Consumers Price Index Revision
Advisory Committee 2004
Measurement limitations in the
Consumers Price Index
Yuong Ha
Sela Xie
Statistics New Zealand
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 2003. 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
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
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
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
Section Three
Item Substitution3
17. 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
Item A
Region
Outlet 1
Region 2
Outlet 2
Subsection B
Item B
Region3
Item C
Item D
Lower level aggregation
Outlet 3
18. 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.4
19. 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 21-23 (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
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.6
23. 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.7
24. 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:
http://www.ilo.org/public/english/bureau/stat/guides/cpi/index.htm)
7
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
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 2.10
33. 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:
http://www.ilo.org/public/english/bureau/stat/guides/cpi/index.htm
11
The underlying cross elasticities of demand are zero, and preferences are described as “Leontief” in
the economics literature.
9
If the price of apples doubles at an outlet, the quantity purchased is halved,
leaving overall expenditure unchanged.12
35. 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 2003. 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 ‘CobbDouglas’. 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
Section Five
New products not being Priced13
39. 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 3032 (see bibliography for full reference).
11
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.15
45. 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.16
46. 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 2006. 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.18
47. 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.19
14
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 38.
12
Section Seven
Quality Change20
48. 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 106-114, with a discussion on hedonics in pages 122-129. A more technical description on
hedonic techniques is provided in Chapter 21 of the CPI manual. Website link:
http://www.ilo.org/public/english/bureau/stat/guides/cpi/index.htm
13
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
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
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:
PFisher = PLaspeyres × PPaasche
International studies21
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 2002. The previous reweight occurred in the June quarter of 1999.
Using the June quarter 2002 weights, a Paasche index was constructed and backcast to
the June quarter 1999. The Fisher index was created as the geometric mean of the
Laspeyres and the Paasche series.22
21
A more detailed overview on bias with references can be found in Chapter 11 of the CPI manual.
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.
22
16
Table 1
Comparison of alternative CPI indexes
Quarter
Index type
Inflation (%)
Jun-99
Jun-00
Jun-01
Jun-02
Jun 99-Jun 02
Laspeyres23
1000.0
1020.0
1053.0
1082.0
8.2
Paasche
1000.0
1014.8
1044.7
1072.4
7.2
Fisher
1000.0
1017.4
1048.9
1077.2
7.7
0
2.6
4.1
4.8
0.5
Laspeyres – Fisher
Figure 2
Alternative CPI indexes
Base: June 1999 quarter (=1000)
1100
Index
Laspeyres
1080
Fisher
1060
Paasche
1040
1020
1000
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 2002.24 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.
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’.
24
17
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
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.
N
M
1
 1 
PDU = ∑  Pi1 / ∑  Pi 0
i =1  M 
i =1  N 
Where:
Pi1 = Price of item i (i=1….N) in period 1
Pi 0 = Price of item i (i=1…M) in the base period
• The arithmetic mean of price relatives (APR) – also known as the Carli formula.
1  Pn1
= ∑ ( ) 0
n =1 N  Pn
N
PCA




Where:
Pn1 = Price of item n (n=1….N) in period 1
Pn0 = 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
 P1  N
PJE = ∏ nN=1  n0 
 Pn 
Where:
Pn1 = Price of item n (n=1….N) in period 1
Pn0 = 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
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
6
7
6
6
2.Outlet B
7
6
7
7
3.Outlet C
2
4
5
2
4.Outlet D
5
5
4
5
5.Arithmetic mean prices
5.00
5.50
5.50
5.00
6.Geometric mean prices
4.53
5.38
5.38
4.53
Current-to-reference quarter (March) price ratios
7.Outlet A
1.00
1.17
1.00
1.00
8.Outlet B
1.00
0.86
1.00
1.00
9.Outlet C
1.00
2.00
2.50
1.00
10.Outlet D
1.00
1.00
0.80
1.00
11.Sum of price ratios
4.00
5.02
5.30
4.00
12.Geometric mean of price ratios
1.00
1.19
1.19
1.00
13.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)
1000
1256
1325
1000
1000
1100
1100
1000
1000
1189
1189
1000
1000
1189
1189
1000
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
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
2003.
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
Inflation %
1102.6
Index point
change
56.5
1046.1
1100.4
54.3
5.2
0
-2.2
-2.2
-0.2
Dec 00
Sep 03
Dutot
1046.1
Dutot/Jevons
Difference
5.4
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
Bibliography
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Statistics New Zealand paper prepared for the 1997 CPI Revision Advisory
Committee.
International Labour Organisation (2003). “International Manual on CPI”, Manual on
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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
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