Measurement limitations in the Consumers Price Index

Transcription

1 Consumers Price Index Revision Advisory Committee 2004 Measurement limitations in the Consumers Price Index Yuong Ha Sela Xie Statistics New Zealand

2 Executive Summary The Consumers Price Index (CPI) provides a measure of representative price change. The issue of bias arises when the practices and decisions of statistical agencies on which items to price, their weights, and where to price those items, become unrepresentative over time. The purpose of the CPI in New Zealand is to measure inflation in the prices of goods and services purchased by consumers. In practice, the CPI measures the price change for an historical basket of goods and services. Any differences between yesterday s and today s expenditure patterns may give rise to a bias. There are inherent measurement limitations in the production of CPIs that can result in bias. These limitations reflect: substitution over time in the items purchased by consumers substitution over time in the outlets where those purchases are made new products entering the marketplace and not being priced in the CPI new outlets entering the marketplace where prices are not being collected making adjustments to reflect changes in the quality of products. This paper reviews and discusses these measurement limitations and also attempts to gauge the importance of item and outlet substitution for CPI calculation in New Zealand. Our results suggest that substitution is not a critical issue affecting the reliability of the CPI. Nevertheless, it is recommended that Statistics New Zealand (Statistics NZ) adopt a different index formula known as the Jevons formula for calculating price indexes for items in the CPI regimen. The Jevons formula is the geometric mean of price relatives. It would provide a more accurate measure of price change when consumers shop around for the best deal. The Jevons formula is unlikely to make a significant difference to the CPI. Analysis indicates that CPI inflation would have been around 0.2 percent lower over the period between the December quarter 2000 and the September quarter However, adopting the Jevons formula would be relatively low-cost and straightforward and bring Statistics NZ s practices in line with international best-practice guidelines. The other measurement limitations are sufficiently well-managed, and Statistics NZ practices conform to best practice guidelines, to ensure the CPI is a fit for purpose measure of household inflation. 2

3 Section One Introduction 1. A CPI is an estimate based on a sample of households to estimate weights, and a sample of zones within regions, a sample of outlets, a sample of goods and services and a sample of time periods for price observation. (ILO resolution paragraph 33) 2. Statistical errors will occur when compiling the CPI (and indeed, any price index) because we only deal with a sample of the universe of transactions. Provided robust frameworks are put in place, however, these errors should not affect the ongoing accuracy and reliability of the CPI. 3. Bias, on the other hand, can affect the integrity of the CPI. Bias occurs when there is a persistent error or systematic deviation between what is actually being measured, and what is intended to be measured. 4. The purpose of the CPI in New Zealand is to measure inflation in the goods and services purchased by consumers. In practice, the CPI measures inflation in an historical, or reference, basket of goods and services. Bias may be an issue if there is a significant and systematic difference between yesterday s and today s expenditure patterns. 5. Most international studies on bias have benchmarked the CPI against a costof-living concept. A cost of living index (COLI) measures the price change of a varying basket of goods and services that deliver a constant level of satisfaction, or utility. When prices for goods and services increase at different rates, consumers tend to substitute towards those items whose prices have increased the least. However, because the CPI prices a fixed basket, it will tend to overstate the actual price change necessary to maintain an unchanged standard of living hence the result that the CPI is biased upwards with respect to a COLI. 6. When the purpose of the CPI is to measure household inflation, the arguments with respect to index bias are the same. Pricing a fixed basket over time is likely to overstate the actual inflation experienced by consumers, because consumers will tend to substitute their purchases towards items that become relatively cheaper. 7. The issue of CPI bias has taken on greater prominence since the time of the Boskin Commission. 1 In 1996, the Commission s report to the US Senate Finance Committee estimated that the US CPI overstated changes in the costof-living by around 1 percent per annum. This had significant flow-on effects for the Federal Budget, given how extensively the CPI was used to index their government programmes. 1 The so-called Boskin Commission was an Advisory Commission to study the US CPI. The Commission was appointed by the Senate Finance Committee and the Commission s recommendations were presented in a December 1996 report (aka The Boskin Report). 3

4 8. Since that time, there has been considerable work that has attempted to quantify the degree of bias in CPIs, and also in developing best-practice guidelines for minimising any bias in the CPI. This is reflected in the recent International Labour Organisation (ILO) resolution on consumer price indexes. This resolution has been supported by the concurrent revision to the reference manual on CPIs by a group of international price index experts. 9. At the time of the 1997 CPI review, Statistics NZ had not undertaken any empirical analysis on CPI bias. The view then was that any bias was likely to be less than the US estimates, given the different methodologies and the more frequent re-weighting that occurred in New Zealand. At the time, the US CPI was re-weighted approximately every 10 years compared with five years in New Zealand. Since then, US revisions occur every two years, compared with three years in New Zealand. 10. The 2004 CPI review provided an opportunity to carry out a more in-depth study on the effect of substitution on the CPI. The following sections review and discuss the sources of bias. Empirical results are detailed. The conclusion is that any bias due to item and outlet substitution is not critically affecting the reliability of the CPI. 11. However, the paper does recommend that Statistics NZ adopt a different formula for calculating elementary price indexes for items in the CPI regimen. The appropriate use of a geometric mean formula (known as the Jevons formula), would produce a more accurate measure of price change when consumers shop around for the best deal and change where their purchases are made. 12. The Jevons formula is unlikely to make a significant difference to the CPI. However, it would be low cost and relatively straightforward to adopt and would bring Statistics NZ s practices in line with international best-practice. 4

5 Section Two Sources of bias 13. The CPI provides an estimate of representative price change the key word being representative. The issue of bias arises where the practices or decisions on which items to price, their weights, and where to price those items, run the risk of becoming unrepresentative over time. 14. In reality, bias reflects the practical constraints faced by statistical agencies in compiling an index. A balance has to be reached between the timeliness and cost of compiling the index, against the quality of that index. For instance, while we can easily collect today s prices for goods and services, for practical reasons, we end up pricing a basket that reflects yesterday's expenditure patterns. The term practical is used in the sense that the CPI in New Zealand is published no later than the eleventh working day after the end of the reference quarter. Statistics NZ, and most other statistics agencies, are not yet in a position to collect and process information on today s expenditure patterns in a sufficiently timely and cost effective manner for CPI publication. 15. Given the advances and uptake of information technologies, it should only be a matter of time before electronically stored information could be used for compiling the CPI. 2 The challenge is for Statistics NZ (and statistical agencies worldwide) to harness that potential into practical and cost effective solutions. 16. There are five sources of bias in the CPI, and we provide an overview of each in turn. The sources of bias in the CPI reflect: item substitution outlet substitution new goods not being priced new outlets not being priced quality change. 2 For instance, supermarket scanner data and EFTPOS transaction data would be a rich source of information for the CPI. 5

6 Section Three Item Substitution There are 672 items in the current regimen and each carries a positive weight, reflecting its expenditure share in some historical period. The prices collected for these items are weighted together accordingly and aggregated through two stages to form the All groups CPI, as shown in figure 1. Figure 1 The hierarchy of the New Zealand CPI All groups CPI Group A Upper level aggregation Sub-group A Section A Subsection A Subsection B Item A Item B Item C Item D Region Region 2 Region3 Lower level aggregation Outlet 1 Outlet 2 Outlet At the initial stage, or the lower level of CPI aggregation, prices collected from outlets are combined to form a regional average price for each item in the index At the second stage, or the upper level of aggregation, price indexes are constructed for each item and these indexes are aggregated through successive stages of the CPI hierarchy to form the All groups CPI (i.e. from region to item, to subsection, to section, to subgroup, to group, to all groups). The CPI weights remain fixed until the time of the next revision. 5 3 Further discussion on substitution can be found in At What Price pages (see bibliography for full reference). 4 There are 15 pricing regions in the CPI: Auckland, Wellington, Christchurch, Hamilton, Tauranga, Napier/Hastings, Dunedin, Whangarei, Palmerston North, Nelson, Invercargill, Rotorua, New Plymouth, Wanganui, and Timaru. For more details on regional coverage in the CPI, see the accompanying paper A review of the Consumers Price Index sample selection framework. 5 CPI weights are published down to the subsection level, with the weights having to remain fixed at the section level. In principle, individual item weights, or subsection weights could be adjusted in between basket revisions to better reflect current expenditure patterns. However, in reality, this rarely occurs due to the lack of information needed at such a detailed level of expenditure. The accompanying RAC paper A review of the Consumers Price Index classification system discusses 6

7 20. Different formulae can be used at each stage of aggregation. At the upper level of aggregation, the CPI is calculated using what is called the Laspeyres formula, where weights reflect expenditures from an historical period. As mentioned previously, this approach does not capture the substitution that occurs towards relatively cheaper items. 21. An alternative approach would be to calculate what is called a Paasche index, where weights reflect current period expenditures. The Paasche index is then projected backwards and provides a comparison of what it would have cost to purchase today s basket at yesterday s prices. 22. In contrast to Laspeyres, the Paasche formula will tend to understate the actual inflation experience of consumers because it makes the assumption that the substitution that occurred in the current period was also happening in the past. As a result of these relationships, the Laspeyres index should exceed the Paasche which international empirical studies have confirmed. This is also true for New Zealand The solution to the problem is to find an index that makes the appropriate allowance for substitution to obtain a representative set of weights the Laspeyres assumes no substitution, while the Paasche assumes full substitution. The solution lies in the use of superlative indexes. There are various superlative index formulae available, such as the Fisher index, or the Tornqvist index. The common feature amongst these indexes is that they involve some averaging across the historical and current expenditure weights. For example, the Fisher index is the geometric mean of the Laspeyres and the Paasche indexes in effect, it is an average of the overstating Laspeyres and the understating Paasche In practice, it is not feasible to produce CPIs using a superlative index formula as Statistics NZ (and other statistical agencies) are not yet in a position to collect information on current household expenditures in a timely and cost effective manner. Most, if not all, statistical agencies use a Laspeyres-type index. 25. It is possible to produce a superlative index CPI after some delay, and comparison between the two indexes is typically used as an estimate of the bias due to item substitution. International studies have found the difference between superlative and Laspeyres indexes to be around 0.1 percent to 0.2 percent per year in inflation rates. In other words, price changes would have been around 0.1 percent to 0.2 percent lower if the CPIs allowed for item substitution. The results for New Zealand suggest that inflation would have been around 0.5 percent lower over the three-year period between June 1999 how moving to a COICOP classification would potentially make it easier to adjust expenditure weights below the published level. 6 See Appendix 1 for more details on the empirical analysis on the New Zealand CPI. 7 A technical discussion on the properties of the Laspeyres, Paasche and Fisher indexes can be found in Chapter 15 of the CPI manual (website link: 7

8 and June 2002 or around 0.16 percent per year (see Appendix 1 for details). These results are consistent with international studies. 26. Under a Laspeyres formula, re-weighting the basket periodically will minimise the problem of item substitution, but cannot eliminate it. The heart of the problem is to recognise that substitution occurs continuously. Therefore any set of weights will become outdated and unrepresentative the longer they remain fixed. And because the differences accumulate over time, the longer the period between basket revisions, the larger the bias. However, given that the best solution of using a superlative index formula is not feasible, the second-best solution is to revise the weights in a Laspeyres index as frequently as possible. 27. Given that the empirical results for New Zealand suggest that the degree of bias is not a significant problem, a three-year revision cycle appears to be adequate for maintaining the integrity of the CPI. 8 Most observers tend to agree that, over shorter time periods, it is relatively more important to obtain good quality data on prices rather than on expenditure weights. 28. Statistics NZ is constrained from shortening the revision cycle further by the three-yearly cycle for the Household Economic Survey (HES). However, the Committee may wish to recommend that Statistics NZ continue to monitor the effect of item substitution in the CPI by constructing a superlative index formula CPI on a retrospective basis at the time of each CPI re-weight. The Committee may also wish to discuss the merits of publishing a superlative index CPI as an analytical series. 29. The next CPI revision is scheduled to occur in 2006, making it a four-year gap since the previous revision. The decision for the one year delay reflected cost considerations. However, the following CPI revision is planned for 2008 to bring the CPI back onto its original three-year revision cycle. 8 In New Zealand, the CPI is re-weighted every three years (prior to 1999, revisions occurred every five years). This is in line with practices for other countries: Australia (five years), US (two years, but previously 10 years) and Canada (four years). The UK is one of a handful of countries that re-weight annually. The ILO draft resolution recommends that weights should preferably be reviewed at least once every five years (para 26). 8

9 Section Four Outlet Substitution 30. At the lower level of aggregation, prices for items in the CPI are collected from a range of outlets where consumers make their purchases, and then combined to form elementary price indexes for the items. 9 Where reliable information is available, outlets are weighted by market share. But for the majority of cases this information is not available, so outlets are equally weighted. 31. The choice of an elementary index formula is important and should reflect the likely degree of outlet substitution. The argument essentially parallels that of item substitution: consumers will tend to shop around for the best deal and substitute more of their purchases towards outlets showing lower relative price change. If the index formula used does not capture consumers shopping patterns, then the resulting CPI could mis-measure the actual degree of price change. 32. Typically there have been three different formulae used to calculate elementary price indexes for individual items: the ratio of arithmetic mean prices (RAP) also known as the Dutot formula the arithmetic mean of price relatives (APR) also known as the Carli formula the geometric mean of price ratios (GM) (or the ratio of geometric mean prices the ratio of means and the mean of ratios are the same) also known as the Jevons formula. A more detailed description of each of these formulas is provided in appendix The Carli formula has traditionally been used by many countries. However, studies have shown that it is likely to produce an upwardly biased measure of price change and, as a result, is no longer recommended. The Dutot and Jevons formulae will produce unbiased estimates of price change. However, each formula carries a different underlying assumption about the degree of outlet substitution. Depending on the real world, using a particular formula may produce inappropriate results. 34. The Dutot formula assumes that the same quantities are purchased at each outlet in each period i.e. no outlet substitution. 11 The Jevons formula, on the other hand, assumes the same expenditure in each outlet in each period. 9 Elementary indexes tend to be regional average prices. An example is that the national index for apples is derived by first calculating average apple prices for each of the 15 regions in the CPI. Movements in these regional prices are then weighted by population shares to form the national price index. In some cases, however, elementary indexes are national prices only, meaning that prices are sampled in a way that does not facilitate the calculation of regional prices. 10 A general discussion on the properties of the various elementary index formulas can be found in chapter 9 of the CPI manual. A more technical treatment can be found in chapter 20. Website link: 11 The underlying cross elasticities of demand are zero, and preferences are described as Leontief in the economics literature. 9

10 If the price of apples doubles at an outlet, the quantity purchased is halved, leaving overall expenditure unchanged Not every item in the CPI will be subject to outlet substitution. For certain items there may be only a few or even a single outlet in a geographical region for the item, limiting or reducing the ability for consumers to shop around. An item that is available through local or even national monopolies will not suffer from outlet substitution (e.g. vehicle licensing fees), and the Dutot formula should be used. However items such as food, which are more frequently purchased and operate in a competitive retail environment, will have a greater tendency for outlet substitution. For these items, the Jevons formula would be preferred. In general, items should be decided on case-by-case and the appropriate formula applied, as reflected in paragraph 43 of the ILO resolution. 36. Many countries, including Australia and the US, are now using a combination of both the Dutot and Jevons formulae. Currently Statistics NZ uses the Dutot formula, implicitly assuming no outlet substitution. This paper recommends that Statistics NZ use the Jevons geometric mean formula, where appropriate. 37. Appendix 2 details some analysis to quantify the effect of different index formulas. Items likely to experience outlet substitution were recalculated using the Jevons formula. The results suggest inflation would have been around 0.2 percent lower over the period between December 2000 and September To put this result into perspective, inflation would have been around 0.5 percent lower over a three-year period, due to item substitution. These results suggest that outlet substitution is of second order importance. 38. Nevertheless, outlet substitution is an issue that can be dealt with in a rather straightforward (and low-cost) manner, unlike item substitution. The recommendation to move to a Jevons formula, where appropriate, makes sense. 12 The underlying cross elasticities of demand are all unity, and preferences are described as Cobb- Douglas. In reality, the degree of outlet substitution is likely to be more complicated than assumed under the geometric means Jevons formula. For example, for some items, changes in relative prices may result in consumers shifting their entire expenditure on that item (or for a group of items) to the relatively lower priced store, rather than maintaining the same expenditure levels. However, it is widely accepted that applying the Jevons formula to the appropriate items will result in an improvement in the accuracy of the CPI. 10

11 Section Five New products not being Priced The introduction of new products into the marketplace can present a significant issue for CPI calculation. New products, by definition, will not be in the historical period basket. If the price change pattern for the new product is the same as that for existing products in the basket, there is no real issue of bias, as the CPI price change will still be representative. 40. However, new products generally enter the market at high prices which fall significantly following their introduction as their market share expands. By not pricing new products, the CPI could overstate the actual price change experienced by consumers if expenditure on these products is significant. 41. To remove or minimise the possibility of new product bias would require an identification of the goods on entering the market, and an accurate tracking of its expanding market share (and hence, basket weight). In practice, this process is managed by Statistics NZ when the CPI basket is reviewed and reweighted every three years. Often, beforehand, Statistics NZ will have an idea of which new products have become increasingly significant. This may be confirmed when HES expenditure data becomes available. 42. No other special procedures are adopted by Statistics NZ to manage new products, and none are specifically recommended in the ILO draft resolution. Paragraph 28 of the resolution does state that new goods should only be included during a basket re-weight. In that respect, Statistics NZ practices are consistent with international best practice guidelines. In general, the shorter the time between basket reviews, the less of a problem from new product bias. And again, the three-yearly re-weight is consistent with ILO guidelines of reweighting at least once every five years. 13 Further discussion on the effect of new goods on the CPI can be found in At What Price pages (see bibliography for full reference). 11

12 Section Six New Outlets not being Priced 43. Prices are collected from a range of outlets that are representative of where consumers make their purchases. The retailing landscape continually changes, but prices are typically collected from a fixed set of outlets to compile the CPI, at least until the periodic outlet reviews are carried out. 44. Like new products, failure to account for new outlets could present an issue for the CPI if expenditure at these outlets is significant and if their price movement differs from existing outlets. 14 In the current environment, the presence of Internet-based retailers may be an area to monitor. The nature of these on-line stores may mean they have different cost structures than traditional retailers, so their pricing behaviour could be different Any bias resulting from the non-pricing of new outlets can be minimised by a robust outlet review framework. The more often the sample of outlets is reviewed, and the closer the match to where purchases are made, the smaller the degree of bias At every second CPI revision (approximately every six years), Statistics NZ formally reviews its outlet sample from which prices are collected in the field. 17 The next review is scheduled for Information on expenditures at the different storetypes is gathered from the HES, and is combined with the judgement of regional field pricing officers and office analysts to determine the specific outlets to collect prices from. In between the formal reviews, outlets are monitored on an ongoing basis and new outlets are included and existing outlets excluded based on the judgement of the pricing officers and office analysts As with most areas of index design, there is a trade-off between cost and accuracy more detailed surveys or data sources could be used more often to identify the relevant outlets, but at a greater cost. However, in the case of a relatively small economy such as New Zealand, relying on the judgement of local pricing officers may be more than adequate Bias due to new outlets not being priced is distinct from bias due to consumer substitution across existing outlets. 15 However, the experience to date suggests that consumers uptake of on-line retailing has been modest. Also, many on-line retailers are simply an extension of traditional retailers services, with little significant difference in price movements. 16 The bias due to excluded new outlets could be minimised somewhat if their presence in the market place causes existing outlets to alter their pricing behaviour. A very recent example is the airfares for trans-tasman and domestic travel. The implication is that the more competitive the market, the more homogeneous the pricing behaviour, and the smaller the bias due to new outlets. 17 In addition to field collections, prices are also collected via postal surveys of outlets. The postal outlet sample is reviewed on a rolling basis. In other words, the overall outlet sample for the CPI will be more current or representative than the six-yearly field outlet review would suggest. 18 Current practice is to include any new significant outlet in a region as early as possible, but only after opening day type specials have ceased so that non-normal price movements are not captured in the index. 19 Statistics NZ practices, in this regard, are consistent with the guidelines in the ILO resolution, paragraphs 37 and

13 Section Seven Quality Change Dealing with quality change is considered as one of the more difficult and least tractable problems in constructing the CPI. Items constantly disappear from the market place and are replaced in the CPI by similar, but somewhat different, items carrying different prices. In a fixed basket, however, the same item should be priced in each period to ensure we are comparing like with like. When new items differ with respect to package sizes, volumes or other characteristics, from the original items they replace, an adjustment should be made to reflect any differences in the quality of the new item. 49. Inappropriate or inaccurate adjustments for changes in quality are a significant issue and can result in the CPI either overstating or understating the true price change. In general, many observers view the bias as upward given the rapid rate of technological advances occurring in the marketplace. 50. In some cases, it is relatively straightforward to adjust for quality. For example, if coffee now comes in a 125g pack instead of the usual 250g, then the obvious adjustment would be to double the price of the new pack and compare it to the price of the old pack. However, in the case when an item being priced is replaced by a new version or model, adjusting for quality changes in the new features is not so straightforward. This is quite often the case in electronic goods, such as personal computers. 51. In the 1997 review, Statistics NZ highlighted the area of quality adjustment as being the most significant for managing overall bias in the CPI. Quality change is an ongoing process that requires price statisticians continual attention. The other sources of potential bias (item and outlet substitution, new goods, new outlets) can be effectively managed by one-off changes or periodic reviews of the CPI basket. 52. Developing solutions and assessing techniques for addressing the problem is difficult. Hedonic techniques currently offer the most promising tool for dealing with quality change. With hedonic techniques, statistical regressions are used to assign monetary values to particular characteristics of a type of product, and to adjust its observed price accordingly, should those features change. 53. Hedonic regressions attempt to uncover any empirical relationship between different prices and different models of a particular product. The underlying principle is that, if consumers face an observable relationship between a product s features and its price, we can use this relationship to disentangle pure price changes from quality changes. 20 Further discussion on the effect of quality change on the CPI can be found in At What Price pages 27-30, and , with a discussion on hedonics in pages A more technical description on hedonic techniques is provided in Chapter 21 of the CPI manual. Website link: 13

14 54. As an example, suppose the original CPI basket only included the prices for a standard personal computer (hard drive, keyboard, mouse, monitor). Suppose nowadays, personal computers are sold without the monitor, allowing the consumer the choice of monitor types (standard CRT, or LCD flat screen). But at the same time, the performance of the computer itself is greatly improved due to range of new features (more memory, faster processing chip etc). In order to price the same quality personal computer in the CPI, an adjustment needs to be made to reflect the value of the monitor and the value of the other performance-enhancing features. If enough prices could be observed over time on computers, hedonic regressions could allow us to assign monetary values to each of the characteristic features on a personal computer. 55. The successful use of hedonic regression relies on the ability to identify and measure the quality-determining features and specify an equation that links these features to the prices of different models for a particular product. For this reason, products that experience frequent but incremental quality change, and for which characteristics changes are easy to measure, are considered the best candidates for hedonic analysis. Consumer electronic goods are considered well-suited for hedonic analysis, but products such as clothing would be more difficult given that quality assessments are often more subjective. The successful use of hedonics also requires a considerable amount of good quality data, which can be costly and time consuming to compile, or unavailable in some cases. 56. At the 1997 CPI review, Statistics NZ made no use of hedonic analysis. Since that time, used cars, refrigerators, and fridge-freezers have been quality adjusted using hedonic techniques and video cameras are likely to be quality adjusted this way in the near future. The work programme is still in its early stages, but eventually hedonic methods are expected to be used for a number of items that experience rapid quality changes (such as personal computers). 14

15 Section Eight Summary 57. While it may be possible to produce the perfect measure of price change, it is highly unlikely that this perfect measure could be produced in a timely and cost effective manner. Most countries publish their CPI with a relatively short lag. This reflects the high value that users place on having timely information about price changes affecting consumers. 58. In the current operating environment, any bias largely reflects the trade-off between the timeliness and cost of production, against the quality of the CPI. In reviewing the sources of bias or measurement limitations, Statistics NZ practices are generally robust and, in all but one area, align with international best practice guidelines: biases due to item substitution and new goods are managed through threeyearly basket and weight revisions bias due to new outlets is managed by a six-yearly sample review, with ongoing inclusions of new outlets where these have been identified by Statistics NZ bias due to quality change is being addressed through the progressive application of hedonic techniques. 59. These processes ensure the New Zealand CPI remains a fit for purpose measure of household inflation this was also the conclusion in Michael Anderson s report, Review of New Zealand s Consumers Price Index. 60. A recommended change is for Statistics NZ to adopt the Jevons geometric mean formula for items that are subject to outlet substitution. Adopting the Jevons formula is likely to have only a small impact on CPI accuracy. Nevertheless, it would be a relatively straightforward and low-cost change to implement and would bring Statistics NZ s practices in line with international best-practice guidelines. 15

16 Appendix One Analysis on Item Substitution in the CPI A Laspeyres index is a fixed-weight basket type index, with the weights reflecting the expenditure patterns in some historical period. As changes occur in the relative prices between substitutable items, and consumers substitute towards those items whose prices have increased the least, these historical weights become less representative of current expenditure patterns. If apple prices increase a lot, but prices for pears increase only a little, consumers may be expected to purchase more pears and fewer apples. Pricing the same quantities of apples and pears at the old prices will overstate the actual price change faced by consumers. Comparing a Laspeyres index to a superlative index, such as the Fisher index, is a way to quantify the effect of item substitution in the CPI. Superlative index formulae average across historical and current expenditures to derive a representative set of weights for index calculation. For example, the Fisher index is the geometric mean of the (upwardly-biased) Laspeyres and (downwardly-biased) Paasche indexes: P = P P Fisher Laspeyres Paasche International studies 21 Studies in the US indicate that for their CPI, a superlative index would have increased by around 0.15 percent less a year than the published CPI over the period from the mid-1980s to the mid-1990s. A Canadian study estimates the bias to be less than 0.2 percent per year for their CPI, and a French study suggests there might be a mild upward bias of around 0.05 to 0.1 percent per year in their CPI. In general, international results suggest that the item substitution results in a Laspeyres based CPI overstating price change by around 0.1 to 0.2 percent per annum. New Zealand estimate The current CPI series was re-weighted in the June quarter of The previous reweight occurred in the June quarter of Using the June quarter 2002 weights, a Paasche index was constructed and backcast to the June quarter The Fisher index was created as the geometric mean of the Laspeyres and the Paasche series A more detailed overview on bias with references can be found in Chapter 11 of the CPI manual. 22 This analysis uses a common sample across both the 1999 and 2002 regimen meaning that those items that disappeared from the 1999 regimen or been added into the June 2002 regimen were excluded from the analysis. The items that disappeared in the 2002 regimen amounted to about 1.3 percent of the total weight in the 1999 regimen, while those items that were added into the 2002 regimen occupied approximately 1.3 percent of the total weight in the 2002 regimen. The weights of the excluded items were not reassigned, but given the relatively small weights involved, it is unlikely to significantly affect the results. 16

17 Table 1 Comparison of alternative CPI indexes Quarter Inflation (%) Index type Jun-99 Jun-00 Jun-01 Jun-02 Jun 99-Jun 02 Laspeyres Paasche Fisher Laspeyres Fisher Index Laspeyres Figure 2 Alternative CPI indexes Base: June 1999 quarter (=1000) Fisher Paasche J 99 S D M 00 J S D M 01 J S D M 02 J The results show that: The Laspeyres index exceeds the Paasche consistent with other studies. The difference in inflation rates between the Laspeyres index and the Fisher index is approximately 0.5 percent over the three-year period from the June quarter 1999 to the June quarter This equates to an annual difference of around 0.16 percent, but the difference is not linear (range 0.6 to 2.6 index points). These results are in line with the results for other countries. The differences between the Laspeyres and Fisher indexes accumulate over time. The longer the period between re-weighting the CPI basket, the larger the bias. The best solution to account for item substitution is to use a superlative index formula, like the Fisher index. Given that this is not feasible to do in real time, the second-best solution is to re-weight the CPI as frequently as possible in order for it to maintain its relevance. However, revising the weights periodically will only minimise, not eliminate, the bias because item substitution is likely to occur 23 Note that this series is the official published CPI. 24 For the June quarter 2002 revision, there were changes in Statistics NZ s methodology for calculating expenditure weights. As a result, the differences between the Fisher and Laspeyres indexes may not be real. 17

18 continuously. Moreover, the pace of substitution will vary over time depending on consumer preferences, income levels and the magnitude of relative price changes. Statistics NZ re-weights the CPI at around three-year intervals, and the ILO recommends at least once every five years. On balance, item substitution is sufficiently well-managed by the current three-year re-weighting to ensure the fitness for use of the CPI as a measure of household inflation. 18

19 Appendix Two Analysis on Outlet Substitution in the CPI Prices for items in the CPI are collected from a range of outlets where consumers make their purchases, and then combined to form price indexes for those items (known as elementary aggregate indexes). Like item substitution, consumers may be expected to substitute their purchases towards outlets whose prices have increased the least. The choice of index formula is important in dealing with outlet substitution. Three index formulae have commonly been used to construct elementary indexes: The ratio of arithmetic mean prices (RAP) also known as the Dutot formula. This is the formula currently used by Statistics NZ to construct all elementary indexes. Where outlet weights are available, they are used otherwise prices from each outlet are equally weighted. P D U = 1 1 P N M 1 Pi / i = 1 N i= 1 M Where: 1 P i = Price of item i (i=1.n) in period 1 0 P i = Price of item i (i=1 M) in the base period 0 i The arithmetic mean of price relatives (APR) also known as the Carli formula. P CA = N n= Pn ( ) N 0 Pn Where: 1 P n = Price of item n (n=1.n) in period 1 0 P n = Price of item n (n=1.n) in the base period The geometric mean of price ratios (GM) (or the ratio of geometric mean prices the ratio of means and the means of relatives are the same) also known as the Jevons formula 1 N 1 N Pn PJE n 1 0 P = = n Where: 1 P n = Price of item n (n=1.n) in period 1 0 P n = Price of item n (n=1.n) in the base period Table 2 provides a numerical example to show how different index formulae can deliver different results. In the example, it is assumed that prices are collected from 19

20 four outlets for a particular item. We also assume no outlet weights are available so the prices are equally weighted. Table 2 Different elementary aggregate index formulae Mar Jun Sep Dec 1.Outlet A Outlet B Outlet C Outlet D Arithmetic mean prices Geometric mean prices Current-to-reference quarter (March) price ratios 7.Outlet A Outlet B Outlet C Outlet D Sum of price ratios Geometric mean of price ratios Carli index (average of price ratios line 11) 14.Dutot index (ratio of arithmetic mean prices line 5) 15.Jevons index (ratio of geometric mean prices line 6) 16.Or Jevons as geometric mean of price ratios (line 12) The Carli formula was traditionally used by many countries. However, it is now recognised as likely to produce an upwardly biased estimate of price change and is no longer recommended for use by the ILO. One of its flaws is the inability to handle price reversals, as highlighted for price changes between June and September, in which the same four prices are observed in both periods but they are switched between the different outlets. The Carli index shows a perverse result, increasing by around 5.5 percent while, whereas the Dutot and Jevons indexes remain unchanged. Most countries now use either the Dutot or Jevons, or a combination of the two. Each carries a different underlying assumption about the degree of outlet substitution (reflecting different consumer preferences). The Dutot formula prices fixed quantities of each item in each period, which carries the underlying assumption that demand is invariant to changes in relative prices i.e. there is no outlet substitution. In contrast, under Jevons, it is the expenditure weight that is held constant, which carries the assumption that demand is inversely proportional to changes in relative 20

21 prices if the item price doubles at an outlet, the quantity purchased halves, leaving expenditure unchanged. The ILO recommends that Jevons be adopted where possible, except in cases where there is little possibility for substitution, or where individual prices may become zero or near zero (since the geometric mean becomes zero). 25 This approach has been adopted by many countries, including the US and Australia, and the recommendation here is for Statistics NZ to do likewise. New Zealand results The process of using the Jevons formula to calculate the CPI is straightforward. The analysis here compares the difference that would have resulted had the Jevons formula been used between the December quarter 2000 and the September quarter of The first step was to identify which of the items in the CPI regimen were unlikely to be subject to outlet substitution, or carried the possibility for zero prices. For those items, the Dutot formula was retained for the calculation of the elementary indexes. The remaining items were then calculated using the Jevons formula. Overall, approximately 65 percent of the regimen, by expenditure weight, was recalculated using Jevons. Table 3 Difference to the CPI under the Jevons geometric mean formula Dec 00 Sep 03 Index point Inflation % change Dutot Dutot/Jevons Difference The results in table 3 suggest that inflation would have been approximately 0.2 percent lower, over the approximately three-year period up to September 2003, had the CPI calculation allowed for outlet substitution. This difference is relatively small when compared to the 0.5 percent difference due to item substitution (comparing Laspeyres to Fisher, see Appendix 1). Similar to item substitution, the conclusion is that outlet substitution is not a critical issue affecting the accuracy of the CPI. Nevertheless, implementing the Jevons formula would be relatively straightforward and bring Statistics NZ in line with international best-practice guidelines. 25 Items that are heavily subsidised (such as child healthcare) often carry zero or near-zero prices. 21

22 Bibliography Morris J (1997). Managing Measurement Limitations in the Consumers Price Index, Statistics New Zealand paper prepared for the 1997 CPI Revision Advisory Committee. International Labour Organisation (2003). International Manual on CPI, Manual on CPI (currently under revision). International Labour Organisation (2003). Resolution concerning consumer price indices, adopted at the Seventeenth International Conference of Labour Statisticians, (replacing the previous resolution adopted in 1987). National Research Council (2002). At What Price: Conceptualizing and Measuring Cost-of-Living and Price Indexes, Panel on Conceptual, Measurement, and Other Statistical Issues in Developing Cost-of-Living Indexes, Charles L. Schultze and Christopher Mackie, Editors. Committee on National Statistics, Division of Behavioral and Social Sciences and Education. Washington DC: National Academy Press Xie S (2003). An Empirical Study on Upper Level Formula Bias in the New Zealand CPI, Internal memo, Statistics New Zealand. Schultze C L (2003). The Consumer Price Index: Conceptual Issues and Practical Suggestions, The Journal of Economic Perspectives, Volume 17: Number 1, Winter 2003, pp