect (other than rounding) on percentage changes, which are calculated from the index numbers.

2.46 The most recent 17th series review was a minor review of CPI, consisting of an update of the expenditure class weights in line with the 2015-16 HES, and a simple examination of structures and methodologies. For more information on the changes resulting from the 17th series review, see Information Paper: Introduction of the 17th Series Australian Consumer Price Index, 2017 (cat. no. 6470.0.55.001).

2.47 The CPI is designed to measure changes in retail prices experienced by metropolitan private households in aggregate. The composition of the basket and the relative importance of items in it relate to this population group as a whole - it represents the expenditures of all inscope households, not the expenditure pattern of the average household or of any particular household type or size. The basket comprises all consumer goods and services acquired over a twelve month period. It includes items acquired infrequently by an individual household (e.g. major electrical appliances, new motor vehicles), items that are acquired almost daily by all households (e.g. bread and milk) and items that are only available at certain times of the year. The basket includes, for example, both rent payments of renting households and the amounts paid by owner-occupier households for the purchase of their principal residence - clearly no individual household can incur both expenses at the same time. Therefore, changes in the CPI are unlikely to reflect exactly the price experience of any particular household.

2.48 The CPI does not measure those changes in living costs which may be experienced by individual households as a direct consequence of their progression through the life cycle. For example younger households may incur a higher proportion of their expenditure on housing and child care while those households entering the older age groups may incur increasing expenditure on medical services. However, changes in the demographic make-up of households in aggregate and differences in expenditure patterns will affect the pattern of total household expenditure recorded in the HES. In turn, these changes will be incorporated in the weighting pattern in the CPI.

2.49 The CPI is not designed to measure price levels; rather its purpose is to measure changes in prices over time. While price levels in country regions often differ from those in metropolitan areas (some higher and others lower), the factors influencing price movements generally tend to be similar. Therefore the CPI can be expected to provide a reasonable indication of the changes in prices in Australia as a whole over the longer term.

2.50 Similarly, the CPI cannot be used to compare price levels between capital cities. For example, the fact that the CPI All groups index in the December quarter 2017 for Melbourne (112.3) was higher than in Adelaide (111.2) does not indicate that Melbourne was more expensive to live in than Adelaide. Rather, it indicates that prices in Melbourne have risen more than in Adelaide since the reference period (2011-12).

2.51 At the end of the day, the CPI is most useful as an indicator of price movements, whether it be for specific items, a particular city, or the economy as a whole. The CPI is not a precise measure of individual household price experiences.

2.52 To illustrate the process used to adjust for changes in the quality of items priced in the CPI, consider the case of a change in the size of a can of tomato soup. In this example, Acme brand tomato soup is priced in three periods (1, 2 and 3) and the size of the can is reduced from 440gms to 400gms between period 2 and period 3:
 

Using the observed prices produces the following measures of price change:

Percentage change from period 1 to period 2 = (2.78 - 3.09)/3.09 x 100 = -10.0%
Percentage change from period 2 to period 3 = (2.85 - 2.78)/2.78 x 100 = 2.5%
Percentage change from period 1 to period 3 = (2.85 - 3.09)/3.09 x 100 = -7.8%.

2.53 However, this does not provide a measure of 'pure price' change because the item priced in period 3 is not identical to the item priced in the previous periods. What is required for period 3 is the 'price that would have been paid for the item that was priced in period 2'. This price can be estimated by adjusting the period 3 price by the ratio of the item's weight in period 2 to its weight in period 3, giving a quality adjusted price of $3.14 ($2.85 x 440/400).

Using this adjusted price in period 3 results in the following correct measures of price change:

Percentage change from period 1 to period 2 = (2.78 - 3.09)/3.09 x 100 = -10.0%
Percentage change from period 2 to period 3 = (3.14 - 2.78)/2.78 x 100 = 12.9%
Percentage change from period 1 to period 3 = (3.14 - 3.09)/3.09 x 100 = 1.6%

2.54 After adjusting for the reduction in quality between periods 2 and 3, the rise in the observed price of 2.5% has been translated into a pure price increase of 12.9%. Similarly, the measure of price change between periods 1 and 3 has been changed from a fall of 7.8% to a rise of 1.6%.

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.

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 reference 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 112.1 in the December quarter 2017 says nothing more than the average price in the December quarter 2017 was 12.1 per cent higher than the average price in the reference year 2011-12 (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.

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 December quarter 2016 and the December quarter 2017. The same procedure is applicable for any other two periods.

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.

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%.

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 2017 would be calculated as the arithmetic average of the index numbers for the March, June, September and December quarters of 2017.

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.

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.

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 December quarter 2017 CPI publication:

3.12 Using only the index numbers themselves, the most that can be said is that between the September and December quarters 2017, the price of Automotive fuel increased by more than the overall CPI (by 10.4% 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 Automotive fuel in the September and the December quarters (given by the points contribution for Automotive fuel divided by the All groups index). For the September quarter, the weight is calculated as 3.10 / 111.4 x 100 = 2.8% and for the December quarter is 3.42 / 112.1 x 100 = 3.1%. Although the underlying quantities are held fixed, the effective weight in expenditure terms has increased due to the price of Automotive fuel 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 Automotive fuel had remained unchanged (given by the points change for Automotive fuel divided by the All groups index number in the previous period). For the December quarter 2017 this is calculated as 0.32 / 111.4 x 100 = 0.29%. In other words, a 10.4% increase in Automotive fuel prices in December quarter 2017 would have resulted in an increase in the overall CPI of 0.3%.

c) Calculate the average percentage change in all other items excluding Automotive fuel (given by subtracting the points contribution for Automotive fuel 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 Automotive fuel are: September quarter 2017, 111.4-3.10 = 108.3; December quarter 2017, 112.1-3.42 = 108.7; and the percentage change (108.7-108.3)/108.3 x 100 = 0.4%. In other words, prices of all items other than Automotive fuel increased by 0.4% on average between the September and December quarters 2017.

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 Automotive fuel was forecast to increase by 25% in the March quarter 2018, then the points change for Automotive fuel would be 3.42 x 0.25 = 0.9, which would deliver an increase in the All groups index of 0.9/112.1 x 100 = 0.8% . In other words, a 25% increase in the Automotive fuel price in the March quarter 2018 would have the effect of increasing the CPI by 0.8%. Another way commonly used to express this impact is ‘Automotive fuel’ would contribute 0.8 percentage points to the change in the CPI.

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 relative 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. An exception to this are the Underlying trend series 'Trimmed mean' and 'Weighted median', which have index numbers published to four decimal places. Index numbers for periods longer than a single quarter (e.g. for financial years) are calculated as the simple arithmetic average of the rounded quarterly index numbers in that period.

3.15 Points contributions are published to two decimal places, except the All groups CPI which is published to one decimal place. Change in points contributions is calculated from the rounded points contributions. Rounding differences can arise in the points contributions where different levels of precision are used.

The following questions and answers illustrate the uses that can be made of the CPI.

3.16 Question 1: What would $200 in 2011 be worth in the December quarter 2017?

3.17 Response 1: This question is best interpreted as asking ‘How much would need to be spent in the December quarter 2017 to purchase what could be purchased in 2011 for $200?’ As no specific commodity is mentioned, what is required is a measure comparing the general level of prices in the December quarter 2017 with the general level of prices in the calendar year 2011. The All groups CPI would be an appropriate choice.

3.18 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 2011. The second is to multiply the initial dollar amount by the ratio of the index for December quarter 2017 to the index for 2011.

3.19 The index for the calendar year 2011 is obtained as the simple arithmetic average of the quarterly indexes for March (98.3), June (99.2), September (99.8) and December (99.8) 2011, giving 99.3 rounded to one decimal place. The index for the December quarter 2017 is 112.1.

The answer is then given by:

$200 x 112.1/99.3 = $225.78

3.20 Question 2: What would be the impact of a 10% increase in vegetable prices on the All groups CPI in the March quarter 2018?

3.21 Response 2: Two pieces of information are required to answer this question; the All groups index number for the December quarter 2017 (112.1), and the December quarter 2017 points contribution for Vegetables (1.45).

3.22 An increase in vegetable prices of 10% would increase vegetables points contribution by 1.45 x 10/100 = 0.15 index points, which would result in an All groups index number of 112.3 for the March quarter 2018, an increase of 0.2%.

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

3.24 Response 3: The All groups CPI measures price change for all goods and services acquired by households. In Table 9 of Consumer Price Index, Australia (cat. no. 6401.0) there are 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.

3.25 Question 4: Household Expenditure Survey data show that average weekly expenditure per household on Food and non-alcoholic beverages increased from $204.20 in 2009-10 to $236.97 in 2015-16 (i.e. an increase of 16.0%). Does this mean that households, on average, purchased 16.0% more Food and non-alcoholic beverages in 2015-16 than they did in 2009-10?

3.26 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).

3.27 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.

3.28 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

3.29 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.

3.30 We now return to the question on expenditure on Food and non-alcoholic beverages recorded in the HES in 2009-10 and 2015-16. 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 group of the CPI for the weighted average of the eight capital cities. The Food and non-alcoholic beverages group index number for 2009-10 is (94.3 + 95.7 + 96.7 + 96.4)/4 = 95.8 and for 2015-16 is (104.0 + 104.3 + 104.1 + 103.8)/4 = 104.1. Using these index numbers, recorded expenditure in 2015-16 ($236.97) can be adjusted to 2009-10 prices as follows:

$236.97/104.1 x 95.8 = $218.08

3.31 The revalued 2015-16 quantities at 2009-10 prices of $218.08 can then be compared to the expenditure recorded in 2009-10 ($204.20) to deliver an estimate of the change in volumes. This indicates a volume increase of 6.8% between 2009-10 and 2015-16. Over the same period food prices increased (104.1 - 95.8)/95.8 x100 = 8.7% and total expenditure (($236.97 - $204.20)/$204.20 x 100) increased 16.0%.

4.1 The CPI has previously been described in terms of a basket of goods and services which is 'purchased' each quarter. As prices change from one quarter to the next so too will the total cost (or price) of the basket. Of the various ways in which a CPI could be described, this description conforms most closely with the procedures actually followed. Using this description, the construction of the CPI can be thought of as being done in four major steps:

1. subdividing the total expenditure into individual items for which price samples can be selected
2. collecting price data
3. estimating price movements for elementary aggregates
4. calculating the current period cost of the basket.

4.2 Based predominantly on the HES, estimates are obtained for total annual expenditure of private households in each capital city for each of the 87 expenditure classes in the CPI. As these estimates relate to the expenditure of households in aggregate, they are referred to as ‘expenditure aggregates’.

4.3 While these expenditure aggregates are derived for well-defined categories of household expenditure (e.g. flooring), they are still too broad to be of direct use in selecting price samples. For this purpose, expenditure aggregates need to be subdivided into as fine a level of commodity detail as possible. As the HES is generally not designed to provide such fine level estimates, it is necessary to supplement the HES data with information from other sources such as other official data collections and industry data. The processes involved are illustrated below by reference to a stylised example for the Carpets and other floor coverings expenditure class of the CPI.

4.4 Suppose that based on information reported in the HES, the annual expenditure on flooring by all private households in Sydney in the September quarter 2017 is estimated at $8 million. Additionally, suppose there exists separately some industry data on the market shares of various types of flooring. In combination these two data sources can be used to derive expenditure aggregates at a much finer level of detail than that available from the HES alone. The results are shown in the following table.

4.5 The next stage in the process involves determining the types of flooring for which price samples should be constructed. This is not as simple an exercise as might be imagined and relies heavily on the judgement of the prices statisticians. In reaching decisions about precisely which items to include in price samples, the prices statisticians need to strike a balance between the cost of data collection (and processing) and the accuracy of the index. Factors taken into account include the relative significance of individual items, the extent to which different items are likely to exhibit similar price behaviour, and any practical problems associated with measuring prices to constant quality.

4.6 In this example, a reasonable outcome would be to construct price samples for items 1, 2, 3 and 4. Separate price samples would not be constructed for types 5, 6 or 7 because of their small market share relative to the other types.

4.7 The items for which it is decided to construct specific price samples are referred to as ‘elementary aggregates’. (There are approximately 800 elementary aggregates for each of the eight capital cities, or approximately 6,400 price samples at the national level.) The expenditure aggregates for the items that are not to be explicitly priced are reallocated across the elementary aggregates of closely related goods or services under the assumption that the price movements for these items are similar. In this example, this would be done in two stages. First, the expenditure aggregate for rugs would be reallocated to carpets, resulting in an elementary aggregate for soft floor coverings. In the second stage, the expenditure aggregates for vinyl and other flooring, which have no closely matching characteristics with any of the other types of flooring, would be allocated proportionally across the remaining elementary aggregates. The process is illustrated in the following table.

4.8 The rationale for this allocation is as follows. The price behaviour of rugs (item 5) is likely to be best represented by the price behaviour of carpets (item 4). The price behaviour of vinyl and other flooring (items 6 and 7) are likely to be best represented by the average price behaviour of all other flooring types.

4.9 Having settled on the items for which price samples are to be constructed, the next step is to determine the outlet types (respondents) from which prices will be collected. In order to accurately reflect changes in prices paid by households for flooring, prices need to be collected from the various types of outlets from which households normally purchase flooring. Data are unlikely to be available on the expenditure at the individual elementary aggregate level by type of outlet. It is more likely that data will be available for expenditure on flooring in total by type of outlet. Suppose industry data indicates that specialty stores account for about 75% of flooring sales, and department stores the remainder. A simple way to construct the price sample for each elementary aggregate that is representative of household shopping patterns is to have a ratio of three prices from speciality stores to every department store price.

4.10 When price samples have been determined, ABS staff determine from which individual speciality stores and department stores the prices will be collected. The individual outlets are chosen to be representative of the two types of outlets taking into account many perspectives. For example, the outlets should be representative of the socio-economic characteristics of the city. The prices are collected each quarter from the same respondents for the same items.

4.11 When a respondent is first enrolled in the collection process, ABS staff will determine, in conjunction with the outlet management, which specific items are best representative of each elementary aggregate. For example, at one outlet it might be decided that porcelain tiles are the most representative tiles, but at another outlet it might be ceramic tiles.

4.12 An important part of the ongoing price collection process is the monitoring of the items for quality change. In the stylised flooring example, quality change could occur in various ways. A possible quality change would be a change in the size (dimensions) of a tile. In this case prices would be adjusted to derive a pure price for the item along the lines illustrated in the example in 2.52. Individual item prices are also compared with prices collected in the previous period to check their accuracy and to verify any large movements.

4.13 Price samples are constructed for the sole purpose of estimating price movements for each elementary aggregate. These estimates of price movements are required to revalue the expenditure aggregates to current period prices in much the same way as illustrated in the example in 3.16. This is achieved by applying the period to period price movement to the previous period’s expenditure aggregate for each elementary aggregate. It provides an estimate of the cost of acquiring the base period quantity of the elementary aggregate in the current quarter.

4.14 There is no single correct method for calculating the price movement for a sample of observations. Four commonly used methods are described below, using as an example, the price observations from two periods for laminate flooring.

4.15 The differences between the four methods involve choices as to:

• whether the price movement for the sample is calculated as the average of each period’s prices or as the average of price movements between periods for each item;
• the type of average used.
   

4.16 The two commonly used forms of average are the arithmetic mean and the geometric mean. For a sample of n price observations, the arithmetic mean is the sum of the individual prices divided by the number of observations, while the geometric mean is the nth root of the product of the prices. For example, the arithmetic mean of 4 and 9 is 6.5, while the geometric mean is 6 (the geometric mean is always less than or equal to the arithmetic mean).

4.17 Based on these options, one method is to construct a ratio of the arithmetic mean prices in the two periods. In the example below the arithmetic mean of prices in period 1 is $61.35 and in period 2 it is $62.62, giving a relative of 1.021 (62.62/61.35) or a percentage change of 2.1%. This method is called the ‘relative of arithmetic mean prices’ (RAP), sometimes referred to as the ‘Dutot’ index formula.

4.18 A second method is to calculate the price movement between periods for each individual item and then take the arithmetic average of these movements. The price movement for each item must be expressed in relative terms (i.e. period 2 price divided by period 1 price as shown in the 'Price relative' column). In the example below the arithmetic average of the price relatives is 1.023, a price change of 2.3%. This method is called the ‘arithmetic mean of price relatives’ (APR), sometimes referred to as the ‘Carli’ index formula.

4.19 A third method is to construct a ratio of the geometric mean of prices in each period. The geometric mean of the sample prices in period 1 is $60.85 and in period 2 it is $62.18 giving a relative of 1.022 (62.18/60.85) or a percentage change of 2.2%.

4.20 The fourth method is to calculate the geometric mean of the price movements for each individual item. Again, the price movements must be in the form of price relatives. In the example below, the geometric mean of the price relatives is 1.022, indicating a price increase of 2.2%, the same as using the ratio of the geometric mean of prices in each period.

4.21 In fact the geometric mean will always produce the same result whether the relative of mean prices or the mean of relative prices is used. These methods are simply referred to as the geometric mean (GM), sometimes called the ‘Jevons’ index formula.

4.22 The method of calculating price change at the elementary aggregate level is important to the accuracy of the price index. The arithmetic average of price relatives (APR) approach has been shown to be more prone to (upward) bias than the other two methods. In line with various overseas countries, the ABS is using the geometric mean formula for calculating elementary aggregate index numbers where practical in the 17th series of the CPI. Where the geometric mean is not appropriate the relative of arithmetic mean prices (RAP) is used. The reasoning behind using geometric means is outlined below.

4.23 At the elementary aggregate level of the index it is usually impractical to assign a specific weight to each individual price observation. The three formulas described above implicitly apply equal weights to each observation, although the bases of the weights differ. The geometric mean applies weights such that the expenditure shares of each observation are the same in each period. In other words the geometric mean formula implicitly assumes households buy less (more) of items that become more (less) expensive relative to the other items in the sample. The other formulas assume equal quantities in both periods (RAP) or equal expenditures in the first period (APR), with quantities being inversely proportional to first period prices. The geometric mean therefore appears to provide a better representation of household purchasing behaviour than the alternative formula in those elementary aggregates where there is likely to be high substitutability in consumption within the price sample.

4.24 The geometric mean cannot be used to calculate the average price in all elementary aggregates. It cannot be used in cases where the price could be zero (i.e. the cost of a good or service is fully subsidised by the government). It is also not appropriate to use geometric means in elementary aggregates covering items between which consumers are unable to substitute. An example of this is local government rates where it is not possible to switch from a high rate area to a low rate area without physically moving location.

4.25 Once price movements are calculated for each elementary aggregate, they can be used to derive the expenditure aggregates that are then summed to derive the current cost of the basket. It is from the expenditure aggregates that index numbers are calculated at any level of the index. The stylised example is continued to show the process for the Carpets and other floor coverings expenditure class.

4.26 The expenditure aggregates are revalued to period 2 prices by applying the movements between period 1 and period 2. The expenditure aggregate for the expenditure class Carpets and other floor coverings is the sum of the expenditure aggregates for the elementary aggregates comprising the expenditure class. Summing the elementary aggregates says that in period 2 it would cost $8.1m to buy the volume of Carpets and other floor coverings in period 1 that cost $8m. The price change for Carpets and other floor coverings between period 1 and 2 is simply the ratio of these expenditure aggregates, that is, a price increase of 1.5% (8.123/8). Thus if the price index for Carpets and other floor coverings was 100.0 in period 1, it would be 101.5 in period 2.

4.27 The derivation of the expenditure class movement as shown above is mathematically equivalent to a weighted average of the price movements for the individual elementary aggregates, that is, a weighted version of the mean of price relatives formula discussed above. In this case period 1 expenditure aggregates are the weights. The same formula is used at higher levels of the index.

4.28 Similar procedures are used to derive price movements at higher levels of the CPI. For example, the current period cost of purchasing items in the Furniture and furnishings sub-group of the CPI is obtained by summing the current period expenditure aggregates of the expenditure classes Carpets and other floor coverings, and Furniture. The ratio of the current and previous period expenditure aggregates for the Furniture and furnishings sub-group gives the price movement for the sub-group.

4.29 Points contributions (see 3.10-3.12) are also calculated using the expenditure aggregates. The current period points contribution of a CPI component, for example the expenditure class Carpets and other floor coverings, is the current period expenditure aggregate for Carpets and other floor coverings relative to the expenditure aggregate for the All groups CPI, multiplied by the current period All Groups index number.

4.30 The CPI publication does not show the expenditure aggregates, but rather the index numbers derived from the expenditure aggregates. Expenditure aggregates vary considerably in size and showing them would make the publication difficult to read and interpret. The published index numbers and points contributions are a convenient presentation of the information.

4.31 The launch of barcode scanner technology in Australia during the 1970s, and its growth in the 20th century, has enabled retailers to capture detailed information on transactions at the point of sale. As such, it is a rich data source for National Statistical Offices (NSOs) that can be used to enhance their statistics, decrease provider burden, and reduce the costs associated with physically collecting data.

4.32 From the March quarter 2014, the ABS significantly increased its use of transactions data to compile the Australian CPI, which now accounts for approximately 25 per cent of the weight. The approach adopted was a 'direct replacement' of observed point-in-time prices with a unit value calculated from the transactions data.

4.33 From the December quarter 2017, the ABS is making greater use of transactions data by implementing a new method to compile components of the Australian CPI. This new method, known as a multilateral index method, utilises a census of products available in big datasets; uses expenditure data to weight products; and further reduces data collection costs.

4.34 For further information on this enhancement, see:

• Information Paper: Making Greater Use of Transactions Data to Compile the Consumer Price Index (cat. no. 6401.0.60.003); and
• Information Paper: An Implementation Plan to Maximise the Use of Transactions Data in the CPI (cat. no. 6401.0.60.004).