6401.0.60.002 - Information Paper: Increasing the Frequency of CPI Expenditure Class Weight Updates, July 2016  
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EMPIRICAL ASSESSMENT


INTRODUCTION

3.1 While HFCE data is the primary source used in this analysis to update expenditure weights for the CPI ECs, to meet the scope and conceptual requirements of the Australian CPI, a range of adjustments are required (see chapter 2). The use of HFCE and other data sources for CPI weighting purposes, together with the impact of revisions (both cyclical and historical), are analysed empirically in this chapter.

3.2 In order to assess each experimental HFCE price index, the ABS Data Quality Framework (DQF) provides a useful starting point to compare the empirical results. With reference to the ABS DQF and other considerations, there were three main criteria used to compare the HFCE vintages. These criteria are:

  • Relevance - the distance between the weight reference and link period;
  • Accuracy - consistency with a superlative(footnote 1) index; and
  • International practice - comparison of other NSOs using HFCE data for CPI weights.


METHODS

3.3 Experimental HFCE price indexes for the period September 2005 to September 2015 have been constructed using a total of 86 ECs. The Deposit and loans EC has been removed from the analysis(footnote 2) and weights for this EC re-apportioned accordingly. This experimental series has used HFCE data as supplied by the National Accounts area of the ABS.

3.4 This analysis uses expenditure aggregates derived at the EC level as weights, and the 16th Series CPICC as the classification standard. This enables a comparison of expenditure with HFCE data and is consistent with the current production approach.

3.5 HFCE data used covers financial years, and are denoted as preliminary (t-1), revised (t-2) and final (t-3). The annual HFCE data is available in October each year, with the experimental HFCE price indexes re-weighted every December quarter(footnote 3) . For example, the weights implemented from December 2014 to September 2015 are derived as follows: t-1 corresponds to preliminary 2012-13 financial year HFCE data, t-2 corresponds to revised 2011-12 financial year. HFCE data, and t-3 corresponds to final 2010-11 financial year HFCE data. The experimental indexes below will be referred to as t-1, t-2 and t-3 respectively.

3.6 HFCE data is available on a financial year basis(footnote 4) which formulates the annual Australian System of National Accounts (cat. no. 5204.0), enabling expenditure weights to be derived annually for this study. The choice of annually re-weighted price indexes is the preferred option to measure consumer expenditure patterns, and is also operationally feasible for the ABS to implement. A price index is constructed for three sets of expenditure weights (one for each HFCE vintage respectively) over the ten year period. HFCE vintages are lagged by one (t-1), two (t-2) and three (t-3) years from the implementation period, indicative of when the data is available.

3.7 In practice, when the weight reference period differs from the price reference period(footnote 5) , in line with ABS and international practice, expenditure weights are price updated(footnote 6) to take into account the price change that has occurred prior to implementation. Given that the weight reference year spans a complete financial year (September quarter to June quarter) a price movement representing the difference between the price reference period (September quarter) and the average price level in the weight reference period (September quarter to June quarter) is applied to the original weights. In practice, quantities pertaining to the t-1, t-2 and t-3 vintages should be revalued at the prices of the price reference period (September quarter) prior to implementation.

The application of price updating to expenditures can be expressed as:

Equation 3.1 shows the price-updating process of the expenditures at the EC level. (3.1)

Where;
      P superscript SQ over subscript i= September quarter (link period) price index for EC i
      AVE (P subscript i under superscript SQ star minus JQ star )= average of price indexes for EC i covering the weight reference period (financial year) and;
      W superscript i over subscript HFCE= original expenditure weights for EC i derived from HFCE data.

3.8 HFCE derived weights are applied to EC price indexes published in Consumer Price Index, Australia (cat. no. 6401.0) at the weighted average of the eight capitals. The only difference between the experimental indexes and the CPI are the upper level weights, since both series use the same published level price movements. Given the experimental index is derived from the EC level, the Lowe index formula is used. The Lowe index formula is defined as:

Equation 3.2 shows the Lowe price index formula used by the ABS and other NSOs. (3.2)

Where;
      Equation: MichaelPtoveri= current period price for EC i
      Equation: 35bP0i= price reference period price for EC i
      Equation: MichaelQboveri= price reference period quantity for EC i
      Equation: 38SobEqPqOverSumPq= price updated expenditure shares for EC i.

3.9 In practice, the availability of annual HFCE expenditure data from September 2005 to September 2015 means ten different CPI weighted baskets are derived, one for each HFCE vintage. In order to form a continuous time series, which takes into account changing purchasing behaviours and product substitution, the experimental HFCE price indexes are chain linked(footnote 7) every September quarter. The application of chain linking can be expressed as:

 Equation 3.3 shows the chain-linking of annual indexes using expenditure from HFCE data. (3.3)

Where;
      Equation I superscript 06/15 over subscript ChLo= continuous chained-linked annual indexes from 2005-06 to 2014-15

3.10 In addition, the ABS has previously constructed a retrospective superlative index to estimate the amount of substitution bias in the CPI following previous series reviews. Superlative indexes allow for substitution as they make use of weights from both the earlier and later periods under consideration. The preferred superlative price index is the Fisher-type index, which is calculated as the geometric mean of the Laspeyres-type(footnote 8) and Paasche-type(footnote 9) indexes. The Fisher-type index formula for any given period t is defined as:

Fisher Equation 3.4 is the Fisher index formula represented as the geometric mean of the Laspeyres and the Paasche index formulas (3.4)

Where;
      Equation: I superscript t over subscript L= Laspeyres-type index at period t
      Equation: I superscript t over superscript P= Paasche-type index at period t

In order to assess the relationship between the experimental HFCE series and superlative index, a Fisher-type index is constructed for the period September 2005 to September 2011(footnote 10) .


EMPIRICAL RESULTS

3.11 A comparison of group level expenditure weights for each of the HFCE vintages and CPI following the 16th Series review is shown in table 3.1 below. The CPI and HFCE vintages show similar expenditure patterns, indicating the methods used to adjust HFCE data for CPI produces consistent expenditure results to those derived from household survey data. The results also indicate the impacts of cyclical revisions are small at the group level.

3.1 Comparison of CPI 16th Series and HFCE weights, proportion (%) of total expenditure - 2011 financial year

GROUP
HES(a)
t-1
t-2
t-3

Food and non-alcoholic beverages
16.95
17.49
17.39
16.76
Alcohol and Tobacco
7.13
6.33
6.46
6.45
Clothing
4.02
4.83
4.68
4.47
Housing
22.47
21.96
23.00
23.32
Furnishing, Household equipment and Services
9.16
8.50
8.37
8.19
Health
5.33
6.38
6.29
6.03
Transport
11.64
11.22
11.25
11.96
Communication
3.07
3.13
3.13
3.01
Recreation
12.68
12.88
12.62
12.76
Education
3.20
3.78
3.68
3.35
Insurances and Financial services
4.35
3.50
3.13
3.70
All groups
100.00
100.00
100.00
100.00

(a) The CPI Group HES weights are taken from Consumer Price Index 16th Series weighting pattern (cat.no.6471) and re-calculated to exclude the weights for the deposit and loans EC.


3.12 Weights for the experimental HFCE price indexes are derived at the EC level for each vintage, which are then applied to the published price indexes (weighted eight capitals). The results at the All groups level are shown below in Figure 3.1, with the experimental HFCE price indexes tracking closely to the CPI. The experimental HFCE series grew by 28.5% (t-1), 29.0% (t-2) and 29.4% (t-3) respectively from September 2005 to September 2015. The CPI grew by a total of 30.1% over the equivalent period.

Figure 3.1: Index comparison between experimental HFCE and CPI series
Graph: Graph The graph shows index comparison between experimental HFCE and CPI series


3.13 The compound annual growth rate (CAGR) is used to derive annual average inflation rates over the analysis period. This measure of average annual household inflation is consistent with previous methods used by the ABS, which accurately account for the effects of compounding when applying annual growth rates to a price index. The experimental HFCE series recorded average annual growth of 2.54% (t-1), 2.58% (t-2) and 2.61% (t-3) respectively from September 2005 to September 2015. The CPI recorded an average annual growth rate of 2.67% over the equivalent period.

3.14 Using EC weights from the 15th and 16th CPI Series reviews, the Fisher-type index rose by a total of 18.5% across the period September 2005 to September 2011(footnote 11) . Across the equivalent period, the experimental HFCE series rose 19.1% (t-1), 19.5% (t-2) and 19.6% (t-3), while the CPI rose by a total of 20.2%, demonstrating all three HFCE experimental indexes lie closer to the Fisher-type index, relative to the CPI.

3.15 In order to quantify the amount of upper level substitution bias, the average annual price changes can be compared to the superlative Fisher-type index. As shown in Figure 3.2, the average annual upward substitution bias for the experimental HFCE series was 0.09% (t-1), 0.15% (t-2) and 0.16% (t-3) higher relative to the Fisher-type index. The CPI recorded a larger substitution bias compared to the experimental HFCE series, with an average annual upward substitution bias of 0.24% relative to the Fisher-type index.

Figure 3.2: Average annual upper level substitution bias
Graph: Graph The graph shows the average annual upper level substitution bias for the t-1, t-2 and t-3, compared to the CPI.


3.16 In addition to the annual normal cycle of revisions to HFCE data, the entire HFCE data series is periodically open for historical revisions, covering the entire Supply-Use time series, and occurs outside the normal cycle of revisions. The headline CPI is only ever revised in exceptional circumstances. HFCE data provide a timelier pattern of household expenditure between HES benchmarks, in comparison to the CPI where it is assumed all of the changes from the previous HES occur at the time the new benchmark is introduced. The impact of historical revisions as shown in this analysis is minimal. Hence, the CPI will maintain its current revisions policy.

3.17 In order to quantify the potential impact of historical revisions to the experimental HFCE price indexes, expenditure weights are derived from the revised series and implemented to determine whether aggregate household inflation measures would have changed. Using the 2010-11 historical revision specifically, the average annual price change for the historically revised series was 2.82% for the period September 2005 to September 2012. This was the same annual growth rate as the t-1 index (2.82%), while the other experimental HFCE indexes reported slightly higher household inflation of 2.88% (t-2) and 2.89% (t-3) per annum respectively. These results suggest that the impact of a historical revision is relatively small, producing an annual inflation rate very close to the t-1 index. This analysis was conducted on other historical revisions to HFCE data, with similar relationships observed for the 2009-10 and 2012-13 historical revisions.

3.18 The Lowe index formula is internationally the most used upper level aggregation formula. The application of the Lowe formula involves price updating expenditures from the weight reference period to the price reference period. The ABS currently implements CPI EC re-weights with an approximate 12 month lag from the weight reference period. If the time between weight and price reference period is long, the impact of price updating may have an upward impact on household inflation measurement. This finding is consistent with other national statistical agencies' investigations into the effects of varying the implementation lag of re-weighting a CPI (Huang et al 2015).

3.19 The analysis shows the t-1 price index lies closer to the historically revised HFCE price index when compared with the other two vintages. This is partially due to the impact of price updating, with the longer implementation lags for t-2 and t-3 vintages having an upward effect on household inflation rates. When the effects of price updating are removed (no implementation lag for all vintages), the t-3 price index reports the lowest rate of household inflation compared to the other two vintages. It also lies closest to the historically revised HFCE price index, providing further evidence of the upward impact price updating over long intervals has on household inflation measurement.

3.20 The t-1 vintage is recommended as the preferred option based on the three main criteria established, specifically; (1) it has the shortest implementation lag between weight reference period and price reference period; (2) it is closest in proximity to a superlative index; and (3) it aligns well with international standards. This is summarised in Table 3.2 below.

3.2 HFCE vintage criteria assessment summary

Criteria t-1 t-2 t-3

Relevance 15 months 27 months 39 months
Accuracy +0.09 p.a. +0.15 p.a. +0.16 p.a.
International practice ONS, Sweden, Netherlands France N/A



1 A superlative index is one of a small group of indexes that makes equal use of prices and quantities, and treats them in a symmetrical manner in each pair of periods under observation. <back
2 This was excluded due to index composition change across the 15th (includes direct and indirect fees) and 16th Series (direct fees only). For more information on the history of deposit and loans see sections 4.29–4.32 of ABS (2010). <back
3 The ABS has typically re-weighted price indexes during the September quarter in past series reviews. Due to availability of HFCE data in October, CPI will be re-weighted in December quarters. <back
4 HFCE data are also estimated quarterly when compiling quarterly GDP. The annual HFCE data are compiled using the Supply/Use framework. <back
5 Price reference period is the period for which prices are used as denominators in the index calculation (ABS 2011). <back
6 A procedure whereby the quantities in an earlier period are revalued at the prices of a later period. For more information, see sections 9.95–9.104 of ILO (2004). <back
7 An index number series for a long sequence of periods obtained by linking together index numbers spanning shorter sequences of periods (ILO 2004, p.491). <back
8 An index in which the basket is composed of the actual quantities of goods and services in the earlier of the two periods compared. In this study, the Laspeyres–type index equivalent to the All Groups CPI (excluding deposit and loans) for the period September 2005 to September 2011. <back
9 An index in which the basket is composed of the actual quantities of goods and services in the later of the two periods compared. In this study, the Paasche–type index derives expenditure weights each quarter using a linear model between the 15th and 16th Series CPI reviews to estimate price change for the period September 2005 to September 2011. <back
10 See detailed information on index theory and aggregation in chapter 4 of ABS (2011). <back
11 The Fisher–type index is retrospectively constructed between September 2005 and September 2011 for the purpose of consistency with the experimental indexes. This assumes that the 15th Series was linked in September 2005 and the 16th Series in September 2011.

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