Course Outline
Course aim
The aim of this course is to provide participants with a basic understanding of
price indexes, the outputs of the Prices business unit and the relationship/link to
other units within Statistics New Zealand.
Pre-course understanding
Prior to undertaking this course it is desirable (although not essential) that
participants have attended the Introduction to Economics for Non-Economists
course or have an equivalent understanding of economic concepts.
Table of Contents
Intermediate Module One .................................................................................. 4
1a: Introduction to the Prices Unit ...................................................................... 6
1b: What is a Price Index?.................................................................................. 6
What does a price index tell us........................................................................... 7
Why they are produced ................................................................................... 8
1c: The Suite of Price Indexes............................................................................ 8
Consumers Price Index & Food Price Index ................................................... 8
Producers Price Index .................................................................................... 9
Capital Goods Price Index .............................................................................. 9
Farm Expenses Price Index ............................................................................ 9
Overseas Trade Price Indexes ..................................................................... 10
Labour Cost Index ........................................................................................ 10
Inflation flows in the economy ....................................................................... 10
1d: Basics of Price Indexes .............................................................................. 11
1e: About the Consumers Price Index .............................................................. 13
1f: About the Producers Price Index ................................................................. 17
1g: About the Capital Goods Price Index ......................................................... 23
1h: About the Labour Cost Index ...................................................................... 25
1i: About the Overseas Trade Indexes ............................................................. 29
1j: Differences Between the CPI, PPI, LCI and OTI ......................................... 33
1k: Price Index Mechanics................................................................................ 36
Index reference period .................................................................................. 36
Price reference period .................................................................................. 37
Weight reference period ............................................................................... 37
Calculating a price index ............................................................................... 38
How an index is read .................................................................................... 38
Price index is about price change NOT price level ....................................... 41
Spatial versus temporal indexes ................................................................... 41
1l: Interpreting Price Index Outputs .................................................................. 43
Visual scan ................................................................................................... 43
Rates of change............................................................................................ 48
Percentage changes and real world price changes ...................................... 51
Contribution information ................................................................................ 52
Module 1 Overview ........................................................................................... 54
2
Intermediate Module Two ................................................................................. 55
2a: Price Index Concepts and Formulae .......................................................... 56
Combining the prices of several items into one price index .......................... 56
Index structure .............................................................................................. 56
Elementary aggregates ................................................................................. 59
Value aggregates .......................................................................................... 61
Price versus volume indexes ........................................................................ 61
Index notations ............................................................................................. 62
Laspeyres price index ................................................................................... 62
The Laspeyres price relative index form ....................................................... 63
Paasche price index ..................................................................................... 64
Fisher ideal index.......................................................................................... 64
The use of the Fisher ideal index .................................................................. 65
Examples of price indexes ............................................................................ 66
Examples of volume indexes ........................................................................ 69
Value movement ........................................................................................... 70
The party index example............................................................................... 71
Index points contribution ............................................................................... 73
Other index forms and chaining .................................................................... 74
2b: From Theory to Practice ............................................................................. 75
Why use the price relative form of the index ................................................. 75
The process of development and maintenance ............................................ 75
Development of a price index - basic steps .................................................. 76
Determining the purpose of the index ........................................................... 78
Module 2 Overview ........................................................................................... 80
Glossary ........................................................................................................... 84
3
Intermediate Module One – Introduction to Prices
Learning outcomes
At the end of this module, participants should be able to
 Understand the Prices unit structure and its work
 Describe what a price index is and its place in the economy
 Explain the basics of each price index output, including their main uses
and coverage
 Discuss the differences between price, weight and index reference
periods
 Interpret price index numbers, percentage changes and index points
contribution.
4
5
1a: Introduction to the Prices Unit
The Prices business unit is part of the Macro Economics and Environment
Statistics Group (MEES). It is divided into three teams:
 CPI Outputs
 CPI/LCI Development
 BLOPI.
The CPI Outputs team is responsible for producing the Consumers Price Index
(CPI) and the Food Price Index (FPI).
The CPI/LCI Development team maintains the medium- to long-term relevance
and quality of the Consumers Price Index (CPI) and the Labour Cost Index
(LCI) by undertaking periodic reviews, to ensure the indexes continue to reflect
household spending patterns (CPI) and business spending patterns on labour
input (LCI).
BLOPI (Business, Labour, Overseas trade Price Indexes) is responsible for
following outputs: the Business Price Index (BPI) suite, consisting of
Producers Price Index (PPI), the Capital Goods Price Index (CGPI) and
Farm Expenses Price Index (FEPI), the Labour Costs Index (LCI) and
Overseas Trade Price Indexes (OTI).
the
the
the
the
1b: What is a Price Index?
Movements in a time series of monetary values can be decomposed into two
elements: changes in price and changes in volume.
Ratio of change in value = ratio of change in price x ratio of change in volume
Example - Sales of Braeburn apples
Variable
Price per kg
Quantity (kg)
Value ($)
Price per kg
Quantity (kg)
Value ($)
Period 0
Period 1
Period 2
1.50
2.00
2.00
100
100
80
150
200
160
Percentage change from previous period
..
33.3
0.0
..
0.0
-20.0
..
33.3
-20.0
6
Period 3
2.60
100
260
30.0
25.0
62.5
All of the change in value from period 0 to period 1 was caused by an increase
in price and all of the change in value between period 1 and period 2 was
caused by a decrease in the quantity of apples sold. The increase of 62.5
percent in value from period 2 to period 3 was caused by increases in both the
price and the quantity. Using the ratio of change formula above, it can be seen
that:
(260 / 160) = (2.60 / 2.00) x (100 / 80)
or
1.625 = 1.300 x 1.250
A price index is a statistic used to measure the overall level of change in prices
being paid by purchasers or being received by sellers, taking into account the
numerous and diverse range of transactions being made.
What does a price index tell us
A price index is a series of numbers that shows how a
whole set of prices has changed over time. The
average price level of goods and services in a single
period, called the index reference period, is assigned
an index number of 1000. The index number for each
subsequent period is calculated such that its ratio to
the index reference period index number is the same
as the ratio of the average price level in that period to
the average price level in the index reference period.
For example, if the index number for a period is 1150, prices for the period are
15 percent higher than in the index reference period. Similarly, if the index
number for a period is 950, then prices are 5 percent lower, on average, than in
the index reference period.
Example - Price index percentage changes
Period 0 (index
reference period)
Period 1
Period 2
Period 3
1000
1100
1150
950
Percentage change from previous period
Price Index
..
10
4.5
-17.4
Percentage change from index reference period
Price Index
..
10
15
-5
Variable
Price Index
An index number on its own means nothing. It must be compared with an index
number from another period to determine the price movement between the
other period and the current period.
7
Why they are produced
Price indexes are used to measured inflation in various parts of the economy.
Common uses of price indexes include:
 to monitor general inflation for monetary policy,
 to adjust (or provide argument for adjusting)
wages and benefit payments to compensate for
any increase in prices of the goods and services
that wages and benefits are spent on,
 to deflate a value series to get a volume series,
 to decompose value change into price change
and volume change,
 to adjust payments to compensate for inflation,
e.g. used in commercial contract clauses,
 to provide evidence of where suppliers are increasing prices faster than
their costs, e.g. telephone charges,
 to provide information of where price increases are coming from. For
example - are import prices rising faster than those for the rest of the
economy? Or is it exports pushing up local prices?
***********************************************************************************
Exercise 1
1. What is a price index?
2. Why are they produced?
3. What are three uses of price indexes? Who might be the users of these
indexes?
***********************************************************************************
1c: The Suite of Price Indexes
Statistics New Zealand compiles a suite of price indexes. Each of these indexes
serves a different purpose. This is explained below:
Consumers Price Index & Food Price Index
The Consumers Price Index (CPI) is a measure of the price change of goods
and services purchased by private New Zealand households. The CPI
measures the changing cost of purchasing a fixed basket of goods and services
8
which represents the average expenditure pattern of New Zealand households
at the index base period.
The Food Price Index (FPI) is a price index that measures changes in the level
of prices of a basket of food goods and services purchased by private
households in the base year of the index. This index represents the Food group
in the CPI.
CPI: Quarterly measure of the price change of a basket of goods and
services purchased by households.
FPI: Monthly measure of price change of a basket of food goods and
services purchased by households.
Producers Price Index
The Producers Price Index (PPI) measures prices relating
to the production sector of the economy. The PPI has two
types of indexes: the outputs indexes which measure
changes in the prices received by producers and the inputs
indexes which measure changes in the cost of production
(excluding labour and capital costs).
Capital Goods Price Index
The Capital Goods Price Index (CGPI) measures movements in the average
levels of prices of physical capital assets within the New Zealand economy.
Farm Expenses Price Index
The Farm Expenses Price Index (FEPI) measures price
changes of fixed inputs of goods and services to the
farming industry. It does not fully measure changes in
the production costs of farming. This is because
production costs are not solely dependent on price
movements but are also dependent on factors that affect
productivity,
such
as
technological
advances,
management efficiency and climate fluctuations.
The FEPI differs from the PPI inputs to agriculture as it
include items such as salaries and wages, local and
central government rates and charges, and interest
rates.
9
Overseas Trade Price Indexes
The overseas merchandise trade price indexes measure changes in the levels
of prices of imports and exports of merchandise trade to and from New Zealand,
on both a quarterly and an annual basis. The overseas services trade price
indexes measure changes in the price levels of services to and from New
Zealand on a quarterly basis.
Labour Cost Index
The Labour Cost Index (LCI) measures changes in base salary and ordinary
time wage rates, overtime wage rates (on a quarterly basis), and the following
non-wage labour-related costs (on an annual basis):
• annual leave and statutory holidays
• superannuation
• ACC employer premiums
• medical insurance
• motor vehicles available for private use
• low interest loans.
Inflation flows in the economy
The price indexes produced by Statistics New Zealand are designed to cover all
the major economic flows, as illustrated in the diagram below.
Inflation Flows in the Economy
Export Price Index
Producers
Price Index
(outputs)
Import Price Index
Production sector
outputs
Expenditure by production/government sector
Labour
costs
Labour Cost Index
Current
costs
Expenditure by household sector
Capital
costs
Producers Price
Index (inputs)
10
Capital Goods
Price Index
Consumers
Price Index
1d: Basics of Price Indexes
When measuring price change between two periods, a common approach is to
compare the expenditure or revenue of a basket of goods and services
purchased or sold in one of the two periods with what the same basket would
have cost or returned in the other of the two periods. This is called a fixedbasket approach to price index construction.
Because expenditure or revenue information at the necessary level of detail to
construct a price index is not generally available in real time, the basket of
goods and services usually relates to some earlier (usually annual) period of
time.
A price index constructed using a fixed basket of goods and services that relate
to some earlier time period is called a base-weighted index. The most
commonly used index of this type is a Laspeyres price index. The Laspeyres
price index formula is:
n
pq
it i 0
It =
i 1
n
p
x 1000
q
i0 i0
i 1
Where:
It = price index for period t
pit = price of ith product in period t
pi0 = price of ith product in base period
qi0 = quantity of ith product in base period
The denominator of the Laspeyres formula is the total expenditure or revenue of
the basket of goods and/or services purchased or sold in the earlier of the two
periods (period 0). The numerator of the formula multiplies the same quantities
sold or purchased in the earlier period (period 0) by the prices prevailing in the
later period (period t), giving an estimate of the cost or revenue of the fixed
basket at current prices.
As indicated above, the formula also scales the ratio of price change to 1000 at
the index reference period (period 0).
A property of the Laspeyres and other price index formulas is that they can be
used to provide an overall measure of price change across a range of different
goods and services expressed in a range of different quantities. For example,
the formula could be used to calculate a measure of overall price change of coal
and hair cuts.
In many situations, it is more feasible to collect expenditure or revenue
information than it is to collect quantity information. The Laspeyres formula
given above can be re-arranged and expressed in the following, algebraically
equivalent price-relative form:
11
 pit 
 
i 1
 pi 0  x 1000
It =
n
 wi 0
n
w
i0
i 1
Where:
It = price index for period t
pit = price of ith product in period t
pi0 = price of ith product in base period
wi0 = expenditure or revenue base weight of ith product
= pi0qi0
This formula is a weighted average price movement, with the weights being the
base-period expenditures or revenues. The base-period expenditure or revenue
weights represent the relative importance of the goods and services in the
weight reference period. For example, households spend more on petrol than
on newspapers, so a 5 percent rise in the price of petrol would have a greater
impact on the Consumers Price Index than a 5 percent increase in the price of
newspapers.
12
1e: About the Consumers Price Index
This section explains the compilation and publication practices of the CPI.
As the Food Price Index is a part of the CPI, in general many of these practices
also apply to the FPI.
Uses and stakeholders
The CPI is used as a measure of inflation, an indicator for monitoring economic
and monetary policy, an indicator of the effect of price change on the
purchasing power of households’ incomes, as a means to adjust benefits,
allowances and incomes, and as a price deflator.
Consumers Price Index: commonly used to monitor monetary policy, adjust
NZ superannuation and benefit payments, and in wage negotiations.
Perhaps its most well-known use is to help with the setting of monetary policy.
There is a Policy Targets Agreement between the Governor of the Reserve
Bank and the Minister of Finance, whereby the Governor aims to keep annual
CPI movements in the range of 1 to 3 percent on average over the medium
term. In doing this, the Governor increases or decreases the official cash rate
and changes in this rate have an impact on mortgage interest rates that
households pay.
Policy Targets Agreement: The Reserve Bank Act requires that price
stability be defined in a specific and public contract. This is called the Policy
Targets Agreement (PTA). The current PTA, signed in December 2008,
defines price stability as annual increases in the Consumers Price Index
(CPI) of between 1 and 3 per cent on average over the medium term.
Another important use of the CPI is that it is used by the government to adjust
New Zealand superannuation and unemployment benefit payments once a
year, to help ensure that these payments maintain their purchasing power.
Another common use is by employers and employees in wage negotiations.
The main reason cited by employers for increasing pay rates is to reflect
changes in the cost of living.
Superannuation and benefit adjustments: The Ministry of Social
Development adjusts payments to superannuitants, students, and people on
Veteran's Pension and benefits annually by the increase in CPI for the year
to 31 December. The adjustments are generally effective from 1 April the
following year.
13
Scope and coverage
The population coverage of the CPI relates to the expenditure of private, New
Zealand-resident households living in permanent dwellings. The reference
population covers approximately 98 percent of the usually-resident population.
There are no exclusions based on income source or geographic location.
The target population for the Household Economic Survey (HES) mirrors the
reference population for the CPI. Some types of expenditure are also excluded
because their price movements cannot be satisfactorily measured nor can they
be related to the price movements of items which are price-surveyed. These
include illicit drugs, pets and other livestock, gambling, most legal services etc.
Structure
The CPI is organised using the New Zealand Household Expenditure
Classification (NZHEC). This classification was adopted in 2006 and is based
on the international standard Classification of Individual Consumption According
to Purpose (COICOP).
There are about 690 goods and services included in the basket. They are
classified into 11 groups:
 Food
 Alcoholic beverages and tobacco
 Clothing and footwear
 Housing and household utilities
 Household contents and services
 Health
 Transport
 Communication
 Recreation and culture
 Education
 Miscellaneous goods and services.
Expenditure weights
Expenditure weights for the CPI are derived mainly from the HES and show the
proportion of average household expenditure made on the items in the regimen.
For some goods and services, the HES does not provide accurate estimates of
expenditure. Respondents tend to under-report expenditure on some goods and
services (such as tobacco and alcohol). Furthermore, large, infrequent
purchases (such as new cars) may not be reported frequently enough by the
sample population (nearly 2,600 households in HES 06/07) to provide accurate
estimates of total household expenditure.
HES data is typically complemented by information obtained from a range of
other sources, including Statistics NZ surveys, government administration data,
retail transaction data and information provided by businesses.
14
CPI basket: There are about 690 goods and services in the basket, broken
down into 11 groups.
Sampling and collection
An accurate measure of the overall level of price change can be calculated by
periodically surveying the prices of a representative sample of goods and
services.
Prices are surveyed by visiting retail outlets, by mail, or directly from collection
agencies (administrative or electronic collection) depending on the item.
Statistics New Zealand employs price collectors who personally visit over 3,000
different shops in 15 main centres throughout the country: Whangarei,
Auckland, Hamilton, Tauranga, Rotorua, Napier-Hastings, New Plymouth,
Wanganui, Palmerston North, Wellington, Nelson, Christchurch, Timaru,
Dunedin and Invercargill. Some examples of the type of outlets visited include
supermarkets, department stores and appliance stores.
In addition to prices obtained by field collectors, there are about 70 different
postal surveys sent out each month, quarter or year. These surveys are used
primarily for collecting the prices of services such as electricity and bus fares.
Some prices are collected each month or quarter from the Internet.
Food prices are collected from about 650 outlets in the
15 surveyed urban areas. Of these, about 75 are
supermarkets, 30 greengrocers, 30 fish shops, 30
butchers, 50 convenience stores (with half being service
stations and the other half being dairies, grocery stores
and superettes), 120 restaurants (for evening meals),
and more than 300 are other suitable outlets (for
breakfast, lunch and takeaway food).
The concept of constant quality
The aim of the CPI is to measure the price change in identical items over time.
Any price movement due to a change in quality should be excluded from the
CPI so that the true price change excluding all other factors is measured.
In practice, it is not always possible to price the same items over time.
Manufacturers regularly change items and other items are no longer produced.
In these cases a change in quality may occur when a substitute item is
introduced.
15
Quality assessments are done to put a monetary value on the change as
perceived by the consumer between the old and new item. Prices are then
adjusted so that no price change is shown that is related to the change in
quality.
Quality adjustment methods are covered in more detail in Prices Advanced:
Module 4.
Processes and calculation
The index is calculated using the price relative form of the base weighted
Laspeyres formula.
Releases
The CPI is produced quarterly and is usually released by the 12th working day
following the quarter. The FPI is produced monthly.
A range of additional analytical measures is released with the CPI each quarter.
This includes:



Tradables and non-tradables series, which decomposes items in the CPI
into two components: one containing goods and services that are
imported or that are in competition with foreign goods either in domestic
or foreign markets (tradables); and goods and services that face no
foreign competition (non-tradables).
Exclusion-based series, which are essentially analytical series showing
the CPI excluding certain items. Examples include CPI less central and
local government charges or CPI less purchase of housing.
Core inflation measures, which are measures of core or underlying
inflation aimed at tracking persistent or generalised trend of inflation.
Trimmed means and weight percentiles are the two core inflation
measures currently produced and published.
16
1f: About the Producers Price Index
This section explains the compilation and publication practices of the PPI.
As the Farm Expenses Price Index is closely related to the PPI, in general many
of these practices also apply to the FEPI.
Uses and stakeholders
The PPI is mainly used as a deflator by National Accounts to calculate real
Gross Domestic Product.
The PPI can be used in the analysis of inflationary trends, in economic
forecasting and in the estimation of real economic growth. The index is also
used to determine the increases/decreases allowable under indexation clauses
in commercial contracts.
The FEPI is mainly used by National Accounts for deflation of intermediate
consumption for the agriculture industry. It is also used by external
organisations such as Federated Farmers and Meat and Wool NZ for
monitoring changes in costs to farmers.
Scope and coverage
Producers Price Indexes
There are two types of PPI indexes: inputs and outputs.
The output indexes are designed to measure price changes at a level
corresponding to the price at the “factory door”, before the addition of
commodity taxes or deduction of subsidies (i.e. the price received by the
producer).
The PPI output and input indexes are arranged to align with the System of
National Accounts concepts of gross output and intermediate consumption,
respectively.
The output indexes cover the prices of:






primary products
manufactured goods
revenue from renting and leasing
the provision of services
capital work undertaken by own employees
margins on goods purchased for resale.
Excluded from the output indexes are:


interest and dividends
royalties and patent fees
17



receipts from insurance claims
government cash grants and subsidies
GST and other indirect taxes.
The input indexes measure price changes in costs of production excluding
labour and depreciation costs.
The input indexes cover the prices of:







materials
fuels and electricity
transport and communication
commission and contract services
rent and lease of land, buildings, vehicles and
plant
business services
insurance premiums less claims.
Excluded from the input indexes are:






wages and salaries (measured in the Labour Cost Index)
capital expenditure (measured in the Capital Goods Price Index)
ACC levies, land tax, government licence fees, road user charges
rates
royalties, patent fees
bad debts and donations.
GST is excluded when measuring input prices for 45 of the 47 industry input
indexes. The assumption is made that those involved in activities in these
industries are ‘registered persons, or businesses’ who provide ‘taxable supply’.
Interest costs are excluded because they are regarded as a cost of capital and
not as a payment for goods or services.
Government charges are excluded when they are used to raise tax revenue
rather than the payment for a good or service purchased from the government.
This is consistent with the System of National Accounts.
PPI input indexes: measure price change in the costs of production faced
by producers.
PPI output indexes: measures changes in prices received by producers.
18
Farm Expenses Price Index
The Farm Expenses Price Index (FEPI) measures price changes of fixed inputs
of goods and services to the farming industry. It does not fully measure changes
in the production costs of farming. This is because production costs are not
solely dependent on price movements, but are also dependent on factors that
affect productivity, such as technological advances, management efficiency and
climate fluctuations.
The FEPI differs from the PPI inputs to agriculture as it
includes items such as salary and wage rates, interest rates
and local and central government rates and fees.
The Labour Cost Index (LCI) is used to provide information
on salary and wage rates related to the farming industry.
Farm Expenses Price Index: measures change in prices of inputs of goods
and services to the farming industry.
Structure
The PPI and FEPI are constructed in a hierarchical manner.
For the PPI, at the lowest level actual price quotes are used to calculate
indexes at the representative commodity level, which then feed into industry
indexes and finally into the All Industries Indexes.
Similarly, the FEPI is constructed by calculating indexes at the input type level,
which then feed into farm type indexes and finally into the All Farms indexes.
An example of this index structure is shown below.
19
Representative
The industry classification used for the PPI is ANZIND96, a National Accounts
variation of ANZSIC96 – the Australian New Zealand Standard Industrial
Classification, 1996.
Expenditure weights
Expenditure weightings are determined by the relative importance of
commodities and businesses within the industry or industry group. Information
from various surveys and censuses and other sources is used to determine the
weightings, such as the Commodity Data Collection (CDC) survey and the
Annual Enterprise Survey (AES).
Sampling and collection
The PPI is calculated quarterly from price quotes, which are collected mainly by
the Commodity Price Survey (CPS). Approximately 10,000 individual
commodity items are surveyed from about 2,500 respondents. Any of the items
from the CPS may be used in the Capital Goods Price Index, Farm Expenses
Price Index, Producers Price Index, or indexes compiled solely for National
20
Accounts. Any given item may be used in more than one of the above index
groups.
Prices are generally collected each quarter with the price
at the 15th of the middle month of the quarter being
collected. Prices may be obtained monthly or annually
depending on the nature of the item.
Some commodities are not directly priced but are derived
from other data sources. For example revenue and volume
data is sometimes used to calculate unit prices.
Other sources of price data used in the PPI include prices collected for the
Consumers Price Index, Labour Cost Index and Overseas Trade Indexes.
Publicly available data is also used, including prices published in regular
publications, meat schedules, and the like.
Price quotes are generally used in more than one outputs industry index,
representing the prices received by producers for both representative and nonrepresentative commodities produced by that industry.
For example wool prices are collected mainly for the livestock
and cropping farming outputs index. However, wool is also
produced by groups like the dairy cattle farming, horticulture
and fruit growing industries, hence wool prices are included in
these indexes as a ‘non-representative’ output.
The price quotes are also used in the input indexes and often occur in more
than one index. For example nearly every industry consumes electricity during
the production process, hence electricity prices are used in nearly every inputs
price index.
Prices for the FEPI are collected as a subset of the Commodity Price Survey
(CPS).
Quality
Price indexes are primarily comparisons of prices. Every attempt is made to
exclude price change that is due to changes in the quality of a commodity. With
quality changes excluded, the price changes should be ‘pure’. Quality
adjustment is a method of adjusting the price so the price change is pure.
Techniques are available to make the appropriate price
adjustment. The most common method is to find a time
period when both the variants of the items are available
and to use the difference in their prices as a measure of
the value of the quality differences between them.
Another common approach is to find out the cost to the
purchaser of the additional features. For example, it may
21
be possible to establish that power steering added $850 to the cost of a new
model car. This value is subtracted from the price of the latest model to get the
price of an equivalent earlier model, without power steering. The adjusted
current period price could then be compared with the earlier price.
A number of quality adjustment methods are used in the PPI. These are
covered in more detail in Prices Advanced: Module 4.
Processes and calculation
The PPI and FEPI are Laspeyres base-weighted price index series.
Releases
The PPI is produced quarterly and is generally released on the same date as
the CGPI. For the FEPI, subindexes that feed directly into the PPI are published
quarterly. The entire FEPI is published in the March quarter only.
22
1g: About the Capital Goods Price Index
Uses and stakeholders
The CGPI is mainly used as a deflator by National Accounts to calculate real
expenditure on Gross Fixed Capital Formation. It can be used as a measure of
price stability like the Consumers Price Index and Producers Price Index. The
asset type indexes can be used in cost indexation clauses for that type of asset,
for inflation accounting as well as in replacement value insurance policies.
Scope and coverage
The price surveys of capital items for the CGPI cannot possibly cover all the
capital goods items purchased by producers.
Some items of Capital Equipment are excluded
from the Capital Goods Price Index. These are:


Large value items that are non-recurring
and / or manufactured to customised
specifications (e.g. Aircraft and Ships).
These have been excluded as comparable
prices for every period are difficult to obtain.
Second-hand equipment is also excluded
from the index.
Capital Goods Price Index: measures change in price of physical capital
assets purchased by producers of goods and services.
Structure
The CGPI All groups index is made up of six asset groups:
Residential Buildings, Non Residential Buildings, Other Construction, Land
Improvements, Transport Equipment, and Plant, Machinery and Equipment.
Expenditure weights
The weights of the commodities are determined by the relative importance
within each of the asset type indexes. Weighting information has been derived
from statistics on external trade, manufacturing and building, and vehicle
registrations, as well as discussions with manufacturers, importers, wholesalers
and retailers. Data for several years have been used, as expenditure on capital
goods can be irregular. GST is excluded from prices used in this index because
it is recoverable for GST-registered businesses.
23
Sampling and collection
It is not necessary to survey the prices of all capital items that producers
purchase, as many related items are subject to similar price movements. The
solution is to survey the prices of a selection of goods and services, which will
represent the price movements of the much wider range of items that
businesses purchase.
The factors, which are to be taken into account when selecting items to be price
surveyed are outlined below. The selected capital items should:




be representative of the capital items purchased by businesses;
have a price history;
have price movements that accurately reflect those of a broad grouping
of similar products; and
have a high probability of being available for a number of years; this
reduces the frequency and subsequent difficulties encountered when
items have to be replaced.
The prices used in the Capital Goods Price Index are collected by the
Commodity Price Survey.
Some prices used in the CGPI are obtained from various other publications.
Most of the ‘outlets’ used within the Capital Goods Price Index are either
manufacturers or wholesalers (e.g. cars). Some retailers also provide prices.
Quality
See the relevant section under About the PPI.
Processes and calculation
The CGPI is constructed using the same calculation methods as the PPI
indexes, i.e. the Laspeyres Price index formula.
Releases
The CGPI is produced quarterly and is generally released on the same day as
the PPI.
24
1h: About the Labour Cost Index
Uses and stakeholders
The index is commonly used in wage negotiations. It is also commonly used in
contract indexation clauses in conjunction with the corresponding Producers
Price Inputs Index (which measures movements in the price of non-labour
production costs) to determine an appropriate cost fluctuation adjustment. The
index is further used by economic forecasters and policy makers to monitor and
forecast wage movements. The Reserve Bank uses the Labour Cost Index, in
conjunction with the Quarterly Employment Survey, to monitor and forecast
changes in unit labour costs and nominal wage inflation, which feed into
monetary policy decisions. The index is used within Statistics New Zealand,
such as in the National Accounts, the Producers Price Index and in the Farm
Expenses Price Index.
Scope and coverage
The index covers jobs filled by paid employees in
all occupations and in all industries except private
households employing staff. Coverage was
extended to include jobs filled by paid employees
under 15 years of age when the index was
reweighted and re-expressed on a base of the
June 2001 quarter (=1000).
In practice, there are few part-time job descriptions in the survey, as it is
assumed that part-time salary and wage rates move in a similar way to full-time
rates for the same job descriptions. Thus, the main effect of the inclusion of
part-timers is their influence in determining the weights for each occupation,
based on their numbers in the Census of Population.
Structure
The Labour Cost Index is published by sector of ownership, by
sector and industry, by sector and occupation, and by industry
and occupation for all sectors combined.
Sector of ownership groupings comprise the local government
sector, central government sector, public sector, private
sector, and all sectors combined.
The industry breakdown consists of 27 published industry
groups, based on the Australian and New Zealand Standard
Industrial Classification (ANZSIC). The ANZSIC-based
industry groups are broadly in line with those used for the Producers Price
Index.
25
Occupation groups are based on the New Zealand Standard Classification of
Occupations 1999 (NZSCO99) and comprise one-digit major groups, selected
two-digit sub-major groups, and the three broader categories of managers,
professionals and technicians; clerks, service and sales workers; and other
occupations.
Expenditure weights
Each job description used in calculating the Labour Cost Index is assigned a
weight which reflects the relative importance of the job description within its
sector of ownership, industry and occupation group.
The main sources of information used in determining these weights include the
Census of Population, Quarterly Employment Survey (QES), Linked EmployerEmployee Database (LEED), Business Frame (BF), and surveyed pay rates
from the Labour Cost Survey (LCS).
Sampling and collection
Information used in calculating the index is obtained by a
quarterly postal survey of employers, called the Labour
Cost Survey (LCS). Salary and wage rates for a fixed set
of job descriptions are surveyed for the pay period which
includes the 15th of the middle month of each quarter.
Information on non-wage labour costs (superannuation,
annual leave, fringe benefits and ACC rates) is collected
in the June quarter each year.
Quality
The index is a quality-controlled measure. Only changes in salary and wage
rates for the same quality and quantity of work are reflected in the index. This is
achieved in practice by asking respondents to provide reasons for movements
in salary and wage rates. If a movement is due to more than one reason, the
respondent is also asked to indicate how much of the movement is due to each
reason.
To further assist the measurement of movements in pay rates
for a fixed level of labour input, job descriptions are specified in
detail. Surveyed job descriptions typically specify the duties
involved, qualifications required, years of service and number
of hours worked.
In theory, these job descriptions should remain fixed between
index reviews. In practice, many descriptions change over
time, usually as a result of changes to contractual
arrangements or because specific employees are being
tracked through time.
26
If a newly negotiated contract involves an increase in the number of ordinary
time hours worked per week, then the description is amended and an
adjustment is made to ensure that the pay rate movement used in the index
relates to the same quantity of work as specified in the new contract.
Similarly, rates being paid for job descriptions in the survey may change partly
or wholly because employees undertaking these jobs have become more
experienced, more (or less) proficient or productive, better qualified, have taken
on additional responsibilities or have been promoted. Components of salary and
wage rate movements which are due to changes of this type in the quality of
work are not reflected in index movements. A policy of excluding increases due
to service increments and merit promotions is consistent with this approach.
Processes and calculation
The index is calculated using the price-relative form of the base-weighted
Laspeyres formula, and is expressed on a base of the June 2001 quarter
(=1000).
Releases
Salary and wage rates indexes are published quarterly, on the same day as the
Quarterly Employment Survey (QES). The LCI and QES share a media release.
The QES and LCI both measure wage growth over time.
However, the two surveys have different approaches to the
measurement of wage growth, and therefore can often have
different results.
The LCI is a quality controlled measure, and calculates the wage
growth for a fixed set of job descriptions, while the QES
measures average wages. When the level or composition of
employment changes, the average earnings data in the QES will
be affected, while the LCI will be unaffected.
LCI indexes of non-wage labour costs and all labour costs are published for
only the June quarter of each year.
The LCI measures changes in pay rates for a fixed set of job descriptions,
while aiming to keep “quality” constant.
The QES measures average hourly earnings and is affected by changes in
the composition of the workforce as well as changes in pay rates.
27
Unadjusted LCI
The LCI (salary and wage rates) measures movements in base salary and
ordinary time wage rates, and overtime wage rates for a fixed quantity and
quality of labour input. This means that changes in pay rates due to the
performance of employees and promotions, among other things, are not shown
in the index. An unadjusted LCI was developed to complement the official LCI in
providing a more comprehensive picture of wage changes. In contrast to the
official LCI, the unadjusted series reflects quality change within occupations.
The published index:
 often tracks employees, but does not show performance-related
increases or service increments
 commonly links in new employees (without showing change).
The analytical unadjusted index:
 often tracks employees, and shows performance-related increments and
service increments
 shows any change when new employees replace incumbents.
From the March 2008 quarter, the unadjusted index has been published as an
analytical series as part of the quarterly LCI (salary and wage rates).
The LCI (salary and wage rates) excludes performance-related changes in
pay rates while the analytical unadjusted LCI includes performance-related
changes in pay rates.
28
1i: About the Overseas Trade Indexes
Uses and stakeholders
The Overseas Trade Price and Volume Indexes are key economic indicators,
which have a variety of applications and uses.
They enable analysts and policy makers to assess the effects of export and
import price and volume level changes on the economy and on the balance of
payments. Changes in export and import price and volume levels can be
monitored and underlying trends analysed for forecasting the prospects of
various sectors of the economy.
Export and import indexes are used to calculate
Expenditure on Gross Domestic Product (GDP) at
Constant Prices, and Indexes of GDP at Constant
Prices by Production Group. Selected price index
series are used to deflate current export and import
values, and some volume index series are used to
extrapolate base period values.
The export and import price indexes can be used to
assess the impact of changes in export and import
price levels on domestic price levels, as they can indicate possible future
inflationary trends.
In conjunction with changes in the nominal exchange rate, the export and import
price indexes can be used to monitor changes and trends in world prices.
Export and import price indexes are also used in escalation clauses in export
and import related contracts.
Scope and coverage
The merchandise trade indexes include all commodities classified as
merchandise trade, although the export indexes exclude re-exports, bunkering,
ships’ stores and passengers’ effects.
The System of National Accounts 1993 (SNA’93) provides the conceptual base
for the services indexes. It establishes the range of services that should be
included in the indexes and key practices, for example the treatment of
insurance.
Effect of exchange rate movement
Changes in export and import price levels reflect movements
in both exchange rates and in the actual foreign currency and
New Zealand dollar prices that goods are bought and sold for.
A decline in the value of the New Zealand dollar has an
upward influence on both export and import price levels, while
29
a rise in the value of the dollar has a downward impact on export and import
price levels.
Structure
The merchandise indexes are classified into commodity groups. Food &
beverages and petroleum & petroleum products are two examples of
merchandise import commodity groups, while dairy products and forestry
products are two examples of merchandise export commodity groups.
For imports, commodities are also published by Broad Economic Categories
(BEC), a classification based on the main end use of commodities. This means,
for example, that all video recorders are treated as consumption goods even
though some are used in business. The BEC categories are arranged to align
with the System of National Accounts categories of capital goods, intermediate
goods, and consumption of goods.
The System of National Accounts 1993 (SNA’93) provides the conceptual base
for the services indexes. It establishes the range of services that should be
included in the indexes and key practices, for example the treatment of
insurance. The four published import and export service categories are:
 Transportation
 Travel
 Other services
 Government services.
Expenditure weights
Value and quantity data used for calculating the merchandise price indexes are
derived from Statistics New Zealand's overseas merchandise trade statistics,
which are in turn processed from export and import entry documents lodged
with New Zealand Customs Service (NZCS) by exporters, importers and their
agents.
Data is classified using the Harmonised System (HS) classification for
processing NZCS entries and publishing overseas trade statistics. There are
about 13,500 10-digit items in the HS classification.
Expenditure weights are assigned at the Harmonised System (HS) 10-digit item
by country level. Item and index weights are not fixed. They vary from quarter to
30
quarter and from year to year as the relative values of goods New Zealand
exports and imports change.
Sampling and collection
The main source of information for the OTI price indexes is unit values derived
from the NZ Customs Service value and quantity data. For basic, homogeneous
commodities not subject to ongoing quality change, unit values provide suitable
indicators of price change.
The unit values data is supplemented by prices directly collected from
businesses and the by international price indexes for some goods.
Prices are collected directly from importers and exporters for selected goods
that are regularly imported or exported in the same form to the same or similar
specification. Directly surveyed prices are collected from importers and
exporters via the Commodity Price Survey used for the Producers Price Index.
The process of adding to the pool of directly surveyed prices should be an
ongoing one that is part of the ongoing overseas merchandise trade index
quality assurance programme.
International price indexes are used selectively as
a proxy to measure price change faced by
importers for goods that are irregularly imported
(for example public transport equipment), imported
to one-off specifications (for example, telephonic
and telegraphic apparatus) and technically
complex goods subject to rapid quality change (for
example computer equipment).
Processes and calculation
Merchandise trade
The merchandise index series are of the chain-linked Fisher Ideal type. The
calculation of a Fisher Ideal index involves first calculating two indexes. One,
the Laspeyres, is base-weighted and uses expenditures from an earlier period
to weight price or volume movements. The other, the Paasche, is currentweighted and uses expenditures from a current period to weight price or volume
movements. The Laspeyres and Paasche indexes are then averaged by
calculating the geometric mean (that is, the square root) of the two indexes to
give the Fisher Ideal index.
Laspeyres, Paasche and Fisher price indexes are covered in further detailed in
Prices Intermediate: Module 2.
31
Services trade
The services indexes are an annually chain-linked Laspeyres price index series.
The weights are determined by the relative importance of services and
businesses within the service industry. Information from various surveys,
censuses and other sources are used to determine the weights.
Releases
Overseas Trade Price Indexes are released quarterly in conjunction with the
volume and value series.
Provisional quarterly and annual price indexes are available within 10 weeks of
the end of the reference quarter. Final indexes are released within 24 weeks of
the end of the reference quarter.
Only final data are released for the services indexes.
Overseas merchandise terms of trade: an index which measures the
changing volume of merchandise imports that can be funded by a fixed
volume of New Zealand's merchandise exports.
32
1j: Differences Between the CPI, PPI, LCI and OTI
The difference between the various indexes is driven primarily by the set of
transactions that each index sets out to measure price change for. The sets of
transactions are bordered by the products origin (domestic or imported);
destination (business, government, consumers or rest of world); and/or end use
(capital, consumption or labour).
The table below attempts to set out the various borders that define the sets of
transactions each index is designed to cover.
Index
PPI - Inputs
PPI - Outputs
CGPI
OTI Export Price Index
OTI Import Price Index
LCI
CPI
Product Properties
Origin
Destination
Either
Government & Business Sectors
Domestic Any
Either
Government & Business Sectors
Domestic Rest of the World
Imported All Domestic
Either
Government & Business Sectors
Either
Household Sector
Use
Intermediate Consumption
Any
Capital Formation
Any
Any
Labour
Final Consumption1
1 includes some capital formation such as owner-occupied housing purchased by households.
If we look at the suite of price indexes produced by Prices in terms of economic
flows we can see that they aim to cover the various parts of the economy as
represented in the flow chart below.
Inflation Flows in the Economy
Export Price Index
Producers
Price Index
(outputs)
Import Price Index
Production sector
outputs
Expenditure by production/government sector
Labour
costs
Labour Cost Index
Current
costs
Expenditure by household sector
Capital
costs
Producers Price
Index (inputs)
Capital Goods
Price Index
Consumers
Price Index
Taking the expenditure by business and government on inputs into their
production process as a starting point we can see that there are three broad
expenditure items: Labour, Capital and Current Costs. Each of these sets of
transactions is covered by a specific price index:
33
Labour Cost Index: The salary and wage rate component of the LCI
measures movement in base salary and ordinary time wage rates, and
overtime wage rates for paid employees in all occupations and in all
industries except private households employing staff. The non-wage
component measures changes in annual leave and statutory holidays,
superannuation, ACC employer premiums and fringe benefits items for the
same population.
Capital Goods Price Index: Provides a measure of the price level changes
for physical capital assets purchased by producers of goods and services
throughout the economy.
Producers Price Index (Inputs): The inputs indexes measure price changes
in costs of production, excluding labour, government charges and
depreciation costs.
Industry (producers) in New Zealand use these inputs to produce outputs which
are then sold onto either consumers, the rest of the world (exports) or back in
NZ industry. The sale of all these products is covered by the Producers Price
Index (Outputs).
Producers Price Index (Outputs): The outputs index measures changes in
prices received by producers for the goods and services they have produced
and sold.
The items which are purchased by consumers are, naturally, covered by the
Consumers Price Index.
Consumers Price Index: measures the rate of price change of goods and
services purchased by households. It includes some capital formation. For
example, net acquisition of assets such as owner-occupied dwellings is
included.
New Zealand’s interaction with the rest of the word is covered by the Export
Price and Import Price Indexes. The Export Price Index is, in scope, a subset
essentially of the Producers Price Index (Outputs), while the items within the
Import Price Index could also fall within the PPI (Inputs), Capital Goods Price
Index or CPI.
Export Price Index: Measures changes in the price levels of exports from
New Zealand. There are separate indexes for merchandise and services
trade.
Import Price Index: Measures changes in the price levels of imports into
New Zealand. There are separate indexes for merchandise and services
trade.
34
In addition to defining the universe of prices to be measured, the scope of the
index also has implications for other aspects of the index such as: how the
prices are collected; the pricing point used; and performing quality adjustments.
The pricing point used in the index is determined by the set of transactions as
covered above. Where we are measuring price changes for ‘purchases’ such as
in the case of the CPI or PPI Inputs, the pricing point used is producer’s prices.
Where we are measuring price changes for ‘sales’ such as in the PPI outputs
basic prices are used.
Producer’s Prices: “the amount paid by the purchaser,
excluding any deductible taxes (GST in New Zealand), in
order to take delivery of a unit of a good or service at the time
and place required by the purchaser.” This means that the
purchaser’s price is equal to the producer’s price plus any
transport charges paid separately by the purchaser in order to
take delivery at the required time and place.
Basic Prices: “the amount receivable by the producer from the purchaser for a
unit of a good or service produced as output minus any tax payable, and plus
any subsidy receivable, on that unit as a consequence of its production or sale.
It excludes any transport charges invoiced separately by the producer.” This
means that the basic price is exactly the amount of money that the producer
earns from the sale of their good or service.
Example: Basic and purchaser’s price
VAT1)
Basic price (excluding deductible
+ Taxes on product, except VAT
- Subsidy on products
= Producer’s price
+ Non-deductible VAT
+ Transport charges and trade margins paid by the
purchaser
= Purchaser’s price
1 VAT = Value Added Tax
Amount
12
1
5
8
2
3
13
In this example, the seller is actually able to retain $12 for the product (basic
price). The sales transaction takes place at $8.00 (producer’s price). The seller
gets an additional $4.00 from the subsidy, less the tax. The purchaser has to
actually expense $13 to take possession of the good (producer’s price), with $5
going to non-deductible taxes and transport charges and trade margins.
The reality is that product subsidies often have to be ignored, because they
cannot be separately identified by producers. For example, bus subsidies may
not be allocated to the ticket price for a particular route. Therefore in many
cases we end up collecting the producer’s price for the PPI, because it is too
difficult to get the basic prices.
35
The two international trade indexes use a slight variation on the above pricing
points:
f.o.b.: the pricing basis used in the Export Price Index is Free on Board which is
the value of the good including the cost incurred in delivering goods on board
ships and aircraft at New Zealand ports.
v.f.d.: the pricing basis used in the Import Price Index is Value for Duty which is
the value of goods excluding the cost of freight and insurance.
************************************************************************************
Exercise 2
1. Why is there a need to produce so many price indexes? Why don’t we
just have one overall price index for the economy?
2. How do price movements in one sector of the economy (e.g. the
production sector) affect another sector (e.g. the households sector)?
3. What is the difference between producer’s prices and basic prices?
************************************************************************************
1k: Price Index Mechanics
A Price Index tells how the value of something at a point in time compares to
the value of the same thing at another point in time.
An index number on its own means nothing. It must be compared with an index
number from another period to determine the price movement between the
other period and the current period.
Thus the standard practice when quoting an index number, is to ensure that the
index reference period and its value are also quoted.
Index reference period
Indexes in New Zealand commonly have an index reference period value of
1000. Other countries may use 100 or 100.0.
This figure is merely a convenient number to which the rest of the index
numbers can be related.
36
It does not matter what number is chosen to represent the reference period,
because the interest is only in the relationship of the other numbers to it.
The index reference period may be changed when an index review or reweight
takes place.
Other names for “Index reference period” are “Expression Base”, “Comparison
Base” or “Reference Base”.
Example
If the index number for a period is 1250, then this means that
prices have increased by 25 percent since the index reference
period.
Similarly, if the index number is 850, then this means that prices
have fallen by 15 percent since the index reference period.
Index reference period: Price indexes produced by Statistics NZ have an
index reference period value of 1000.
Price reference period
The price reference period of an index is the reference time period (i.e. month
or quarter) in which the base period prices are selected, that is, where the price
is = p0.
It is normally set in the latest reference period for which pricing information is
available at the time an index is redeveloped.
Weight reference period
The weight reference period of an index refers to the year or years from which
the weighting data was derived.
It is normally set as the period which the main weighting source information
relates to.
***********************************************************************************
Exercise 3
1. What are the differences between index reference period, price reference
period and weight reference period?
2. How would you go about determining what each of these periods should
be?
************************************************************************************
37
Calculating a price index
Simplistically, a price index can be calculated for a single item by:
Taking a time series of prices:
Month >>
Price ($ per Kg)
Jan
5.00
Feb
5.60
Mar
6.00
Apr
7.00
Choosing an index reference period - In this case, we chose January but could
have been any month in the series.
Index Base Jan
1000
Increasing the index reference period index number by the increase in the price
from the index reference period - For this example, the index for February
has been calculated below:
Month >>
Jan
Index Series on Base 1000
Jan
Feb
1000 
5.60
 1120
5.00
Mar
c
Apr
d
***************************************************************************************
Exercise 4
Index Calculation
Fill in the cells c and d above for March and April indexes, respectively.
Note that we have a time series about a price movement from an index
reference period of 1000. By convention, we do not include a comma in the
1000.
****************************************************************************************
How an index is read
Percentage change
A price index is read to get information about how the price
of something is changing over time. The changes are
commonly expressed as percentage changes.
Example
In the earlier example in Exercise 5, by what percentage
has the price of the coffee in month 2 increased over its
38
price in month 1? The index has increased from 1000 to 1500 in index number
terms.
Method:
The original value of 1000 has increased by 500 which is 50% of itself i.e. a
50% increase.
i.e.
1500 - 1000 = 500
500 / 1000 = 0.50
0.50 x 100 = 50%
Percentage calculation
A percentage change expresses the difference between two numbers as a
proportion of one of those numbers.
In price index work, it is conventional to express the later period index as a
percentage of some earlier period, i.e., the difference between the earlier and
later period as a proportion of the earlier period. (That proportion being on the
basis of per hundred rather than per one.)
The percentage change from the previous period t-1 to the current period t is =
It
 I t 1
I t 1
 100
Cumulative percentages
Indexes represent the prices of goods at different months or quarters of the
year.
As well as the price movement between quarters of the year, the price
movement for the whole year may need to be known. A common mistake is to
add the percentage movements of the four quarters together to arrive at the
annual movement.
Index movements cannot be calculated by adding the percentage results
between the intervening index periods. Movements must always be calculated
between the extremes of the period under consideration, because of the
compounding characteristic of index numbers.
39
***********************************************************************************
Exercise 5
More Index Movements
Consider the following index series:
Quarter
Index
number
Mar-03
Jun-03
Sept-04
Dec-04
Mar-04
1000
1030
1500
1700
1900
Quarter
change (%)
A
B
Sum of
Change from
quarters (%)
base (%)
3.0
45.6
13.3
11.8
1. Fill in column A by entering the cumulative sum of percentages of the
quarters.
2. Fill in column B by entering the change of the index for each quarter from
the base.
The percentage movements for the quarters are:
March to June 3.0% [ ie.( 1030-1000) x 100 ]
1000
June to September 45.6% [ ie. (1500 - 1030) x 100 ]
1030
September to December 13.3% [
ie. (1700 - 1500) x 100 ]
1500
December to March 11.8% [ ie. (1900 - 1700) x 100 ]
1700
The sum of the quarterly percentage movements is 73.7%.
However, the index has moved from 1000 to 1900 for the year,
which is an increase of 90%. [ ie. (1900 - 1000) x 100 ].
1000
Clearly, the sum of the quarterly movements does NOT equal the annual
movement.
****************************************************************************************
40
The interpretation of indexes
Caution should be exercised when comparing two or more price indexes. Since
we say it measures price movements, it should not be misinterpreted as actual
price levels.
Example
Suppose that the index numbers for petrol and bread for the June 1994 quarter
are 1300 and 1150 respectively (December 1993 quarter = 1000).
This does not mean that the price of petrol is higher than the cost of bread.
What it does say is that since the December 1993 quarter, the price of petrol
has risen by more (up 30 percent) than the price of bread (up 15 percent).
Price index is about price change NOT price level
Suppose you have a series of index numbers that represents the
price of a packet of coffee over three months (the same size and
brand is priced each time, same outlets, same group of people
buying). The price of the coffee is expressed as follows:
Index Movement
Month 1
Month 2
Month 3
Index
number
1000
1500
1650
Percentage
change (month to
month)
Percentage
change(base to
current month)
50
10
50
65
It can be seen from this series that the price of this particular brand of coffee
increased by 50% between the first and second months. In month 3, the price
was 10% more than it was in month 2 and 65% greater than it was in month 1.
However, nothing is known about the actual price of the coffee. It may have
been $8.00 in month 1 and increased to $12.00 by month 2, or it may have
started at $15.00 and increased to $22.50. The index numbers provide no
information about the actual price of the coffee.
Spatial versus temporal indexes
The CPI, PPI, FEPI, CGPI, OTI and LCI are indexes which track price changes
of a set of goods and/or services over time. These are known as temporal
indexes. For example, they cannot be used to draw inferences about whether
prices in one region are any higher or lower than prices in any other region.
41
Another type of index, called spatial indexes, compares price levels at a given
point in time across regions or countries.
The essential difference between temporal and spatial comparisons of prices is
that in the former the objects of comparison are different periods of time while in
the latter it is regions which are being compared. While temporal comparisons
measure the difference in price levels over time, spatial comparisons measure
the difference in price levels across space.
The 2004 CPI Revision Advisory Committee concluded that there would be
some interest in a spatial index which compares regional differences at a point
in time in the cost of living, for example between Auckland and Wellington.
Statistics New Zealand currently does not produce any spatial indexes. We are
however involved in the Organisation for Economic Co-operation Development
(OECD)’s Purchasing Power Parity (PPP) programme.
OECD PPP programme: PPPs are a measure of the relative domestic
prices of the components that form GDP in each country and allow intercountry comparisons of price levels. The well-known ‘Big Mac Index’,
published in The Economist magazine, is an example of a PPP comparison.
42
1l: Interpreting Price Index Outputs
As producers and/or users of price indexes, it is obviously important to be able
to understand index movements and perform analysis of the results. This can
also help to assure the quality of the published indexes.
Assuming that the individual prices have passed through quality checks, the
probability that the index is incorrect is relatively low. But relatively low is not
quite good enough. It is normal for producers of indexes to carry out 'macro
edits' of the finished product. This includes the following:



visual scan (of tables and graphs) to see if everything looks reasonable
calculation of percentage changes
examination of the significant contributions of regimen sets to the
movements of higher-level indexes.
Visual scan
Experienced statisticians can, by just looking at a table, pick up apparent
anomalies. That is practice and experience. An alternative is to graph the series
and look for irregular peaks and troughs. Excel can create graphs very quickly
and you can get data into Excel from any other
electronic format.
When graphing it is best to have a minimum of
three years data as there may be seasonal
patterns, which can only be identified with a
minimum of three and ideally five years’ data. If
there is an apparent seasonal pattern the eye may
not see anomalies. In these situations there are
advantages in doing a seasonal analysis.
Examining the low level index series is more likely to find anomalies. In the
higher level indexes such anomalies may be hidden.
Anomalies may of course be a reflection of what is happening out there in the
real world, in which case they are accepted but probably require a mention in
the media release.
Because price index samples are generally quite small, and because we are
basing index calculations on a sample of transactions from a sample of
providers at a sample of points of time, for a sample of products within a sample
of goods and services, we must always be prepared to question whether outlier
movements are representative of the wider population of transactions.
43
Quarter
Veg
Jun-99
Sep-99
Dec-99
Mar-00
Jun-00
Sep-00
Dec-00
Mar-01
Jun-01
Sep-01
Dec-01
Mar-02
Jun-02
Sep-02
Dec-02
Mar-03
Jun-03
Sep-03
Dec-03
Mar-04
Jun-04
Sep-04
Dec-04
Mar-05
Jun-05
Sep-05
Dec-05
Mar-06
Jun-06
Fruit
1000
1002
902
886
934
1054
1066
1075
1096
1242
1163
1096
1039
1245
1163
1051
1076
1154
1148
1148
1176
1277
1184
1084
1059
1131
1091
1055
1177
1069
1201
1146
1059
1098
1236
1103
1034
1025
1261
1217
1128
1102
1381
1285
1151
1129
1229
1179
1147
1095
1267
1157
995
910
1008
1023
987
1000
Vegetables and Fruits
Quarterly indexes
1600
1400
1200
Index
1000
Veg
800
Fruit
600
400
200
Ju
nSe 9 9
pDe 99
c
M -99
ar
J u 00
nSe 0 0
p
De -00
c
M -00
ar
J u 01
nSe 0 1
p
De -01
c
M -01
ar
J u 02
nSe 0 2
p
De -02
c
M -02
ar
J u 03
nSe 0 3
p
De -03
c
M -03
ar
J u 04
nSe 0 4
p
De -04
c
M -04
ar
J u 05
n
Se -0 5
p
De -05
c
M -05
ar
J u 06
n06
0
Quarter
The time series above are typical of price indexes of vegetables and fruits. It
shows that prices tend to peak every September quarter.
The graph shows more clearly than the table that there is a rise and fall that has
some seasonality.
44
***********************************************************************************
Exercise 6
Group Discussion
1. Given the graphs below, what can you say about the price movements of
this particular item?
CPI Subsection Index
1160
1140
1120
Index
1100
Index Number
1080
1060
1040
1020
Jun-02
Sep-02
Dec-02
Mar-03
Quarter
CPI Subsection Index
1200
1180
1160
1140
Index
1120
Index Number
1100
1080
1060
1040
1020
1000
Jun-02
Sep-02
Dec-02
Mar-03
Jun-03
Quarter
45
Sep-03
Dec-03
Now that you can see more observations, what can you say?
CPI Subsection Index
1200
1180
1160
1140
Index
1120
Index Number
1100
1080
1060
1040
1020
1000
Jun-02
Sep-02
Dec-02
Mar-03
Jun-03
Sep-03
Dec-03
Mar-04
Quarter
CPI Subsection Index
1400
1200
1000
800
Index
Index Number
600
400
200
0
Mar-94
Mar-95
Mar-96
Mar-97
Mar-98
Mar-99
Mar-00
Mar-01
Mar-02
Mar-03
Mar-04
Mar-05
Mar-06
Quarter
The graphs above refer to Writing Pads and Refills.
Below is the corresponding time series data of Writing Pads and Refills from the
December 1993 quarter to the June 2006 quarter.
2. Discuss: What further observations do you have on the index movements
based on the time series data? What do you think are the reasons for the
decreases in prices of writing pads and refills every March quarter? What
has happened over time to the size of the March quarter decreases?
46
What do you think are the reasons for this? How might you go about
finding out more about the reasons?
Writing pads and refills (I1A1)
Quarter
Index Number
Dec-93
923
Mar-94
739
Jun-94
886
Sep-94
877
Dec-94
934
Mar-95
813
Jun-95
881
Sep-95
932
Dec-95
988
Mar-96
842
Jun-96
992
Sep-96
1020
Dec-96
1019
Mar-97
743
Jun-97
919
Sep-97
953
Dec-97
967
Mar-98
777
Jun-98
941
Sep-98
990
Dec-98
1023
Mar-99
795
Jun-99
1000
Sep-99
1014
Dec-99
1015
Mar-00
831
Jun-00
971
Sep-00
1011
Dec-00
1030
Mar-01
888
Jun-01
1099
Sep-01
1104
Dec-01
1101
Mar-02
950
Jun-02
1097
Sep-02
1122
Dec-02
1139
Mar-03
1063
Jun-03
1145
Sep-03
1158
Dec-03
1173
Mar-04
1128
Jun-04
1176
Sep-04
1158
Dec-04
1169
Mar-05
1058
Jun-05
1167
Sep-05
1212
Dec-05
1208
Mar-06
1124
Jun-06
1202
Percentage Change
(Prev Period)
-19.9
19.9
-1.0
6.4
-12.9
8.4
5.8
6.0
-14.8
17.7
2.9
-0.1
-27.1
23.7
3.7
1.5
-19.7
21.1
5.2
3.3
-22.3
25.8
1.4
0.0
-18.1
16.8
4.1
1.9
-13.9
23.9
0.4
-0.2
-13.7
15.4
2.3
1.4
-6.6
7.7
1.1
1.3
-3.9
4.2
-1.5
1.0
-9.5
10.3
3.8
-0.3
-7.0
6.9
47
Percentage Change
(Annual)
1.2
10.0
-0.6
6.2
5.9
3.6
12.5
9.4
3.1
-11.8
-7.4
-6.6
-5.1
4.6
2.4
3.9
5.8
2.4
6.3
2.5
-0.8
4.5
-2.9
-0.3
1.6
6.8
13.2
9.2
6.9
7.1
-0.2
1.7
3.4
11.9
4.4
3.2
3.1
6.1
2.7
0.0
-0.3
-6.2
-0.7
4.6
3.3
6.2
2.9
****************************************************************************************
Rates of change
Rates of change are ratios of total change in a specified time reference period
to values at the beginning of the period or at a specified earlier time reference.
These can be observed by simply looking at the slopes of the index graphs.
***********************************************************************************
Exercise 7
3. Which index changes more rapidly:
a) the one that decreases by each quarter 68 index points, or,
b) the one that decreases by 20.0 percent each quarter?
Through visual scan of the line graphs, the overall rates of change indicate that
the one that decreased by 20.0 percent quarterly (or Figure 1 below) declines
more rapidly than the one that decreased by 68 index points quarterly (or Figure
2 below).
The slope of Figure 1 shows a rapid decline from the December 2003 quarter to
the September 2005 quarter but began to slow down from the September 2005
quarter to the March 2007 quarter. The slope of Figure 2, on the other hand,
decreased at a constant slope but has actually caught up with Figure 1 in the
March 2007 quarter and surpassed the rate of change beginning in the
September 2006 quarter (which is 21.3 percent versus the previous quarter
compared with 20.0 percent of Figure 1).
Quarter Figure 1
Dec-03
1000
Mar-04
800
Jun-04
640
Sep-04
512
Dec-04
410
Mar-05
328
Jun-05
262
Sep-05
210
Dec-05
168
Mar-06
134
Jun-06
107
Sep-06
86
Dec-06
69
Mar-07
55
Figure 1
Figure 2
vs. Previous vs. Previous
Figure 2
(%)
(%)
1000
932
-20.0
-6.8
864
-20.0
-7.3
796
-20.0
-7.9
728
-20.0
-8.5
660
-20.0
-9.3
592
-20.0
-10.3
524
-20.0
-11.5
456
-20.0
-13.0
388
-20.0
-14.9
320
-20.0
-17.5
252
-20.0
-21.3
184
-20.0
-27.0
116
-20.0
-37.0
48
Rates of Decrease
Figure 1 and Figure 2
1200
1000
Index
800
Figure 1
600
Figure 2
400
200
D
ec
-0
3
M
ar
-0
4
Ju
n04
Se
p04
D
ec
-0
4
M
ar
-0
5
Ju
n05
Se
p05
D
ec
-0
5
M
ar
-0
6
Ju
n06
Se
p06
D
ec
-0
6
M
ar
-0
7
0
Quarter
4. The same concept applies with increasing rates of change. For example,
which index changes more rapidly:
a) the one that increases by 15.0 percent each quarter, or,
b) the one that increases by a 400 index points each quarter?
Without looking at the graphs, the numbers can be quite misleading. Although
400 index points quarterly sounded like a huge increase per quarter, the
increase of 15.0 percent quarterly actually rises by about the same amount
overall because of the compounding effect of incremental increases from
quarter to quarter (see graphs below).
Figure 1 (which increases 15.0 percent per quarter), started more slowly but
eventually caught up with Figure 2 (which increases by 400 index points per
quarter). In the table, Figure 2's rate of change showed a continuous decline
and became lower than 15.0 percent starting in the June 2005 quarter.
Quarter
Figure 1
Dec-03
1000
Mar-04
1150
Jun-04
1323
Sep-04
1521
Dec-04
1749
Mar-05
2011
Jun-05
2313
Sep-05
2660
Dec-05
3059
Mar-06
3518
Jun-06
4046
Sep-06
4652
Dec-06
5350
Mar-07
6153
Figure 1
Figure 2
vs. Previous vs. Previous
Figure 2
(%)
(%)
1000
1400
15.0
40.0
1800
15.0
28.6
2200
15.0
22.2
2600
15.0
18.2
3000
15.0
15.4
3400
15.0
13.3
3800
15.0
11.8
4200
15.0
10.5
4600
15.0
9.5
5000
15.0
8.7
5400
15.0
8.0
5800
15.0
7.4
6200
15.0
6.9
49
Rates of Increase
Figure 1 and Figure 2
7000
6000
Index
5000
4000
Figure 1
Figure 2
3000
2000
1000
D
ec
-0
3
M
ar
-0
4
Ju
n04
Se
p04
D
ec
-0
4
M
ar
-0
5
Ju
n05
Se
p05
D
ec
-0
5
M
ar
-0
6
Ju
n06
Se
p06
D
ec
-0
6
M
ar
-0
7
0
Quarter
In summary, an index that grows or declines each quarter by the same
percentage has a concave shape when graphed (blue line). An index that
grows or declines each quarter by the same number of index points has a
straight-line shape when graphed (pink line).
Remember
An index that grows or declines each quarter by the same percentage has a
concave shape when graphed.
An index that grows or declines each quarter by the same number of index
points has a straight-line shape when graphed.
50
Percentage changes and real world price changes
Using the computer to establish the level of change can assist in finding errors.
Such percentage changes will also be used in the media release. GIFT provides
some facilities for this. Again Excel can be used and can be set up to identify
changes above a preset level.
Being aware of real world price changes and looking
to establish if they are reflected in the percentage
changes in the relevant time series is important. Petrol
price changes are a regular in those examinations.
Reading through price collectors’ reports and
respondent comments will also put one “on enquiry”
for changes.
Unrounded or rounded index numbers
So which is right? The percentage changes calculated from the unrounded
index numbers, or the percentages calculated from the index numbers which
have been rounded to the nearest index point. In the final analysis, the error
margin of the index time series would almost always be greater than the
difference between the rounded and unrounded index numbers.
The usual practice for the CPI, PPI and LCI is to publish index numbers
rounded to the nearest index point, and to calculate percentage changes from
the rounded index numbers. When index numbers are extracted from the GIFT
index calculation system, rounding is done only at the level that index numbers
are output. Product total calculations at all levels of the hierarchical index
structures are made using unrounded numbers stored to the highest level of
precision possible.
For the OTI, published percentage changes have, for some years, been
calculated from unrounded index numbers.
When the index reference period (or expression base) of the CPI or the LCI is
updated, the previously published index numbers rounded to the nearest index
point are rescaled, and decimal places are retained to preserve the originally
published percentage changes exactly.
Short cuts in calculating percentage changes
There are short cuts in calculating percentages.
I
I
If there is an increase then dividing t by t  n , deducting 1 and sliding the point
mentally speeds the process. Using the June 1996 quarter to the September
1996 quarter from the example below 1057 / 1002 = 1.055, deduct the 1 gives
0.055, slide the point two spaces (i.e. multiply by a hundred) gives an answer of
5.5 percent – an increase between the June 1996 quarter and the September
1996 quarter of 5.5 percent.
51
Quarter
Price Index
Mar-96
Jun-96
Sep-96
Dec-96
1020
1002
1057
1138
Percentage
Change over
Previous Period
-1.8
5.5
7.7
If there is a decrease then the procedure is similar. Note: The denominator
MUST be the earlier period not the lower index number. Using the March 1996
quarter to the June 1996 quarter, we have 1002 / 1020 = 0.982, deduct 1 gives
-0.018, slide the point gives -1.8. That is a decrease between the March 1996
quarter and the June 1996 quarter of 1.8 percent.
The alternative formula for the percentage change from the previous period t-1
to the current period t is =
 It

 I t 1



1


 100
Contribution information
Examining contributions allows us to assess the impact of price movements in
the context of their relative importance within the indexes they contribute to.
The main analysis tool for this purpose is to look at “index points contribution”
that a regimen set makes to an index.
Index points contribution is the term given to the number of index points that a
component of a wider index caused the wider index to move by.
Examples
 What was the impact of coffee on the total movement in the Food Price
Index from one month to the next?
 What contribution did public sector salary and wage rates have on the
Labour Cost Index from one quarter to the next?
The index points contributions of the components to the wider index may be
upward or downward and they add to the change (in index points) of the wider
index.
The contribution of a component to a change in a wider index is dependent on
both the size of the percentage change for the component and the relative
weight of the component. For example, if newspapers and petrol both
increased 5 percent in the CPI, petrol would have made a bigger contribution to
the overall CPI because of its higher relative weight.
52
Index points contribution is both a tool for searching out anomalies and a means
of explaining to users what has made the index move, or not move, in the latest
period.
The calculation of index points contribution is covered in Prices Advanced:
Module 3.
Index points contribution: The contribution of a component to a change in
a wider index is dependent on both the size of the percentage change for
the component and the relative weight of the component.
53
Module 1 Overview

The Prices unit consists of three teams: CPI Outputs, CPI/LCI
Development and BLOPI.

A price index tells how the price of a set of goods and/or services has
changed over time, or differs across space.

There are many uses of price indexes. Some of which include: to monitor
general inflation, for wage adjustment/negotiation, to deflate a value
series to get a volume series, to provide information of where price
increases are coming from.

A common approach to measuring price change over time is the fixedbasket approach, which compares the expenditure or revenue of a
basket of goods and services purchased or sold in one of the two periods
with what the same basket would have cost or returned in the other of
the two periods.

The basket of goods and services generally relates to some earlier
period of time, as accurate expenditure or revenue information is not
usually available in real time. This type of index is called a base-weighted
index and the most commonly used index of this type is Laspeyres price
index.

The Prices business unit produce a suite of price indexes and each of
these indexes serves a different purpose. The indexes produced are: CPI
and FPI, PPI (inputs and outputs), CGPI, FEPI, OTI and LCI (salary and
wage rates, and non-wage).

A price index is about price change and not about actual price level.

Methods to interpret price index outputs include: visual scan of tables
and graphs, calculation of percentage changes and examining
contribution information.

Index points contribution refers to the number of index points that a
component of a wider index caused the wider index to move by.
54
Intermediate Module Two – Introduction to Prices
Learning outcomes
At the end of this module, participants should be able to
 Understand common index formulae and their concepts
 Distinguish the differences between index formulae described in this
module
 Describe how a index formula can be applied
 Understand how a price index is constructed
 Understand the process of developing and maintaining a price index.
55
2a: Price Index Concepts and Formulae
This module outlines the processes required to develop and maintain a price
index. It builds on the theory in Module 1 and goes on to discuss the first step –
determining the use of the proposed index. The module following provides
some elaboration on these processes.
Combining the prices of several items into one price
index
In the previous module we learned about the basics of a price index. In practice,
a price index is usually for a set of items. This set is known as the “regimen”
and sometimes as the “basket”. The regimen is a set or quantity of items. The
price index for a regimen represents the change in the monetary value of that
set over time.
Hence constructing a price index requires that a regimen be selected and then
priced consistently. Consistency requires the same quantity and quality of each
regimen item be selected each time and that they be priced at the same place
each period. We need to look at the options for combining the price movements
of the individual regimen items.
REMEMBER
An index number on its own means nothing. It must be compared with an
index number from another period to determine the price movement
between the other period and the current period.
Index structure
The index structure uses either a hierarchical additive structure or building
blocks to move from the individual price of a reference commodity through to
the aggregate index.
The index structure is usually hierarchical, whether an additive or building block
structure, based on aggregating up through levels of a classification eg.
Commodity, industry or occupation.
When a building block approach is used expenditure or revenue weights are
assigned for inputs into each index at each level in the structure.
The PPI structure is an example of “building blocks”. This structure allows a
block (aggregated prices of commodity) to be used for different sets of
commodity classification. For example, electricity can be used for both transport
and construction.
56
The benefits of the building block structure include the
fact that reweighting can be done for isolated indexes at
any level. In practice, reweighting at the working
industry level and above will occur during
redevelopments of the PPI and users will be advised
before the weight change occurs. Changes at the
commodity index level are usually made to maintain the
representativeness of the commodity indexes. For
example, changes in respondents, changes in the
quality of the priced item and discontinued or additional
priced items may result in weight changes. These
changes may not necessarily be advised.
For a hierarchical additive structure, expenditure or revenue weights are
assigned at the elementary aggregate level and are additive at higher levels in
the structure.
The CPI uses “hierarchical additive structure” for its upper-level aggregation.
For example, regular and premium petrol become petrol, which then becomes a
part of an index for the transport group, in turn becomes an index for the
national CPI. Expenditure weights are explicitly assigned at the regional
average price level. Once expenditure weights have been used to calculate
Laspeyres product totals at the next level, the product totals can be simply
summed to derive product totals at higher levels of aggregation through the
hierarchical New Zealand Household Expenditure Classification (NZHEC).
Structure
Hierarchical
additive structure
Pros
-Simple and transparent.
Hierarchical
building block
structure
-More flexible.
-Allows prices or indexes to
be reused with different
weights.
-Allows a range of weighting
sources to be used without
the need to ensure
consistency across indexes.
57
Cons
-Requires a single
weighting source across
the whole regimen or
adjustments to different
sources to give
consistency across the
whole regimen.
-Complex and not
transparent.
In every level of the index structure, some sort of averaging process combines
the "building blocks" or price observations.
For the CPI, the items collected at the lowest level are weighted based on the
importance of each type of outlet for the regimen group or "regimen set" that
the item represents.
At the next levels, we use population and expenditure weights to combine the
building blocks.
58
Elementary aggregates
The initial aggregation of prices for a particular
item below the level for which expenditure weights
are available is called the elementary aggregate
(EAs).
EAs are the only elements for which an index may
be derived by direct reference to a sample of price
observations.
Some key points to note:

Elementary aggregates should consist of groups of goods or services
that are as similar as possible, and preferably fairly homogeneous.

They should also consist of items that may be expected to have similar
price movements. The objective should be to try to minimise the
dispersion of price movements within the aggregate.

The elementary aggregates should be appropriate to serve as strata for
sampling purposes in the light of the sampling regime planned for the
data collection.
Selection of goods and services
There are compromises choosing between the representative goods and
stable goods. Some representative goods or services are not always
available over a long period of time, such as PlayStation, while there are
less representative goods or services that are steadily available in the
market over a long period of time.
Each elementary aggregate, whether relating to the whole country, an individual
region or group of outlets, will typically represent a very large number of
individual products. In practice, only a small number can be selected for pricing.
When selecting the products, the following considerations need to be taken into
account:

The products selected should be ones for which price movements are
believed to be representative of all the products within the elementary
aggregate.

The number of products within each elementary aggregate for which
prices are collected should be large enough for the estimated price index
to be statistically reliable. The minimum number required will vary
between elementary aggregates depending on the nature of the products
and their price behaviour.

The object is to try to track the price of the same product over time for as
long as the product continues to be representative. The items selected
59
should therefore be ones that are expected to remain
on the market for some time, so that like can be
compared with like, and problems associated with
replacement of products reduced.
In the general case, EAs also represent the lowest level for
which weighting information is available. At this level
however, expenditure weights are often not available. Hence
outlet or population weights are used for the aggregation.
Different formulae are used in the aggregation of data and
this depends on where you are in the index structure.

Within the elementary aggregates, Dutot, Carli or Jevons is used.

Above the elementary aggregates, index formulae are used. Typically,
this would be Laspeyres, Paasche or Fisher for Statistics New Zealand.
But there are other index formulae, namely, Walsh, Tornqvist-Theil,
Marshall Edgeworth, etc.
The Dutot formula is the ratio of the simple arithmetic mean of prices in the
current period divided by the simple arithmetic mean price in the calculation
base period. Use of the Dutot elementary aggregate formula implies that equal
quantities were purchased from each outlet in the base period. In the CPI, most
of the price quotes obtained through postal surveys is aggregated using Dutot.
The Jevons formula calculates the geometric mean of the price relatives. A
price relative is the price of the item at a particular store divided by the price of
that item at that store in the base period. Use of the Jevons elementary
aggregate formula implies an equal expenditure share for each outlet in the
base and current period. The formula allows for substitution by redistributing
underlying quantity weights in favour of outlets exhibiting lower rates of price
change.
The Carli formula uses a simple arithmetic mean of price relatives. A price
relative is the current price of the item at a particular outlet divided by the price
of that item at that outlet in the base period. The use of the Carli elementary
aggregate formula implies that equal expenditure was made at each outlet in
the base period. In the case of the LCI, the same expenditure on labour input is
made in the base period by each employer.
For CPIs, it is recommended that the 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). The Dutot formula continues to be used for other items where
outlet substitution is not possible (eg local authority rates), where it is not
currently practical to adopt the Jevons formula, for fresh fruit and vegetables (as
the first stage of aggregation is across both outlets within each region and
across weeks within each month), and where prices are subsidised and may fall
to zero (eg GPs' fees) due to a property of geometric means.
60
Try this in Excel in your own time. Put 0 in cell A1, and 9999 in cell A2. Then in
cell A3 put =geomean(A1:A2). You will see an error message in Excel, because
the square root of 0 is still 0.
Elementary Aggregates
For the CPI, the Jevons formula has been used since the 2006 review as
recommended by the Revision Advisory Committee. The Dutot formula
continues to be used for other items where outlet substitution is not possible,
where prices are subsidised and may fall to zero, for fresh fruit and
vegetables (as the first stage of aggregation is across both outlets within
each region and across weeks within each month), and where it is not
currently practical to adopt the Jevons formula.
More details about Elementary Aggregate Formulae will be covered in Prices
Advanced – Module 2.
Value aggregates
The dollar value obtained from the aggregation in time value t, derived by taking
the quantities in the weighting base period and the prices in period t, is called
the value aggregate (VAs) or product total.
What is important about VAs is that the value represents expenditure (or
revenue) and that the VA of any one component can be directly compared to
the VA of any other component. For this to be true however the index structure
should be hierarchical additive and the expenditure or revenue weights are
expressed in dollars. If a building block structure is used, with weights summing
to an arbitrary or conventional number, this is not the case.
Price versus volume indexes
The work of Prices Business Unit is concerned with price indexes.
Price Indexes show the changing costs of a fixed basket of goods, or the
changing value of a fixed level and mix of production.
Price index measures price movement.
Volume index measures quantity movement.
Volume Indexes show the changing volume of goods at constant prices or the
changing levels and mixes of production at constant prices.
61
Index notations
The symbols are those conventionally used although like most conventions
there are variations. You will come across these in the literature and even in
other publications of Statistics New Zealand.
L
 The superscripts on the I (for Index) are
to say that it is Laspeyres
Index and
index
q
p
to say that it is a price index rather than a quantity
.
m

m

is read as “The sum of items i from 1 ( i 1 ) to m ( )”, i.e., sum the
part of the equation that follows for all items in the regimen 1 to m.

The lower case p with the subscript it in the part of the equation it io
represents the price of an individual item, i, of the regimen or basket at
the time period, t, which the index number being calculated represents.

Similarly, lower case q with the subscript io is the quantity of an individual
item of the regimen or basket at the time period that is the weight or price
reference period for the index number being calculated. Strictly, “o” is the
period of the weight or price reference. For the moment, this is
immaterial as the price reference and index reference periods are the
same in the examples we are using.
i 1
p
q

Laspeyres price index
This form of price index is the common index used in
Statistics New Zealand to construct price indexes. Named
after the person who first formalised this method, the
Laspeyres Price Index measures the changing cost of a
fixed basket of goods or services. In this case the basket or
regimen represents the quantity of goods that was
purchased/sold in the weight reference period. I.e., the
index has fixed base period quantities.
Under normal economic conditions, consumers react to
changes in relative prices by substituting goods and
services that have become relatively less expensive for those that have become
relatively more expensive. For example, if the price of chocolate biscuits
increases more quickly than the price of plain biscuits, then the quantity of plain
biscuits will tend to rise and the quantity of chocolate biscuits will tend to fall.
Under this condition, the Laspeyres index overstates price change because it
tends to overweight goods and services showing higher relative price change.
The upward substitution bias caused by use of a Laspeyres price index formula
can be minimised by updating the expenditure weights used in the formula as
frequently as possible, to ensure they are as representative as possible of
current expenditure or revenue patterns. For the CPI, this is done every two to
62
three years, and the next review is due in 2011, as the last two reviews were
done in 2008 and 2006.
This is the form of the index:
  pit qio 
m
Index I Lp 
i 1
m
  pio qio 
1000
i 1
.
Where
pit
= Price of item i(i = 1,…,m) in period t ,
pio
= Price of item i(i = 1,…,m) in period 0,
qio
= Quantity of item i(i = 1,…,m) purchased in period
0, and
I Lp =
Index of the price of all items i to m in period t,
on base period 0 equals 1000, where the price index is a weighted
average of the price relatives and each item carries a weight equal
to the expenditure or revenue in the base period.
The Laspeyres price relative index form
The way the standard Laspeyres Price Index is written implies that quantities of
each regimen item have to be obtained. E.g., grams of butter, kgs of potatoes,
pairs of trousers, kilometres travelled on a suburban bus, numbers of haircuts,
services of a lawyer, etc. This is not a practical proposition but we can get over
that difficulty by some algebraic manipulation of the index formula so that it can
use dollars spent on each regimen item. (For example, dollars spent is what we
get from the Household Economic Survey.)
The transformed formula is:
m
p 
  Eio it 
P
i 1
Index I Lp   m io  1000
 Eio
i 1
Where
pit
= Price of item i (i = 1,…,m) in period t,
pio
= Price of item i (i = 1,…,m) in period 0,
Eio
= Expenditure on item i in period 0, =
pio  qio
Laspeyres price relative form is the modified version of the Laspeyres
index formula that does not require explicit quantities, and this helps since
obtaining quantity information is not always feasible.
63
What is done here is to take the expenditure in the base period for each item
and move it by the change in the price of that item between the base and
current period.
Those of you with a little algebra can try converting the formula in the Price
relative form to the original we discussed in the Laspeyers Price Index section.
The same process can be done with the Paasche index. In practice, all the price
indexes compiled by statistics offices are done in this way.
Paasche price index
The Laspeyres price index uses the base period quantities
to determine the content of the regimen and the weights for
each item in the regimen. An alternative is to use the
current period quantities. This is done with the Paasche
Index:
  pit qit 
m
Index I Pp 
i 1
m
  pio qit 
 1000
i 1
The notation is the same but note that q the quantity is
now subscripted it representing quantities in the current period (rather than io
representing the base period as in the Laspeyres Index). This index tends to
understate price change as opposed to the Laspeyres index, because it tends
to overweight goods and services showing lower relative price change.
Laspeyres index tends to overstate price change.
Paasche index tends to understate price change.
Fisher ideal index
The Fisher Ideal Index is one of several possible steps towards improving the
representativeness of the regimen. Fisher’s formula recognises that the relative
importance of what people buy changes over time. With Laspeyres and
Paasche, there is an assumption that the same goods are purchased in the two
periods being compared.
Index ... I
Fp
=
Laspeyres index x Paasche index =
I Lp  I Pp
That is the geometric average of the Laspeyres and Paasche indexes.
Fp
This formula is read as "the Fisher Ideal Index ( I ) is the square root (
the product of the Laspeyres and Paasche price indexes”.
) of
Try writing this out in full using the notation for the Laspeyres and Paasche
price indexes.
64
The use of the Fisher ideal index
If the current period weights are readily available, a
“cross-weighted” index can be used as a better
indication of price movements.
Such a “cross-weighted” index, the Fisher Ideal
Index, is used in the overseas trade indexes (OTI).
Its usage was made possible thanks to the latest
information of price and volume by sourcing data
from Customs. This gives us enough time to analyse
and implement new weights into the index structure.
The CPI cannot currently use this form in real time,
or the Paasche, as it would take too long to collect
information of the current spending patterns of households (expect a year and a
half whilst we ran and processed the Household Economic Survey). However,
Statistics New Zealand does produce a retrospective superlative index for the
CPI because once each new set of CPI expenditure weights has been
calculated it is possible to make use of the existing and new weights to
calculate a 'superlative' index on a retrospective basis.
Fisher ideal index is the only superlative index currently used in Statistics
NZ; other superlative indexes include Walsh, and Tornqvist-Theil. More
details about superlative indexes are covered in the glossary.
Try to think and discuss possible ways to adopt the Fisher Ideal Index in our
indexes.
65
Examples of price indexes
The following example provides a simple illustration of how indexes are derived.
The data in table 1 below indicate the prices and quantities of materials used by
a construction company for two consecutive years, which are to be considered
respectively as the base year (year o) and the current year (year 1).
Table 1
Material
Prices
Quantities
po
50
30
40
10
Cement
Steel
Brick
Other
Material
Cement
Steel
Brick
Other
po qo
3,500
1,500
800
300
6,100
m

Sum of Products
pt
50
20
20
20
po qt
4,000
1,800
2,000
200
8,000
qo
70
50
20
30
pt qo
3,500
1,000
400
600
5,500
i 1
m
p q 

Laspeyres Price Index
it
i 1
m
p
i 1
=
io
q
io io

x 1000
5,500 x 1000 = 901
6,100
m
Paasche Price Index

p q 
i 1
m
p
i 1
=
it it
q
io it

x 1000
6,600 x 1000 = 825
8,000
Fisher Ideal Price Index

I Lp x I Pp
 901 x 825
= 862
66
qt
80
60
50
20
ptqt
4,000
1,200
1,000
400
6,600
Note that all are different and that the Fisher Ideal is between the two. Under
normal economic conditions demand is relative to the price of goods or
services. When using quantities from the current period, any price movement
related to price change will be somewhat muted.
On the other hand, using quantities from the base period will somewhat overemphasise the price change, because it does not take quantity change into
account. Hence the expenditure will be higher than a value based on the basic
economic model that people buy relatively less of products that become
relatively more expensive.
For the example above, why has the Paasche index risen by less than the
Laspeyres index?
67
******************************************************************************************
Exercise 1
Labour Cost Index:
Try calculating labour cost indexes using the same formulas but with the
following prices and weights. (Hint: Enter the column headings to guide you
through the index calculation. Some column headings have been filled out as
examples.)
Table 2:
Wages
Wage/Salary
Base
quarter
p0
$20
$18
$24
$12
$15
Carpenter
Bricklayer
Foreman
Pay Clerk
Driver
Current
quarter
$22
$20
$30
$12
$18
Weekly hours worked by
each trade
base quarter
current
quarter
qt
105
140
80
80
40
38
12
12
60
80
p0q0
Carpenter
Bricklayer
Foreman
Pay Clerk
Driver
Sum of Products
Price Indexes on base in period 0 = 1000
Laspeyres
= ____________ x 1000
= ....................
Paasche
= ____________ x 1000
= .....................
Fisher
=
x
= .....................
*****************************************************************************************
68
Examples of volume indexes
The volume index formulas (or formulae if you wish – it's
optional) are much the same as the price index formulas.
The difference is that for a volume index you keep the
price terms in the numerator and denominator for the
same period and have the quantity terms for the base
and current period.
Example (using data from table 2)
m
p

Laspeyres Volume Index
p
q
io io
i 1

q
io it
i 1
m
= 1172
m
 p

Paasche Volume Index
i 1
m

it
 p
i 1
it
qit
7404
 1000
6334

i 1
p
x
io
qio
I Lq x I Pq
m
 pio qit
p
x 1000
= 1169
Fisher Volume Index


qio. 
Index... I Pq
i 1
m

x 1000
6496
 1000
5544
Index... I Lq
m

i 1
m
it
p
i 1
it
qit
qio
Then, what is it equal to?
Index... IFq
=
= 1170
69
Value movement
Value movements can be decomposed into the
respective price and volume movements.
The price movement can be derived by using the
price index calculation (change in the prices
between two periods), whereas the volume
movement can be derived by using the volume
index calculation (change in volume between two
periods).
To illustrate, let's look at the percentage increase of wages of the given
occupations above between the base and current quarters:
Percentage increase in the sum of wages paid =
(7404 - 5544) x 100
5544
=
33.5%
This increase in value is due to a 14.1% rise in prices and a 17.0% rise in
volumes. These decomposed figures were taken from the following indexes:
Fisher Price Index = 1141
Fisher Volume Index = 1170
When we compound the two component increases, we should arrive back at the
total movement.
p0 q0 x
pq
Where 0 0 =
period 0,
pt qt =
period t,
Fp
It
=
Io
It
It
Fp
Io
Fp
x
It
Fq
Io
Fq

pt qt
price of item in period 0 multiplied by quantity of item in
price of item in period t multiplied by quantity of item in
Fisher price index in period t,
Fp
=
Fisher price index in period 0,
=
Fisher volume index in period t,
=
Fisher volume index in period 0,
Fq
Io
Fq
Applying the above equation gives us:
5544 x 1141 x 1170 = 7404
1000 1000
Please note that the relationship is multiplicative (i.e. we cannot simply add
percentage price and quantity movements).
70
In a similar way, value movements can be decomposed into Paasche price and
Laspeyres volume movements, and into Laspeyres price and Paasche volume
movements.
The party index example
Let's look at an example of comparing the costs of a party held in 1998 and a
party held in 2008:
Drink
wine
beer
juice
The 1998 Party
Unit Price Quantity
Po
Qo
$2.50
25
$4.50
10
$0.60
10
The 2008 Party
Unit Price Quantity
Pn
Qn
$3.00
30
$6.00
8
$0.84
15
The goods are:
•wine - bottles (small and cheap); mixed red and white wines are the same price
•beer - six packs; all the same price
•juice - litre bottles; all flavours are the same price
Calculate the simplest possible index of the changing cost of the
party.
How much more expensive was it to run the party in 2008 than in
1998 according to the expenditure index?
Method:
The simplest possible expenditure index would be to calculate the
index of 2008 cost on 1998 cost:
∑PnQn x 1000 =
(3 x 30) + (6 x 8) + (0.84 x 15) x 1000 = 1327
∑PoQo
(2.5 x 25) + (4.5 x 10) + (0.6 x 10)
Therefore, the increase in cost is 32.7%.
But what have we done?
 We’ve allowed for the differing quantities of wine, beer and juice by
multipyling unit prices by their quantities.

A simpler aggregative index would be (3+6+0.84)/(2.5+4.5+0.6) x 1000 =
1295. This would exclude the quantities and ignore the differences in the
units.

The answer would be different if we used a single can of beer rather than
the six-pack.
Single can of beer in 1998 = $0.75
Single can of beer in 2008 = $1.00
71
Excluding quantities, the aggregative index would be:
Index =
(3+1.00+0.84)
x 1000 = 1257
(2.5+0.75+0.6)
******************************************************************************************
Exercise 2
What's the index if we use the base-weighted price index or Laspeyres price
index?
The 1998 Party
Drink
Unit Price Quantity
Po
Qo
wine
$2.50
25
beer
$4.50
10
juice
$0.60
10
Value Agg. ∑PoQo =
Laspeyres Price Index =
The 2008 Party
Unit Price Quantity
Pn
Qo
$3.00
25
$6.00
10
$0.84
10
∑PnQo =
∑ PnQo x 1000 = ________
∑ PoQo
*****************************************************************************************
Exercise 3
What's the index if we use the current period weighted price index or Paasche
price index?
The 1998 Party
Unit Price Quantity
Po
Qn
wine
$2.50
beer
$4.50
juice
$0.60
Value Agg. ∑PoQn =
The 2008 Party
Unit Price Quantity
Pn
Qn
$3.00
$6.00
$0.84
∑PnQn =
Drink
∑ PnQn x 1000 = ________
∑ PoQn
*******************************************************************************************
Paasche Price Index =
72
Index points contribution
Index points contribution is a quantitative expression
of how much each component contributes to the
magnitude of the all groups index number. The
simplest way of calculating this is:
Points Contribution = Component Value Aggregate
Total Value Aggregate
x Index Number
For the labour cost example above, the points contribution of the occupation
'carpenter' in the base and current quarters using Laspeyres are:
in period 0, Points Contribution
=
=
in period t, Points Contribution
=
=
20 x 105
5544
379
x 1000
22 x 105
6334
416
x 1142
The table below is an example from Table 8 of the quarterly Consumers Price
Index release.
From previous quarter
Percentage
Index points
points
contribution(1)(3)
contribution(1)(3)
2.42
0.226
1.29
0.121
-0.23
-0.021
0.56
0.052
0.12
0.011
0.41
0.039
-2.47
-0.230
-0.02
-0.002
-0.60
-0.056
0.79
0.074
Food group
Alcoholic beverages and tobacco group
Clothing and footwear group
Housing and household utilities group
Household contents and services group
Health group
Transport group
Communication group
Recreation and culture group
Education group
Expenditure
(weight)
June 2008
quarter(1)
17.83
6.76
4.48
22.75
5.26
5.09
16.18
3.21
9.54
1.78
Percentage
change(2)
1.2
1.8
-0.4
0.3
0.2
0.8
-1.5
-0.1
-0.6
4.2
Miscellaneous goods and services group
7.12
0.9
0.69
0.064
23.3
100.00
0.3
2.97
0.277
100.0
Group
All groups
Percentage
contribution(1)(3)
81.6
43.6
-7.7
18.8
4.1
14.0
-83.2
-0.8
-20.3
26.6
Index points contribution is covered in more detail in Price Advanced – Module
3.
73
Other index forms and chaining
There are other index forms. Some of these involve
geometric or arithmetic averaging in one form or
another. You will see them in the glossary under
“Ideal Index”.
Most of the effort in refining index formula is
directed at the inaccuracies introduced with
changing regimens over time. There is an
alternative when we can only get regimens for a
past period. This is to “chain” indexes. In practice, this means starting a new
index every few years based on a regimen perhaps a year or two earlier and
then linking these indexes together.
The recent CPI reweight in 2008 involved chaining of the index. Up to the June
2008 quarter, old weights were used to calculate the price movement from the
March 2008 quarter to the June 2008 quarter. From the September 2008
quarter, the new weights and regimens were applied to the June 2008 quarter
then the price movement was obtained by measuring price change from the
June 2008 quarter to the September 2008 quarter. This ensures the continuous
time series of the index while preserving the previous time series.
Further information about chaining is described in the glossary.
74
2b: From Theory to Practice
Why use the price relative form of the index
The price relative form of the Laspeyres index does not
require information on the quantity, or the conversion of
expenditure into a price and notional quantity. Obtaining
information about expenditure on, say, meat from
households is feasible. Asking a household to state the
quantity of meat purchased in a week is unlikely to get a
reasonable response. Further there are some purchases
when quantity is not easily identifiable, e.g. a consultation
with a lawyer could be of any length and quality. This form
also allows expenditures to be aggregated.
The process of development and maintenance
Moving clockwise around the formula serves to show the steps required to set
up and run an index such as the CPI, LCI and PPI.
3. Determine the
regimen groups
and the
transactors
1. Determine the
purpose or use of
the index
2. Determine the
form of the index.
Laspeyres,
Paasche, Fisher,
other?
4. Determine the base period.
Estimate the expenditure (E)
on each regimen group in the
base period.
m
Index I Lp 
  Eio
i 1
m
pit
Pio


 1000
 Eio
8. Set up the collection of
prices of the representative
items on a regular basis, and
i 1
7. Set up an
index
calculation
system.
9. Set out procedures for
adjusting for quality and
availability
5. Determine (i) the
item to price to
represent each
regimen group.
And
6. Determine a
method of getting
prices for each
representative
item (i.e. what
geographic areas
and what outlets
and then how to
combine these
prices to a single
price relative).
10. Finally determine the method of publishing the index.
m

Note that the i in i 1 is a group of items, whereas the i in
price representative of the group.
75
Pit
Pio is an item-to-
Development of a price index - basic steps
New price indexes are developed occasionally and the existing ones are subject
to review.
There is an organisation-wide generic Business
Process Model that can be applied to the
development of a price index.
In Statistics New Zealand reviews are conducted as
frequently as possible to maintain the quality of
indexes. Be it a new index or a review, the process
is the same. The boxes around the formula from the
diagram on page 78 summarise the steps that have
to be taken for a new index or when one is
reviewed. To elaborate a little here and then take
each part of the process separately
i.
Determine the purpose of the index. What is it to be used for?
This is the “Need” step in the Generic Business Process Model. In this
step, need and use of indexes can be identified. This step will also help
determine the appropriate conceptual approach (ie. Whether it will be
either actual-outlays, acquisition, or consumption approach). More details
are in the glossary.
ii.
Determine the formula of the index. This requires knowledge of the use
and, more importantly, the information that is and will be available in the
permissible time frame.
This is the “Develop and Design” step in the gBPM. The use and purpose
identified in the previous step can be taken into account to design an
index, and the formula can be decided upon, depending on the
availability of resources to set up an index. Once purpose of an index is
decided, it’s important to think about the conceptual approach mentioned
in the previous step.
iii.
Determine the regimen groups and the transactors. Establish the buyers
and or sellers whose exchanges are to be covered by the index and the
goods and services to be included in the regimen, dividing the regimen
items into groups.
This is the “Develop and Design” step in the gBPM. Some compromises
will be made due to costs and shortage of other resources.
iv.
Determine the expenditure on each regimen group in the base period.
76
This is the “Develop and Design” step in the gBPM. For the CPI, HES is
one of the most representative methods of obtaining the expenditure
weights. For the LCI, the Census can be used.
v.
Determine items-to-price that are representative of the regimen groups.
This is the “Develop and Design” step in the gBPM. The selection of
representative commodities is based on a mixture of analysis of available
information and judgement. There are compromises due to the same
reasons as in step iii. Such a problem as choosing between
representative vs stable goods is a good example.
vi.
Determine a method of getting prices for each representative item; that is,
where prices are to be collected, and if more than one price is needed,
then how these are to be brought to a single figure. This may be a simple
average, or a form of weighted average (steps iv, v and vi are often an
iterative process). If there is to be some weighting then these weights
have to be obtained.
This is the “Develop and Design” step in the gBPM. This step also
involves methods of obtaining reliable weights, and in the case of the
CPI, this would be the Household Economic Survey (HES)
vii.
Set up a system for calculating the index. In Statistics New Zealand this
will normally be GIFT (Generalised Index Facility Toolbox). There are
simpler systems, which we may use for demonstrating what happens in
the calculation process, such as Excel.
This is the “Build” step in the gBPM. For some lower level aggregations,
it may be easier to use spreadsheets before entering price data into
GIFT.
viii.
Set up a collection system. This requires questionnaires, an integrated
data collection system (IDC) and maybe staffing and managing a field
collection on a continuing basis.
This is the “Collect” step in the gBPM. Collection methods vary
depending on frequency, timing, cost etc. Field collection is a standard
method for goods and services that are susceptible to change in
behaviour of consumers that are likely to exhibit frequent outlet changes.
For some prices, administrative data or internet collection will be used.
ix.
Set up the procedures for routine processing of collected prices,
determining the practices for adjusting for quality change in items priced,
and for replacing items-to-price that are no longer available.
77
This is the “Process” and “Analyse” step in the gBPM. This is also about
consistency of an index. Once an index is finalised, it’s important to make
sure that the time series is continuous and consistent, also ensuring the
important property of an index that the utility value of selected products
should remain consistent over a period of time.
x.
Finally, determine the method of publication or dissemination and the
necessary steps to implement this.
This is the “Disseminate” step in the gBPM. Currently web-based
publication is one of the most cost-effective ways of dissemination. In the
case of the CPI, a media conference is held on the day of its release due
to interest from the public and the media.
There may also be steps required to obtain the finance, consultation with stake
holders, training staff, documenting the procedures and archiving information.
Determining the purpose of the index
This is not as simple as it sounds. BUT it is necessary to establish what goods
and services should be covered and whose transactions are to be included. To
make informed decisions it is also necessary to
determine what use is to be made of the index.
For example: The Consumers Price Index is used,
supposedly, as the measure of the price change of
goods and services purchased by households. This
requires a definition of households and a definition of
what goods and services are to be included. To
answer those questions one has to be aware of the
intended uses.

IF the use is to adjust wage rates to maintain purchasing power, then
perhaps we only need the expenditure patterns on wage earners.

IF the CPI is to be the control measure for the Reserve Bank’s inflation
target, we need to exclude interest – a monitoring/control measure
should not include the operational adjuster.
78
********************************************************************************
Exercise 4
As an exercise, think of some other uses for the CPI
and then uses of the PPI, LCI and OTI that may
conflict with the main purpose of each.
The use of the index will influence every step of the
process:

Who are the transactors (e.g. should the CPI
include prison inmates)?

What are the transactions? What commodities and services are included
(e.g. should bonuses be in the LCI)?

The choice of the representative “items to price”

The type of “outlets” where prices are obtained -- the relative importance
of each type (e.g. shop, mail order, e-mail purchase)

The geographic regions where goods are obtained and the relative
importance of each (e.g. every main town, rural/urban representation)

The transaction level of the price (e.g. free on board ship, on the wharf,
at the wholesale, factory door, retail shop?)

The way in which quality adjustments and substitutions of priced items
are made

Who gets the results (e.g. public good in the Hot off the Press or is it a
private index)?
What can we do about this – to meet as many needs as possible?
For class discussion – Using the white/black board and drawing ideas from the
class
What are the uses of the other indexes such as PPI, LCI and OTI?
Do those uses require conflicting index properties?
**********************************************************************************
79
Module 2 Overview

Indexes are calculated in two steps, with the first
being the elementary aggregates, and the
second being higher-level indexes calculated by
averaging the elementary aggregates.

There are three widely used elementary
aggregate formulae, Carli (simple arithmetic
mean of price relatives), Dutot (simple arithmetic
mean of prices), and Jevons (geometric mean of
the price relatives).

Laspeyres index tends to overstate price change, while Paasche index
tends to understate price change.

It is not practical to use the Fisher ideal index for the CPI in real time due
to the difficulty of obtaining the latest expenditure information in a timely
manner. For the OTI the Fisher index is used thanks to up-to-date value
and volume information supplied by New Zealand Customs Service.

Discrepancies between the Laspeyres index and Fisher Ideal index can
be minimised by updating expenditure weights as frequently as possible.

The Laspeyres price relative index form is the most widely used at
Statistics New Zealand, because it does not require quantity information,
only information on expenditures.

Development of a price index requires careful planning, and the first step
is to determine the purpose. This should also be in line with Statistics
New Zealand’s organisation-wide Generic Business Process Model
(gBPM).
80
Glossary
This glossary provides a list of the terms and the main formulas used in Price
Index work in Statistics New Zealand. Like most glossaries it can never be
complete. Suggestions for correction, additions and elaboration are welcome.
All Groups Index
The index series showing price movements for the weighted combination of all
goods and services priced for the CPI.
ANZSIC
See Australian and New Zealand Standard Industrial Classification.
Arithmetic mean
An arithmetic mean of a set of n numbers is calculated by adding the numbers
together and dividing by n.
e.g. Given the numbers 3, 6, 8, 4, 3, 2 then n = 6 (i.e. there are 6 numbers
listed)
3 68 4  3 2
6
Arithmetic average =
=
4.33
Cf Weighted average
Actual-outlays approach (payments or money outlays approach)
A conceptual base in which the expenditure weight for a commodity is based on
payments made for the commodity in the weighting base period, regardless of
when the commodity was actually acquired or consumed.
Cf Consumption approach and Acquisition approach.
Acquisition approach
A conceptual base in which the expenditure weight for an item is based on the
actual cost of a good or service acquired by households in the weighting base
year, regardless of when the good is consumed or paid for.
The New Zealand CPI has been acquisition based since the 1974 revision.
Cf Actual outlay approach and Consumption approach.
Australian and New Zealand Standard Industrial Classification (ANZSIC)
A classification of industrial activity used in Statistics New Zealand
classifications of businesses and business activity. It is used in the Producers
Price Index and in the Labour Cost Index.
The same classification is used in Australia and New Zealand.
Every New Zealand business on the Statistics New Zealand register of
businesses (See Business Frame) has an ANZSIC classification.
81
Base period
The period at the beginning of the lifetime of a price index. Unless other wise
specified, it is the period on which an index time series is set at 100 or 1000.
This is the 'expression base period' or the 'index reference period'. The
expression base period for the CPI is the June 2006 quarter.
The 'weighting base period' or 'weight reference period' is the period in which
the regimen and regimen weight are drawn from. In the CPI the weighting base
is the year ended June 2004 inflated to prices ruling in the June 2006 quarter.
For the PPI the expression base is currently the December quarter 1997 but the
weighting comes from several years around this period. The Capital Goods
Price Index has an expression base of September quarter 1999. The Labour
Cost Index has an expression base of the June 2001 quarter and the Farm
Expenses Price Index has an expression base of December 1992 quarter.
The 'calculation base' or 'price reference' refers to the period for which prices
are compared with current prices when an index is calculated. This will differ
from the expression base when an index is chain linked to form a continuous
series on a common expression base. The Overseas Trade Price Index is
expressed on the June 2002 quarter but, being a chain-linked index, has a
series of calculation bases.
For comparison purposes many of the price indexes produced by Statistics New
Zealand are converted to an expression base of the June 2006 quarter (See
Table 6.01 in Key Statistics).
Basket of goods and services
The goods and services represented in a price index. The basket of goods and
services selected for the New Zealand CPI is essentially fixed, i.e. the goods
and services are selected in the expenditure base year, and remain more or
less constant for the life of the index. Of the Statistics New Zealand price
indexes only the Overseas Trade Price Index uses current as well as base
weights.
In the LCI the regimen is made up of employees in specified occupations and
industries. In the PPI the regimen is the goods and services purchased and sold
by businesses and those purchased by government.
The basket is sometimes referred to as the regimen of the index. (See
Regimen).
There is a distinction between the basket, which is ALL goods and services
covered by the index, and the items priced to represent them. The latter are
referred to as the representative items of the basket.
Benthamite utility
A utility theory from Jonathan Bentham also called "the greatest happiness
principle". He wrote that:
82
"Nature has placed mankind under the governance of two sovereign
masters, pain and pleasure. It is for them alone to point out what we ought to
do, as well as to determine what we shall do. On the one hand the standard
of right and wrong, on the other the chain of causes and effects, are
fastened to their throne. They govern us in all we do, in all we say, in all we
think..." - Jeremy Bentham, The Principles of Morals and Legislation (1789)
Ch 1, p 1
Roughly, this proposed that people ought to desire those things that will
maximise their utility.
(Source: Daniel Read, Utility theory from Jeremy Bentham to Daniel Kahneman,
www.lse.ac.uk/collections/operationalResearch/pdf/working%20paper%20OR64
.pdf)
See Utility.
Bias
An increase or decrease in an index series caused by some deviation from the
theoretical ideal method at any stage of index compilation. This may be caused
by regimen selection, price collection, the method of adjusting for changes in
the representative items priced, the mathematics of averaging prices and index
calculation.
See Elementary index bias, Commodity substitution bias, New goods bias,
Outlet substitution bias,Quality adjustment bias and Theoretical index bias.
Boskin report
A report released in the mid-1990s by the Commission to Study the Accuracy of
the Consumer Price Index chaired by Michael Boskin of Stanford University.
The Commission estimated that the U.S. CPI was upward biased by 1.1
percentage points per year. This is a large error when the measured annual rate
of consumer inflation since 1991 has averaged 2.6 percent per year.
Although the main focus of the Commission’s report was possible overstatement in the escalation of income payments to U.S. Social Security
recipients, CPI components are used for deflation of components of the national
accounts, not only in the United States, but in every country. The Commission’s
estimate implied that output growth was understated in the United States,
though the precise amount is difficult to determine, since national accounts
deflation does not use the overall CPI, but rather its components, and other
price indexes are also used (Producer Price Index components, for example).
Nevertheless, the Commission’s estimate, if accurate, had strong implications
for productivity measurement, whether or not the price indexes used for
deflating capital and other inputs had their own biases.
The Commission’s report had a tremendous impact, not only in the United
States, but also internationally because economists in other countries rightly
saw that CPI measurement error was not specific to one country.
(Source: Jack E. Triplett, The Boskin Commission Report After a Decade:
Introduction to the Symposium and Implications for Productivity)
83
The
Boskin
Commission
Report
http://www.ssa.gov/history/reports/boskinrpt.html
is
available
at
Business Frame
The name given to the Statistics New Zealand register of all significant
businesses and government organisations operating in New Zealand. Besides
the name of the business the Business Frame holds the Industry, Institutional
Sector, geographic location and the numbers employed by each establishment
belonging to an enterprise. The register is maintained on a continuing basis.
The list of organisations is used as the frame for business censuses and
surveys carried out by Statistics New Zealand.
Business Price Indexes (BPI)
This is a general term used to cover those price indexes compiled by Statistics
New Zealand relating to business activity. It embraces the Producers Price
Index (PPI), Capital Goods Price Index (CGPI) and the Farm Expenses Price
Index (FEPI).
In the GIFT system the BPI subject area also includes the Overseas Trade in
Services Prices Index.
Butting
A method used for substituting the price of a new item for an existing similar
item in the calculation of a price index. The price of the new commodity is
inserted directly into the index as a replacement with no adjustment made to
compensate for quality change (i.e. it is assumed that there is no quality
change).
Capital Good Price Index
A price index series compiled by Statistics New Zealand to cover the prices paid
by businesses and government for goods purchased as capital items. The flows
measured are equivalent to the national accounting flow fixed capital formation.
The commodities covered are durable goods that are to be used over a period
of more than one year to produce other goods and services. Cf the Producers
Price Indexes, which measure the price change of goods and services that are
used up in the productive process.
Carli elementary aggregate/index
A method of aggregating prices collected for an individual item where reliable
expenditure weights are not available – this will often be the case where the
level of expenditure is low or information is not available.
The Carli formula uses a simple arithmetic mean of price relatives.
A price relative is the current price of the item at a particular outlet divided by
the price of that item at that outlet in the base period. The Carli formula is
sometimes referred to as the price relatives formula and is given by:
84
1  pit 


i 1m  pio 
m
Carli elementary aggregate/ index  
Where
(period t)
pit
=
Price of item i (i = 1,...,m) in the current period
pio
=
Price of item i (i = 1,...,m) in the base period (period
0)
 pit 


pio 

Note that :
is a price relative.
The use of the Carli elementary aggregate formula infers that equal expenditure
was made at each outlet in the base period. In the case of the LCI that the
same expenditure on labour input is made in the base period by each employer.
Cf Dutot elementary aggregate and Jevons elementary aggregate.
Chain linking
When an index is revised, the new series is calculated using a new regimen and
a new set of expenditure weights. This is linked to the old series to form a
continuous long-term series by chain linking. The new index may be given an
expression base value of 1000, and all index numbers based on the
superseded regimen are scaled to the same base as the new (rebased) index.
e.g. If, in the re-base year, the existing index was 1350, then this figure would
be reset to 1000 by multiplying it by 1000/1350. All existing index numbers
based on the superseded regimen would be adjusted by this same link factor.
Commodity
In the technical language of price indexes and National Accounts a commodity
is any good or service that is bought and sold at market price. Goods and
services provided free or at significantly reduced price, such as government
provided health and education services, are referred to as “Other goods and
services” in National Accounts parlance.
Commodity substitution
The change in the composition of purchases by transactors in response to
changes in the relative prices of the commodities purchased.
For example households will substitute trainers for leather shoes because the
price of trainers rises less that the price of leather shoes. The fixed weight
pattern of the CPI assumes that the same quantity of leather shoes is being
purchased over the life of the index.
Commodity substitution bias (or product substitution bias)
This is the bias that occurs in a price index when a change in consumer
preferences is not reflected in the index.
See Bias and Commodity substitution.
85
Consumers Price Index
A series of price indexes compiled by Statistics New Zealand that measures the
price change of goods and services purchased by New Zealand noninstitutionalised households. The CPI coverage approximates to the national
account flow of Final Consumption Expenditure by Private Households.
Consumption approach (or economic cost of use)
A conceptual base in which the weight of a commodity is the amount of a good
or service consumed (or used) in the base period, regardless of when it was
acquired or when payment was made. When dealing with housing, there is a
variant of this consumption approach referred to as rental equivalence.
Cf Actual outlay approach and Acquisition approach.
Cost of living index
An index measuring the changing cost of purchasing a varying set of
commodities which will provide a fixed level of consumer satisfaction in line with
changing householders’ tastes. No cost of living index is produced in New
Zealand.
The Consumers Price Index is NOT a Cost of Living Index as the commodities
priced are held constant over the life of the index.
Current-weight price index
This can mean a price index in which the quantity of each commodity in the
regimen is assumed not to be constant, i.e. the weights change each period. It
can also refer to an index where the quantity of each commodity in the regimen
is taken to be that of the last period in the time series.
The term is used for a Paasche Index where the weights applied to each period
of an index time series are the expenditure pattern of that period.
Cf Laspeyres Index.
Deflation
This has two meanings:
1. The opposite of inflation where the value of money relative to goods
and services is rising. In inflation the quantum of goods and services
that a nominal amount of money can buy falls.
2. The use of a price index to adjust the nominal money value of a set of
goods and services to a value expressed in the prices of some
previous period.
For example it is possible to determine that a small car purchased by a
business at the beginning of 2001 for $25,000 would have cost
approximately $23,018 two years ago. Deflating the current value
using the indexes 1072 in March 2001 and 987 in March 1999 does
this. The price indexes are from the Capital Goods Price Index – “Cars
1600cc and under”
86
The
calculation
is
IndexfortheEarlierPe riod
Current Pr ice 
 Pr icefortheEarlierPeri od
Indexforthecurrentperiod
987
25,000 
 23,017.7
1072
That is
Cf Inflation.
Democratic weighting
A method of expenditure weighting in which each transactor (household in the
case of the CPI) is given an equal weight regardless of how much each
transactor actually spends. It involves calculating, for each transactor, the
proportion of the total expenditure it incurs on each commodity and then
averaging these proportions across all transactors.
This method is not used in the New Zealand CPI. The Household Economic
Survey, from which weights are drawn, does not provide these proportions.
Cf Plutocratic weighting.
Dutot elementary aggregate/index
A method of aggregating prices collected for an individual item where reliable
expenditure weights are not available or the cost-benefit does not warrant a
more elaborate method. This will often be the case where the level of
expenditure is low or information is not available.
The Dutot formula is the ratio of the simple arithmetic mean aggregate of prices
in the current period divided by the simple arithmetic mean aggregate price in
the calculation base period. The Dutot formula is given by:
m 1
 pit
Dutot elementary aggregate/ index  im1m
1
 pio
i 1m
pit
Where
=
Price of item i (i = 1,...,m) in the current period
(period t)
pio
=
Price of item i (i = 1,...,m) in the base period (period
0)
The Dutot formula is widely used in the CPI for combining prices from outlets in
the same region. However, where the relative importance of individual outlets or
of outlet types can be determined then outlet weights, based on the proportion
of sales, are used to calculate weighted arithmetic means of prices.
Use of the Dutot elementary aggregate formula implies that equal quantities
were purchased from each outlet in the base period.
Cf Carli elementary aggregate and Jevons elementary aggregate.
Economic cost of use
See Consumption approach.
87
Economy-wide measure of inflation
A measure of inflation that encompasses all aspects of an economy. It includes
prices paid by households, producers, private non-profit organisations and the
government sector for goods and services including capital purchases.
The National Accounts Implicit Price Indexes of Gross Domestic Product and
Gross National Expenditure can be regarded as such. (See Implicit Price
Index).
Elementary aggregate
The initial aggregation of prices for a particular item where expenditure weights
are not available – this will often be the case where the level of expenditure is
low or information is not available. See Module 1.2. There are three main
formulae that can be used to calculate elementary aggregates: Carli (arithmetic
mean of price relatives); Dutot (relative of arithmetic mean prices); and Jevons
(geometric means).Statistics New Zealand uses both the Dutot and Jevons
formulae. It implicitly used the Carli for the LCI and in some cases for the PPI.
Elementary index bias (elementary aggregate bias or formula bias)
The bias resulting from the process of averaging prices at the lowest level. See
how this occurs in Module 1.2.7.
See Bias.
Expenditure approach
A conceptual base in which a price index is based on expenditure (rather than
consumption). There are two basic variants of the expenditure approach - actual
outlays and acquisitions.
See Actual outlay approach and Acquisition approach.
Expenditure weight
Each item included in the basket of goods and services making up a price index
regimen is weighted according to its relative importance. (See Laspeyres
index.)
For the CPI these weights are based on household expenditure information
collected by Statistics New Zealand. This is supplemented by information from
direct enquiry of businesses and from export and import statistics.
For business price indexes information on purchases and sales are collected in
business surveys such as the Annual Enterprise Survey and the Commodity
Data Collection. This is supplemented by information from direct enquiry of
businesses, import and export statistics. The Inter Industry Study reconciles
purchases and sales – this improves the regimen weights for each industry and
provides the weights for use in combining industry indexes.
Similarly the Labour Cost Index uses quantity information from the Population
Census, the Business Frame and Government departments.
“Price”
information, i.e. wages, salaries, and other labour costs come from businesses
and government.
88
The OTI (Overseas Trade Price Index) uses the value of imports and of exports
as the weight.
Factor Reversal Test
The factor reversal test requires that multiplying a price index and a volume
index of the same type should be equal to the proportionate change in the
current values (e.g. the “Fisher Ideal” price and volume indexes satisfy this test,
unlike either the Paasche or Laspeyres indexes).
Farm Expenses Price Index
A series of price indexes compiled by Statistics New Zealand covering the noncapital expenditure of farm operation. This index series covers goods and
services including salary and wages but excluding the remuneration of farm
owners. Livestock purchases are covered but an All Inputs Excluding Livestock
is calculated as part of the series.
Fisher, Irving
Irving Fisher (1867-1947) was the American economist who made significant
and original contributions in the fields of economics, mathematics, statistics,
demography, public health and sanitation, and public affairs. He was born in
Saugerties, N. Y., on Feb. 27, 1867. Fisher received his doctoral degree in
mathematics at Yale in 1891. From 1892 until 1895 he taught mathematics at
Yale; in 1895 he joined the faculty of political economy, where he remained until
his retirement as professor emeritus in 1935.
Fisher made significant and original contributions in statistical theory,
econometrics, and index number theory. The Making of Index Numbers (1922)
became a standard reference on the subject. After a methodical and
quantitative analysis of various index number formulations, he developed his
"ideal" index, the geometric mean of the Paasche and Laspeyres indexes. He
considered this formulation "ideal" because it met his "time reversal" and "factor
reversal" tests.
(Source: Answers.com, Irving Fisher, http://www.answers.com/topic/irvingfisher)
See Factor Reversal Test.
See Time Reversal Test.
Fisher Ideal Index
See Ideal Index.
Fixed-weight price index (or base weighted index)
This term normally refers to a price index in which the quantity of an item
purchased is assumed to be constant or fixed at the base period for the life of
the index. The CPI, Business Price Indexes and the Labour Costs Index are
fixed weight indexes. The life of a CPI is now three years, i.e. weights are
revised every three years.
See also Laspeyres Index.
89
Fringe Benefit Tax
A tax on payments in kind provided by employers to employees designed to
counteract avoidance of income tax. This tax is payable on such benefits as the
provision of a car for private use.
General measure of inflation
A measure of the prevailing level of price change in an economy. It is designed
to measure the market prices for goods acquired at a point in time by all
transactors in the economy. See Economy-wide measure of inflation.
Geometric mean
A geometric mean of a set of n numbers is calculated by multiplying the
numbers together and taking the nth root.
e.g.Given the numbers 3, 6, 8, 4, 3, 2
n = 6 (i.e. there are 6 numbers listed)
 3  6  8  4  3  2
1
6
Geometric average =
= 3.89
A geometric mean of prices will always be equal to or lower than an arithmetic
mean of the same prices.
GIFT
The Generalised Index Facility Toolbox is a computer system used to calculate
all price indexes in Statistics New Zealand except the Overseas Trade Price
Index. This was developed in house during 1997 to 1999.
Hedging
A procedure whereby purchasers and sellers protect themselves against future
changes in prices.
There are two common ways used to hedge – one by fixing a future price for a
commodity the other by fixing a future price for the foreign exchange that a
commodity is to be sold or purchased with. Sometimes these two approaches
may be combined.
Commodity Price Hedging
Large electricity consumers might contract with an electricity supplier to
buy up to a certain quantity of electricity for the coming year at a set price
(the “futures price”). The contracting purchaser will get that quantity of
power at the contracted price even though the price in the market (the
“spot price”) might rise considerably.
Currency Hedging
A firm selling lamb to the United States may contract to sell an agreed
tonnage in a period six months in the future at a US dollar price per kilo.
The selling firm may protect itself from currency fluctuations by taking a
“forward” contract with a bank to sell the expected US dollars for NZ
dollars at an agreed exchange rate.
90
In this way the firm is passing the risks associated with foreign exchange
transactions to the bank and will pay a fee for this service.
Hedonic regression
A method for calculating the value of the quality change of an item by a
regression technique. This involves assigning values to each of its main
characteristics. e.g.with respect to motor-cars it may include engine size,
passenger capacity, fuel type and fuel consumption.
Household Economic Survey (HES)
A survey of households carried out by Statistics New Zealand that collects
information on the spending patterns of private New Zealand households. The
results are now produced once every three years. People in institutions such as
hospitals and prisons are not covered by this survey.
This survey was previously called the Household Expenditure and Income
Survey (HEIS).
Ideal index
A price index formula that meets a range of tests or axioms which have been
identified as important for indexes is termed an ideal index. The most well
known ideal index is the Fisher ‘Ideal’ Index, which is the geometric mean of the
Paasche and Laspeyres indexes.
The Fisher Ideal Index formula is given by:
Laspeyres index x Paasche index =
Fp
Index I =
I Lp  I Pp
Other ideal index formulae are:
The Marshall-Edgeworth Index formula, which takes an arithmetic
mean of quantities in periods 0 and t, is given by:
 qio  qit 


2 

i 1
 1000
m
 qio  qit 
pio 


2


i 1
=
m
p
MEp
Index I
Where
it
pit
=
Price of item i (i = 1,…,m) in period t
pio
=
Price of item i (i = 1,…,m) in period 0
qit
=
Quantity of item i (i = 1,…,m) purchased in the
=
Quantity of item i (i = 1,…,m) purchased in the base
(current) period t
qio
period 0, and
91
I MEp =
Index of the price of all items i to m in period t, on
base period 0 equals 1000, and each item carries a
weight equal to the average quantity in the base
and current period.
The Tornqvist Index (also known as Tornqvist-Theil Index) formula,
which is a weighted geometric mean of price relatives, with the weights
being the arithmetic mean of expenditure shares in periods 0 and t, is
given by:
m
Index I Tp =
Where
w
p 
  it  1000
i 1 pio 
w
=




 pio qio  pit qit   1
m
 m
 2
   pio qio    pit qit  
i 1
 i 1

pit
=
Price of item i (i = 1,…,m) in period t
pio
=
Price of item i (i = 1,…,m) in period 0
qit
=
Quantity of item i (i = 1,…,m) purchased in the
=
Quantity of item i (i = 1,…,m) purchased in the base
=
Index of the price of all item i to m in period t, on
base period 0 equals 1000, where the price index is
the result of a geometric weighted mean of price
relative and each item’s weight is the arithmetic
mean of the item’s expenditure shares in the base
and current periods.
Note
that
m
w 1
the
i 1
Where
(current) period t
qio
period 0, and
I Tp
This may also be expressed as:
Index I
Where
Tp
 S i 0  S it 


2

 pit  

 
p
= i 1  io 
m
 1000
Si0
=
Expenditure shares of item i (i = 1,…,m) in period 0
S it
=
Expenditure shares of item i (i = 1,…,m) in period t
The Walsh Index formula, which uses a geometric mean of quantities in
periods 0 and t, is given by:
92
m
Index
I Wp 
 p q
i 1
m
i0
qit  2
1
i0
 p q
i 1
Where
it
qit  2
1
i0
pit
=
Price of item i (i = 1,…,m) in period t
pio
=
Price of item i (i = 1,…,m) in period 0
qit
=
Quantity of item i (i = 1,…,m) purchased in the
=
Quantity of item i (i = 1,…,m) purchased in the base
=
Index of the price of all item i to m in period t, on
base period t equals 1000, and each item carries a
weight equal to the geometric mean of the
quantities of the base and current periods.
(current) period t
qio
period 0, and
I Wp
This may also be expressed in terms of expenditure shares and price
relatives:
1
S
1
 
2
it  
S
1
 
2
it  
m
Index
I
Wp

 S
i 1
i0
m
 S
i 1
Si0
Where
S it
i0


 pit  2


 pi 0 
 pi 0 


p
 it 
1
2
=
Expenditure shares of item i (i = 1,…,m) in period 0
=
Expenditure shares of item i (i = 1,…,m) in period t
Implicit Price Index
An index derived by comparing the current and constant price values of a time
series of the same flow or stock. In such cases a price index can be derived
from these two values.
  pit qit 
m
IndexI Ip 
i 1
m
  pio qit 
i 1
1000
that is
The current price value of a flow or stock of commoditie s
 1000
= The value of the same commoditie s in prices of the chosen base period 0
93
Where
period
pit
=
Price of item i (i = 1,…,m) in period t, the current
pio
=
Price of item i (i = 1,…,m) in period 0, the period in
which constant price is expressed
qit
=
Quantity of item i (i = 1,…,m) purchased in the
period t, the current period
I Ip 
Implicit price index of all items i to m in period t, on
base period 0 equals 1000, where each item carries
a weight equal to the expenditure in the current
period t. That is the implicit price index is a Paasche
Index.
Implicit Price indexes are often derived from the current and constant price
estimates of GDP (Gross Domestic Product). Summing deflated smaller
elements using price indexes such as the CPI and PPI derives these National
Accounting constant price values.
Implicit weighting
This occurs when an arithmetic mean is taken of a set prices. It becomes
apparent when one of the prices is significantly different from the others. This
different price exerts, proportionally, more influence on the overall average and
hence over any derived price relative.
e.g. Given the following prices: $12.00, $12.40, $12.35 and $19.50
12.00 + 12.40 + 12.35 + 19.50
Average =
4
= $14.0625
Clearly the $19.50 figure has had considerable effect on the mean calculation
making this mean price considerably higher than any of the first three prices or
their mean ($12.25). A given percentage change in a price with a high implicit
weight has a greater effect on the movement in the mean prices than the same
percentage change in a price with a lower weight.
Implicit weighting can lead to over or understatement of price change in some
circumstances. It is appropriate where:
• the sample is properly self weighted,
• where prices are weighed using accurate quantities, or
• where price relatives are weighted using accurate expenditure.
(See Weighted average)
Using the example above,
If the base prices were: $10.00, $9.80, $12.10 and $ 18.00
Then, the arithmetic mean base price would be $12.475 and the price
index would 1.127, or 1127 on base 1000
Taking the price relatives of the individual prices and averaging them we
have:
94
 12 .00 12 .40 12 .35 19 .50 




4
 10 .00 9.80 12 .10 18 .00 
= 1.2  1.2653 1.0207  1.083  4
base 1000
=
4.5693  4
= 1.1423, or 1142 on
Imputation
The estimation/calculation of an unknown quantity, value or price based on
relevant available information. E.g., the price change in one outlet, that is
unavailable at the time an index must be calculated, may be imputed from the
movement in another outlet. A price may also be imputed by carrying forward
the previous period’s price and assuming no price change.
Index population (or reference population or target population)
The population of transactors covered by a price index.
For the CPI, the index population is private resident households in New
Zealand.
For the Farm Expenses Price Index the index population is all farms in New
Zealand excluding some in smaller farm activities.
Similarly the PPI and CGPI are all businesses.
For the OTI the transactor coverage is implicitly all exporters and all importers.
For the LCI the coverage is all employers.
Industry Classification
See Australian and New Zealand Standard Industrial Classification.
Index number
In respect of prices - the ratio of current expenditure to base expenditure
multiplied by 1000 (or some other convenient base expression).
Index number series
A series of numbers measuring movement over time from a base period value.
The base period value is normally represented by an index number of 1000.
Indexation
The periodic adjustment of a money value by the change in a selected price
index. This money value may be, for example, a wage, a construction or
maintenance contract fee, a property rent or a payment under a matrimonial
settlement.
For example an index composed of relevant parts of the LCI and PPI inputs
index could be compiled and be written into a five-year Lift Maintenance
Contract. Each year the original contract price would increase by this index.
95
If the original price in, say, 1997 was $5,500 and the index has moved from
1100 in December 1996 to 1500 in December quarter 2000 then the price for
the services under the contract during 2001 would be:
2001 Contract Pr ice  1997 Contract Pr ice 
$5,500 
December 2000 quarterIndex
December1996 quarterindex
1500
1100
=
= $7,500
(Note the lag built into the contract. This is needed so that the parties
have certainty as progress payments are made during the 2001 year.
They cant wait until January 2002 to know what is payable in February
2001.)
Inflation
Inflation is a general term referring to an increase in the general or average
level of prices of goods and services over a period of time.
Cf Deflation.
Irregular movements (of a time series)
Movements in a series not due to ongoing trends or regular seasonal variation.
These movements can be due to one-off events.
Item substitution
The replacement of a priced item by another in the basket of goods and
services when an originally selected item to price is no longer available.
Item to price
A good or service chosen to represent a regimen set (one or more goods or
services) that is priced from period to period to provide a price relative for that
regimen set.
“Representative items” or “Representative commodity” has the same meaning.
Item weights
Estimates of the overall significance of each of the different items in the price
index baskets of goods and services. The weight will be based on the
proportion of the total weight of an index that the priced item represents. More
than one price may be collected for the same item to obtain a more
representative price relative for a regimen set. In such cases the item weight is
applied to some average of these prices or their price relatives.
Jevons elementary aggregate/index
A method of aggregating prices collected for an individual item. The Jevons
formula calculates the geometric mean of the price relatives. A price relative is
the price of the item at a particular store divided by the price of that item at that
store in the base period. The Jevons formula is given by:
Jevons elementary aggregate/index  m
 pit 

i 1  io 
m
 p
96
Where
(period t)
pit
=
Price of item i (i = 1,...,m) in the current period
pio
=
Price of item i (i = 1,...,m) in the base period (period
=
is the symbol for multiply
0), and

 pit 


p
Note that :  io  is a price relative.
Use of the Jevons elementary aggregate formula implies an equal expenditure
share for each outlet in the base and current period. The formula allows for
substitution by redistributing underlying quantity weights in favour of outlets
exhibiting lower rates of price change.
Use of Jevons formula is recommended by the International Labour Office for
goods and services where households are able to substitute towards outlets
showing lower relative price change.
Cf Carli elementary aggregate and Dutot elementary aggregate.
Labour Cost Index
A price index series compiled by Statistics New Zealand of the salaries, wages
and other labour costs paid by businesses and government.
The index covers salaries and wage rates and such costs of employing labour
as annual leave, statutory holidays, ACC employers’ premiums, medical
insurance, motor vehicles available for private uses and low interest loans to
employees.
Laspeyres, Étienne
(Ernst Louis) Étienne Laspeyres (Halle an der Saale, November 28, 1834 –
August 4, 1913) was Professor ordinarius of Economics and Statistics or State
Sciences and cameralistics in Basel, Riga, Dorpat (now Tartu), Karlsruhe and
finally for 26 years in Gießen. Laspeyres descended from the Huguenot family
of originally Gascon descent which had settled in Berlin in the 17th century, and
he emphasised to maintain Occitan pronunciation (Lass-pey-ress).
Laspeyres is mainly known today for the index number formula for determining
the price increase which he developed in 1871, and which is used until this day.
Other than that, he may count as a father of business administration as an
academic-professional discipline in Germany, and as one of the main unifiers of
economics and statistics by "developing ideas which are today by and large
nationally and internationally reality: quantification and operationalization of
economics; expansion of official statistics; cooperation of official statistics and
economic research; and integration of the economist and the statistician in one
person." (Rinne 1983) In economics, Laspeyres was to some extent a
representative of the Historical School and certainly of Kathedersozialismus.
(Source:
Wikipedia
the
Free
Encyclopedia,
Étienne
Laspeyres,
http://en.wikipedia.org/wiki/Etienne_Laspeyres)
97
Laspeyres Index
A price index measuring the changing cost over time of purchasing the same
basket of commodities as was purchased in some historical period (the
expenditure base period).
The expenditure aggregate Laspeyres form of the index is:
  pit qio 
m
Index I Lp 
i 1
m
  pio qio 
1000
i 1
.
Where
pit
=
Price of item i (i = 1,…,m) in period t
pio
=
Price of item i (i = 1,…,m) in period 0,
qio
=
Quantity of item i (i = 1,…,m) purchased in period 0,
I Lp
=
Index of the price of all items i to m in period t, on
base period 0 equals 1000, where the price index is
the sum of the current expenditure on the regimen
in the current period divided by the sum of the
expenditure on the same regimen items in the base
period, multiplied by 1000.
and
An alternative form of the Laspeyres index formula, the price relative form, is
used by Statistics New Zealand in the calculation of the CPI. This is given by
the formula:
m
Index I Lp 
  Eio
i 1
pit
Pio
m


 1000
 Eio
i 1
Where
pit
=
Price of item i (i = 1,…,m) in period t
pio
=
Eio
=
Price of item i (i = 1,…,m) in period 0,
pio  qio
Expenditure on item i in period 0 =
I
Lp
=
Index of the price of all items i to m in period t, on
base period 0 equals 1000, where the price index is
a weighted average of the price relatives and each
item carries a weight equal to the expenditure in the
base period.
Linking (of Index Series)
The technique used to join a new index series (e.g. one having a changed
composition and weighting pattern) to an old index series to form one
continuous series. The technique should ensure that the resultant linked index
reflects only price level variations, and that the introduction of the new items
and weights does not in itself affect the level of an index.
98
Market price
The price of a good or service that a willing seller will pay to a willing buyer
where the buyer and seller are “at arms length” i.e. are financially independent
of each other, not members of the same family or companies with shared
ownership.
It is implicit in price indexes that the price measured is the market price. This
will include commodity taxes such as GST where the purchaser cannot recover
the tax back, this is the case with the CPI. In Business Prices Indexes the seller
collects the GST and passes it to government and the purchaser pays GST but
can claim this back from government. Hence Business Price Indexes, such as
the PPI and CGPI, use prices exclusive of such taxes.
Marshall-Edgeworth Index
See Ideal Index.
National average price
The average price of a good or service which is not aggregated up from
regional prices. This can be a price that is collected at one place (“outlet”) and
regarded as being applicable to the whole country, e.g. motor vehicle
registration is the same price nation-wide, i.e. it is a national price.
It can also be an average price for the whole country where a survey sample is
drawn on a national basis. This is the situation with postal survey items in the
CPI.
New goods bias
Bias caused by the failure of a price index to account for the introduction of new
goods/services into the market.
See Bias.
New Zealand Household Expenditure Classification (NZHEC)
Used in the CPI (since the review implemented in 2006) and the Household
Economic Survey (HES) since the 2006/07 survey. NZHEC is based on an
international standard - ie the United Nations COICOP classification, with
stands for the Classification of Individual Consumption According to Purpose. It
is recommended for use in CPIs by the International Labour Office.
Nominal
“Nominal” is used to describe values measured in current money values. This
compares with the “constant” price values obtained when a current value is
deflated using the movement in a price index.
Non-representative expenditure
Expenditure made by transactors covered by an index which is not represented
in the index. This exclusion may be for conceptual reasons, or for practical
reasons. In the CPI gambling and works of art are excluded because of the
practical difficulty of obtaining a price. Interest is excluded from the all groups
CPI on conceptual grounds.
99
Non-response
Non-response results when a respondent fails to provide information when
contacted by the survey.
Non-sampling errors
Any error not caused by the collection of information from a sample, rather than
the whole population. The main non-sampling errors affecting the reliability of
the CPI are under-coverage; non-represented consumption; non-response and
the practical limitations of collecting certain data. Other Statistics New Zealand
indexes have the same non-sampling errors. In the Overseas Trade Indexes all
goods exported and imported are supposedly covered but some are not
represented because they are only traded in some periods.
Cf Sample error.
Notional transaction
An estimate of a real transaction, not based on direct measurement. The rental
equivalent value of the owner-occupied dwelling is an example.
New Zealand Standard Occupational Classification NZSCO
The standard classification of occupation used in Statistics New Zealand
surveys where an individual is to be classified by occupation or job. This
standard is used in the Labour Cost Index, Population Census, Household
Economic Survey and Household Labour Force Survey.
Occupation Classification
See New Zealand Standard Occupational Classification.
OECD-Eurostat Purchasing Power Parities Programme
A Purchasing Power Parities (PPP) programme established in the early 1980s
to compare on a regular and timely basis the GDPs of the Member States of the
European Union (EU) and the Member Countries of the OECD. This remains
the purpose of the Programme, although its coverage has been broadened to
include countries that are not members of either the European Union or the
OECD.
The objective of the Programme is to compare the price and volume levels of
GDP and its expenditure components across the countries participating in it.
Before such comparisons can be made, it is first necessary to express the
GDPs – which are in national currencies and valued at national price levels - in
a common currency at a uniform price level. To do this, Eurostat and the OECD
use purchasing power parities (PPPs).
See Purchasing power parities.
Outlet
An individual, organisation or business enterprise from which goods or services
may be purchased or sold and that can provide a price for such goods or
services. For the CPI an outlet can be a shop, a service provider, such as a
plumber, petrol station, an administrative source or any other place where
prices are obtained.
100
Note that an “Outlet” may, in the context of the Producers Price Index Inputs
Index and the Labour Cost Index, be a purchaser rather than seller. For the
Overseas Trade Index the “outlets” can be regarded as all exporters and
importers.
Outlet sample
The outlets selected by purposive sampling (Which see)of a population of
outlets.
Outlet substitution bias
Bias caused by the exclusion of price changes due to changes in outlets from
which purchasers make their purchases. For example in recent years petrol
stations have replaced convenience stores and corner dairies.
Some commodities are now bought and sold through the Internet which are
having to be increasingly included in the outlets for Statistics New Zealand price
indexes.
See Bias.
Outlet type
A group of outlets that is regarded as relatively homogeneous for pricing
purposes. For example in the CPI supermarkets are one outlet type. Specialist
stores are another. In the Producers Price Index and Labour Cost Index all
businesses in a particular industry may be regarded as a type of outlet.
Outlet weights
A measure of importance (or weight) given to a particular type of shop or
“outlet”. In the CPI these are based on national expenditure patterns and market
share or may be self-weighting. For Business Price Indexes weights are based
on market share.
In the CPI weights are allocated to supermarkets in a region as well as being
used to weight average prices from different store types in a region. The latter
are also known as store type weights (Which see).
For example, many consumers tend to buy dairy products from supermarkets
rather than other outlet types such as convenience stores. Hence a
supermarket will have a higher outlet weight for dairy products than a
convenience store.
Outlet weights are generally applied only to food and non-food groceries in the
CPI. Information on other expenditure groups and other Statistics New Zealand
indexes is not so complete, so that self-weighting within outlet types (which are
generally weighted) is the norm.
Paasche, Hermann
Hermann Paasche (1851-1925) was a German economist. He is best known for
his Paasche Index, which provides a calculation of the Price Index. Paasche
studied economics, agriculture, statistics and philosophy at University of Halle.
101
In 1879, he became a professor of political science at Aachen University of
Technology. Paasche died in 1925 in Detroit, Michigan, United States.
(Source:
Wikipedia
the
Free
Encyclopedia,
Hermann
Paasche,
http://en.wikipedia.org/wiki/Hermann_Paasche)
Paasche Index
A price index which compares the cost of purchasing the current basket of
goods and services with the cost of purchasing the same basket in an earlier
period.
The Paasche Index formula is given by:
  pit qit 
m
Index I Pp 
i 1
m
  pio qit 
 1000
i 1
Where
pit
=
Price of item i (i = 1,…,m) in period t
pio
=
Price of item i (i = 1,…,m) in period 0
qit
=
(current) period t, and
I Pp =
Quantity of item i (i = 1,…,m) purchased in the
Index of the price of all items i to m in period t, on
base period 0 equals 1000, where the price index is
a weighted average of the price relatives and each
item carries a weight equal to the expenditure in the
current period.
The Paasche Index can also be expressed as a Price relative formula.
m
E
i 1
m
Index I
Where
Pp

 Eit
i 1
m
p 
  Eit io 
pit 
i 1
Eit
=
 1000
or
it



m 
 Eit 

 pio 
i 1
 p 
 it 
 1000
Expenditure on item i in period t, =
pit  qit
Partial splicing
A method used for substituting the price of a new priced item for an existing
similar item in the calculation of a price index so as to remove the effect of any
quality change. The price difference between the replaced commodity and its
replacement is attributed to a combination of quality differences and a genuine
price change.
See Splicing.
102
Percentage change
The change in an index series from one period to another expressed as a
percentage of its value in the first of the two periods.
Percentage contribution
This is the term given to the number of index points that a component of a wider
index caused the wider index to move by, divided by the number of index points
that the wider index moved by in total, expressed as a percentage.
For example, the index of all labour costs may have increased from one quarter
to the next by 5 index points. Salary and wage rates may have made an
upward contribution of 4 index points and non-wage labour costs may have
accounted for the remaining 1 index point. Therefore, the increase in salary and
wage rates accounted for 80 percent of the increase in labour costs and the
rise in non-wage labour costs accounted for the remaining 20 percent.
The percentage contributions of the components of the wider index may be
upward or downward, and add to 100 percent. Percentage contributions can
not be calculated if the wider index shows no change.
The percentage contribution of a component to a change in a wider index is
dependent on both the size of the percentage change for the component and
the relative weight of the component.
Points effect
This is the term given to the number of index points that a component of a
wider index caused the wider index to move by.
For example, the index of all labour costs may have increased from one quarter
to the next by 5 index points. Salary and wage rates may have made an
upward contribution of 4 index points and non-wage labour costs may have
accounted for the remaining 1 index point. The index point contributions of the
components to the wider index may be upward or downward and they add to
the change (in index points) of the wider index.
The contribution of a component to a change in a wider index is dependent on
both the size of the percentage change for the component and the relative
weight of the component.
Plutocratic weighting
A method of expenditure weighting in which expenditure weights are derived
from estimates of average (or total) household expenditure on the commodities
covered by the index. This means that households with expenditure levels
which are above average have a greater influence in the determination of the
weights than those households which spend less.
Cf Democratic weighting.
Policy Targets Agreement
An agreement signed by the Governor of the Reserve Bank and the Minister of
Finance requiring the Reserve Bank to achieve and maintain price stability. The
103
RBNZ uses the CPI and other statistics to monitor price stability. For the
purpose of the agreement, the target is to keep future all groups CPI annual
movements between 1 per cent and 3 per cent on average over the medium
term.
Population weighting
A measure of importance of a particular region based on the population of that
region compared to the overall population. Population weights are used in the
CPI to allocate national expenditure weight estimates to the regions. All other
Statistics New Zealand price indexes are national and do not use population
weights to aggregate regional estimates.
The Labour Cost Index uses population information to weight the number of
employees in each industry and occupation.
Price change measure
A measure of the changes in the prices of a set of items. This set of items could
be all household expenditure as in the case of the CPI All Groups, or of a set of
distinct transactions such as telecommunication charges.
Pricing centre
One of the 15 urban areas from which prices are collected for the calculation of
the CPI.
Price deflators
Factors that, when applied to a related time series of values allows a valid
comparison of the true underlying change in quantity free from the influence of
price movements. Deflators may be price relatives of a single commodity or an
index combining many commodity price changes.
Price index
A numerical index indicating how a set of prices has changed between time
periods.
Price Parity Index
A Price Parity index is an index comparing the price of the same goods and
services in different geographic areas or between different transactors.
New Zealand is one of many countries that provide price information to an
OECD initiated project to compare consumer prices between countries. This
provides information on the relative purchasing power of currencies in their
home country. This can differ considerably from the foreign exchange rate.
Price Reversal Test
A test that may be used under the axiomatic approach which requires that the
quantity index remains unchanged after the price vectors for the two periods
being compared are interchanged.
104
Probability sampling
A statistical selection of items in which each item has a certain chance
(probability) of being selected.
Cf Purposive sampling.
Producers Price Index
A series of price indexes compiled by Statistics New Zealand covering the
goods and services produced by businesses and purchased by businesses, by
non-profit establishments, and by government. The flows measured are
equivalent to the national accounting flows of Intermediate Inputs and Gross
Outputs.
Durable goods purchased as capital assets and salary and wage costs are
excluded.
Purchasing power measure
A measure of how much a set amount of money will purchase, usually
expressed in ‘real dollar’ terms. Price indexes are used to adjust money values
to establish the purchasing power.
Purchasing power parities (PPP)
1. PPP - OECD: Purchasing power parities (PPPs) are the rates of currency
conversion that equalise the purchasing power of different currencies by
eliminating the differences in price levels between countries. In their simplest
form, PPPs are simply price relatives which show the ratio of the prices in
national currencies of the same good or service in different countries.
2. PPP - SNA: A purchasing power parity (PPP) is a price relative which
measures the number of units of country B’s currency that are needed in
country B to purchase the same quantity of an individual good or service as
1 unit of country A’s currency will purchase in country A.
See OECD-Eurostat Purchasing Power Parities Programme.
Purposive sampling
The selection of items to price or of outlets using information from a variety of
sources including interviewers and field testing. It involves an element of
judgement in the selection process.
Cf Probability sampling.
Pure Price Change
The change in the price of a good or service after removing any variation in
price attributable to a change in quantity or quality.
Quality adjustment
The elimination of the effect that changes in the quantity or composition of an
item has on the price of an item, in order to isolate the pure price change.
See Pure price change.
105
Quality adjustment bias
Bias occurring in a price index when full or accurate assessment of quality
adjustment is not made to allow for a priced item being replaced by a new
version or model which may show an increase or decrease in quality.
See Bias.
Quality change
In a purchase price index such as the CPI, LCI and the Producers Input price
indexes quality change is any perceived difference in quality by the consumer
for a good or service. In expenditure price indexes such as the as the Producers
Output price index the quality change is that perceived by the producer or seller.
Real Dollar Terms
An amount expressed in “real dollar terms” has been adjusted for the changing
purchasing power of money. For example, the actual money value of the gross
domestic product may increase over a period of time, but the extent to which
this increase is “real” depends upon the change in the value of money over the
same period. “Real” values are expressed using a particular year as the “base
year”, i.e. the year to which the values in other years are related in order to
discount movements in prices.
Rebase
To change the expression base period of an index series, which is done when
an index review or reweight takes place.
Reference population
See Index population.
Regimen
This term is used with several different, although related, meanings. The first is
the generally favoured use in Statistics New Zealand.
1. The selection of goods and services for which representative items are
priced for the purpose of compiling a price index. The goods and services in
the regimen of (i.e. covered by) the CPI are classified into 11 groups, 44
subgroups, 105 classes, 176 sections, and 215 subsections, 487 items
covering about 685 subitems.
The regimen of the LCI and business price indexes is divided into industry
classes using ANZSIC (Which see).
Regimen has the same meaning as the “Basket of goods and services”
(Which see) when used in this way.
2. Some authorities restrict the use of the term “Regimen” to those goods and
services that are priced. They then say that the items priced carry the
regimen weights.
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Regimen level
This term is used to define the index classification levels that can be published.
They remain fixed for users and are subject to change at the discretion of the
statistical agency. In Statistics New Zealand, we publish only down to the class
level of the CPI and this allows us to restructure the lower levels (unpublished)
to introduce new and replacement items without apparently affecting the
published series.
Regimen set
This term is used in the training modules to refer to the smallest grouping of
items of a regimen or basket such that the price change of that group is
represented by one or few representative items. This is generally the lowest
level of aggregation of items in an index.
Regional expenditure
In the CPI, the national expenditure is allocated to regions in proportion to their
population in the weighting base period. This effectively provides population
weights to each region in calculating the national CPI series.
Relevance
How well a representative price (Which see) or index approximates the concept
desired to be measured i.e. the difference between what is attempted to be
measured and what is wanted to be measured.
Relevance is determined by how closely the most reliable available priced item
or price index will approximate the concept desired. The practical difficulties and
cost of obtaining a time series of prices have an affect on relevance.
Reliability
The likelihood that what is actually measured is what the index seeks to
measure. This is dependent on sampling and non-sampling errors, the items
priced and weights determined for each item. The relevance (Which see) of the
items priced will also impact on reliability.
Rental equivalence approach
A variant of the conceptual consumption approach (Which see) in which it is
assumed that the money value of the consumption of shelter services is
equivalent to the market price (= rent) that could be charged for the property if it
were rented to the household occupying it.
Representative commodity (- item)
A good or service chosen to represent a regimen set (one or more goods or
services) (Which see). The identical item is priced from period to period to
provide a price relative for that regimen set. Alternatively a replacement item
has to be substituted. (See Substitution)
“Representative item” and “Item to price” have the same meaning.
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Salary and wages rates
The measure of “price” used in the Labour Cost Index. Measured as the dollars
per period, (e.g. per hour) paid.
Sample frame
In the context of price indexes, sample frame is a comprehensive list of all
existing outlets (Which see) from which a statistical sample can be selected.
Sampling error
Any error resulting from the collection of information from a sample, rather than
the whole population. Mathematical techniques are available to measure and to
reduce the probability of sample error.
Cf Non-sampling errors.
Seasonal adjustment
This is a statistical technique that removes the seasonal pattern from prices,
price relatives or from the resultant price index so that the series is free from
fluctuations due to seasonality.
Seasonal adjustment is not currently used in Statistics New Zealand price
indexes at publication, although users may seasonally adjust these for their own
use.
Seasonal commodity
A good or service with seasonal fluctuations in the quantity purchased
throughout the year. These commodities may also, but not necessarily, have
seasonal fluctuations in their price during the year.
Seasonal fluctuations (of a series)
Regular fluctuations that occur with a similar magnitude at the same time every
year. This occurs particularly with fruit and vegetables in the CPI.
Note that the peaks and troughs may occur early or late because of changes in
the weather. Such influences may be disasters, such as hailstorms or just a late
or early spring. This can make seasonal adjustment difficult.
Self weighting
A loose term indicating that weighting is implicit in the number of outlets of a
particular type from which a price is collected.
In the CPI, if supermarkets account for 80% and specialty stores for 20% of the
expenditure on an item then the simple arithmetic mean of a price collected at
eight supermarkets and two dairies would give a price representative of the
prices of that item paid by all consumers. In so far as the number of outlets
priced is not in proportion to the expenditure then errors may be introduced.
Similar situations can occur in other indexes were the price of a representative
item is collected from several outlets or regions.
Cf Weighted averages
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Specification
The detailed description of the characteristics of a good or service to be priced.
This description will define the nature of the commodity, its weight or quantity,
any associated service and also packaging where relevant. The description may
include a brand name. The outlet is included explicitly or implicitly in the
description.
Splicing
In the context of price indexes this is a method used for substituting the price of
a new representative item for an existing similar item.
The ratio of the price of the replaced commodity (Which see) to that of the
replacement commodity at the changeover period is calculated and all future
prices of the replacement commodity are scaled accordingly. This may assume
that any price difference between the replaced and replacement commodities is
entirely due to quality difference.
A quality adjustment can be allowed for at the same time as the replacement
item is introduced by splicing.
Statistical sampling
Any sampling technique based on a statistical selection of items. Probability
sampling (Which see) is an example of statistical sampling.
Storetype weights
For some representative items, the CPI applies weights to the prices collected
from types of stores to arrive at the average price of an item in a region (Which
see). These weights are based on turnover as measured in retail trade surveys
or expenditure measured in the Household Economic Survey carried out by
Statistics New Zealand.
Substitution
The replacement of one representative priced item in a price relative time series
by another item-to-price. This is normally done when the originally priced item
becomes unavailable.
Various techniques are used to ensure that the price relative from the
replacement item results in a time series that reflects only the price change in
the regimen set represented and not those due to substitution.
Superannuitants Price Index (SPI)
An index measuring price movements for goods and services purchased by
superannuitant households. This index is no longer produced.
Superlative indexes
Superlative indexes treat prices and quantities equally across periods. They are
symmetrical and provide close approximations of cost of living indexes and
other theoretical indexes used to provide guidelines for constructing price
indexes. All superlative indexes produce similar results and are generally the
favoured formulas for calculating price indexes.
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A superlative index is defined technically as an index that is exact for a flexible
aggregator. A flexible aggregator is a second-order approximation to an
arbitrary production, cost, utility or distance function. Exactness implies that a
particular index number can be directly derived from a specific flexible
aggregator.
The Fisher price index, the Törnqvist price index and the Walsh price index are
superlative indexes. A basic characteristic of these indexes is that they are
symmetric indexes.
See Ideal Index.
Target population
The population which a survey aims to represent:
• For the CPI this is all resident private households in New Zealand;
• For the Producers Price Indexes (PPI) this is all market-oriented businesses
in New Zealand and, for the input indexes, this includes government;
• For the LCI all labour employed by New Zealand enterprises and
government; and,
• For the OTI all commodity exports and imports.
Terms of Trade
An index comparing one price index with another to show the extent to which
prices of one regimen are rising or falling relative to those of another regimen.
Such comparisons can be made between any two price indexes.
In New Zealand a comparison between the price indexes of merchandise
exports and merchandise imports is commonly used to show the deterioration
or improvement in the quantity of goods New Zealand can buy overseas with
the goods being exported.
A comparison of farm outputs and farm inputs is also common.
Theoretical index bias
That part of the cumulative difference, between the actual level of price change
experienced by the target population (Which see) and the published index that
is due to the construction of the price index. There are five types of theoretical
bias: Commodity substitution bias; Outlet substitution bias; New goods bias;
Elementary index bias; and Quality adjustment bias. (Which see).
Time Reversal Test
A test that may be used under the axiomatic approach which requires that if the
prices and quantities in the two periods being compared are interchanged the
resulting price index is the reciprocal of the original price index.
When an index satisfies this test, the same result is obtained whether the
direction of change is measured forwards in time from the first to the second
period or backwards from the second to the first period.
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Tornqvist Index (or Tornqvist-Theil Index)
See Ideal Index.
Transactor
A person, company or organisation that buys, sells or otherwise exchanges
goods and services for value.
In the CPI, the transactors are NZ private resident households on the one hand
and the shops, government agencies and businesses that sell goods and
services on the other hand. In the Producers Price Indexes, the transactors are
all New Zealand resident businesses and their customers and suppliers.
For the LCI, the transactors for the wage and salary element can be regarded
as New Zealand businesses and government on the one hand and the persons
providing labour on the other. Note, however, that there are other transactors
involved in the costs of accident insurance, fringe benefit tax, etc.
Trend (of a series)
The steady underlying long-term movement and shorter-term movements in a
series. This is most easily calculated as a four quarter moving average of a time
series. EXCEL provides more sophisticated options to measure trends. The
Trend is also a by-product of seasonal adjustment calculation. (Which see).
Under-coverage
A form of non-sampling error which occurs when the sample frame from which a
survey is selected does not completely cover the population of interest.
Underlying inflation
In New Zealand, this was used in the Reserve Bank’s monitoring of the
economy. It was a measure of the prevailing level of price change in the
economy excluding major price shocks, factors beyond New Zealand control,
effects of government charges, and effects of credit services charges. A
numerical measure of this type is no longer produced. However, trimmed mean
and weighted percentile measures are being produced by Statistics NZ and
used by the Bank.
Utility
It is the satisfaction derived from consumption of a good or service.
Walsh Index
See Ideal Index.
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Weighted average
A means of averaging a set of values where each value carries a different
weight. This weight reflects the importance of each value relative to the other
values in the set.
e.g.
A
Given a set of numbers
3
6
8
4
3
2
B
2
3
1
4
1
1
8
16
3
2
And given weights
Then multiplying the values by the weights gives
C
Sum of numbers times
weights
6
18
Then the sum of the weight in row B is 12 (i.e. 2 + 3 + 1 + 4 + 1 + 1).
The sum of the products of weight time value is 53 (i.e. 6 + 18 + 8 + 16 + 3 + 2).
And the weighted average is obtained by dividing the sum of the products by
the sum of the weights
= 53/12 = 4.42
In mathematical notation, the weighted average of a set of m numbers =
m
 vi wi
i 1
m
 wi
i 1
Where
vi
wi
=
=
is the value of the item i (i = 1 …m), and
is the weight of the item i (i = 1 …m)
In indexes produced by Statistics New Zealand the weight is often related to the
expenditure or sales receipts of the item valued.
In the CPI, population is used to allocate expenditure weights to regions.
See also Democratic weighting, Expenditure weight, Implicit weighting, Item
weight, Outlet weight, Plutocratic weighting, Population weighting, and
Storetype weight.
Cf Arithmetic mean.
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