TABLE OF CONTENTS
INTRODUCTION ......................................................................................................................... 3
Purpose ...................................................................................................................................... 3
How the manual was written ..................................................................................................... 3
Contents of the Manual .............................................................................................................. 4
CHAPTER 1 COVERAGE AND CLASSIFICATION OF CAPITAL STOCKS ...................... 6
Coverage .................................................................................................................................... 6
Classification ............................................................................................................................. 8
CHAPTER 2 CAPITAL STOCK AND RELATED FLOWS: CONCEPTS AND USES ........ 12
Valuing capital stocks .............................................................................................................. 12
Gross Fixed Capital Stock ....................................................................................................... 14
Consumption of fixed capital................................................................................................... 15
Net capital stock ...................................................................................................................... 18
Capital services ........................................................................................................................ 20
Summary .................................................................................................................................. 23
CHAPTER 3 OVERVIEW OF MEASUREMENT METHODS ............................................. 24
Gross capital stock ................................................................................................................... 24
Net capital stock ...................................................................................................................... 25
Consumption of fixed capital................................................................................................... 25
Capital services ........................................................................................................................ 26
CHAPTER 4 PERPETUAL INVENTORY METHOD ............................................................ 27
Introduction.............................................................................................................................. 27
Gross capital stock ................................................................................................................... 27
Consumption of fixed capital................................................................................................... 43
Net capital stock ...................................................................................................................... 43
Alternative application of the PIM .......................................................................................... 43
CHAPTER 5 MEASURING CONSUMPTION OF FIXED CAPITAL .................................. 46
Introduction.............................................................................................................................. 46
Empirical evidence .................................................................................................................. 47
Capital service value profiles, asset prices and depreciation ................................................... 48
Depreciation methods .............................................................................................................. 56
How well do depreciation methods perform in practice? ........................................................ 58
Summary .................................................................................................................................. 61
CHAPTER 6 SURVEYS AND OTHER DIRECT MEASUREMENT METHODS............... 62
Introduction.............................................................................................................................. 62
Published company accounts ................................................................................................... 62
1
Balance of Fixed Assets........................................................................................................... 63
Statistical surveys in market economies .................................................................................. 64
Administrative records............................................................................................................. 67
Summary .................................................................................................................................. 67
CHAPTER 7 CAPITAL SERVICES ........................................................................................ 69
Introduction.............................................................................................................................. 69
Stocks or flows ........................................................................................................................ 69
Capital services ........................................................................................................................ 70
Summary .................................................................................................................................. 72
LIST OF ANNEXES ................................................................................................................... 74
Annex 1. Glossary of Terms: Capital Stocks and Related Statistics ....................................... 75
Annex 3. Service lives of assets used in four countries .......................................................... 81
Annex 4. Questionnaire forms used by New Zealand and the Netherlands ............................ 91
Annex 5. Graph Showing Impact of Different Service Lives and Interest Rates
on Asset Values Implied by Five Capital Service Value Profiles. (Service Lives 15 and
50 Years; Interest rate 5% and 10%) ....................................................................................... 91
Annex 6. Asset prices and depreciation implied by four capital service value profiles. ......... 91
2
INTRODUCTION
Purpose
1.
This manual serves two complementary purposes: to clarify the conceptual issues concerning
stocks and flows of fixed capital in the national accounts and to provide practical guidelines for
estimation.
2.
The nature of capital and its contribution to production has long been a contentious issue for
economists but there is now a good measure of agreement on definitions of the stock of fixed capital
assets and capital consumption in the context of the national accounts. The 1993 System of National
Accounts (1993 SNA) includes stocks as an integral part of the accounting system and shows how the
opening and closing stocks are reconciled by transactions in assets and other changes. The 1993 SNA
also provides detailed definitions on the scope of fixed capital formation, stocks of fixed assets and
consumption of fixed capital. These guidelines provide the basis for the recommendations in this
Manual.
3.
Three documents have been produced by international organisations on the estimation of
capital stock statistics. The first was published in 1976 by the Organisation for Economic
Co-operation and Development (OECD) – “The Measurement of Capital; The Methodology of Capital
Stock Estimates in OECD Countries” (Michael Ward, 1976). This dealt with both conceptual and
measurement issues and marked the beginning of work in the Organisation to encourage more
Member countries to compile capital stock statistics. The second was published in 1979 by the
United Nations - “Guidelines on Statistics of Tangible Assets” (United Nations, 1979). While mainly
concerned with clarifying the accounting role and classification of stocks in the 1968 SNA, this
publication also contains useful suggestions on sources of data and estimation procedures. The third
was published by the OECD in 1993 - “Methods Used by OECD countries to Measure Stocks of Fixed
Capital” (OECD, 1993). This deals exclusively with the estimation of capital stocks by the “Perpetual
Inventory Method” (PIM) and is confined to practices in Member countries of the OECD. This
Manual is somewhat broader in both respects because it reflects experience in non-OECD countries
and considers methods of estimation other than the PIM. The manual does, however, draw on
information in these earlier OECD publications and in the United Nations publication.
How the manual was written
4.
With encouragement from the United Nations Statistical Commission, the Australian Bureau
of Statistics (ABS) organised a meeting on capital stock statistics in Canberra in early 1997. The
participants agreed that it would be useful to produce a Manual dealing with conceptual and
measurement aspects of capital stock statistics and a Steering Group was appointed to draw up an
outline for such a manual. This shaped the agenda for the next meeting of the “Canberra Group on
Capital Stock Statistics” which was organised by the ABS at the Organisation for Economic
Co-operation and Development (OECD) in Paris in September 1998. The papers presented at these
3
two meetings and the discussions they provoked have provided most of the input for this Manual
which was drafted at the OECD during the first half of 1999. The draft Manual was circulated for
comment to the Canberra Group participants in mid- 1999 and completed during the Canberra Group's
third and final meeting, which was co-hosted by the United States Bureau of Economic Analysis
(BEA) and the Bureau of Labor Statistics (BLS) and held in Washington D.C. November 1999. In
all, representatives from XXX countries and ZZZ international agencies took part in these meetings
and contributed to the production of this Manual.
5.
An annotated bibliography at the end of this Manual describes the contributions by members
of the Canberra Group. All papers presented at the three meetings of the Canberra Group, together
with the reports on those meetings, are available in the electronic version of this Manual.
Contents of the Manual
6.
Chapter 1, Coverage and Classification of Assets, explains that the manual deals only with
stocks of fixed assets as these are defined in the 1993 SNA. Data on inventories and on non-produced
assets are also required for the balance sheets of the 1993 SNA but are not covered in this manual.
Classifications of both assets and asset owners are given in the 1993 SNA and these should be the
starting points for the classification of capital stocks. It is, however, unlikely that any country will be
able to apply the full detail of these classifications and suggestions are given for a more aggregated
breakdown of assets and asset owners and users.
7.
Chapter 2, Capital Stocks and Related Flows;Concepts and Uses, starts by explaining the
valuation principles and gives numerical examples of how stocks are valued at historic cost and at
current and constant replacement costs. The chapter then gives the basic definitions of the gross and
net stocks; consumption of fixed capital and capital services and explains their uses.
8.
Chapter 3, Overview of Measurement Methods, reviews the basic data sources that may be
used to estimate capital stocks, consumption of fixed capital and capital services. The gross capital
stock can be estimated either by surveys of enterprises or by the “perpetual inventory method” (PIM).
Company accounts give estimates of both net stocks and consumption of fixed capital but these are not
generally suitable for national accounts purposes; both of these need to be estimated by statistical
agencies, usually starting with the gross capital stock. Capital services can be directly observed when
assets are leased but most assets are owned by their users and capital services have to be estimated
indirectly.
9.
Chapter 4, Perpetual Inventory Method, describes the basic requirements for the PIM,
namely statistics on gross fixed capital formation, price indices for capital assets, and information on
average service lives for assets and on how retirements are distributed around these averages. The PIM
is essentially used to estimate the gross capital stock; the same methods are used to calculate
consumption of fixed capital and the net capital stock whether the gross capital stock is obtained by
the PIM or from direct observation through surveys. This chapter also describes an innovative
application of the PIM, which has been developed by the United States Bureau of Economic Analysis
(BEA); this method generates estimates of the net capital stock and consumption of fixed capital
without an explicit calculation of the gross stock.
10.
Chapter 5, Measuring Consumption of Fixed Capital, reviews the empirical evidence about
how assets lose their value over the course of their service lives. It notes that there are many “capital
service value profiles” that are consistent with this empirical evidence. Three depreciation methods
are then introduced and each is tested to see how well they approximate the depreciation that will
4
theoretically occur for assets that have service value profiles that are consistent with the empirical
evidence.
11.
Chapter 6, Surveys and Other Direct Measurement Methods, considers other ways of
estimating capital stocks that may avoid the uncertainties inherent in the perpetual inventory method.
(These relate, in particular, to assumptions about service lives and mortality patterns.) It concludes
that there is a case for wider use of direct survey methods. The main impediment to the use of surveys
is their high cost but this can be reduced by a “rolling benchmark” survey of the kind that has been
introduced in the Netherlands. Another alternative to the PIM is the “ balance of fixed asset” survey
that is carried out in several transition economies.
12.
Chapter 7, Capital Services, notes that in studying the productivity of capital, a flow rather
than a stock measure is required. There is now general agreement that this flow should be measured
as: ft = (dt + r) Vt where f is the value of the capital service provided in period t, d is the rate of
depreciation, r is the rate of return and V is the capital stock. The chapter then discusses alternative
ways of measuring the rate of return and the capital stock.
13.
Annex 1 is a glossary of terms used in the literature or the measurement of capital. It
includes terms used in the 1993 SNA as well as other terms commonly encountered in the literature.
The other 5 annexes are supporting material which are referred to in the text.
5
CHAPTER 1
COVERAGE AND CLASSIFICATION OF CAPITAL STOCKS
Coverage
1.
The stock and flow measures considered in this manual relate to the physical objects that are
included in gross fixed capital formation as defined in the 1993 SNA. Table 1 gives the full listing of
non-financial assets recognised in that system, and those which form the subject of this manual are
printed in bold.
2.
It is clear from Table 1 that a relatively small subset of all non-financial assets is dealt with
in this manual. The 1993 SNA requires that stocks of all non-financial assets shown in Table 1 should
be included in the Balance Sheets of the system. There are several reasons why this manual is
restricted to stocks of fixed assets:
In almost all countries fixed assets account for by far the largest part of total stocks of
non-financial assets. The only exceptions are countries with a small industrial base and
large stocks of sub-soil assets.
No consumption of fixed capital is calculated in respect of inventories and valuables or for
any of the non-produced assets. This eliminates one of the major problems in calculating
stock values for the balance sheets.
Fixed assets are usually used as the capital variable in productivity studies. Other
non-financial assets such as valuables, sub-soil assets, biological resources and water
resources have rarely been suggested as candidates to explain economic growth. On the
other hand, both land and inventories have often been included in the capital variable
used in productivity studies.
Stocks of assets of non-financial assets not covered in this manual generally present either
less severe problems of estimation than those that are included or they are estimated by
methods that are quite different from those discussed here. For example, the value of
stocks of land can usually be obtained directly from administrative sources, although
these values will often need major adjustments to bring them to market values; the value
of sub-soil assets is usually estimated by calculating the discounted present value of
expected income flows, a procedure that is rarely used for fixed assets.
3.
In summary, this manual concentrates on the kinds of non-financial assets, the stocks of
which are particularly difficult to estimate, which are a very large component of total stocks, which
6
require that estimates be made for consumption of fixed capital in addition to estimates of stocks and
which are particularly useful for economic analysis.
Table 1. SNA Classification of Non-Financial Assets
AN.1
Produced assets
AN.11
Fixed assets
AN.111
Tangible fixed assets
AN.1111
Dwellings
AN.1112
Other buildings and structures
AN.11121 Non-residential buildings
AN.11122 Other structures
AN.1113
Machinery and equipment
AN.11132 Other machinery and equipment
Mineral exploration
AN.1122
Computer software
AN.1123
Entertainment, literary or artistic
originals
AN.132
Antiques and other art objects
AN.139
Other valuables
AN.2
Non-produced assets
AN.21
Tangible non-produced assets
AN.211
Land1
AN.2119 Other land and associated surface
water
AN.11142 Vineyards, orchards and other
plantations of trees yielding
repeat products
AN.1121
Precious metals and stones
AN.2113 Recreational land and associated
surface water
AN.11141 Livestock for breeding, dairy,
draught, etc.
Intangible fixed assets
AN.131
AN.2112 Land under cultivation
Cultivated assets
AN.112
Valuables
AN.2111 Land underlying buildings and
structures
AN.11131 Transport equipment
AN.1114
AN.13
AN.212
Subsoil assets
AN.2121 Coal, oil and natural gas reserves
AN.2122 Metallic mineral reserves
AN.2123 Non-metallic mineral reserves
AN.213
Non-cultivated biological resources
AN.214
Water resources
AN.1129
Other intangible fixed assets
AN.22
Intangible non-produced assets
AN.12
Inventories
AN.221
Patented entities
AN.121
Materials and supplies
AN.222
Leases and other transferable contracts
AN.122
Work-in-progress
AN.223
Purchased goodwill
AN.1221
Work-in-progress on cultivated assets
AN.229
Other intangible non-produced assets
AN.1222
Other work-in-progress
AN.123
Finished goods
AN.124
Goods for resale
1.
Only “land improvement” is included in the capital stock and not the land itself. Land improvement
covers levelling, terracing, fencing, drainage and similar works.
7
Classification
4.
This section deals with the classifications used for publishing capital stock statistics. Three
1993 SNA classifications are relevant – the Classification of Assets, the Classification of Institutional
Sectors, and the International Standard Classification of All Economic Activities (ISIC, Revision 3).
These are used in different combinations for the gross capital stock, the net capital stock, consumption
of fixed capital and capital services.
5.
The net capital stock and consumption of fixed capital appear as entries in the 1993 SNA and
this determines the classifications to be used. Both are to be classified by the institutional sector that
owns the assets. This is the appropriate classification for the net capital stock, which is needed for the
Balance Sheets of the system and for the consumption of fixed capital, which is needed for the nonfinancial accounts i.e. the Distribution and Use of Income Accounts and for the Accumulation
Accounts.
6.
Capital stock statistics also serve a number of analytic uses, such as calculating capital
output ratios and studying capital or “multi-factor” productivity. For these purposes, it is usually
preferable to classify assets according to the kind of activity of the owner and by type of asset. This
involves a cross-classification by ISIC and by the Classification of Assets.
7.
For some purposes it may also be useful to classify assets according to the kind of activity of
the user of the asset rather than that of the owner. It should be noted, however, that when assets are
classified by user, the statistics cannot be related to other flows in the national accounts because these
are compiled on an “ownership” basis. For example, the distribution of value added among different
kinds of activities depends on asset ownership rather than on asset use. If assets are rented, the income
generated by the asset appears in the value added of the owner and not that of the user. This is
because the rental payment is deducted as intermediate consumption from the gross output of the user
and appears in the gross output of the owner.
8.
In practice, countries that use the perpetual inventory method can usually only classify assets
according to the activity of the owner because this is how statistics on capital formation are reported.
Assets can only be classified by the activity of the user if the capital stock estimates are based on
enterprise surveys in which respondents are required to report both values of assets owned and of
assets that are rented.
Classification by type of asset
9.
The part of the 1993 SNA Classification of Assets covering non-financial assets is given in
Table 1 above. At its most detailed level it distinguishes 12 types of assets. Most countries use an
asset breakdown that is far less detailed than this. The standard questionnaire that is used by the
international organisations to collect annual statistics according to the 1993 SNA uses a three-way
breakdown – machinery and equipment, buildings and structures and other assets. Many users would
certainly want more detail than this. National publications usually distinguish transport equipment
from other types of machinery and equipment and dwellings from other buildings and structures. It is
also common for non-residential buildings to be shown separately from other structures. Intangible
assets are a new feature of the 1993 SNA, so it would be useful to show these separately to provide
comparison with earlier stock data which excluded these assets.
8
10.
With these considerations in mind, the following (bold) headings are recommended for
classifying assets:
Dwellings
Non-residential buildings
Other structures (including land improvement)
Transport equipment
Other machinery and equipment
Cultivated assets

Livestock for breeding, dairy, draught, etc.

Vineyards, orchards and other plantations of trees yielding repeat products
Intangible assets

Mineral exploration

Computer software

Entertainment, literary or artistic originals

Other intangible fixed assets
Classification by institutional sectors
11.
The 1993 SNA identifies five institutional sectors:
Non-financial corporations
Financial corporations
General government
Households
Non-profit institutions serving households
The sixth pseudo-sector “Rest of the World” is not relevant in the present context because all fixed
assets are, by convention, considered to belong to the five “domestic” sectors. These sectors are
further broken down to give a total of 36 sub-sectors at the most detailed level.
12.
The level of detail to be used for classifying the net capital stock and consumption of fixed
capital depends entirely on the degree of sector detail that is used in the Balance Sheets (for net stock)
and in the non-financial accounts (for capital consumption). The few countries that compile balance
9
sheets at the present time mostly classify stocks according to the five institutional sectors, but with
some breakdown of general government by level - central, local, social security funds, for example.
A similar breakdown is used by most countries for the non-financial accounts, although the Financial
Corporations sector is sometimes broken down to distinguish between depository institutions (i.e.
banks) and non-depository institutions.
13.
The questionnaire used by the international organisations to collect 1993 SNA statistics calls
for the non-financial accounts to be sub-sectored as follows and this determines the institutional sector
detail for classifying consumption of fixed capital:
Non-financial corporations
Financial corporations
Central government
State government
Local government
Social security funds
Households
Non-profit institutions serving households
In practice, the above list represents a target classification. Not all member countries of the OECD can
yet meet this requirement and for most other countries the five main sectors represent a more realistic
target for capital stock statistics.
Classification by kind of activity
14.
Capital stock and flow statistics classified by kind of activity are used mainly for analytic
work. As a general rule, the more detailed the activity breakdown, the more useful will the statistics
be for such purposes. On the other hand, practical considerations limit the amount of detail that can be
shown. For example, if the PIM is used, the kind of activity breakdown cannot be more detailed that
the kind of activity classification used for gross fixed capital formation. If the latter is very detailed,
transfers of used assets between producers in different kinds of activities will affect reliability and
reduce the amount of detail that can reasonably be shown.
15.
The annual 1993 SNA questionnaire calls for capital stock statistics to be broken down by 17
kinds of activities. These are the 17 “tabulation categories” of the ISIC (revision 3). It would be
possible to make this list more useful by distinguishing the principal activities within manufacturing
(which is a single tabulation category) and by grouping some of the categories covering service
activities. A classification that may be useful for countries starting capital stock statistics is given in
Table 2.
10
Table 2. Suggested activity classification for capital stock statistics.
ISIC
tabulation
categories
Description
A+B
Agriculture, hunting, forestry and fishing
C
Mining and quarrying
D
Manufacturing, with 4 or 5 important activities separately identified.
E
Electricity, gas and water supply
F
Construction
G+H
Wholesale and retail trade, repair of vehicles and household goods, hotels and restaurants
I
Transport, storage and communications
J+K
Financial intermediation, real estate, renting and business activities
L
Public administration, defence and social security
M,N + O
Education, health and social work, other community, social and personal service activities
11
CHAPTER 2
CAPITAL STOCK AND RELATED FLOWS: CONCEPTS AND USES
1.
This chapter describes the definitions and the main uses of the gross and net capital stocks
and of two important flow measures derived from them, namely consumption of fixed capital and
capital services. First, however, it is necessary to consider the three different ways in which stocks can
be valued.
Valuing capital stocks
2.
Stocks of capital assets can be valued at three kinds of prices:
Historic prices, which means that the value of the stock of assets is obtained by aggregating
them at the prices at which each asset was originally (i.e. “historically”) acquired.
Current replacement prices, which means that the value of the stock of assets is obtained
by aggregating them after each asset has been revalued to the prices of the current year.
Constant replacement prices, which means that the value of the stock of assets is obtained
by aggregating them after each asset has been revalued to the prices of a selected year.
3.
It is important to note that price indices are required for valuation at current replacement
prices as well as valuation at constant replacement prices. In the first case, assets have to be revalued
each year to bring them to the prices of the current year; in the second case, assets have to be revalued
to convert the prices actually paid to those of the selected year. It is only in the case of valuation at
historic prices that no price indices are required because the prices at which the assets were originally
acquired continue to be used in every year in which the assets remain in the capital stock.
4.
Table 1 shows how the stock of a group of assets is valued at each of these three kinds of
prices. The assets are assumed to each have a life of five years and to have been acquired in three
successive years. In table 1, the stocks of assets are valued “gross” i.e. before deducting consumption
of fixed capital or “depreciation” as it is more commonly called.
12
Table 1. Calculation of a capital stock at historic, current and constant prices
year
1
6
7
Assets purchased in year 1
Assets purchased in year 2
Assets purchased in year 3
Stock at historic prices
2
3
4
5
At actual prices paid i.e. at historic prices
10.0
10.0
10.0
10.0
10.0
20.0
20.0
20.0
20.0
5.0
5.0
5.0
10.0
30.0
35.0
35.0
35.0
20.0
5.0
25.0
5.0
5.0
Asset price
100
112
114
118
Assets purchased in year 1
Assets purchased in year 2
Assets purchased in year 3
Stock at current replacement prices
10.0
At replacement prices of the current year
10.3
10.5
11.0
11.2
20.0
20.4
21.4
21.7
5.0
5.2
5.3
10.0
30.3
35.9
37.6
38.3
22.1
5.4
27.6
5.6
5.6
Assets purchased in year 1
Assets purchased in year 2
Assets purchased in year 3
Stock at constant replacement prices
10.0
At constant prices of year 1
10.0
10.0
10.0
19.4
19.4
19.4
4.8
4.8
10.0
29.4
34.2
34.2
19.4
4.8
24.2
4.8
4.8
103
105
110
10.0
19.4
4.8
34.2
5.
To obtain the stock at historic prices, the assets acquired in years 1, 2 and 3 are valued at the
prices prevailing in each of these years and continue to be valued at these same prices during the five
years that they remain in the capital stock.
6.
Table 1 shows that the asset price has been rising over the period from 100 in year 1 to 118
in year 7. In order to obtain the value of the stock at current replacement prices the assets need to be
revalued -- in this case increased in price -- in line with the rise in asset prices. Note that in year 2, the
assets acquired in that year (to the value of 20) are already at the prices of year 2 and do not therefore
need to be revalued in that year. For subsequent years, however, they must be multiplied by pt /103
where pt is the asset price index in year t; similarly the assets, valued at 5, acquired in year 3 must be
multiplied by pt /105 for years 4 through 7.
7.
In order to obtain the value of the stock at constant replacement prices -- in this example at
the prices of year 1 -- all assets acquired after year 1 must be deflated to bring them down to year 1
prices. Thus the assets acquired in year 2 are multiplied by 100/103 and those acquired in year 3 by
100/105. The assets acquired in year 1 are, by definition, already at year 1 prices.
8.
The last line of Table 1 shows the ratio of the asset stock at current prices to the stock at
constant prices. It is of course identical to the asset prices given in the table. This indicates that the
rather laborious procedure for calculating the capital stock at current prices can be avoided by first
estimating the stock at constant prices and inflating with price indices. This is the usual procedure in
practice.
9.
Valuation at historic prices is the usual procedure in company accounts. This is done
because historic prices can be objectively verified by examining the invoices relating to asset
purchases, while valuation at either current or constant replacement prices introduces uncertainty into
the stock valuation because there are always error margins attached to price indices. Commercial
accountants may also prefer historic prices because they give a conservative valuation of assets. These
advantages, however, are offset by the fact that assets which have been acquired at different dates are
being valued at different prices so that when prices are rising/falling assets acquired more recently are
13
implicitly given a higher/lower weight than those acquired in earlier periods. Capital stocks valued at
historic prices cannot be compared with national accounting or other economic statistics which are
calculated at either current or constant prices. Nevertheless a few countries calculate and publish
stocks and depreciation at historic prices because they believe that many businesses use stock and
depreciation estimates at historic cost for management decisions. They may, therefore, be useful in
explaining the behaviour of businesses.
10.
The adjective “replacement” is conventionally applied to qualify the current and constant
prices used to value capital stocks because the objective is to value the asset stock at what it would
cost to replace it in the sense of buying an identical set. There are, however, difficulties in the notion
of a replacement price. These arise because capital assets may remain in the capital stock for several
years and it will often happen that it is impossible to replace assets several years after they were
originally installed because the assets concerned are no longer being produced; there are no true
“replacement” prices at which they can now be valued. In practice, assets which are no longer being
produced have to be revalued to current replacement prices using price indices that are calculated from
price changes of assets that are still in production.
Gross Fixed Capital Stock
11.
The gross fixed capital stock is the value, at a point in time, of assets held by producers with
each asset valued at “as new” prices -- i.e. at the prices for new assets of the same type, regardless of
the age and actual condition of the assets. It is a “gross” measure of the stock in the sense that it is
calculated before deducting consumption of fixed capital.
12.
Two points should be noted about the coverage of the assets to be included in the gross
capital stock.
First the assets included in the stock may be owned by the enterprises that use them in
production or they may be rented out to producers by their owners. Certain types of
assets, such as commercial and residential buildings, road vehicles and construction
equipment are commonly rented in many countries.
Second, not all the assets included in the gross stock may actually be in use to produce goods
and services. Some assets may have been “moth-balled” or held in reserve to meet
unexpected surges in demand. Others may be kept in reserve as insurance against the
breakdown of critical pieces of equipment. Assets that are rented to producers may spend
idle periods between customers. In order to be counted as part of the capital stock all that
is required is that assets are present at production sites and capable of being used in
production or they are available for renting by their owners to producers.
13.
If the gross stock is valued at historic prices the prices that were actually paid to purchase the
assets are used when the assets are added up to obtain the stock. If the gross capital stock is valued at
current replacement or constant replacement prices, the assets must be revalued or deflated using asset
price indices in the manner shown in Table 1 above.
14.
The gross capital stock is not a part of the System of National Accounts and it is not shown
in company accounts. Gross capital stocks have sometimes been used to represent capital input in
studies of “multi-factor” productivity (or “total factor productivity” as it is also termed) but this is not
recommended in this manual because it is argued here that the required measure of capital for
productivity studies is the services provided by the stock of assets rather than the stock itself.
14
However, although the gross capital stock has no role in national or company accounts and serves few,
if any, analytic purposes it is the conventional starting point for calculating consumption of fixed
capital and the net capital stock. Both these latter aggregates have important analytic and accounting
roles as explained below.
15.
The role of the gross capital stock as the starting point for estimating consumption of fixed
capital has an important implication for the way in which “replacement” prices are defined for valuing
the gross capital stock. The problem is caused by obsolescence.
16.
Obsolescence is the loss in value of an old asset because a newly introduced asset of the
same kind contains improvements in productiveness or efficiency or suitability in production.
Obsolescence in an old capital asset is closely linked to quality change in newer capital assets of the
same kind; a striking example of loss in value due to of obsolescence is provided by computer
equipment. Obsolescence may also occur because of changes in relative factor prices; for example an
asset that was designed to economise on raw materials by using more labour will fall in value due to
obsolescence if labour becomes more costly relative to raw materials. Finally, an asset will suffer
obsolescence if there is a fall in demand for the good or service that it was designed to produce.
17.
Note that obsolescence does not involve any physical deterioration in the asset itself. The
asset may still be functioning as well as when it was first acquired but its value has declined because
technical improvements in newer models have rendered the older model less attractive to purchasers,
or because of changes in relative prices, or because of shifts in demand for the asset’s output. It is, of
course, possible that obsolescence as here defined may actually increase the value of an asset. A rise in
demand for an asset’s output or relative price movements could conceivably make an older asset more
valuable than its newer rival, but “negative obsolescence” is likely to be a rare event and it is here
assumed that obsolescence generally reduces the value of older assets.
18.
The question that arises is whether the replacement prices used to value the gross capital
stock should reflect declines in the value of older assets due to obsolescence. Specifically, in
estimating the replacement price of an asset which is no longer available on the market (but which still
remains in the capital stock) should the “as new” price of that asset be reduced to reflect the fact that
potential buyers could only be persuaded to buy the older model if the price were reduced? The answer
given here is that no reduction should be made in respect of obsolescence. The reason for this is that
the gross capital stock is used to derive consumption of fixed capital. If the gross capital stock is
valued at replacement costs which have been reduced by obsolescence, it cannot then used to derive a
measure of consumption of fixed capital which includes obsolescence as one of its components. In
consequence, the estimate of consumption of fixed capital will be too low when estimated at current
prices and too high at constant prices. Similar errors, but with opposite signs, will also be carried
through to estimates of the net capital stock.
Consumption of fixed capital
19.
The general definition of consumption of fixed capital is given in the 1993 SNA,
paragraph 6.179.
[Consumption of fixed capital] may be defined in general terms as the decline, during the course
of the accounting period, in the current value of the stock of fixed assets owned and used by a
producer as a result of physical deterioration, normal obsolescence or normal accidental
damage. It excludes the value of fixed assets destroyed by acts of war or exceptional events
15
such as major natural disasters which occur very infrequently. Such losses are recorded in the
System in the account for “Other changes in the volume of assets”.
20.
Some clarifications are needed.
First, the decline in the current value of the stock of assets must be calculated using inflationadjusted prices to value the opening and closing stocks. Changes in the value of fixed
assets arising from changes in the general price level are recorded in the revaluation
accounts and do not form part of consumption of fixed capital.
Second, “used by a producer” must be interpreted to include situations where assets have
been purchased by a producer but which for any reason have not yet been employed in a
production process. This clarification is needed because consumption of fixed capital can
occur in respect of assets which are available at the producer’s establishment for use in
production but which are kept idle for some reason. For example, in some centrally
planned economies it was customary for producers to hold a surplus stock of assets for
use in the event of unexpected breakdown of working assets, as insurance against
interruption in the future supply of particular kinds of assets, or to cannibalise for spare
parts. Assets held by producers but which have not been, or may never be, employed for
productive purposes may nevertheless fall in value because of obsolescence and these
falls in value must be included in consumption of fixed capital.
Third, “physical deterioration” refers to wear and tear that is not made good by repairs or by
replacing worn components. Some assets may not suffer any physical deterioration
because the asset owner makes good all wear and tear through careful maintenance. In
such cases the fall in asset value over time measured by consumption of fixed capital will
be due only to obsolescence or to normal accidental damage.
Fourth, “normal accidental damage” refers to the kinds of accidents which are commonly
insured against. Accidental damage includes cases where the asset has been so badly
damaged that it has to be prematurely scrapped. Transport equipment is particularly
vulnerable to damage of this kind and when service lives are estimated for such assets
they must reflect the probability of premature scrapping through accidental losses.
Finally, the above definition implies, without explicitly stating so, that abnormal
obsolescence is also excluded from consumption of fixed capital. Abnormal
obsolescence may occur either because of unexpected technological breakthroughs or
because of sudden changes in the relative prices of inputs. The introduction of electronic
calculators in the 1960s is an example of an unforeseen technological development,
which resulted in a sudden and sharp fall in the existing stock of electro-mechanical
calculators. The 1974 oil-shock is an example of a drastic shift in relative input prices,
which led to premature replacement of inefficient oil-using equipment by more efficient
models or by assets using alternative energy sources. Premature scrapping of assets,
which arises from abnormal obsolescence, is treated in the same way as losses of assets
due to wars or natural calamities and is shown in the account for “Other changes in the
volume of assets”.
21.
The definition of consumption of fixed capital -- as the decline during the accounting period
in the market value of assets excluding any exceptional losses -- is simple, but measuring consumption
of fixed capital in the same way as it is defined is not possible in practice. Some assets are, of course,
sold on second hand markets so that market prices become available from time to time. However, to
16
measure consumption of fixed capital using actual market prices for all assets would only be feasible if
producers were to sell and buy back all their capital assets at the end of each period of account. In the
absence of market prices for most capital assets in the periods following their installation, both
national accountants and commercial accountants are forced to assume that assets decline in value in
some systematic way over the course of their service lives. Several “depreciation patterns” are used by
accountants for this purpose and they are described in a later chapter. For now it is sufficient to note
that the two commonest depreciation patterns are “straight-line” and “geometric”; the first assumes
that assets decline by a constant amount, namely 1/L (where L is the expected service life of the asset),
while geometric depreciation assumes that asset values decline at a constant rate. The calculation of
consumption of fixed capital is demonstrated in Table 2 using straight-line depreciation.
Table 2. Consumption of fixed capital at historic, current and constant replacement prices
year
Assets purchased in year 1
Assets purchased in year 2
Assets purchased in year 3
Gross capital stock at historic prices
1
2
3
4
5
6
Gross capital stock at historic prices (i.e. at prices actually paid)
10.0
10.0
10.0
10.0
10.0
20.0
20.0
20.0
20.0
20.0
5.0
5.0
5.0
5.0
10.0
30.0
35.0
35.0
35.0
25.0
5.0
5.0
CFC on assets purchased in year 1
CFC on assets purchased in year 2
CFC on assets purchased in year 3
Total CFC at historic prices
Consumption of fixed capital at historic prices
2.0
2.0
2.0
2.0
4.0
4.0
4.0
1.0
1.0
2.0
6.0
7.0
7.0
Asset price
100.0
103.0
105.0
110.0
7
2.0
4.0
1.0
7.0
4.0
1.0
5.0
1.0
1.0
112.0
114.0
118.0
Assets purchased in year 1
Assets purchased in year 2
Assets purchased in year 3
Gross capital stock at current replacement prices
Gross capital stock at replacement prices of the current year
10.0
10.3
10.5
11.0
11.2
20.0
20.4
21.4
21.7
5.0
5.2
5.3
10.0
30.3
35.9
37.6
38.3
22.1
5.4
27.6
5.6
5.6
CFC on assets purchased in year 1
CFC on assets purchased in year 2
CFC on assets purchased in year 3
Total CFC at replacement prices of current year
Consumption of fixed capital at replacement prices of current year
2.0
2.1
2.1
2.2
2.2
4.0
4.1
4.3
4.3
4.4
1.0
1.0
1.1
1.1
2.0
6.1
7.2
7.5
7.7
5.5
1.1
1.1
Assets purchased in year 1
Assets purchased in year 2
Assets purchased in year 3
Gross capital stock at constant replacement prices of year 1
Gross capital stock at constant replacement prices of year 1
10.0
10.0
10.0
10.0
10.0
19.4
19.4
19.4
19.4
4.8
4.8
4.8
10.0
29.4
34.2
34.2
34.2
4.8
4.8
CFC on assets purchased in year 1
CFC on assets purchased in year 2
CFC on assets purchased in year 3
Total CFC at constant replacement prices of year 1
Consumption of fixed capital at constant replacement prices of year 1
2.0
2.0
2.0
2.0
2.0
3.9
3.9
3.9
3.9
3.9
1.0
1.0
1.0
1.0
2.0
5.9
6.8
6.8
6.8
4.8
19.4
4.8
24.2
22.
In Table 2, annual consumption of fixed capital is obtained by dividing the gross capital
stock series by 1/5 because straight-line depreciation is being used in this example and because the
assets last for five years. When valued at historic prices and at constant replacement cost, consumption
of fixed capital is constant for each group of assets throughout their lifetimes. For the calculations at
current replacement prices, consumption of fixed capital rises in line with the re-valued prices of the
assets.
17
1.0
1.0
23.
Table 2 demonstrates why the gross stocks must be valued at prices that are not reduced to
reflect obsolescence. If the asset prices were so reduced -- i.e. if the asset price index was growing
more slowly than shown here -- the straight-line depreciation factor of 1/5 would have been applied to
a base that was too low in the case of the current price estimates and too high in the case of the
constant price estimates. The “as new” prices used to calculate gross capital stocks must not reflect
any parts of the fall in market values which are to be captured by the depreciation factor.
24.
Consumption of fixed capital has three roles in the 1993 SNA:
It is deducted from gross measures of product, income and saving to arrive at net measures
of these aggregates. In recognition of the difficulties that many countries have in
calculating consumption of fixed capital, the SNA provides for all balancing items in the
Production Account and in the Distribution and Use of Income Accounts to be recorded
on either a gross or net basis. However, SNA para. 6.203 indicates a preference for the
net measures: “In general, the gross figure is obviously the easier to estimate and may,
therefore, be more reliable, but the net figure is usually the one that is conceptually more
appropriate and relevant for analytical purposes.” As the terms are used in economics,
saving and income are almost always understood as excluding consumption of fixed
capital.
Consumption of fixed capital is one of the cost items required to estimate output and valueadded of government and other non-market producers. Some countries at the present
time use consumption of fixed capital at historic prices taken from accounting records to
estimate government output and value added. This is likely to lead to underestimation of
both aggregates. It should also be noted that the 1993 SNA has considerably expanded
the scope of consumption of fixed capital for government by transferring some durable
military goods from intermediate consumption to capital formation and by requiring that
consumption of fixed capital be calculated in respect of roads, dams, bridges and similar
structures.
Finally, consumption of fixed capital is an entry in the Capital Account. It is one of the
transactions that explain the differences between the opening and closing stocks of fixed
assets.
25.
Consumption of fixed capital is an “imputed” flow. It is not a transaction between two
parties which can be measured by observing a monetary transaction. It is an imputed transaction
which is internal to the unit; in this sense it is similar to the consumption of food that has been grown
by household members. This does not make consumption of fixed capital a less “real” or “genuine”
transaction, but it does create practical measurement problems.
Net capital stock
26.
The net capital stock is the value at a point in time of assets at the prices for new assets of the
same type less the cumulative value of consumption of fixed capital accrued up to that point. It is
obtained from the gross capital stock and consumption of fixed capital as shown in Table 3. For
example, the net capital stock at current replacement prices for year 3 is shown in Table 3 as 20.4.
This is derived from the gross capital stock at current replacement prices, i.e. 35.9, by deducting
accumulated depreciation on the assets purchased in year 1 (2.1 x 3), plus accumulated depreciation on
18
the assets purchased in year 2 (4.1 x 2) plus accumulated depreciation on the assets purchased in year
3 (1.0 x 1). Observe that accumulated consumption of fixed capital at current replacement prices is
calculated using the prices of the year in question; it cannot be obtained by adding up the consumption
of fixed capital calculated for earlier years because these amounts are valued at the prices of several
different years.
Table 3. Net capital stock at historic, current and constant prices.
year
Assets purchased in year 1
Assets purchased in year 2
Assets purchased in year 3
Gross capital stock at historic prices
1
2
3
4
5
6
Gross capital stock at historic prices (i.e. at prices actually paid)
10.0
10.0
10.0
10.0
10.0
20.0
20.0
20.0
20.0
20.0
5.0
5.0
5.0
5.0
10.0
30.0
35.0
35.0
35.0
25.0
5.0
5.0
CFC on assets purchased in year 1
CFC on assets purchased in year 2
CFC on assets purchased in year 3
Total CFC at historic prices
Consumption of fixed capital at historic prices
2.0
2.0
2.0
2.0
4.0
4.0
4.0
1.0
1.0
2.0
6.0
7.0
7.0
2.0
4.0
1.0
7.0
4.0
1.0
5.0
1.0
1.0
Assets purchased in year 1
Assets purchased in year 2
Assets purchased in year 3
Net capital stock at historic prices
Net capital stock at historic prices
8.0
6.0
4.0
16.0
12.0
4.0
8.0
22.0
20.0
2.0
8.0
3.0
13.0
0.0
4.0
2.0
6.0
0.0
1.0
1.0
0.0
0.0
110.0
112.0
114.0
118.0
Asset price
100.0
103.0
105.0
7
Assets purchased in year 1
Assets purchased in year 2
Assets purchased in year 3
Gross capital stock at replacement prices of the current year
Gross capital stock at replacement prices of the current year
10.0
10.3
10.5
11.0
11.2
20.0
20.4
21.4
21.7
5.0
5.2
5.3
10.0
30.3
35.9
37.6
38.3
22.1
5.4
27.6
5.6
5.6
CFC on assets purchased in year 1
CFC on assets purchased in year 2
CFC on assets purchased in year 3
Total CFC at replacement prices of the current year
Consumption of fixed capital at replacement prices of current year
2.0
2.1
2.1
2.2
2.2
4.0
4.1
4.3
4.3
4.4
1.0
1.0
1.1
1.1
2.0
6.1
7.2
7.5
7.7
5.5
1.1
1.1
Assets purchased in year 1
Assets purchased in year 2
Assets purchased in year 3
Net capital stock at replacement prices of the current year
Net capital stock at replacement prices of the current year
8.0
6.2
4.2
2.2
0.0
16.0
12.2
8.5
4.3
4.0
3.1
2.1
8.0
22.2
20.4
13.9
6.5
0.0
1.1
1.1
0.0
0.0
Assets purchased in year 1
Assets purchased in year 2
Assets purchased in year 3
Gross capital stock at replacement prices of year 1
Gross capital stock at replacement prices of year 1
10.0
10.0
10.0
10.0
10.0
19.4
19.4
19.4
19.4
4.8
4.8
4.8
10.0
29.4
34.2
34.2
34.2
19.4
4.8
24.2
4.8
4.8
27.
The net stock, at current replacement prices, appears in the opening and closing balance
sheets of the 1993 SNA. Table 4 shows the connection between these opening and closing balances in
the system.
19
Table 4. Links between opening and closing stocks of fixed assets
The net value of the stock of the asset at its current price at the beginning of the period
plus gross fixed capital formation, i.e., acquisitions less disposals of the asset in transactions
with other units
minus consumption of fixed capital incurred during the period
plus the total value of other positive or negative changes in the quantity of the asset : i.e.,
changes which are not attributable to the use of the asset in production or to transactions
with other units (e.g. the physical destruction of an asset as a result of a natural
disaster or the premature scrapping of assets because of unforeseen obsolescence),
plus the total value of the positive or negative holding gains accruing during the period as a
result of changes in the price of the asset,
equals the net value of the stock of the asset at its current price at the end of the period.
28.
The net stock is the market value of fixed assets owned by the different institutional sectors
and the nation as a whole. As such, it is a measure of wealth and it is usually the largest part of
national net worth in industrialised countries. Ratios of the net stock of fixed assets to value added are
used to compare economic efficiency over time and between countries. As will be seen from the next
section, the net capital stock is also relevant for measuring capital services.
Capital services
29.
Producers purchase fixed assets because they expect them to provide a flow of services into
the production process. In principle, these capital services can be broken down into quantity
components -- such as ton-kilometres provided by a freight truck or cubic feet of storage space
provided by a warehouse -- and corresponding price components. Capital services are sometimes
traded between asset owners and the producers who need to use them. However, most capital services
are produced for own consumption within producers’ establishments. Because the producers own their
capital assets there is no explicit market transaction. As a result it is not generally possible to observe
quantities and prices of capital services directly. The following paragraphs show how capital services
can be measured indirectly.
30.
The value of an asset depends on the services which it is expected to provide over its
expected working life or “service life”. More specifically, the price of an asset (V) at time (t) is equal
to the sum of the capital services (f) that the asset is expected to generate from time (t) up to the end of
its expected service life (T) after these service flows have been reduced (or “discounted”) by a rate of
interest (r). If the asset is expected to have a scrap value (S) at the end of its service life this must be
added (after discounting) to the asset price. The price of an asset at time t can therefore be written as:
T
Vt  
t
ft
1  r 
t

S
(1)
1  r T t
20
31.
Equations such as (1) are commonly used by business accountants to determine whether or
not their company should purchase an asset. They do this by guessing at the likely pattern of capital
service flows (f) over the expected lifetime (T) of the asset and the probable scrap value (S) at the end
of its working life. As the market price of the asset (V) is known, equation (1) can be solved to
determine r -- the internal rate of return, i.e. the annual profit margin that the asset is likely to earn. If r
is higher than the rate of return that the company could earn on alternative investments, such as the
purchase of a competing model of the asset or investing in securities, the accountant will conclude that
the company should buy the asset. If the calculation suggests that r is very high, i.e. that the
investment is likely to be unusually profitable, then provided that markets are relatively open, one or
both of two things can be expected to happen. Either demand for the assets will rise and bid up the
price (V) or increased investment in the asset, either by existing producers or by new entrants, will
raise output supply and force down the value of the capital services (f) that the asset can earn. In
general, there will be both a rise in V and a fall in f, but whatever happens the result will be a fall in
the rate of return (r) to a normal or average rate for the economy as a whole. If, on the other hand, the
solution of equation (1) yields a value of r that is regarded as too low, either the asset price (V) must be
reduced in order to persuade investors to buy the asset or the asset will be withdrawn from the market.
In practice, the producers of assets will themselves have usually made a calculation such as that in
equation (1) before producing the asset and would not have decided to proceed with its production
unless the price at which it would have to be sold seems likely to yield a satisfactory rate of return to
prospective investors. Equation (1) can therefore be seen as a very plausible explanation of the way in
which asset prices are determined under normal market conditions.
32.
Vt 
Following (1), the value of an asset at any time during its service life can be written as:
ft
f
f
fT
S
 t 1 2  t  2 3  ....... +

T
1  r  1  r  1  r 
1  r  1  r T t
(2)
And its value in the next period is:
Vt 1 
f t 1
f
fT
S
 t  2 2  ........ +

T 1
1  r  1  r 
1  r 
1  r T t 1
(3)
Dividing (3) by 1  r  gives:
Vt 1

1  r 
f t 1
1  r 
2

f t 2
1  r 
3
 ......... +
fT
1  r 
T

S
1  r T t
(4)
Subtracting (4) from (2) gives:
Vt 
Vt 1
ft

1  r  1  r 
(5)
Rearranging the terms gives:
f t  Vt  Vt 1  rVt
(6)
21
However, since:
Vt  Vt 1  Dt ,
(7)
where Dt is depreciation in year t, i.e. the fall in the value of the asset between the beginning and end
of the year, equation (6) can be rewritten as:
f t  d t  r Vt
(8)
where d t is the rate of depreciation in period t and dtV= Dt.
33.
What (8) shows is that the value of the service rendered by a capital asset (ft ) is equal to
consumption of fixed capital (Dt) plus the rate of return (r) times the value of the asset (Vt). In other
words the capital service provided by an asset is equal to an amount that will compensate the owner
for the fall in the market value of the asset over the accounting period (consumption of fixed capital)
and also provide the owner with a net return on the value of the asset. The right hand side of (8) is
variously referred to as “ the cost of capital”, the “user cost of capital” and “asset rental values”. In this
Manual it is referred to as “capital services”.
34.
It was noted above that capital services are, in general, not directly observable, but equation
(8) provides a practical, though indirect, method of measuring them. Several points should be noted:
First, the Vt in equation (8) is the depreciated value of the asset -- or the net capital stock if
equations (2) through (8) are aggregated across all assets. Some practitioners have
preferred to use an alternative measure of the stock in (8) which is obtained from the
gross capital stock by adjusting the “as new” prices of assets by factors which reflect the
decline with age in their productive efficiency. This alternative way of using (8) is
discussed in Chapter 7.
Second, when each Vt is multiplied by the appropriate d t  r  and then added to obtain a
total, that total can be described in either of two ways -- as the capital stock weighted by
the gross return on each asset or as the total capital services provided by the assets during
the period. In the first case, the gross rate of return, i.e. the rate of depreciation plus the
rate of return, is being regarded as the weight; in the second case, the asset values are
taken as the weights. The preference in the United States seems to be for the stock
terminology. This manual uses the alternative term and refers to “capital services”
because this is more consistent with the flow versus stock distinction made in the System
of national Accounts.
Third, the principal difficulty in applying (8) to measure capital services is to determine the
rate of return (r). There seem to be two choices -- either to use national accounts
statistics on property income flows as a ratio of the capital stock or to base it on market
interest rates that appear to be relevant for investment decisions. This issue is discussed
in Chapter 7.
Finally, the rate of depreciation (d) in (8) is shown as varying over time. This would be the
case if, for example, straight-line depreciation is used but consumption of fixed capital
can also be calculated at a constant rate in which case the time subscript is superfluous.
22
Summary
35.
This chapter has presented a framework linking capital stocks with consumption of fixed
capital and capital services. Note that this is a perfectly general framework and is not linked to any
particular method of estimation, such as the perpetual inventory method or a direct survey approach. In
summary:
Capital assets held in producers’ establishments are valued at “as new” prices to obtain the
gross capital stock.
The gross capital stock is multiplied by a “depreciation factor” to estimate consumption of
fixed capital.
Consumption of fixed capital is accumulated over the years that each asset has been in use
and deducted from the gross capital stock to obtain the net capital stock.
Capital services -- defined as the periodic (e.g. annual) contribution of capital assets to the
production process is calculated by applying a gross rate of return to either the net or the
“productive” capital stock.
23
CHAPTER 3
OVERVIEW OF MEASUREMENT METHODS
1.
This chapter reviews the methods that are available for measuring gross and net capital
stocks, consumption of fixed capital and capital services.
Gross capital stock
2.
The gross capital stock can be estimated in at least three ways. By far the commonest is the
“perpetual inventory method” (PIM) which involves accumulating past capital formation and
deducting assets that have reached the end of their estimated service lives. Both capital formation and
discards are revalued either to the replacement prices of the current year (current replacement prices)
or to the prices of a single year (constant replacement prices).
3.
Survey methods can also be used. Enterprises are asked to report the historic values of all
assets still in use and the dates when they were installed or constructed. The assets are then revalued
to current or constant replacement prices either by the statistical agency or by the respondents
themselves using revaluation coefficients supplied by the statistical agency.
4.
A method that lies between the PIM and survey methods is the “balance of fixed assets”. In
many centrally-planned economies, enterprises were required to keep a running inventory of their
fixed capital assets, tracking outflows as well as inflows. The results of these calculations were
reported regularly to the central statistical agency which obtained the total capital stock by simple
addition. Although they have moved away from central planning, several of these countries have
continued to calculate the balance of fixed assets. Correctly applied, this method can be seen as an
ideal form of the PIM; ideal because it substitutes actual retirements for the assumed retirements used
in the conventional PIM.
5.
Finally, the gross stocks of certain kinds of assets can be estimated using administrative
records on the numbers of assets together with price information obtained by the statistical agency.
Assets for which administrative records are often available include road vehicles and dwellings
6.
The gross capital stock is essentially a statistical artefact which has no value in the
commercial world. It does not appear in business accounts and is compiled only by statistical agencies
which use it as the starting point for estimating the net capital stock and related flows.
24
Net capital stock
7.
By contrast, the net capital stock is a concept familiar to commercial accountants and
company balance sheets invariably record the value of assets on a net basis. Unfortunately company
accounts use a number of conventions in calculating net asset values which render them unsuitable for
national accounts purposes; the main problem is the use of historic valuation which means that the
stock of assets is valued at a mixture of prices.
8.
For use in national accounts, the net stock is usually derived from the gross stock (obtained
either by the PIM or from a survey) by deducting accumulated consumption of fixed capital. Note that
while the gross capital stock may be derived from a survey, survey methods are not suitable for
obtaining the net capital stock. This is because a consistent method must be used to estimate
consumption of fixed capital, but companies’ accounts may use a variety of depreciation methods.
9.
There are two other possible sources for net stock estimates. First, insurance companies
record the current replacement costs of commercial properties insured against damage by fire or other
catastrophes. However, properties are sometimes under-insured so that insurance values will
understate the net stock. Under-insurance is less likely to happen with assets exposed to a high risk of
loss, such as road vehicles and ships. Insurance values for assets of this kind may provide a realistic
estimate of net stocks and could be used as a cross-check on net asset stocks estimated by other
methods.
10.
Second, an estimate of the market values of a company can be obtained by multiplying the
number of shares outstanding by the share price. To obtain the net value of the tangible fixed assets
owned by the company, both the value of financial assets (less liabilities) and the market value of
land, valuables and intangible assets must be deducted. This method is only applicable for companies
with publicly quoted shares and such companies may cover only a small part of the capital stock in
some countries. Another problem is that share prices can be heavily influenced by future profit
expectations. For these reasons, this is not likely to be a very useful approach.
Consumption of fixed capital
11.
As noted, company accounts routinely report consumption of fixed capital, or depreciation
as it is usually called. Unfortunately, in almost all countries it is calculated by reference to the historic
cost of assets and so is effectively calculated using a mixture of prices and when there is inflation use
of historic prices will lead to substantial understatement of depreciation. Another problem is that
most countries allow companies to use a variety of depreciation methods so they cannot properly be
aggregated across companies. Finally many countries have used “accelerated depreciation” schemes as
a means of encouraging investment, with the result that reported depreciation bears no relation to the
actual decilnes in asset values. Despite these problems, several countries use depreciation reported by
companies in their national accounts. Such estimates cannot even be justifies as crude approximation
to consumption of fixed capital as defined in the SNA.
12.
For the national accounts, consumption of fixed capital can only be obtained by applying
depreciation factors to the estimated gross values of assets; gross here means the “as new” values
obtained by revaluing the historic cost of assets to current or constant replacement costs. The gross
value of assets may have been obtained either through a survey or by the PIM. The various ways of
calculating consumption of fixed capital are explained in Chapter 5.
25
Capital services
13.
The contribution of capital to production is here referred to as capital services. Transactions
in capital services occur when assets are leased by their owners to other producers. (Capital service
transactions occur only in the case of “operational leasing”; in the case of a “financial lease” the asset
is treated as being owned by the user.) Operational leasing is quite common for certain kinds of assets
– road vehicles, aircraft, buildings and some types of construction equipment are examples. The price
of a lease will include other costs in addition to the pure price of the capital service, such as insurance
and the cost of storing equipment in a convenient location and transporting the assets to and from the
producer’s site. These costs could of course be estimated so that, in principle, capital services for
several types of assets could be obtained by direct observation. In practice, national statistical offices
have not used this approach. Chapter 2 has described an indirect approach using the value of the asset
stock, consumption of fixed capital and the estimated rate of return and this is further developed in
Chapter 7. It could, however, be useful to compare capital services estimated by indirect methods with
capital services that have been directly observed.
26
CHAPTER 4
PERPETUAL INVENTORY METHOD
Introduction
1.
The Perpetual Inventory Method (PIM) generates an estimate of the capital stock by
accumulating past purchases of assets over their estimated service lives. The standard procedure is to
use the PIM to estimate the gross capital stock, apply to it depreciation factors to calculate
consumption of fixed capital and obtain the net capital stock by subtracting accumulated capital
consumption from the gross capital stock. This chapter follows this sequence but it has a final section
which describes an alternative way of applying the PIM that has been devised by the United States
Bureau of Economic Analysis (BEA). This method moves directly to the measurement of consumption
of fixed capital without first estimating the gross capital stock.
Gross capital stock
2.
The basic requirements to apply the PIM to estimate the Gross Capital Stock are:
 An initial bench-mark estimate of the capital stock.
 Statistics on gross fixed capital formation (GFCF) extending back to the bench-mark, or,
if no bench-mark is available, back over the life of longest-lived asset.
 Asset price indices.
 Information on the average service lives of different assets.
 Information on how assets are retired around the average service life.
Initial estimate of the capital stock
3.
Provided the capital stock series go back as many years as the longest-lived asset, it is
possible to estimate the capital stock without having an initial bench-mark estimate. However, as the
longest lived assets, usually structures, may have service lives in excess of 100 years, most countries
need to start their PIM estimates with a bench-mark estimate, at least for structures and other assets
with long lives. Possible sources for bench-mark estimates include:
27
 Population censuses.
 Fire insurance records.
 Company accounts.
 Administrative property records.
 Share valuations.
None of these sources will give an accurate estimate of precisely what is required -- namely
the “as new” values of assets in place at a point in time.
4.
Population census records usually provide information on the numbers of dwellings of
different types. Estimated values will have to be assigned to the various types of dwellings identified
in the Census records. Fire insurance records normally refer to the net values of assets at current
prices and will have to be adjusted to gross valuation. They are usually incomplete because small
companies may not insure their assets at all and very large enterprises and government bodies often
prefer to bear the risks themselves and so will also be excluded from fire insurance records. Company
accounts give asset values at depreciated historic costs and will need adjusting both to bring them up
to gross values and to “as new” replacement prices. An additional problem is that they are only
available for the corporate sector. Administrative property records typically record residential and
commercial buildings at values which purport to be current market prices but which are actually
historic prices periodically revalued to current prices. An additional problem is that they are only
available for the corporate sector. The share valuation of a company’s fixed assets can be obtained by
multiplying the number of shares issued by a company by the share price and subtracting financial
assets net of liabilities. The resulting values should reflect the current market values of the company’s
fixed capital assets but the valuation will also be affected by various unquantifiable factors such as
“good-will”, differences in entrepreneurial skill and the general business climate. In addition, this
approach can only be used in countries with active stock markets and then will only provide valuations
for corporate enterprises.
5.
It is clear that a bench-mark estimate based on any of these sources will be highly
approximate but the importance of any error introduced into the stock figures will diminish over time
as the base period is left further behind.
Gross fixed capital formation
6.
Gross fixed capital formation is defined as the acquisition, less disposals, of tangible and
intangible fixed assets plus land improvement. These are the assets denoted in bold in Table 1 of the
Chapter 1. The assets acquired may be new or they may be used assets that are traded on second-hand
markets; the assets disposed of may be sold for continued use by another producer or they may be sold
as scrap-- i.e. to be broken down into reusable components, into recoverable materials, or into waste
products.
7.
Assets acquired are valued at prices which include installation costs and transfer fees.
Disposals are valued at the amounts received by the sellers before deducting any costs born by the
sellers to dismantle the equipment or remove it from their property. (These latter costs are treated as
negative capital formation and not as current production expenses.)
28
8.
The fact that GFCF involves transactions in used assets, which are valued at less than the
prices of new assets, causes problems for PIM estimates of the gross capital stock. Suppose, for
example, that enterprise A sells a used asset to enterprise B. Enterprise A will report the sale of the
asset at its current market value and not at the “as new” price which is required for valuation of the
gross capital stock. This means that the GFCF reported by Enterprise A (its acquisitions less disposals
of assets) will be too large for use in the PIM because its disposals are valued at (low) market prices
instead of at (high) “as new” prices. At the same time, Enterprise B will report its acquisition of the
used asset from A at the current market price which is lower than the “as new” price required for the
gross capital stock. B’s reported GFCF (its acquisitions less disposals) will be too small for use in the
PIM.
9.
The errors caused by the way that A and B report transactions in a used asset will cancel out
if the records for the two enterprises are consolidated because the overstatement of A’s reported GFCF
is exactly matched by the understatement in B’s reported GFCF. There are, however, circumstances in
which there will be no compensating errors of this kind:
 Capital stock statistics need to be classified by institutional sector and by kind of activity.
If transactions in used assets occur between units that are classified to different
institutional sectors or activities, errors will be introduced into the sectoral or activity
distribution of the capital stock.
 Second, used assets may move into and out of the domestic economy via imports and
exports. If a used asset is imported, the acquisition will be recorded at the current market
value of the asset and GFCF will be understated (for PIM purposes); if a used asset is
exported, the disposal will be valued at current market value and GFCF will be
overstated (for PIM purposes). In neither case are there any offsetting errors because the
other partners to the transactions are outside the domestic economy.
 Finally, used assets may move from productive to non-productive uses. In particular,
they may move between the government or corporate sectors and the household sector.
Perhaps the commonest example is the sale of used vehicles by car-hire companies to
households. In this case there is no offsetting entry to the overstatement of GFCF by the
car-hire companies because the purchase of the used cars by households does not count
as capital formation.
10.
How important are the errors that may be introduced into the gross stock estimates because
of transactions in used assets? And what can be done about them?
11.
As regards errors in the distribution of the stock by sector and activity, the importance of the
problem depends partly on the degree of detail in the sectoral or activity breakdowns that are used.
This suggests that countries should be modest in the amount of activity detail given in their stock
estimates, at least in the initial stages of developing these statistics. The importance of the problem
also depends on the extent to which assets can be used in different industries. Most plant and
machinery is probably industry-specific but buildings may often move between sectors and activities;
a shop may become a bank, a factory may be used for different types of manufacturing or a railway
station may become a museum. Annex 1 describes two methods of dealing with this problem that have
been devised by the Australian Bureau of Statistics. They depend on identifying transactions in used
assets separately from transactions in new assets.
12.
Imports and exports of used assets may be quite significant for some countries but they do
not cause problems additional to those mentioned above. Whether a producer sells a used asset to
29
another domestic producer or to abroad, all that is required is to identify the sale as that of a used asset
and make whatever upward adjustment is required to the disposal value. Similarly, if a producer
purchases a used asset from abroad exactly the same kind of adjustment is required as when the asset
is acquired from a domestic source.
13.
As regards movement of assets from producers to households, it seems likely that in most
countries, the only significant transactions are in used vehicles sold by producers to households.
A reasonable assumption that could be made here is that all sales of used passenger cars by producers
are to households. Provided that sales of used cars can be identified in the records of producers it
should be possible to adjust disposal values to “as new” prices and eliminate this source of error.
Asset price indices
14.
The problems of separating value changes into price and volume components are generally
agreed to be more difficult for capital goods than for other goods and services because many capital
goods are unique. This is the case, for example, with most buildings, construction work, special
purpose industrial plant, aircraft and ships. The errors that may be introduced into capital stock
estimates through incorrect price deflators may be as large as errors caused by the use of incorrect
service lives and mortality functions. (Note, too, that direct survey methods are equally affected by
errors in price deflators because these have to be used to move from historic to current and constant
prices.) However, these are here regarded as problems of price statistics in general. They are not
peculiar to capital stock statistics and are not discussed in this manual. One special problem does,
however, need to be addressed - namely the estimation of prices for capital assets which are no longer
available on the market in a new condition but which still remain in the capital stock.
15.
The objective in estimating the gross capital stock at replacement prices is to value all assets
in the stock at prices that would have to be paid to purchase them in their new condition. For
estimates at current replacement prices the prices will refer to the current period and for estimates at
constant replacement prices the prices will refer to those of the base year. However, the “as new”
prices used for the gross capital stock estimates must not be reduced for any element of depreciation
because depreciation is to be calculated only after the gross capital stock has been estimated. In
particular this means that assets in the stock which are no longer available in a new condition in the
market must not be written down by valuing them at prices reflecting their partial obsolescence.
16.
The “as new” prices which are to be used to value assets that are no longer in production are,
of curse, fictitious prices; they are the prices at which they would be sold in a new condition if the
technical progress or other events which have rendered them obsolete had not occurred. They are
neither hypothetical producers prices - what producers would still be willing to produce them for - nor
hypothetical purchasers prices - what purchasers would still be willing to pay for them new. They are
the prices at which they would be traded if the world had stood still. The fact that a large part of the
gross capital stock is being valued at these fictitious prices simply underlines the artificial nature of the
gross capital stock. It is a statistical artefact that is used only to obtain depreciation and the net capital
stock.
17.
Asset price indices are necessarily based on the prices of the goods that are entering the
capital stock in the current period and they cannot include prices for goods which are no longer
available. In constructing price indices, the standard practice is to replace items which are no longer
available on the market by newer items in the same product group. This means that the prices of the
discontinued models are assumed to change, in the years after they cease to be available, in the same
way as the prices of similar assets that are still available. In general, therefore, the standard procedures
30
for constructing price indices seem to be consistent with the requirement noted above that the prices of
assets that are no longer available on the market should not be written down to reflect their partial
obsolescence. The qualification “in general” is required because there are certainly many differences
between countries in the ways in which replacements are handled and how prices of newer models are
linked with those of discontinued models.
Service lives of assets
18.
The accuracy of capital stock estimates derived from a PIM are crucially dependent on
“service lives” -- i.e. on the length of time that assets are retained in the capital stock. The first section
below looks at the sources that are available to estimate service lives; the next section considers
evidence that service lives may be changing over time, and a final section looks at how errors in
service life assumptions may affect reliability of capital stock estimates. Annex 2 gives detailed
estimates of service lives used by four countries which have investigated service lives with particular
care. These are the United States, Canada, the Netherlands and the Czech Republic.
Sources for estimating service lives
19.
The main sources for estimating service lives are asset lives prescribed by tax authorities,
company accounts, statistical surveys, administrative records, expert advice and other countries’
estimates.
 Tax-lives
20.
In most countries, the tax authorities specify the number of years over which the depreciation
of various types of assets may, under normal circumstances, be deducted from profits before charging
taxes. Many countries -- including Australia, United States, Germany and the United Kingdom for
example -- make some use of them, either to estimate the service lives of assets for which no other
source is available, or to provide a general credibility check on service life estimates obtained by other
methods.
21.
The interesting question is what sources are used to estimate tax-lives in the first place. In
general, it appears that tax-lives are based on a variety of sources of differing reliability including
expert opinion, ad hoc surveys of particular assets in particular industries and advice from trade
organisations. In general, the accuracy of tax-lives will depend on the extent to which they are actually
applied in tax calculations. Some governments use various systems of accelerated depreciation to
encourage investment with the result that tax-lives become irrelevant to the calculation of tax
liabilities, and neither tax collectors nor tax payers have any incentive to see that they are accurate and
kept up-to-date. In many countries, however, tax-lives are based on periodic investigations by the tax
authorities and can be assumed to be realistic.
22.
In some cases, the statisticians have concluded that the pattern of tax lives across industries
or asset types are fairly realistic but that there is a tendency for an overall bias in one direction or the
other. They therefore systematically apply an upward or downward correction factor before using
them for their PIM estimates.
31
 Company accounts
23.
Company accounts often include information on the expected service lives that they are
using to depreciate assets. Singapore and Australia have both made use of service lives reported in
company accounts. The International Accounting Standards Committee (ICAS) has for some years
been encouraging member countries to adopt common standards for company accounting and ICAS
rules require companies to report asset service lives used to calculate depreciation in their accounts.
Company accounts could, therefore, become a better source of information in the future.
24.
Company accounts almost always record stocks of assets at historic (or ‘‘acquisition’’)
values, and while this is a disadvantage for many purposes, it does not necessarily prevent them from
being used to estimate asset lives. Current price estimates of GFCF are, by definition, also valued at
acquisition prices and are therefore consistent with stock estimates in company accounts. If the latter
can be converted to a gross basis by adding back depreciation (which is also recorded at historic prices
in company accounts) service lives can be estimated by comparing the gross stock in each year with
the sum of investments during a varying number of previous years until finding how many years’
cumulated investments most nearly equal each year’s capital stock. This technique has been used in
France, Italy and the United States.
 Statistical surveys
25.
Two kinds of surveys are relevant to the estimation of asset service lives -- those which ask
producers about discards of assets during some previous accounting period and those which ask
respondents to give the purchase dates and expected remaining lives of assets currently in use. The
Netherlands has been carrying out a discards survey (“desinvestments” in their terminology) for some
years and the Czech Republic has recently added questions about discards to its annual capital
expenditure survey. The United Kingdom, on the other hand, recently investigated the feasibility of a
discards survey but concluded that very few respondents would be able to provide reliable information
about assets that had already been discarded from the stock.
26.
The results of the Netherlands discards survey have been used directly to estimate asset
survey lives, but Statistics Netherlands now prefers to use an indirect approach. The value, at “as new”
prices, of reported discards of a given type of asset installed in a given year are divided by each year’s
gross stock of assets each year of that same asset and same vintage. This gives an estimate of the
“hazard rate” defined as the risk that an asset of that particular type and “vintage” (i.e. year of
installation) will be discarded in each year following its installation. The hazard rates are then used to
estimate the parameters of a Weibull probability function which is assumed to give a good
approximation to the way in which a group of assets installed in a given year are discarded. The
average service life of the assets is determined from the estimated Weibull parameters.
27.
Several countries carry out surveys of the second kind -- i.e. those asking respondents about
expected lifetimes. Korea and Japan have carried out large-scale investigations of capital stocks and
asset service lives covering most kinds of activities. Canada, Italy and Spain have added questions
about expected service lives to ongoing surveys of capital investment or industrial production. The
United States carried out a number of industry-specific surveys in the 1970s with a view to updating
the service lives used for tax purposes. A recent survey carried out in New Zealand on behalf of the
tax authorities concentrated on 250 specified types of plant, machinery, transport and other types of
32
equipment. For each asset type, a target group of producers was identified which could be expected to
use that particular type of equipment and respondents were asked to report the year of purchase and
expected remaining life of one individual asset of that type. By confining the investigation to a single
asset the survey achieved a good response rate; an example of the questionnaire used for this survey is
attached in Annex 3.
28.
Producers of capital goods need to know the age structure of the asset stock in order to
forecast future demand. For this reason, trade associations and publishers of technical journals
sometimes carry out surveys which may provide information on service lives. For example the trade
journal American Machinist has carried out several surveys of the age distribution of metal working
machines in each of the principal user industries, and the journal Metalworking Production publishes
the results of a similar survey for the United Kingdom. Information from these sources does not seem
to have been widely used by statistical agencies but it may well be that similar information on
particular kinds of assets is available from trade and technical publications in other countries.
 Administrative records
29.
For some assets, government agencies maintain administrative records that can be used to
estimate service lives. In many countries vehicle registration records track the service lives of road
vehicles. Aircraft and ships are often subject to similar controls. Regulatory bodies in power
industries, railways and telecommunications are also a possible data source.
 Expert advice
30.
Most countries appear to base at least some of their asset lives on ‘‘expert advice’’. The term
is ambiguous. At its best, the use of ‘‘expert advice’’ may involve seeking advice from a panel of
production engineers familiar with conditions in a representative cross-section of industries, or asking
firms that produce capital assets for the expected or normal service lives of different sorts of
equipment. At the other extreme, ‘‘expert advice’’ may be no more than a euphemism for pure
guesswork by the statisticians responsible for the capital stock series.
 Other countries’ estimates
31.
It is probable that most countries periodically review estimates used by other countries to
ensure that their own estimates are not too far out of line with those of neighbouring or similar
countries. Certainly, when countries first estimate capital stocks, they invariably search the literature
or contact other statistical offices directly to find out the service lives used elsewhere.
Changes in service lives
32.
Estimates of service lives are rarely updated in most countries. The “fixity” of service lives
has been criticised because it is alleged that service lives are tending to fall over time. Two main
reasons are given for this:
 It is argued that “product cycles” are becoming shorter. Consumer tastes in many
countries may be changing more rapidly than in the past so that manufacturers are forced
to introduce new versions and models more quickly and to bring new products onto the
33
market more often than before. This could require producers to retool their production
lines more frequently.
 It is also argued that capital goods prices are rising less rapidly than in the past and in
some cases are actually falling. This is certainly the case with computers and related
equipment and may also be true for the increasing range of assets that incorporate
computer technology; numerically-controlled machines, communications equipment, and
robotised production systems are examples. If the price of an asset rises more slowly
than the prices of the goods and services it is producing, the initial investment can be
recouped over a shorter period than before and service lives will fall.
33.
As against this, some assets are certainly becoming more durable. Road vehicles and
commercial aircraft are two examples. In addition, there has been considerable progress in recent year
in the development of “flexible” production systems which allow manufacturers to rapidly switch
between alternative models without the need to retool. Shorter production cycles do not, therefore,
necessarily imply shorter asset lives.
34.
There appear to be very few empirical studies relevant to the question of changes in asset
lives. In Germany the Federal Ministry of Finance first began to publish tables of service lives to be
used for tax purposes in 1957 and they have been regularly updated since then. The German
Statistisches Bundesamt notes that officials of the Ministry of Finance are in regular contact with firms
about changes in asset lives. The information obtained by the officials may be impressionistic rather
than scientifically-based, but the Statistisches Bundesamt considers that it is nevertheless sufficiently
well-founded to detect the direction of changes in service lives and the approximate size of such
changes. A number of changes to tax lives are reported in these tables and, with the exception of
commercial aircraft, all are reductions. Examples include farm-buildings (from 50 to 25 years), woodworking machinery (reduced by one or two years), machines in the precision industries (reduced from
10 to 8 years), and machines in the optical industries (reduced from 8 to 7 years).
35.
Most countries appear to keep asset lives fixed for their PIM estimates, but there are some
exceptions. In the capital stock estimates of Australia and the United Kingdom, the lives of most assets
are assumed to have been gradually declining since the 1950’s. In the PIM estimates for Australia,
service lives are assumed to be declining by about 5% each decade, while in the United Kingdom’s
estimates, service lives of most types of long-life assets are reduced by just over 1% each year. The
German Statistisches Bundesamt uses falling service lives for housing, farm buildings, motor vehicles
and certain types of industrial equipment. Finland assumes that service lives for machinery and
equipment were falling by 0.8% to 1% per year from 1960 to 1989 and at about half that rate since
1990.
36.
It seems probable that these reductions in asset lives are introduced not because the
statisticians believe that service lives of particular kinds of assets are falling but rather that the asset
groups identified in their PIM models are thought to contain increasing shares of shorter life assets. In
particular, assets containing computerised components are generally assumed to have shorter lives
than other types of equipment and the share of such assets in some asset groups is almost certainly
rising in all countries. Thus, even in the absence of information about asset lives of specific assets, it
may be right to assume declining service lives for groups of assets. Clearly the importance of this
“composition” effect will depend on the degree of detail in the asset classification that is being used.
37.
The United States uses a rather detailed asset classification for stock estimates and certain
changes in the service lives of specific assets lives are incorporated in its current PIM model. For
example the Bureau of Labor Statistics assumes the following reductions in service lives for office
34
computer and accounting equipment. (The changes are discrete, rather than continuous as the
examples given above.)
Mainframe computers:
Printers:
years before 1970 8
years before 1976 10
1970 - 1979
7
1976-1980
8
1980 and after
5
1981-1985
6
1986 and after
4
Direct access storage devices:
years before 1981 8
1981-1985
7
1986 and after
5
Terminals:
years before 1981 9
Tape drives:
1981-1985
8
1986 and after
6
years before 1981 8
1981 and after
7
38.
There are fewer examples of increasing service lives. In Germany the service lives of
commercial aircraft are assumed to have been between 5 to 8 prior to 1976 and 12 years for aircraft
purchased since then. In the United States electric light and power equipment was assigned a service
life of 40 years before 1946 and 45 years for all later years. Commercial aircraft are also assigned
longer lives in later years -- 12 or 16 years prior to 1960 and 15 or 20 years since then.
Effect of errors in service life estimates
39.
Ideally, what is required for accurate implementation of the PIM is a set of service lives for
narrowly-defined asset groups that are used in different sectors and kinds of activity. Moreover, this
set of service lives should be updated regularly to reflect cyclical or longer term changes in the lengths
of time that assets remain in the stock. From the review of the sources above it is clear that the
information actually available falls far short of this ideal. Service life estimates are generally available
only for broad asset groups, there is limited information available on differences in lives of asset
groups between sectors and kinds of activity and service lives are updated at rare intervals in most
countries. This section considers how errors in service lives may affect levels and growth rates of
capital stocks derived from the PIM.
40.
The effect of errors in the average service lives used in the PIM can be gauged through
“sensitivity studies” by running the PIM model with alternative estimates of service lives. Results of
recent sensitivity studies for Canada and the Netherlands are described below.
41.
Statistics Canada has estimated the gross capital stock in manufacturing with its standard
PIM model but using service lives that increased from 0.5L to 1.5L, with L the average service life
presently being used in Canada. The tests were run for the period 1950 to 1998. Predictably, changing
service lives changes the level of the capital stock in the same direction. Using the shortest lives (0.5L)
35
reduced the level of the stocks by up to 50% and using the longest lives (1.5L) increased the level by
up to 40%. With less extreme changes -- 0.9L and 1.1L -- the size of the stock is reduced by about 8%
and raised by about 7%; assuming that service lives used for PIM estimates are not usually wrong by
more than 10%, the Canadian study therefore suggests that stock levels may have error margins of
+/-8%.
42.
Analytic studies often use growth rates rather than stock levels. The effect of changing
service lives has an unpredictable effect on growth rates because service lives act like weights. An
upward revision to the service life of a particular asset increases the share of that asset in the total
stock. An upward revision to a faster (slower) growing component of the stock will raise (lower) the
growth rate of the capital stock as a whole. In the Canadian study, reducing service lives generally
increased capital stock growth rates during the period 1950 to 1970 but decreased them from 1971 to
1998.
43.
The study carried out by Statistics Netherlands focused on stocks of machinery in the
chemical industry and covered the period 1978 to 1995. Five different service lives were used -- 10,
15, 20, and 25 years (the average service life actually used is 19 years). While the Canadian study
deals only with estimates of the gross capital stock, the Netherlands study looked at the effects on both
gross and net stocks and on consumption of fixed capital.
44.
The level of the gross stock again changes in the same direction as the changes to service
lives. Consumption of fixed capital, however, generally changed in the opposite direction; that is,
increasing the service lives reduced the amount of consumption of fixed capital. This happened
because, with longer service lives, each asset is written off over a longer period and this outweighs the
increase due to the fact that longer service lives mean that there are more assets in the stock. In some
years, however, the increase in the number of assets in the stock due to the use of longer service lives
outweighed the reduction in the amounts of consumption of fixed capital charged to each asset and
total consumption of fixed capital increased with longer service lives.
45.
Net capital stock is obtained by deducting accumulated consumption of fixed capital from
the gross stock. Since longer service lives will always increase the gross capital stock and will usually
decrease consumption of fixed capital, the net capital stock will tend to increase when longer service
lives are used. Moreover, the increase in net capital stock as service lives are lengthened will be
relatively larger than in the case of the gross capital stock.
46.
A final conclusion from the Netherlands study is that growth rates of gross and net stocks
and of consumption of fixed capital becomes less volatile as service lives are lengthened. With longer
service lives any lumpiness in investment flows into and out of the stock tends to be dampened by the
larger size of the stock.
47.
To summarise the results of these two sensitivity studies:
 Longer service lives always increases the size of the gross capital stock.
 Longer service lives usually reduce consumption of fixed capital.
 Longer service lives usually increase the size of the net capital stock and by relatively
more than in the case of the gross capital stock.
 Longer service lives have an unpredictable effect on growth rates.
36
 Longer service lives reduce the volatility over time in the growth of stocks and capital
consumption.
Mortality patterns
48.
This section looks at the assumptions made about the distribution of retirements around the
average service life. “Retirements” and “discards” are here used interchangeably to mean the removal
of an asset from the capital stock, with the asset being exported, sold for scrap, dismantled, pulled
down or simply abandoned. As used here retirements and discards are distinguished from “disposals”
which may includes sales of assets as second-hand goods for continued use in production.
49.
Four types of mortality patterns are discussed -- simultaneous exit, linear, delayed linear, and
bell-shaped. The mortality functions and survival functions corresponding to these four patters are
displayed in Figure 1. The mortality functions (first column) show rates of retirement over the
lifetimes of the longest-lived member of a group of assets of a particular type that were installed in a
given year. They are probability density functions with the area under each curve equal to unity. The
survival functions (in the second column) show what proportion of the original members of the group
of assets are still in service at each point during the lifetime of the longest-lived member of the group.
50.
The simultaneous exit mortality function assumes that all assets are retired from the capital
stock at the moment when they reach the average service life for the type of asset concerned. The
survival function therefore shows that all assets of a given type and vintage remain in the stock until
time L, at which point they are all retired together. This retirement pattern is sometimes referred to as
‘‘sudden exit’’ but this term is ambiguous. Whatever mortality pattern is used, individual assets are
always retired suddenly; the distinguishing feature of this mortality function is that all assets of a given
type and vintage are retired simultaneously.
Linear
51.
With a linear retirement pattern, assets are assumed to be discarded at the same rate each
year from the time of installation until twice the average service life. The mortality function is a
rectangle whose height -- the rate of retirement -- equals 1/2L where L is the average service life: the
survival function shows that the surviving assets are reduced by a constant amount each year, equal to
50/L% of the original group of assets. A linear retirement pattern assumes that retirements start
immediately after they are installed and this is generally regarded as an unrealistic assumption.
Delayed linear
52.
A delayed linear retirement pattern makes the more realistic assumption that discards occur
over some period shorter than 2L. Retirements start later and finish sooner than in the simple linear
case. Suppose for example that it is assumed that the assets are retired over the period from 80% to
120% of their average service life. The rate of retirement in the mortality function is then equal to 1/L
(1.2-0.8) or 250/L% per year during the period when the retirements are assumed to occur.
37
Chart A. Four Mortality and Survival Functions
Mortality Functions
Survival Functions
1. Linear
R - rate of retirement
Percent surviving
100%
L - average service life
L - average service life
2. Delayed linear
R
100%
L
L
3. Bell shaped
R
100%
L
L
4. Simultaneous exit
R
100%
L
L
38
Bell-shaped
53.
With a bell-shaped mortality pattern, retirements start gradually some time after the year of
installation, build up to a peak around the average service life and then taper off in a similar gradual
fashion some years after the average. Various mathematical functions are available to produce bellshaped retirement patterns and most provide considerable flexibility as regards skewness and
peakedness (or “kurtosis”). They include gamma, lognormal, quadratic, Weiull and Winfrey functions.
The last two are probably most widely used in PIM models and deserve special mention.
 Winfrey curves
54.
Winfrey curves are named after Robley Winfrey, a research engineer who worked at the
Iowa Engineering Experimentation Station during the 1930s. Winfrey collected information on dates
of installation and retirement of 176 groups of industrial assets and calculated 18 ”type” curves that
gave good approximations to their observed retirement patterns (see box). The 18 Winfrey curves give
a range of options for skewness and kurtosis and remain the only retirement patterns that are based on
an extensive empirical study of asset discards. They are used in PIM models by several countries.
55.
The Winfrey symmetrical curves are written as:

x2 
y x  yo 1  2 
a 

m
(1)
where y x  ordinate to the frequency curve at age x (origin at the mean age),
y o = ordinate to the frequency curve at its mode, and a and m are parameters ranging from,
respectively, 10 to 7 and 0.7 to 40.0, which determine the peakedness (kurtosis) and the
skewness of each curve.
56.
The skewed curves are considerably more complicated and use up to 12 parameters. The
more peaked of these curves are obtained by superimposing a “minor” curve on a “major” curve.
39
WINFREY MORTALITY FUNCTIONS
During the 1920s and 1930s, Robley Winfrey assembled information on retirements of 176 different
kinds of assets. Data were “accumulated from many sources, representing the following industries: gas,
electric light and power, railway, telephone, telegraph, water supply, agricultural implement, motor
vehicle and street pavement” (Statistical Analyses of Industrial Property Retirements, Robley Winfrey,
page 59). His data sources included many of the major companies of the time -- the American
Telephone and Telegraph Company, the Atchison, Topeka and the Santa Fe Railway and the Pacific
Gas and Electric Company. He also used information from the Chicago Water Works System and other
municipal enterprises and he examined Iowa State vehicle registration records covering a wide range of
“motor trucks” and “motor cars” -- the latter including over 6 000 Model-T Fords and 5 000 cars of
other makes.
His interest was in the ways in which a group of assets -- e.g. creosoted cross-ties (sleepers), motor
cars, waterworks boilers, asphalt pavements -- that had been installed or constructed in a given year
were retired over their total life-span. Winfrey plotted the 176 individual mortality functions showing
when each member of each “cohort” (group of assets installed in a given year) was retired from the
capital stock and concluded that they could be grouped into 18 ”type” curves which he denoted by L, S
and R for left-modal, symmetrical and right-modal and by the numbers 0 through 6 for the flattest to
the most peaked curves. The table below shows how the 176 different kinds of assets were assigned to
his 18 type curves. The assets were fairly evenly spread between the L, S and R curves but slightly
more assets were assigned to the left-modal group -- i.e. mode to the left of the mean. Over half of
them had rather peaked mortality functions (numbers 3 to 6) indicating that most retirements happen
within a short space of each other
ALLOCATION OF 176 ASSETS TO THE 18 WINFREY “TYPE CURVES
Left modal
Symmetric
Right modal
LO
7
SO
6
L1
15
S1
13
R1
L2
17
S2
13
L3
15
S3
L4
8
L5
3
....
Total 65 (37%)
Total
....
3
(7%)
5
33
(19%)
R2
5
35
(20%)
7
R3
19
41
(23%)
S4
9
R4
24
41
(23%)
S5
3
R5
6
12
(7%)
S6
1
....
1
(1%)
Total 59 (33%)
176
(100%)
Total 52 (30%)
57.
When Winfrey curves are used in a PIM model, the usual procedure is to calculate the
percentage of assets of a given vintage that are discarded at different ages defined as percentages of
the average service life. Table 1 below shows how a Winfrey curve was used by the BEA for discards
of most types of plant and machinery. This is a truncated version of the Winfrey S-3 curve. Discards
start at 45% of the average age and continue to 155% of the average, by which time all the assets of a
given vintage have been discarded.
40
Table 1. Example of a Winfrey Retirement Pattern
Percent
of Cumulative
Percent
of Cumulative
Percent
of Cumulative
average
percent
of average
percent
of average
percent
of
service life
original
service life
original
service life
original
expenditures
expenditures
expenditures
discarded
discarded
discarded
Less than 45
0.0
80
24.6
120
81.3
45
1.2
85
31.2
125
86.3
50
2.4
90
38.4
130
90.3
55
4.1
95
46.1
135
93.5
60
6.5
100
53.9
140
95.9
65
9.7
105
61.6
145
97.6
70
13.7
110
68.8
150
98.8
75
18.7
115
75.4
155
100.0
 Weibull distribution
58.
The Weibull function has been widely used in studies of mortality in natural populations. It
is a flexible function that can adopt shapes similar to those designed by Winfrey and it is used by
several countries for PIM estimates. The Weibull frequency function is written as:
f w  x    .  x 
 1
. e   x 

(2)
where x is the number of years since the asset was installed, and  and  are parameters
which jointly determine kurtosis and skewness.
59.
The frequency function at (2) can be used to calculate the percentage of assets of a given
vintage that are discarded at different ages as shown in Table 1 above for the Winfrey mortality
pattern.
60.
Statistics Netherlands has used data from surveys of discards to estimate Weibull discard
patterns for a wide range of assets. They report values of  ranging from 0.015 to 0.033. The 
parameter can be interpreted as a measure of changes in the risk of an asset being discarded.
0 <  <1
indicates that the risk of discard decreases over time,
 1
indicates that the risk of discard remains constant through the lifetime of the asset,
1<<2
indicates that the risk of discard increases with age but at a decreasing rate,
 2
indicates a linearly increasing risk of discard, and
>2
indicates a progressively increasing risk of discard.
61.
Most of the  values reported by Statistics Netherlands lay between 1 and 2 except for
computers where values just over 2 were reported. The older the computer, the higher the risk that it
will be obsolete and have a high risk of being discarded.
41
Which mortality pattern is the best?
62.
Of the four discard patterns considered above, the first two -- simultaneous exit and linear
decline -- are clearly unrealistic. It is simply not plausible to assume that all assets of a given vintage
will all be withdrawn from the stock at the precise moment when they reach the average service life
for that asset type. Like people, some assets will be discarded before they reach the average age
because they are overworked, poorly maintained or fall victim to accidents, while others will continue
to provide good service several year beyond their average life expectancy. Simultaneous exit must be
regarded as an inappropriate retirement pattern.
63.
It is almost as implausible to assume that an equal number of assets of a given vintage are
discarded each year beginning in the first year that they are installed. Assets are by definition expected
to remain in use for several years and discards in the years immediately after installation are likely to
be rare for most assets. Linear retirement also fails the test of plausibility.
64.
The remaining discard patterns -- delayed linear and bell-shaped -- are clearly more realistic
models. Delayed linear assumes that once retirements begin, equal parts are discarded until the entire
vintage has disappeared and this may be less plausible than the assumption of a gradual build-up of
discards in the early years and a gradual slowdown in later years, which is implied by bell shaped
distributions.
65.
Winfrey curves were specifically developed to reflect the way that assets are discarded and
they are used by several countries in their PIM models. Winfrey’s research is, however, more than
60 years old and his 176 asset groups included many items that have long since disappeared -- Model
T Fords and wooden railway bridges for example. In addition relative factor prices have changed
considerably since the 1930s and this may have affected discard practices. For example, in Winfreys
day cross-ties for rail tracks were replaced individually as they wore out; this is a labour intensive
operation and a common practice now is to replace complete sections of rail tracks at fixed intervals.
The rather flat discard patterns that Winfrey observed for cross-ties will now have been replaced by a
more peaked distribution..
66.
To summarise:
 A delayed linear pattern is easy to implement and it avoids giving the appearance of
spurious precision. Its very simplicity is a signal to users that estimating capital stocks is
a precarious undertaking.
 Winfrey curves were designed for the purpose at hand but may no longer be appropriate
for modern capital stocks and factor prices.
 Weibull functions are easy to implement and studies at Statistics Netherlands have
shown that they can satisfactorily replicate observed discard patterns. The problem is that
very few countries have any information on discard patterns and so cannot select
appropriate parameters for the Weibull function.
 For countries with no direct empirical evidence on discard patterns, it may be best to use
a moderately peaked symmetrical Winfrey curve -- say S-2 or S-3 -- or a Weibull
function with a similar shape to these.
42
Consumption of fixed capital
67.
Consumption of fixed capital is not generally observable and is usually estimated on the
assumption that asset prices decline in a systematic way over the course of the asset’s service lives.
Note that consumption of fixed capital almost always has to be estimated in this way whether the gross
capital stock is obtained by the PIM or by some kind of survey method.
68.
Several techniques have been developed for estimating consumption of fixed capital and
these are explained in the next chapter. When there is empirical evidence about how particular kinds of
assets lose their value, that information should obviously determine the choice of depreciation method.
In the usual situation where there is little or no information about actual depreciation, it is argued that
the “sum of the digits” methods will produce estimates that are least likely to be wrong.
69.
Once an appropriate method has been selected, consumption of fixed capital is calculated by
applying the depreciation factor to the gross capital stock. The simplest method, straight-line
depreciation, depends only on the initial value of the asset and the estimated service life. The other two
methods, sum of the digits and geometric depreciation depend also on the age of the asset because they
assume that depreciation falls as the asset ages. A numerical example of the calculation of
consumption of fixed capital was given in Chapter 2 and is not repeated here.
Net capital stock
70.
The net capital stock is defined as the value of fixed assets at their market prices, either at the
average prices of a selected year or at the average prices of the current year. These market prices are
lower than the “as new” prices used for the gross capital stock because of wear and tear, obsolescence
and other components of consumption of fixed capital. These market values are estimated by
deducting accumulated consumption of fixed capital from the gross capital stock. The net capital stock
has to be estimated in this way whether the gross capital stock is obtained by the PIM or through a
survey. A numerical example of the calculation of the net capital stock was given in Chapter 2 and is
not repeated here.
Alternative application of the PIM
71.
In 1997, the United States Bureau of Economic Analysis (BEA) published revised estimates
of the capital stocks and consumption of fixed capital, which were based on a perpetual inventory
model, but which omitted the first step of explicitly calculating the gross capital stock. This alternative
approach goes directly to the calculation of consumption of fixed capital which is then cumulated and
subtracted from the sum of past investments to obtain the net capital stock.
72.
Because the step of calculating the gross capital stock is missed out, there is no explicit use
of a mortality function. However, a mortality function still has to be incorporated in the model because
the value of a group of assets declines because some members of the group are discarded each year
and not only because those that remain in use suffer wear and tear, obsolescence and accidental
damage. A mortality function must, therefore, be built into the depreciation factor. The depreciation
factors used by BEA are based on studies of the prices of assets that are being traded on the second
hand market and of the prices of the assets that have been discarded. In these studies, the unobservable
(zero) prices of the latter assets are added to the observed prices of the former assets on the assumption
that discards follow a symmetrical Winfrey distribution.
43
73.
Table 2 is a worksheet showing how this version of the PIM is implemented.
Table 2. Direct calculation of consumption of fixed capital and net capital stock without
calculating gross capital stock
year
1
Gross fixed capital formation at year 1 prices:
In year 1
In year 2
In year 3
Net stock at end of:
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
etc
74.
3
4
5
6
7
8
etc
10
20
5
Depreciation factor (1-d)
Consumption of fixed capital on assets purchased in:
Year 1
Year 2
Year 3
Total consumption of fixed capital
Accumulated consumption of fixed capital
2
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
5.000
2.500
10.000
5.000
5.000
12.500
17.500
1.250
5.000
2.500
8.750
26.250
0.625
2.500
1.250
4.375
30.625
0.313
1.250
0.625
2.188
32.813
0.156
0.625
0.313
1.094
33.906
0.078
0.313
0.156
0.547
34.453
0.039
0.156
0.078
0.273
34.727
...
...
...
...
...
10
10 + 20
10+ 20 + 5
10+ 20 + 5
10+ 20 + 5
10+ 20 + 5
10+ 20 + 5
10+ 20 + 5
10+ 20 + 5
minus
minus
minus
minus
minus
minus
minus
minus
minus
5.000
17.500
26.250
30.625
32.813
33.906
34.453
34.727
...
equals
equals
equals
equals
equals
equals
equals
equals
equals
5.000
12.500
8.750
4.375
2.188
1.094
0.547
0.273
...
To understand the worksheet:
 The worksheet shows expenditures on a particular type of asset in years 1, 2 and 3
amounting to 10, 5 and 20 respectively. The expenditures were converted to the constant
prices of year 1 before being entered in the worksheet.
 The depreciation factor (d) is shown as 0.5. This was obtained by the double declining
balance method as d = 2/L where (L) -- the average service life -- is 4 years (BEA uses a
modified version of the double declining method in which 2 is replaced by numbers that
are derived from studies of second-hand asset prices).
 Consumption of fixed capital in year 1 is obtained by multiplying the expenditure on the
asset in year 1 by the depreciation factor 1-d = 0.5. (Note that this worksheet implies that
the asset was purchased at the beginning of the year so that it falls in value by a whole
year’s depreciation. It would be more realistic to assume, as does the BEA, that assets are
purchased in the middle of the year so that only half of a full year’s capital consumption
would be charged in the first year.)
 Consumption of fixed capital in all subsequent years is obtained by multiplying the
previous year’s consumption of fixed capital by the depreciation factor.
 The net capital stock at the end of a given year is the sum of all past expenditures on the
asset minus the consumption of fixed capital accumulated up to the end of that year. For
example, the net capital stock at the end of year 2 is the sum of the expenditures in
44
years 1 and 2 (10+20 = 30) minus the consumption of fixed capital accumulated up to the
end of year 2 (17.5). (From year 4 onwards the total expenditures on the asset remain at
10+5+20 = 35 because in this example there were no further purchases of this asset after
year 3.)
 Note that the worksheet takes no explicit account of the average service life of the assets.
Even though the average service life of these assets is here assumed to be only four
years, they continue to contribute to consumption of fixed capital and to the net capital
stock for all future periods. These contributions decline asymptotically and in this
example they become negligible after a few years because the worksheet uses assets with
a very short service life. For buildings and other long-lived assets, however,
contributions to capital consumption and the net capital stock may continue to be
significant for many years after their average service lives.
 Finally, the price index for this asset is used to inflate capital consumption and net stocks
to obtain estimates at current replacement cost. (This stage is not shown in the
worksheet).
45
CHAPTER 5
MEASURING CONSUMPTION OF FIXED CAPITAL
Introduction
1.
Hitherto the term consumption of fixed capital has been used in accordance with the
terminology used in the System of National Accounts. As it is defined in this System, consumption of
fixed capital is in fact identical with depreciation as this term is understood in economics. In this
chapter the two terms are used interchangeably.
2.
The aim of this chapter is to identify the depreciation methods that are most likely to reflect
the ways in which assets lose their value over time. The chapter is divided into four sections:
The first reviews the empirical evidence about how assets lose their value during the course
of their service lives. This evidence comes from studies mainly carried out in
North America on the prices of second-hand assets.
The next section shows that there are many capital service value profiles that will produce
age-price profiles for assets that are consistent with the empirical evidence drawn from
the prices of second hand assets. The best known of these is probably the “geometric”
profile in which the value of the capital service falls at a constant rate over the lifetime of
the asset, but there are several other capital service profiles that are consistent with the
empirical evidence on asset prices. Each of these capital service profiles implies a
particular pattern of depreciation.
The third section describes three common depreciation methods, which are used by both
national accountants and business accountants. These are straight-line, sum-of-the-digits
and geometric depreciation.
The fourth section tests how well these three depreciation methods measure depreciation for
assets which have capital service profiles that are consistent with the age-price profiles
that have been observed for second-hand assets.
3.
The conclusions reached in this chapter on the best way to measure consumption of fixed
capital are equally relevant whether capital stocks are being measured by surveys methods or by the
PIM. Consumption of fixed capital cannot generally be observed and so it has to be estimated by
assuming that assets decline in value over time in a systematic way.
46
Empirical evidence
4.
If the price level is stable, consumption of fixed capital is simply the change, in the market
value of an asset, or group of assets, from one accounting period to the next. The prices of
second-hand assets will therefore cast light on depreciation. Specifically, second hand asset prices,
adjusted to eliminate changes in price levels, can be used to establish age-price profiles for particular
types of asset that were produced or installed in a given year. For example they can be used to show
how farm tractors of a particular make and model and produced in a given year lose their value as they
become older.
5.
Virtually all studies of second hand asset prices have been made in the United States,
perhaps because second-hand asset markets are more highly developed in that country. It is not certain
that the age-price profiles identified for assets in the United States are also typical for other countries,
although the few studies carried out elsewhere, Canada, United Kingdom and Japan, for example, have
found similar age-price profiles.
6.
Ideally, these studies should use actual transaction prices. A few studies have done this by
using auction prices. This is often the case in studies of farm equipment because auctions are a
common way of disposing of assets when farms go out of business. Other studies have tried to obtain
transaction prices from second-hand asset dealers through surveys. Most studies, however, have been
based on “list prices”. These are the offer prices published by dealers and, because bargaining is
common in asset markets, they may overstate actual transaction prices. In almost all cases, the first
price in the age-price profile -- the new price of the asset -- is almost always a list price even when the
subsequent observations are real transaction prices. Finally, at least one study has used insurance
values. This was a study of fishing boats and because they run substantial risks of accidental loss, both
owners and insurers have a keen interest in ensuring that insured values are realistic; this is not always
the case for assets which face lower accident risks.
7.
Questions have sometimes been raised whether assets traded on second-hand markets are
representative of the entire asset stock, including the large majority of assets that remain in the
possession of their original owners until they are scrapped. In particular, it has been suggested that
assets are put on the second-hand market because they are defective in some way; this is sometimes
referred to as the “lemons” theory. Even if most second hand assets are in fact not “lemons”, so long
as some prospective buyers fear that there may be some defective ones among the assets on offer,
prices will be depressed and the prices of assets traded on second-hand markets will understate the
market values of assets not so traded. The opposite suggestion has also been made; namely that used
assets are usually put on the market in order to raise finance and so firms will sell their best assets
rather than their worst ones. Attempts to determine the validity of these and other theories about the
extent to which second-hand assets are representative of the total asset stock are inconclusive.
8.
A significant source of bias, about which there is no dispute, arises from the fact that
second-hand asset prices necessarily refer only to assets that have not yet been retired from the capital
stock. Within the entire group of farm tractors of a given make, model and year of manufacture, there
will be some whose second-hand prices are zero because they have been scrapped. A minority of
studies has tried to correct for this bias by adding some (unobserved) zero prices to the observed set of
non-zero prices. It is usually assumed that the assets with zero prices were withdrawn following a bellshaped mortality function. While this is a reasonable assumption, it means that the studies are no
longer strictly empirical since they include assumptions about the pattern of discards.
47
9.
As regards age-price profiles, three main conclusions can be drawn:
First, different kinds of assets exhibit a very wide range of age-price profiles. If price is
plotted on the vertical axis and age horizontally, studies have found age-price profiles
that are concave to the origin, that are horizontal lines, that fall in a straight line and that
are convex to the origin. The studies have covered a wide range of industrial, agricultural
and construction machinery, commercial and industrial buildings and transport
equipment and it is therefore no surprise that they have not identified a single, standard
pattern for the age-price profile of assets.
Second, notwithstanding the above, by far the commonest age-price profile is a line which
falls over time with some convexity towards the origin. This is particularly the case for
machinery and equipment and is generally the case for buildings.
Third, the downward sloping convex curve, which is most often detected in these studies,
does not follow any simple mathematical law. Many of the studies have tested whether
their observed age-price profiles follow one of two simple models -- geometric (i.e. asset
prices falling by a constant rate each year) or straight-line (i.e. asset prices falling by a
constant amount each year) Statistical “goodness of fit” tests almost invariably reject
both of these simple models, although straight-line is usually rejected more firmly than
the geometric model. Some studies have successfully fitted Box-Jenkins curves to the
asset price data; these are flexible functions which can take a range of forms including
straight lines and geometric curves. The fact that Box-Jenkins curves may fit the data
quite well is simply confirmation that age-price profiles follow complex paths. This is
again not a cause for surprise. It would be astonishing if the multitude of factors that may
influence asset prices -- shifts in demand, relative factor prices, technological
developments to mention a few -- combined to produce age-price profiles that follow
some simple mathematical model.
Capital service value profiles, asset prices and depreciation
10.
The relationship between the value of the capital services produced by an asset (f) and the
price of that asset (V) is described by equation (1) which was introduced in Chapter 2.
T
Vt  
t
ft
1  r 
t

S
(1)
1  r T t
11.
In what follows the second term on the right-hand side of (1) -- the discounted value of the
scrap value -- will be ignored. This is done to simplify the arithmetic but it may not be unreasonable in
practice. Note that S is the amount that can be recuperated when an owner sells the asset to be broken
down, recycled or otherwise reduced to its component parts. S does not refer to the much higher values
that may be realised when an asset is sold to other producers for continued use in production. Note too
that the scrap value of an asset can be negative as well as positive; the cost of dismantling or removing
an asset from its site may be higher than the value of any parts or materials that can be salvaged. (See
box).
48
Assets with very high scrapping costs
Some assets may have very high scrapping costs. Two obvious examples are nuclear power stations
and marine oil-rigs. The high costs of dismantling such assets will mean that towards the end of their
service lives, and certainly in the last year of operation, their net values are likely to be negative; as the
end of their service lives approaches, the discounted value of the S term in equation (1) will exceed the
sum of the remaining capital service values. In principle, the fact that scrap values may be negative
does not cause any particular problem for measuring asset values or depreciation provided the true
scrapping costs were correctly anticipated and built into the initial asset price.
In practice, the costs of scrapping may not have been known at the time the assets were first acquired.
In the case of the earliest generation of nuclear power stations, for example, the costs of
decommissioning have increased significantly since the time when they were first brought into service
because governments and the general public now demand higher safeguards against the the long term
health risks of contamination. In the case of oil-rigs, the original disposal plans appear to have been to
sink them in deep water, but this scrapping method is meeting growing opposition from environmental
lobbies in many countries. Oil companies are being forced to incur very high costs of dismantling the
rigs and extracting waste products.
If the true costs of scrapping turn out to be substantially higher than were originally thought at the time
when the assets were acquired, formula (1) implies that the assets were overvalued at the time they
entered the capital stock as gross fixed capital formation. This overvaluation should be corrected by
negative entries in the “other changes in assets account”, with the adjustment being made at the time
when it becomes apparent that substantially higher scrapping costs will be incurred than had originally
been expected. These negative entries are similar to unforeseen obsolescence.
12.
In this section, (1) is used to show how the age price profile of an asset will change from
year 1 to T (the last year of its service life) under alternative assumptions about the profiles of the
service values generated by the asset over its lifetime. The purpose is to identify service value profiles
which seem plausible on a priori grounds and which generate age-price profiles which are consistent
with the empirical evidence discussed above -- namely that these profiles are usually downward
sloping and with some convexity towards the origin.
13.
Table 1 shows the calculation of the age-price profile of an asset, which produces service
value that declines geometrically by 10% per year. The discount rate (r) is assumed to be 5% per year
and the asset has a lifetime of 15 years. To understand the table:
The service value generated each year is shown in the second column: It is 100 in the first
year and falls by 10% to 90 in the second year, by a further 10% to 81 in the third year
and so on throughout its life.
Because these service values are generated in sequence and are not all available in the first
year, their present value (i.e. what the future service flows are worth at the beginning of
year 1 when the asset is installed) has to be obtained by discounting each year’s service
value by the discount factor (1+r), i.e. 1.05 in this example.
The third column shows the value in year 1 of the service values, which are expected to be
received in each of the 15 years of the asset’s life. This example assumes that service
values are received at the end of each year and so the first year’s value of 100 is only
49
worth 100/1.05 = 95.2 at the beginning of year 1. Similarly the service value of 90 which
is expected at the end of year 2 is worth only 90/1.052 = 81.6 at the beginning of year 1.
The total of these discounted service values gives the value of the asset at the beginning
of year 1, i.e. 600.6.
The fourth column shows the service values generated by the asset now that it is one year
old. The first year’s value of 100 has been used up so the price of the asset will be lower
for this reason although this is partly offset by the fact that by the beginning of the
second year all the capital services expected from year 2 through to year 15 are now one
year nearer and so will be discounted one less time. The total of these discounted service
values gives the price of the asset at the beginning of year 2, i.e. 530.7.
The last row in the table is depreciation and it is obtained as the difference between
consecutive asset values. Depreciation in the first year is therefore 600.6 - 530.7 = 70.0
(rounded)
Table 1. Calculation of Asset Value and Depreciation
Service value (f) declines by 10% annually. Discount rate is 5%
Year
Annual
service
value
(f)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
100.0
95.2
2
90.0
81.6
85.7
3
81.0
70.0
73.5
77.1
4
72.9
60.0
63.0
66.1
69.4
5
65.6
51.4
54.0
56.7
59.5
62.5
6
59.0
44.1
46.3
48.6
51.0
53.6
56.2
7
53.1
37.8
39.7
41.6
43.7
45.9
48.2
50.6
8
47.8
32.4
34.0
35.7
37.5
39.3
41.3
43.4
45.6
9
43.0
27.7
29.1
30.6
32.1
33.7
35.4
37.2
39.0
41.0
10
38.7
23.8
25.0
26.2
27.5
28.9
30.4
31.9
33.5
35.1
36.9
11
34.9
20.4
21.4
22.5
23.6
24.8
26.0
27.3
28.7
30.1
31.6
33.2
12
31.4
17.5
18.3
19.3
20.2
21.2
22.3
23.4
24.6
25.8
27.1
28.5
29.9
13
28.2
15.0
15.7
16.5
17.3
18.2
19.1
20.1
21.1
22.1
23.2
24.4
25.6
26.9
14
25.4
12.8
13.5
14.2
14.9
15.6
16.4
17.2
18.1
19.0
19.9
20.9
22.0
23.1
24.2
15
22.9
11.0
11.6
12.1
12.7
13.4
14.0
14.7
15.5
16.3
17.1
17.9
18.8
19.8
20.7
21.8
600.6
530.7
467.2
409.6
357.1
309.4
265.8
226.0
189.4
155.9
124.9
96.3
69.7
45.0
21.8
70.0
63.5
57.6
52.4
47.8
43.6
39.9
36.5
33.6
30.9
28.6
26.6
24.8
23.2
21.8
Value of the asset
Depreciation
50
14.
As noted, Table 1 shows asset values and depreciation for an asset, which capital service
value that declines geometrically by 10% each year. This particular service profile has often been used
in theoretical studies of asset prices and depreciation because it has the property, in certain
circumstances, of producing asset values and depreciation both of which also decline geometrically2.
However, the fact that it is a convenient assumption for analytic purposes is not a relevant
consideration in the present context. The important question here is whether geometric decline in
service values is a realistic assumption in practice.
15.
In considering alternative profiles of the capital service values, it is helpful to decompose
them into their quantities and prices. Denoting the value of capital services provided in period t by ft
and their price and quantity by pt and qt respectively, we have ft = ptqt. The capital service value
profile is then:
p1q1,, p2q2,, p3q3,, …….., pTqT.
This value profile can be decomposed into the capital service price profile:
p1,, p2,,
p3,, ……….., pT
and the capital service quantity profile,
q1,,
q2,,
q3,, ……….., qT.
16.
This last profile is also referred to as the efficiency profile of an asset as it is a measure of
the technical performance of an asset in production. Many types of assets produce a nearly constant
flow of service quantities over their lifetimes, but a constant quantity, or efficiency, profile does not
imply a constant value profile since this also depends on the price profile. For example a computer
may be able to produce a constant quantity of services almost indefinitely but its service value profile
may fall rapidly because the market price of those services is being constantly eroded by competition
from more technically advanced equipment.
17.
A constant efficiency profile needs to be carefully interpreted. It means that the asset
provides a constant quantity of services for the same amount of inputs; an efficiency profile is not
constant if the asset can only maintain the same level of physical output through ever increasing inputs
of materials or labour. The efficiency profile of an asset may vary for several reasons:
Most assets suffer from what can be termed “input decay” meaning that they require more
labour or material inputs to maintain their performance. For, example a freight truck may
use more oil as it ages or require more extensive maintenance work and therefore more
inputs of labour. Input decay will result in a declining efficiency profile.
Assets may also suffer from “output decay” as they age. This may take several forms. An
older asset may produce more defective products which have to be rejected, or its
2.
One example of geometric depreciation in which depreciation and asset prices are never geometric is
when the rate of decline in service values is set to zero. This is the “one-hoss shay” case and, as can
be seen from Figure 1 below, depreciation is an upward sloping curve and asset prices follow a
declining path which is concave to the origin. In order for depreciation and asset prices to decline
geometrically several conditions are required – both the decline in service values and the rate of return
must be positive and relatively high (for example, if both are 8% or more) and the asset must have an
infinite life. This last condition is approximately met for assets whose service lives exceed 20 years.
51
productive capacity could be lowered because it needs to spend more time under repair
and less time in production.
Some assets may require a running-in period during which technical adjustments are made to
maximise performance. Others may require the operators to learn new skills. In either
situation the efficiency profile could be expected to rise during the early period of use.
This could be described as “negative” decay.
18.
A constant service value price profile also need careful interpretation. It means that the
relative price of the capital service remains constant, i.e. after removing the effects of changes in the
overall price level. Relative prices of capital services may change for several reasons such as falling
demand for the goods or services produced by the asset and, especially important for technically
advanced assets, because of obsolescence; the asset faces competition from newer models which
produce a more desirable output.
19.
With these considerations in mind, we next consider five standard service value profiles:
Constant service value. This is sometimes referred to as the “one-hoss shay” pattern after the
mythical horse-drawn cart in “The Deacon’s Masterpiece”, a poem by Oliver Wendell
Holmes (see Box). The deacon built his cart so well that it ran perfectly for a hundred
years without need for repair, thus providing a constant value of transport services until
the day when it suffered catastrophic failure. During its service life the one-hoss shay
neither input decay nor output decay reduced the quantity of services provided and it
must be assumed that the relative price of the transport services it provided also remained
constant. There are probably rather few assets that produce the same value of capital
services every year throughout their working lives. Light-bulbs are sometimes cited as
potential one-hoss shays, but light-bulbs are too short-lived to be classified as capital
goods. More serious contenders might be bridges or dams. With a constant level of
maintenance these structures may continue to provide constant service values for very
long periods always assuming, of course that the service price profile also remains
constant. In general, however, the one-hoss shay, is regarded as a textbook curiosity with
few examples in the real world.
Service values fall at a constant rate each year. This is usually referred to as geometric
decline. In the example discussed below, the service value falls by 10% per year. There
is some evidence that assets that are particularly vulnerable to obsolescence exhibit
service value profiles of this kind. Obsolescence results in rapid falls in the service price
profile as newer, more technically advanced models produce improved outputs.
Computer equipment is sometimes cited as an example of geometric decline in service
values. Note that geometric decline implies that the service values generated by the asset
fall by a decreasing absolute amount each year. In the example given in Table 1, the
service value fell by 10 units in the second year but by only 2.5 units in the last year.
Since input decay can be expected to increase in absolute terms with age (thereby
reducing the efficiency profile), this suggests that the geometric profile may not be
relevant for assets that experience significant input decay.
Service values fall by a constant amount each year. A linear fall in service values could
occur with linear falls in the efficiency profile and the price profile or with various
combinations of non-linear efficiency and price profiles. The linear pattern means that
52
14The Deacon’s Masterpiece or the Wonderful “One-Hoss Shay”
Oliver Wendell Holmes’ poem tells of a Deacon
who decides to build a “shay” that would have no
weak spots so that it would never break down. (Shay
is a corruption of the French chaise, which is an old
English abbreviation of “post-chaise” or stagecoach.)
Now in building of chaises, I tell you what,
There is always somewhere a weakest spot,In hub, tire, felloe, in spring or thill,
In panel or cross-bar, or floor or sill,
In screw, bolt, thoroughbrace, - lurking still,
Find it somewhere you must and will.
First of November fifty-five,
This morning the parson takes a drive….
The parson was working his Sunday’s text,Had got to “fifthly”, and stopped perplexed…
All at once the horse stood still.
Close by the meet’n’-house on the hill.
First a shiver and then a thrill,
Then something decidedly like a spill,And the parson was sitting upon a rock,
At half-past nine by the meet’n’-house clock,Just the hour of the Earthquake shock!
Notice that, while the one-hoss-shay suffered
neither input decay nor output decay during its
hundred year service life, this does not mean that it
was immune to wear and tear. It clearly did suffer
wear and tear, which is why it suddenly fell apart.
The wear and tear took the form of metal fatigue
and similar subtle changes in the molecular
structure of the wood and leather. These changes
were imperceptible to the naked eye (although they
could have been discovered by microscopic
investigation), and they in no way affected the
ability of the shay to provide a steady flow of
unchanged transport services. But the changes
nevertheless guaranteed that, sooner or later, the
shay would fall apart.
The Deacon assembles the hardest timbers, the
finest steel, the toughest leather and the work
begins.
Seventeen hundred and fifty-five,
Georgius Secundus was then alive.Stuffy old drone from the German hive.
That was the year when Lisbon town
Saw the earth open up and gulp her down,….
It was on that terrible Earthquake day
That the Deacon finished the one-hoss shay.
The shay outlives the Deacon:
She was a wonder and nothing less,
Colts grew horses, beards turned gray
Deacon and deaconess dropped away,
Children and grandchildren - where were they?
But there stood the wonderful one-hoss shay
As fresh as on Lisbon Earthquake day!
This point is not trivial because it is sometimes
alleged that one-hoss shays, such as light-bulbs, lose
their value only because the failure point grows
nearer as each year passes. From this it has been
concluded that the passage of time is a cause of
depreciation in itself, in addition to the causes
identified in the SNA, namely wear and tear,
obsolescence and accidental damage. This is a
mistake. If the light-bulb is not suffering wear and
tear - through leakage of the inert gas or oxidisation
of the filament, for example - it will go on working
forever and the passage of time becomes irrelevant.
Ageing, or exhaustion as it sometimes called, may
be a useful rule of thumb for determining how much
wear and tear has occurred but is not, in itself, a
cause of depreciation.
But still, nothing last for ever, and by its
hundredth year:
There are traces of age in the one-hoss shay,
A general flavour of mild decay,
But nothing local as one may say.
There couldn’t be- for the Deacon’s art
Had made it so like in every part
That there wasn’t the chance for it to start.
Finally, disaster:
53
service values fall at a faster rate as the asset ages. In the example below, the service
value is assumed to fall steadily by 5 units per year.
Service values falls hyperbolically. With this profile, service values decline slowly in the
earlier period and at an increasing rate towards the end of the assets life. There is some
evidence from the United States that this may be a common efficiency profile for many
kinds of assets including both structures and plant and machinery. It will produce a
hyperbolic value profile if the relative output prices are stable or themselves falling
hyperbolically. The value of the capital service (f) in year t is obtained as:
f t  V0 T  t  / T  t 
where V 0 is the initial value of the asset, T is the service life and  takes a value
between 0 and 1. In the example given below  is set at 0.5.
Two-step service value. In many countries there is an increasing trend towards integrated
production systems in manufacturing. There may be many separate pieces of equipment
in such a system, each of which must operate without failure since the entire system will
shut down if any single component malfunctions or produces defective outputs. Many of
these systems are robotised with little human intervention and they may be operated
almost continuously rather than in shifts. The successful operation of such systems
requires that maintenance is minimised and is carried out to a strict schedule. Typically,
the component machines in such a system will be expected to operate without failure for
several years, at which point the investment manager will decide either to undertake
necessary repair work in order to keep the machines in the integrated system or to
remove it from the main production system. In the latter case it may either be sold to
another producer or it may be assigned a less demanding role, such as developing
prototypes or filling special orders. Assets incorporated into integrated production
systems may be expected to have a capital service profile that:
 Increases in the first period as the system is run-in, i.e. “negative” output decay.
 Remains constant during the several years in which it is a part of an integrated system,
i.e. a one-hoss shay profile.
 Declines abruptly when the machine is withdrawn from the integrated system.
In the example given below, the service value is assumed to rise by 5% in the first year,
to remain steady for the next 7 years when it operating in an integrated system and to
then become substantially lower and decline linearly for the remainder of the asset’s
service life. This “two-step” value profile may be appropriate for an increasing
proportion of plant and machinery in manufacturing industries.
20.
The calculations shown in Table 1 above have been repeated using the five service value
profiles described above; the same service life (15 years) and discount assumptions (5% interest rate)
are used as in Table 1. The time profiles of service values, asset values and depreciation are shown in
Figure 1 with all three flows scaled to equal 100 in the first year.
54
Figure 1. Asset values and depreciation profiles implied by five standard income profiles
Capital service value
250
Constant service value.
Asset Value
Depreciation
200
150
100
50
0
1
120
2
120
Service value falls by 10% per year.
100
100
80
80
60
60
40
40
20
20
3
4
5
6
7
8
9
10
11
12
13
14
15
13
14
15
Service value falls by 5 units per year.
0
0
1
2
120
3
4
5
6
7
8
9
10
11
12
13
14
1
15
2
3
160
Service value falls hyperbolically.
4
5
6
7
8
9
10
11
12
Two step: constant then falling.
140
100
120
80
100
80
60
60
40
40
20
20
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1
15
2
3
4
5
6
7
8
9
10
11
12
13
14
15
21.
The empirical evidence on second hand assets that was reviewed in the first section of this
chapter shows that asset values generally fall over time with some convexity towards the origin. The
first service value profile in Figure 1 -- Constant service value -- gives a time profile for the asset
value which is the opposite shape -- i.e. it is concave to the origin. It can therefore be concluded that
one-hoss shays are rare in the real world. The other four service value profiles, however, all produce
time profiles for asset values that are consistent with the empirical evidence. The two-step service
profile gives a time profile for the asset value that has an inflection towards the origin rather than the
smooth convexity produced by the other service value profiles but it is still broadly consistent with the
empirical evidence
22.
As explained, the calculations underlying Figure 1 used a service life of 15 years and a
discount rate of 5%. How far are these results sensitive to these two assumptions? Annex 5 graphs the
55
results of calculations based on service lives of 15 and 50 years and discount rates of 5% and 10%.
These alternative calculations show that the overall shape of the time profiles of asset prices is not
affected by a longer service life or by a higher discount rate. The only exception is with the hyperbolic
profile where the asset price loses its convexity when the service life is extended to 50 years and the
discount rate is set at 10%. The other interesting finding from Annex 5 is that while the geometric
decline in service values produces both asset price and depreciation profiles that are close to geometric
when the service life is lengthened, with a service life of 15 years neither depreciation nor asset prices
follow a geometric path.
23.
The conclusion of this section is that there are several capital service value profiles that are
consistent with the empirical evidence based on studies of second hand asset prices. In reality, it is
unlikely that any assets produce service flows that correspond precisely with any of these patterns. It is
much more likely that they produce flows of capital services that are combinations of these, and other,
patterns during different parts of their life cycles. There will, therefore, be an infinite number of
service profiles and depreciation profiles that are consistent with the empirical evidence on asset
values.
Depreciation methods
24.
In calculating depreciation, business accountants face the same problem as national
accountants; except in the usually rare circumstance where they are buying or selling used assets, they
do not know the market values of their company’s asset stock. They have, therefore, devised a number
of methods for estimating how asset values decline over their lifetimes. Some of these methods use
information about the usage or performance of the asset; for example, depreciation may be assumed to
be proportional to the hours of usage in the accounting period compared to the total hours that the
asset was expected to be in use when it was originally purchased; another method essentially involves
an annual updating of the present value of expected capital service flows over the remaining service
life of the asset using the standard equation for the value of an asset (equation (1) above ). In the vast
majority of cases, however, business accountants use one of the following three depreciation methods
which all assume a systematic decline in the value of an asset over time and which depend only on the
initial value of the asset and its expected lifetime:

Sraight-line depreciation.

Sum-of-the-digits depreciation.

Geometric depreciation.
25.
With straight-line depreciation , the market value of an asset is assumed to decline by the
same amount each period. This amount is equal to 1/Tth of the initial value of the asset, where T is the
average service life for that type of asset.
26.
With the sum-of-the-digits method, the market value is assumed to fall by an amount which
declines linearly over the lifetime of the asset. Specifically, depreciation (D) in year t is calculated as:
Dt = V[T-t+1] / [T(T+1)/2], where V is the initial price of the asset and T is the service life.
For example, if the service life is 15 years, depreciation in the first year will be 15/120th of V,
in the second year it will be 14/120th of V, etc. The denominator is the standard formula for
the sum of an arithmetic progression -- i.e. 15 + 14 + 13 +...+ 1 = 120. This gives the method
56
its name and ensures that the total depreciation calculated over the lifetime of the asset fully
exhausts its initial value.
27.
With geometric depreciation, the market value is assumed to decline at a constant rate in
each period. The depreciation factor can be written as R/T where T is the service life and R is the
“declining balance rate”. Depreciation for period t is obtained by multiplying the written down value
of the asset in the period t-1 by the depreciation factor, R/T. There are several ways of calculating the
declining balance rate (R):
A method commonly used by commercial accountants is known as the “double declining
balance” method. With this method, R is set at 2. The effect of this is that, in the first
period, depreciation will be twice as large as depreciation calculated by the straight-line
method. (It is for this reason that the method is referred to as double-declining.)
Another approach is to set R at a value that ensures that the asset’s initial value will have
been reduced to a predetermined percentage (g) of that value by the time it reaches the
end of its expected service life. In other words, a value of R is required such that:
V (1 - R/T)T = gV.
Dividing by V and solving for R gives:
R = T(1 - g1/T).
With g set at 0.1 (i.e. 10% of the initial value remains at time T) a service life of 15 years
gives R = 2.135 which implies slightly more rapid depreciation than the double-declining
method; R increases as service lives get longer and for a 50 year service life, R rises to
2.250.
28.
A third approach is to use evidence drawn from empirical studies of second-hand asset prices
to determine the declining balance rate appropriate to each asset. This has been done in the
United States where the Bureau of Economic Analysis (BEA) uses R values that range from 0.8892 for
most office and commercial buildings to 2.1832 for office machinery. An R value of 1.6500 is used for
most types of industrial machinery and equipment.
29.
It is interesting to note that the R values used by BEA are generally lower for long-lived
assets compared with assets that have short lives. As noted above, when R is set so that a
predetermined share of the initial value remains at the average service life, R is an increasing function
of the service life. The R values used by BEA mean that, for assets with long lives, quite large
percentages of the initial value still remain in the stock after the assets have reached their average
service life. In the case of commercial warehouses, for example, over 40% of the initial value still
remains in the stock when the average service life of 40 years has been reached.
30.
Geometric depreciation will never exhaust the full value of an asset because the depreciated
value of the asset falls asymptotically, approaching, but never reaching, zero. This is a disadvantage
for commercial accountants because accounting rules almost always require that, whatever system of
depreciation is used, total depreciation calculated over the expected life of the asset must equal the
initial price of the asset. It can also be seen as a disadvantage for national accountants because it is
clearly not the case that a group of assets installed in a given year will continue contributing to
production in all future periods. There are at least three ways of dealing with this problem.
57
31.
The first is to ignore it. The new PIM-based estimates by the United States BEA calculate
consumption of fixed capital using the standard “infinite” version of geometric depreciation. They
acknowledge that it is unreasonable to assume that assets continue contributing to production ad
infinitum but argue that, because of the high R values assigned to short-life assets, this contribution
becomes negligible soon after the asset reaches the average service life. Long-life assets, however,
such as buildings and other structures, which are assigned much lower R values will continue to
significantly influence the levels of depreciation and the net capital stock for up to twice the average
service life.
32.
The use of infinite geometric depreciation may also introduce a bias into time series of net
capital stock and depreciation. The early part of a time series of depreciation will necessarily exclude
depreciation on assets that were installed prior to the year of the earliest observation even though an
asset stock must have existed before that point in time. The most recent part of the time series,
however, will include depreciation on all assets installed since that time. In the case of the
United States this may not be a serious problem, at least for the more recent part of the time series,
because the time series of capital formation on which their estimates are based covers a long historical
period. It could however be seen as a serious drawback for countries that do not have long time series
on capital formation.
33.
The second approach is to treat all the remaining value of the asset as depreciation in the last
year of the asset’s service life. This is the standard approach of commercial accountants and is also
used by several countries that use geometric depreciation for their PIM estimates. These countries also
set the declining balance rate (R) so that a predetermined portion of the original asset value remains at
the end of the service life. Ten percent -- i.e. g = 0.1 -- is usually selected as the share of the original
asset value that is to remain at age T.
34.
The third approach is to arbitrarily adjust the rate of geometric depreciation so that the full
initial value of the asset is exhausted when it reaches the end of its service life. The box describes the
method used in Canada but there are several other adjustment techniques that could be used. What all
these methods have in common, however, is that they necessarily change the depreciation pattern so
that it is no longer geometric. If it succeeds in fully exhausting the initial asset value, the adjusted
depreciation pattern must be faster than geometric over at least some part of the asset’s lifetime.
How well do depreciation methods perform in practice?
35.
The question addressed in this section is how well the depreciation methods discussed above
will approximate the depreciation that should, theoretically, occur for assets whose age-price profiles
are consistent with the evidence on second-hand asset prices. “Theoretically” means that these are the
amounts calculated using the standard equation for the value of an asset (equation (1) above). Assets
that were earlier shown to be consistent with this evidence are assets that generate one of four service
value profiles -- geometric, linear, hyperbolic and “two step”.
36.
Three depreciation models will be considered:

Straight line.

Sum-of-the-digits.

Geometric.
58
37.
For the geometric method, the declining balance factor (R) is set to leave 10% of the initial
value of the asset at the end of its service life and all the remaining value of the asset is treated as
depreciation in the last period. This form geometric depreciation is often used in practice.
Statistics Canada’s version of “finite geometric” depreciation
In the following example the asset is assumed to have a service life of 10 years and an initial value of
100. Depreciation is first calculated by the normal method which implies an infinite life and infinite
depreciation. The double declining formula is used so that the geometric depreciation factor is 12/10 = 0.8. The amounts of depreciation are shown in the second column of the table. In the third
column, these values have all been reduced by the amount of depreciation calculated for the 11th year
-- i.e. 2.147. In the final column, the amounts shown in column 3 have been scaled up to 100 by
dividing them by 67.788/100.
Age
Depreciation
Column 2
Adjusted
minus
"geometric"
by the
depreciation
depreciation
double-
in 11th year
calculated
declining
(column 3
i.e. 2.147
divided by
formula
total of
column 2
times 100)
1
20.000
17.853
26.336
2
16.000
13.853
20.435
3
12.800
10.653
15.715
4
10.240
8.093
11.938
5
8.192
6.045
8.917
6
6.554
4.406
6.500
7
5.243
3.095
4.566
8
4.194
2.047
3.019
9
3.355
1.208
1.782
10
2.684
0.537
0.792
11
2.147
0.000
:
etc
total
67.788
total
100.000
Note that the adjusted “geometric” depreciation shown in the fourth column falls more sharply than
the original infinite geometric depreciation shown in the second column. Clearly the adjusted
depreciation is no longer geometric in the strict sense.
38.
Table 2 shows the amounts of annual depreciation for four assets which each last for
15 years and each produce 100 units of service value in the first year, but which thereafter generate
different service profiles -- geometric decline by 10% per year, linear decline by 5 units per year,
hyperbolic decline with  = 0.5, and the two-step service profile described above. The amounts shown
as depreciation in the first case (10% geometric decline) are taken from Table 1. The amounts of
depreciation shown for the other service value profiles were calculated in the same way, all using a 5%
discount rate. (The service value profiles and corresponding asset values and amounts of depreciation
are given in Annex 6).
59
39.
Table 2 compares the amounts of actual (or “theoretical”) depreciation with the estimates of
depreciation that will be obtained using each of the three depreciation methods. The success of each
method in approximating actual depreciation is evaluated by calculating the absolute mean of the
differences between the actual and estimated amounts of depreciation.
40.
The test results are given in Table 3, which also gives the ranking of each depreciation
method for each service value profile.
41.
The mean of the absolute differences in Table 3 shows the average of the annual errors in
estimates of depreciation when each of the three methods is used. The smaller the number, the better is
the depreciation method at measuring actual (i.e. theoretical) depreciation.
42.
The sum-of-the-digits method is clearly the best. It gives the smallest errors compared with
straight line and geometric in all cases except for the asset with a linear decline in service values.
Moreover, sum-of-the-digits gives mean differences that are substantially lower in cases a), c) and d)
than those obtained using the other methods.
43.
The straight line method is best in case b), linear decline in service value, but in the other
three cases there is little to choose between straight line and geometric. They both perform badly
compared with sum-of-the-digits.
Table 3. Relative performance of three depreciation models
Mean of absolute
differences value
Geometric by 10% per year
Straight
Sum
line of the
Geometri
digits
Linear decline
c
Straight
Sum
line of the
Geometri
digits
Hyperbolicc decline
Straight
Sum
line of the
Geometri
digits
Two step: cconstant then linear
decline Straight
Sum
line of the
Geometri
digits
rank
13
7
11
3
1
2
9
13
19
1
2
3
16
7
18
2
1
3
24
17
23
3
1
2
44.
The relatively poor performance of the geometric method may appear to be due to the fact
that depreciation in the last year of the asset’s life includes the 10% of the asset’s original value as
well as the amount of depreciation calculated for that year. However, it should be noted that an
“infinite” geometric method would not result in a better performance than the “finite” version used
here. The only difference when geometric depreciation is taken to infinity is that instead of the asset
value remaining at year T all being treated as depreciation in that year, this same amount is spread
over the period from T+1 to infinity. Since the asset no longer exists after T, and actual depreciation
60
must therefore be zero, the absolute error summed to infinity is the same as when the finite version is
used.
45.
To see why the sum-of-the-digits method performs better than the straight line and geometric
methods, it is helpful to turn back to Figure 1 which shows the time-paths of actual depreciation for
each of the four assets. In all cases, depreciation is lower at the end of the period than at the beginning.
This works against the straight line method, which gives constant depreciation throughout the period.
For the assets where capital services decline linearly and hyperbolically depreciation follow curves
which are concave to the origin. This works against the geometric method, which gives a convex
depreciation pattern. The sum-of-the-digits method captures the downward trend of actual depreciation
shown by all four models but does not presuppose either convexity or concavity.
46.
One point in favour of the geometric method is that, unless the discount rate is constant over
time, it is the only one of the three methods that, in theory, allows simple aggregation of different
vintages of assets over time. This is because only geometric depreciation gives a constant rate of
depreciation in all periods. When the discount rate is changing, it can be shown that the use of either
the straight line or sum-of-the-digits methods, assets of different ages should be aggregated using a
superlative index, such as Fisher or Tornquist. In practice, the errors introduced by failure to aggregate
different vintages using a superlative index will not be large unless changes in the discount rate are
large or erratic and they are likely to be swamped by the numerous other errors inherent in the
measurement of capital stocks.
Summary
47.
Four capital service value profiles have been identified that generate age-price profiles for
assets that are consistent with the empirical evidence about the prices of second hand assets.
48.
The sum-of-the-digits method best approximates the actual (or “theoretical”) ways in which
these four assets depreciate over time. Sum-of-the-digits is commonly used by commercial accountant
but has not so far been used by national accountants in estimating consumption of fixed capital.
49.
Straight line and geometric methods are widely used by national accountants but, according
to the test described above, they are clearly inferior to the sum-of-the-digits. Straight line is the
simplest method and performs at least as well as geometric. The geometric method has the theoretical
advantage that it allows simple aggregation of assets of different vintages but has the awkward
property of never exhausting the initial value of the asset without resorting to one of the artificial
methods described above.
61
CHAPTER 6
SURVEYS AND OTHER DIRECT MEASUREMENT METHODS
Introduction
1.
Most countries estimate capital stocks and related flows by the perpetual inventory method
(PIM), which was described in Chapter 4. The PIM is a cheap and convenient method, but it requires
many assumptions and the estimates obtained are probably less reliable than most other official
statistics. This chapter reviews other, possibly more reliable, procedures that may be used to estimate
capital stocks.
2.
One possible procedure would be to make an inventory of all the objects considered to be
capital assets through physical inspection by teams of enumerators. This was one of the methods used
to compile the Domesday Book in England, but seems not to have been tried since then. Four possible
data sources are reviewed in this chapter:
Use of published company accounts.
Enterprise surveys used in centrally planned economies to measure the “balance of fixed
assets”.
Statistical surveys carried out in market economies.
Administrative records on the stocks of particular types of assets.
Published company accounts
3.
In almost all countries enterprises are required to keep accounts for tax purposes and these
accounts normally include balance sheets showing the opening and closing stocks of capital assets
owned by companies and used in the production of goods and services. Can these statistics, which are
readily accessible, be used to estimate capital stocks for national accounts purposes?
4.
A first problem is that accounts including balance sheets are usually only available for
corporate enterprises. Unincorporated enterprises are not generally required to keep accounts for their
capital assets and so even if company accounts can be used for the corporate sector it would be
necessary to devise other methods to cover capital stocks of unincorporated enterprises.
5.
In general, capital assets are defined in company accounts as covering physical objects of
the kind defined in the SNA as tangible fixed assets. There are some differences from SNA
definitions, and between countries, in the treatment of capital repairs and transfer costs and in the
capitalization of interest payments on loans used to purchase assets. These differences, however, are
relatively minor and do not rule out the use of company accounts for direct estimates of capital stocks.
62
6.
A more serious problem lies in the way that assets are valued. In virtually all countries the
standard method of valuing assets is “depreciated historical cost”. A few countries that have
experienced long periods of high inflation specify that assets must be revalued to current purchasing
power using the consumer price index or other general inflation measure; current purchasing power is
a different concept from current replacement cost as required for national accounts. Most countries
also allow companies to revalue assets to current replacement cost. Usually companies have
considerable freedom to decide whether to revalue assets to replacement values, but several place tight
restrictions on this option and only allow revaluations after extended periods of high inflation, or as
part of the restructuring of a company following a merger or bankruptcy.
7.
Methods by which historical costs are depreciated in the accounts also vary. Most countries
allow companies to use any method to depreciate fixed assets provided that it will exhaust the full
value of the asset and will do it in a systematic way. In practice “straight-line”, “sum-of-the-digits”
and “double-declining balance” are the commonest methods.
8.
Finally, in many countries it appears that assets often continue to be used in production for
several years after they have been fully written-off in the company accounts. It may sometimes be that
this is because the accountants have used conservative estimates of the probable service lives when the
assets were initially installed. However, this can also be due to various “accelerated depreciation”
schemes that governments use to encourage capital investment . Allowing countries to write off their
assets over short periods reduces net profits and, therefore, taxes is a strong incentive to invest.
9.
It is clear from the above that asset values reported in company accounts cannot simply be
aggregated to obtain estimates of the net capital stock. Historical costs are not suitable for national
accounts purposes because assets are then being valued at a mixture of prices, and the use of different
depreciation methods adds a further element of non-comparability from one company to another. The
same problems also render depreciation reported in company accounts unsuitable for national accounts
purposes.
10.
The above comments refer to the published accounts of companies. Of course, companies
keep many other records relating to the purchase and use of capital assets and these have been found,
in several countries, to be suitable for capital stock estimates appropriate for national accounts
purposes. As explained below, these records provide the essential basis for statistical survey methods.
Balance of Fixed Assets
11.
The “balance of fixed assets” is the term used to describe the annual enquiries traditionally
carried out by the centrally planned economies of central and eastern Europe. They were
comprehensive surveys of all fixed assets used in state enterprises. These enterprises accounted for
most production in these countries so that the total balance of fixed assets was virtually the same as the
nation’s total capital stock. The main omission was assets used on private farms, where these were
permitted. Several transition countries have continued these surveys.
12.
To obtain the “balance of fixed assets”, enterprises were required to report the stock of fixed
assets at the beginning of the year, the acquisitions during the year (including new assets), withdrawals
(including liquidation) of fixed assets and the value of the stock of fixed assets at the end of the year.
The balance is compiled at both full (non-depreciated) replacement value and remaining replacement
value, i.e. after subcontracting consumption of fixed capital. The full replacement value is defined as
the value of expenditures which is needed to acquire and put into operation new fixed assets in the
present circumstances.
63
13.
The “balance of fixed assets” could be seen as an ideal form of the perpetual inventory
method in which companies rather than statistical offices keep a running total of additions to, and
withdrawals from the capital stock. It is an “ideal” form because it uses information on actual
retirements of assets and does not require assumptions about service lives and mortality functions.
14.
Until the changes which started in 1990s, the prices of domestically produced assets were
“plan prices” which would reflect the “plan cost” of producing them. Imported assets were valued at
the prices paid, which could be market prices if imported from market economies. Prior to transition,
prices were relatively stable so that for many assets there was little difference between historic costs
and current prices. In the early 1990s, however, most of these countries experienced rapid inflation
and it became necessary to revalue assets each year to current replacement costs. The revaluations are
carried out by the enterprises themselves either using coefficients supplied to them by the statistical
agency or on the basis of information about the current market prices of the assets. The coefficients
varied from one type of an asset to another but not from one enterprise to another. Thus, the gross
value of an asset at the beginning of each would either be equal to its original price of acquisition
multiplied by the cumulative product of all the revaluation coefficients applied up to that point of time
or, alternatively, it would be equal to the estimated current market price of a replacement asset.
15.
These countries used a definition of capital consumption that was narrower than the one
required for national accounts. It covered only wear and tear and excluded any fall in value due to
obsolescence. Estimates of capital consumption obtained from these surveys is not, therefore, suitable
for national accounts purposes but, provided revaluations were carried out regularly, the balance of
fixed assets could, in principle, be used as an estimate of the gross capital stock.
16.
In practice, there are at least three problems with these data:
First, the coverage of the surveys has deteriorated with the growth of private sector
enterprises. These new enterprises may be included in the surveys but are often
unwilling or unable to supply detailed data on their asset stocks.
Second, the very high rates of inflation in the early years of transition made it very difficult
for the statistical agencies to provide realistic coefficients for revaluing assets. The
current replacement costs at which the balance of fixed assets is supposed to be valued
are highly suspect in many of the countries concerned. (The unreliability of asset price
indices will affect PIM estimates in exactly the same way).
Third, doubts have been raised about the true values of many of the assets held by state
enterprises. Much of the older plant and equipment in heavy industries may no longer
have been used in production but was still being included in the balance of fixed assets at
its revalued historic costs.
This said, even if these statistics are now of doubtful value, the balance of fixed assets which was
calculated in the early 1990s before inflation became rampant could be used as bench-mark estimates
of the gross capital stock and could then be updated by the PIM for the current period.
Statistical surveys in market economies
17.
In addition to the centrally planned economies, two other counties, Japan and Korea, have
traditionally carried out surveys of the capital stock. Both are described as “National Wealth Surveys”
and are designed to provide estimates of the national balance sheet. In addition to fixed assets they
64
also covered inventories and net foreign financial assets. Both surveys were carried out at
approximately 10-year intervals. The last Japanese survey was held in 1983 and there are no plans to
repeat the survey; the Korean surveys are continuing and the latest was held in 1998.
18.
The Korean survey covers all sectors, including general government, government business
enterprises, incorporated and unincorporated enterprises and non-profit institutions serving
households. It has a reasonably detailed coverage of fixed assets, including buildings, other structures,
machinery and equipment, ships, vehicles and other transport equipment, tools and furniture, and
construction work in progress. Almost 8 000 incorporated enterprises, and 160 000 unincorporated
enterprises were sampled in the last survey, along with 62 000 households. A comprehensive survey of
the government sector is conducted.
19.
The Netherlands is the only other country that carries out capital stock surveys on a regular
basis. The survey is annual and covers mining and manufacturing. However the survey does not
cover all mining and manufacturing activities each year. Instead, different subsectors are covered each
year in such a way that all activities within mining and manufacturing are surveyed every five years.
Stock estimates for the inter-survey years are derived by adding gross fixed capital formation and
subtracting discards. Discard figures are obtained using the discard survey. For national accounting
purposes the Netherlands intends to use the survey results as benchmarks for the PIM.
20.
The survey uses eight asset classes: sites (only purchase and sale), industrial buildings, civil
engineering works, external means of transport (e.g. excavators), internal means of transport (e.g.
assembly lines), computers, other machinery and other equipment, and other tangible fixed assets (e.g.
furniture, silos, etc).
21.
Both the Korean and Netherlands surveys collect the following information:
Type of asset.
Original (historic) value.
Year when the asset was installed or constructed.
Whether the assets were purchased new or second hand.
Whether the assets are owned or leased.
In both cases, revaluation to replacement values is done by the statistical agencies using asset price
indices. Annex 4 contains the questionnaire used by Korea for non-financial enterprises.
22.
Note that because these surveys distinguish between owned and leased assets, they can
provide estimates of the capital stock on both an ownership and user basis. This is an advantage
compared with the PIM which gives stock estimates only on ownership basis, because this is how
capital formation is normally reported.
23.
Like all statistical inquiries, the reliability of the results depends on the quality of the survey
procedures and on the ability of respondents to supply the information requested.
24.
Both the Korean and Netherlands surveys involve visits by enumerators. Experience has
shown that it is not usually possible to collect the necessary information by mail questionnaire. For
the Korean survey, the work of enumeration is so great that is divided up between several government
65
agencies. In the Netherlands the high cost of on-site investigation by skilled enumerators is the main
reason that the five-year “rolling benchmark” method is used.
25.
The ability of respondents to provide the information depends on the quality of their
accounting records. The following problems have been encountered in the Netherlands:
Companies do not always capitalize major alterations to assets.
Most companies use value cut-off points in deciding whether expenditure is capital or
current. In some cases these are so high that they exclude some items that should be
treated as capital assets according to the SNA.
Company records do not always distinguish new from second-hand assets.
Some companies pick arbitrary dates, such as the end of the Second World War, as
installation dates for very old assets; others may report the year of a revaluation as the
installation date for assets that were actually installed before that date.
Large installations consisting of several separate pieces of equipment, which were actually
acquired at different times, may be assigned a single installation date.
Replacement parts may be capitalized but the part it replaces may not be recorded as a
discard.
An asset may cease to be used in production but is not physically removed from the site and
so is not recorded as a discard.
26.
In the Netherlands, capital stocks are estimated by updating the stock (adding gross fixed
capital formation, subtracting discards) for years between the five-year survey benchmark estimates.
When new survey results become available quite large discrepancies have been found for some
industries between the PIM projection and the survey results. These discrepancies have been
interpreted as showing the weaknesses of the PIM, but it is clear that some of them may also be due to
errors in the survey results arising from problems with the accounting records.
27.
Some of these difficulties may be alleviated in the future by an interesting development
reported in the United Kingdom. Most large companies now maintain computerized asset registers
using standard software developed for this purpose. These records may improve the accuracy of the
records and, equally important, may make it possible to measure capital stock without the need for onsite investigation by enumerators. The high cost of doing this is one of the main impediments to the
wider use of surveys to measure capital stocks.
28.
Finally, mention should be made of a survey procedure being developed in Canada, called
the “Fixed Asset Accounting Simulation Model” (FAASM). The starting point is a survey in which
enterprises are asked to report the gross values of their fixed assets at historic costs. These are then
aggregated by type of asset and kind of activity. Long time series of gross fixed capital formation are
then aggregated in the same way and are compared to the gross capital stocks at historic prices to
determine what the service lives of the assets must have been in order to reconcile capital formation
with the gross capital stocks. In making this reconciliation, it is assumed that assets are retired from
the stock following a truncated normal distribution around the average service life but this particular
“mortality” pattern is not an essential feature of FAASM and other patterns could be used, such as
Winfrey curves or the Weibull distribution. Gross capital stocks are then revalued from historic prices
66
to current and constant prices and the estimated service lives are used to calculate consumption of
fixed capital and net capital stocks. FAASM has been tested in Canada and the results are said to be
encouraging.
Administrative records
29.
In most countries, administrative records are maintained on the stocks of certain types of
assets. This may be done because ownership or use of the asset in question is taxed; examples are
motor vehicles and residential buildings. Administrative record may also be kept on assets that
represent health hazards or whose use is regulated for safety or environmental reasons; examples
include nuclear fuel rods, passenger aircraft and fishing vessels.
30.
These records usually give the numbers rather than values of the assets concerned, but if the
records give additional information on their technical specifications they can be valued either at
current values to obtain the net capital stock or at historic values updated to the current year to obtain
the gross stock. Several countries use administrative sources where they are available and estimate
other asset stocks by the PIM.
31.
In some cases administrative records may be available only for selected years. For example,
detailed information on the housing stock may be available only for population census years. In these
cases the stock of assets in the inter-censal periods can be obtained by the PIM. Using a combination
of benchmark estimates and PIM estimates provides an opportunity to test the critical parameters of
the PIM mode, notably service lives and mortality functions.
Summary
32.
There are a number of alternatives to the PIM for estimating capital stocks. The first method
considered, use of published company accounts, is clearly an inferior method and is not
recommended here. Although accounting practices vary between countries a common feature is that
stock and depreciation are calculated using historic costs. For national accounts purposes current or
constant replacement costs must be used. Several countries do in fact use data from company
accounts, particularly for their estimates of consumption of fixed capital, but these will, at best, be
crude approximations to what is required for the national accounts and will often be highly misleading.
33.
A survey method that is well established in central and eastern Europe is the balance of
fixed assets. Provided that prices are correctly revalued each year, this method can, in principle,
provide suitable estimates of the gross capital stock. In practice, there are severe practical difficulties
in applying this method at the present time; these include growing rates of non-response, difficulties in
measuring asset prices under high inflation and the over-valuation of older assets. It may, of course,
be possible to overcome these problems by redesigning the surveys and improving enumeration
procedures and these surveys would then be a valid alternative to the PIM.
34.
Korea and the Netherlands are the only two other countries that use statistical surveys at the
present time. Both appear to be successful although the costs are high, particularly for the National
Wealth Survey carried out in Korea. The success of survey methods depends crucially on the quality
of the asset records maintained by companies. These vary so significantly from country to country that
generalizations cannot be made about the potential of survey methods for any particular country.
35.
There is no doubt that capital stock surveys can be expensive and the results can be of
questionable quality. It is probably not cost effective to apply it to all sectors, for all asset types for
67
every time period. The most cost-effective strategy is likely to be using survey methods selectively
and periodically, and use them in combination with the PIM. This is essentially the approach adopted
by the Netherlands.
36.
FAASM is an original approach but is still in the experimental stage. As with other surveys,
much depends on the quality of the records maintained by enterprises. FAASM appears to be feasible
in Canada but may not be exportable to other countries.
37.
Administrative records can be used in some countries to estimate stocks of certain types of
assets, notably road vehicles, dwellings, aircraft, and nuclear fuel rods. Such estimates are usually to
be preferred to estimates based on the PIM, but they will only cover a small part of the total stock.
68
CHAPTER 7
CAPITAL SERVICES
Introduction
1.
This chapter considers how to measure the contribution of capital to the production of goods
and services. The contribution of labour is relatively easy to measure because both the quantities
provided (hours worked) and the prices paid (wages and salaries) are readily observable. But in the
case of capital assets, quantities and prices of inputs can only be observed when a producer rents an
asset so that there is a purchase and a sale of a capital service which can, in principle, be recorded by
the statistical agency.
2.
The definition and measurement of the contribution of capital to production has been a
controversial issue in economics, but a measure of agreement has been reached in recent years on
some of these issues. The sections below identify areas of agreement and describe the solutions that
have been suggested for the outstanding issues.
Stocks or flows
3.
The term “growth accounting” is used to describe attempts to determine the causal factors of
economic growth. Growth accounting requires a measure of the contribution to economic growth
made by capital assets and the theoretical development of ways to measure this contribution is due to
the work of economists, mainly working in North America, who are commonly referred to as “growth
accountants”.
4.
Although some prominent growth accountants have long argued that a measure of capital
services is required, most growth accounting studies have used the gross capital stock to represent the
contribution of capital. A few experimented with the net capital stock and, occasionally, an average of
the net and gross stocks was used. The gross stock was generally preferred because it was believed
that valuing assets at their “as new” prices was more likely to reflect their contribution to production
over time; if they are properly maintained, most assets retain their original efficiency for much of their
working lives. The depreciated prices used for the net stock were thought to undervalue the productive
capacity of assets.
5.
One problem in using stocks, whether net or gross, is that the other variables in the growth
accounting model are all flows. These include labour inputs and intermediate consumption as
independent variables and value added or gross output as dependent variables. The “dimensions “ of
the variables are therefore inconsistent. In practice, almost all growth accounting models relate the
changes in the independent variables -- such as capital and labour -- to changes in the dependent
variable -- value added or gross output. Changes in the capital stock can, of course, be regarded as
69
flows; the change in the gross capital stock is gross fixed capital less discards and the change in the
net capital stock is gross fixed capital less consumption of fixed capital or “net capital formation” as it
is usually termed. But the dimension problem remains because a first-order flow – namely a change in
a stock -- is now being used together with second-order flows, namely changes in the flow of labour
inputs or the flow value added.
6.
Growth accountants have recognised this problem and have often explained that what they
were really looking for were measures of the services provided by capital assets. They used the capital
stock as an approximation to the service measure they really needed. One solution that has been
occasionally tried is to use capital consumption in place of capital stocks. This overcomes the problem
of inconsistent dimensions because capital consumption is a first order flow on a par with the other
variables in the model. Below it is shown that, while consumption of fixed capital may be a better
measure of capital services than capital stocks, it is an incomplete one.
Capital services
7.
Chapter 2 introduced the standard equation that relates the price of an asset to the value of
the services that it is expected to provide over its working life. This equation was then manipulated to
show that these services can be expressed as the product of the capital stock and the sum of the rate of
depreciation and the net rate of return to the asset owner. Specifically, Chapter 2 showed that:
ft = (dt + r) Vt ,
(1)
where ft is the value of the capital service provided in period t,
Vt is the value of the asset in period t,
dt is the rate of depreciation in period t, and
r is the rate of return.
8.
Equation (1) shows why consumption of fixed capital alone is not a good measure of the
services provided by capital assets. It measures only a part of these services and omits the net return
(rVt) that the asset provides in addition to depreciation.
9.
Measuring capital services (f) using equation (1) requires estimates of depreciation (dt), the
rate of return (r) and the value of the asset stock (Vt). The previous chapter has discussed the various
ways to measure depreciation. Measurement of the rate of return and the appropriate way to represent
the asset stock in equation (1) are addressed below.
Rate of return (r)
10.
There are essentially two approaches to the measurement of the rate of return -- the use of
national accounts statistics on property incomes or the use of market interest rates.
11.
The income and outlay accounts record payments by institutional sectors of interest and
dividends and other types of property income. These can be related to the capital stock to obtain a
measure of the actual, ex-post, rates of return earned by capital. The System of National Accounts, as
well as most national systems, record transactions in property incomes for institutional sectors such as
70
“general government” and “non-financial enterprises” because payments and receipts of property
income are made by institutional units and not by production units. This means that national accounts
data can only be used to calculate rates of return at a rather aggregated level. For many purposes,
estimates of capital services are required according to kind of activity. An average rate of return
calculated for an institutional sector such as non-financial corporations may not be appropriate for the
many different kinds of activities in which non-financial enterprises engage, including agriculture,
mining, manufacturing, utilities and services.
12.
An alternative is to estimate the rate of return from market interest rates. The logic behind
this is that interest rates play a key role in determining rates of return. First, the decision to purchase a
capital assets is based on a comparison between the rate of return that the asset is expected to earn and
the income that could be earned from alternative uses of the funds. These alternative uses include
investment in financial assets. Second, investment in capital assets is often financed through
borrowing and a producer will not borrow to buy an asset unless the expected rate of return exceeds
the interest that has to be paid on the loan.
13.
The fact that both the interest that could be earned and the interest that would have to be paid
seem equally relevant for investment decisions poses a problem. Which should be used for estimating
the rate of return? One possibility is to use the average of these two rates as an estimate of the rate of
return. This average can be seen as an estimate of the “pure” rate of interest, i.e. the compensation that
lenders demand for postponing consumption to a future period. The difference between this and the
interest actually paid can be regarded as a service charge levied by financial intermediaries for
arranging loans to borrowers and managing the accounts of lenders.
14.
An advantage of calculating rates of return from market interest rates is that, in some
countries, statistics on interest payments are available according to activity categories. It would,
therefore, be possible to estimate activity-specific rates of return rather than using overall averages for
broadly defined institutional sectors.
Capital Stock (Vt)
15.
Equation (1) shows that Vt , which is the current market value of assets, i.e. the net capital
stock, is required for calculating capital services. That is the logical conclusion starting from the
standard equation which relates the value of assets to the value of the capital services they are
expected to provide. Some analysts, however, have argued that when a measure of capital services is
required for productivity analysis, the capital stock should not be valued at current market prices but
at prices which reflect their efficiency in production. Researchers at the BLS have developed an
alternative measure of the capital stock, which they use for measuring capital services in their
extensive work on productivity in the business sector. This alternative is referred to by BLS as the
“productive capital stock”.
16.
The difference between the productive capital stock and the net capital stock (which BLS
refers to as the “wealth capital stock”) is that in the former, assets are valued at prices which reflect
their efficiency in production, while in the latter, assets are valued at prices which reflect their current
market values. These two sets of prices are identical in the year when the assets are installed but may
follow quite different paths during the remainder of their service lives.
17.
The evidence on second hand asset prices reviewed in Chapter 5 shows that, when asset
prices are plotted on the vertical axis and time on the horizontal axis, market prices of assets usually
fall along a path that is convex to the origin. The absolute fall in market prices is larger in the earlier
71
period than towards the end of the asset’s service life. The efficiency profile (the sequence of of the
qt’s), on the other hand, is likely to decline in a quite different way over time. A one-year old asset will
usually be just as efficient, in terms of the quantities of output produced, as when it was new. Indeed,
if there is a learning process involved the asset may be even more productive a few years after
installation than when it was first acquired. Investigations by BLS and discussions with production
engineers and managers in manufacturing industries have confirmed that most assets lose their
productive efficiency by smaller amounts in the early part of their lives compared with later year. In
other words, when productive efficiency is plotted on the vertical axis and time on the horizontal axis,
efficiency profile declines along a path that is concave to the origin.
18.
In passing, it should be noted that there is no inconsistency between these contrary timeprofiles for productive efficiency on the one hand and market prices on the other. Figure 1 in
Chapter 5 gives examples of assets whose efficiency profiles were assumed to decline by smaller
amounts in the early years compared to later periods but which generate asset values that fall by larger
amounts in the early years compared to later periods; i.e. the efficiency profile is concave but the
profile of ass et prices is convex. Figure 1 of Chapter 5 shows that this is the case with hyperbolic
decline in service values and two-step model.
19.
The BLS calculates the productive capital stock using a hyperbolic function of the kind that
was used in Chapter 5 in the discussion of capital service value profiles. In calculating the productive
capital stock BLS defines the value (Vt), of each asset in the stock at time t as:
Vt = V0 (T - t)/(T - t), with 0 <  > 1.
(2)
Here V0 is the initial value of the asset and T is the service life. BLS currently sets  at 0.50 for most
types of plant and equipment and at 0.75 for structures.
20.
The gross capital stock is the starting point for calculating the productive capital stock.
Instead of reducing the value of assets by one of the depreciation methods described in Chapter 5, the
gross stock is “depreciated” using the hyperbolic function in (2). Inverted commas are needed because
the productive capital stock does not represent the depreciated value of the asset stock as this term is
generally understood. The writing down of the gross stock to arrive at the productive capital stock
reflects the decline in the productive efficiency of assets. It has nothing to do with the decline in
market values.
21.
In the BLS methodology, the components of the productive capital stock are multiplied by
the capital services they are assumed to provide, i.e. by (dt + r). (These capital services are estimated
by BLS from national accounts statistics on property income transactions.) The BLS describes the
result as the productive capital stock (weighted by capital services). As was noted in Chapter 2, when
two vectors are multiplied, either vector can be described as the weights and the term preferred in this
manual is capital services (weighted by the capital stock).
Summary
22.
As regards the definition and measurement of capital services, there are two areas of
agreement:
The contribution of capital to the production of goods and services should be represented by
the services they provide rather than by the value of the asset stock.
72
These services cannot usually be observed but they can be indirectly estimated. Starting from
the standard equation which shows how asset prices are determined by the values of the
capital services expected during the asset’s service life, the value of capital services (ft)
can be derived as ft = (dt + r) Vt . Here d is the rate of depreciation, r is the net rate of
return to the asset owner and Vt is the value of the asset.
23.
Two areas may still be open to debate:
The net rate of return (r) can be estimated either from national accounts statistics on
transactions in property incomes as a ratio of the capital stock, or they can be based on
market interest rates. With the second approach, an average of the borrowing and lending
rates faced by producers seems to be a practical solution that is consistent with the way
that the 1993 SNA distinguishes between pure interest and charges for financial services.
The choice between using property income flows from national accounts or averages of
interest rates may be a practical rather than a theoretical issue. Perhaps it should be
decided by data availability.
The standard equation for the price of an asset seems to require that capital services should
be calculated by reference to the net capital stock, i.e. to the current market prices of the
stock of assets. Casual observation, backed up by a canvass of expert opinion in the
United States, strongly suggests that the efficiency profile of assets declines much more
slowly in the early years than their market prices. This has lead BLS to devise an
alternative measure of capital, which they refer to as the “productive capital stock”. Is
this a better measure to use in calculating capital services rather than the net capital stock
which seems to be required in theory?
73
LIST OF ANNEXES
1. Glossary of Terms: Capital Stocks and Related Statistics.
2. Methods of adjusting capital stock estimates for transactions in used assets. (Not yet
available)
3. Service lives of assets used in four countries.
4. Examples of questionnaires: New Zealand survey of asset lives; Netherlands
questionnaires used for discard and stock, discard and investment surveys.
5. Graphs of asset service lives implied by five capital service profiles: service lives 15 and
50 years; interest rate 5% and 10%.
6. Asset prices and depreciation implied by four capital service value profiles.
74
Annex 1. Glossary of Terms: Capital Stocks and Related Statistics
Introduction
This Glossary is divided into two parts. Part 1 lists terms used in the 1993 System of
National Accounts. It is based on the complete “Glossary of Terms in the 1993 System of National
Accounts”, OECD, Paris, 1999.
Part 2 is based on the “Dictionary of Usage on Capital Measurement”(Jack Triplett,
Brookings Institution, United States) presented at the Second Meeting of the Canberra Group on
Capital Stock Statistics, September 1998, Paris. This part of the Glossary contains terms that are not
found in the SNA but which are commonly used in the literature on capital measurement. The
Dictionary itself is organised in an analytic framework which distinguishes between terms related to
physical concepts and those related to value concepts, but in Part 2 below, the terms are listed in
simple alphabetic order. The Dictionary also contains detailed notes on how the terms have been used
(and mis-used) by different authors. These are not reproduced here but they are a valuable guide for
readers interested in the development of concepts in the area of capital measurement.
Part 1. Terms Used in the 1995 System of National Accounts
Term
Assets
Definition
Assets are entities that must be owned by some unit, or units, and from
which economic benefits are derived by their owner(s) by holding or
using them over a period of time.
SNA paragraph
1.26
Balance sheet
A balance sheet is a statement, drawn up at a particular point in time, of
the values of assets owned by an institutional unit or sector and of the
financial claims - liabilities - against the owner of those assets.
13.1
[1.11, 2.93, 10.1]
Catastrophic losses
The volume changes recorded as catastrophic losses are unanticipated
losses resulting from large scale, discrete, and recognisable events that
may destroy assets within any of the categories of assets.
12.35
Computer software
Computer software consists of computer programs, program
descriptions and supporting materials for both systems and applications
software.
(AN.1122) - Annex
to chapter XIII
Consumption of fixed
capital
Consumption of fixed capital represents the reduction in the value of the
fixed assets used in production during the accounting period resulting
from physical deterioration, normal obsolescence or normal accidental
damage.
10.27
[6.179, 10.118]
Dwellings
Dwellings are buildings that are used entirely or primarily as residences,
including any associated structures, such as garages, and all permanent
fixtures customarily installed in residences; movable structures, such as
caravans, used as principal residences of households are included.
(AN.1111) - Annex
to chapter XIII
75
Entertainment, literary or
artistic originals
Entertainment, literary or artistic originals are the original films, sound
recordings, manuscripts, tapes, models, etc, on which drama
performances, radio and television programming, musical performances,
sporting events, literary and artistic output, etc are recorded or
embodied.
(AN.1123) - Annex
to chapter XIII
Existing fixed asset
An existing fixed asset is one that has already been acquired by at least
one resident user, or produced on own account, and whose value has,
therefore, already been included in the gross fixed capital formation of
at least one user at some earlier point in time in the current or some
previous accounting period.
10.39
Fixed assets
Fixed assets are tangible or intangible assets produced as outputs from
processes of production that are themselves used repeatedly or
continuously in other processes of production for more than one year.
10.33
[1.49, 10.7, 10.26,
13.15, (AN.11) Annex
to chapter XIII]
Gross capital formation
Gross capital formation is measured by the total value of the gross fixed
capital formation, changes in inventories and acquisitions less disposals
of valuables for a unit or sector.
10.32
Gross capital stock
Gross capital stock is the value of all fixed assets still in use when a
balance sheet is drawn up, at the actual or estimated current purchasers’
prices for new assets of the same type, irrespective of the age of the
assets.
6.199
Gross fixed capital
formation
Gross fixed capital formation is measured by the total value of a
producer’s acquisitions, less disposals, of fixed assets during the
accounting period plus certain additions to the value of non-produced
assets (such as land or subsoil assets) realised by the productive activity
of institutional units.
10.33
[10.26]
Historic cost accounting
Historic cost accounting is a valuation method which requires goods or
assets used in production to be valued by the expenditures actually
incurred to acquire those goods or assets, however far back in the past
those expenditures took place.
1.60
Intangible fixed assets
Intangible fixed assets are non-financial produced fixed assets that
consist of mineral exploration, computer software, entertainment,
literary or artistic originals and other intangible fixed assets intended to
be used for more than one year.
(AN.112) - Annex
to chapter XIII
Land
Land is the ground, including the soil covering and any associated
surface waters, over which ownership rights are enforced.
(AN.211) - Annex
to chapter XIII
[13.54]
Livestock for breeding,
dairy, draught, etc.
Livestock for breeding, dairy, draught, etc consist of livestock that are
cultivated for the products they provide year after year.
(AN.11141) - Annex
to chapter XIII
Machinery and equipment
Machinery and equipment consist of transport equipment and other
machinery and equipment other than that acquired by households for
final consumption.
(AN.1113) - Annex
to chapter XIII
Major renovations or
enlargements
Major renovations or enlargements are activities which increase the
performance or capacity of existing fixed assets or significantly extend
their previously expected service lives; the decision to renovate,
reconstruct or enlarge a fixed asset is a deliberate investment decision
which may be undertaken at any time and is not dictated by the
condition of the asset.
6.162
76
Mineral exploration
Mineral exploration consists of the value of expenditures on exploration
for petroleum and natural gas and for non-petroleum deposits.
(AN.1121) - Annex
to chapter XIII
Net capital stock
The sum of the written-down values of all the fixed assets still in use
when a balance sheet is drawn up is described as the net capital stock
6.199
Net fixed capital
formation.
Net fixed capital formation consists of gross fixed capital formation less
consumption of fixed capital.
10.27
Net value of a fixed asset
The net (or written-down) value of a fixed asset is equal to the actual or
estimated current purchaser’s price of a new asset of the same type less
the cumulative value of the consumption of fixed capital accrued up to
that point in time.
6.199
Net worth
Net worth is the value of all the non-financial and financial assets
owned by an institutional unit or sector less the value of all its
outstanding liabilities; it is a measure of the wealth of a unit or sector at
a point in time.
3.68 and 10.1
[13.10, 13.82]
Non-produced assets
Non-produced assets are non-financial assets that come into existence
other than through processes of production.
(AN.2) - Annex to
chapter XIII, 10.6
[10.8, 13.17]
Non-residential buildings
Non-residential buildings are buildings other than dwellings, including
fixtures, facilities and equipment that are integral parts of the structures
and costs of site clearance and preparation.
(AN.11121) - Annex
to chapter XIII
Other buildings and
structures
Other buildings and structures consist of non-residential buildings and
other structures, such as civil engineering works.
(AN.1112) - Annex
to chapter XIII
Other changes in the
volume of assets account
The other changes in the volume of assets account records the changes
in assets, liabilities, and net worth between opening and closing balance
sheets that are due neither to transactions between institutional units, as
recorded in the capital and financial accounts, nor to holding gains and
losses.
Other intangible fixed assets are new information, specialised
knowledge, etc, not elsewhere classified, whose use in production is
restricted to the units that have established ownership rights over them
or to other units licensed by the latter.
Other machinery and equipment consist of machinery and equipment
not elsewhere classified.
12.4
[1.9, 3.58 - 3.61]
Other intangible fixed
assets
Other machinery and
equipment
Other structures
Other structures consist of structures other than buildings, including the
cost of the streets, sewers and site clearance and preparation other than
for residential or non-residential buildings.
Perpetual inventory
method (PIM)
The perpetual inventory method (PIM) requires an estimate to be made
of the stock of fixed assets in existence and in the hands of producers;
this is done by estimating how many of the fixed assets installed as a
result of gross fixed capital formation undertaken in previous years have
survived to the current period.
Produced assets are non-financial assets that have come into existence
as outputs from processes that fall within the production boundary of the
SNA.
Straight-line depreciation is a depreciation profile based on a constant
annual amount of capital consumption over the life of the asset.
Produced assets
Straight-line depreciation
Tangible fixed assets
Tangible fixed assets are non-financial produced assets that consist of
dwellings; other buildings and structures; machinery and equipment and
cultivated assets.
77
(AN.1129) - Annex
to chapter XIII
(AN.11132) - Annex
to chapter XIII
(AN.11122) - Annex
to chapter XIII
6.189
10.6
[13.14, (AN.1) - Annex
to chapter XIII]
6.193
(AN.111) - Annex
to chapter XIII
Transport equipment
Transport equipment consists of equipment for moving people and
objects.
Written-down (net) value
of a fixed asset
The written-down (net) value of a fixed asset is the actual or estimated
current purchaser’s price of a new asset of the same type less the
cumulative value of the consumption of fixed capital accrued up to that
point in time.
(AN.11131) - Annex
to chapter XIII
6.199
Part 2. Terms not used in the SNA but commonly found in the literature on capital stock and
related flows.
Age-price profile--a schedule showing the decline (normally) in the value of an existing capital good
as it ages. In principle, the age-price profile might look like a used-car price book, if no quality change
occurred in automobiles. A 1997 price book, for example, might contain prices for 1996, 1995, 1994,
and so forth model cars. From such a schedule, an owner of a fleet of vehicles of a variety of ages
could calculate the current value of the fleet by looking up each vehicle and valuing it according to the
age-price profile.
Capital services--the productive input, per period, that flows to production from a capital good. If two
or more types (or ages) of capital asset are aggregated, the capital service measure is also an
aggregation, combining services provided by the separate kinds of assets. Capital service is the
appropriate measure of capital input for estimates of multi-factor productivity (MFP) measurement.
Capital service price-- the unit cost for the use of a capital good for one period--that is, the price for
employing or obtaining one unit of capital services. The service price is also referred to as the "rental
price" of a capital good, or the “user cost of capital”.
Capital used up in production--the loss of capital services, over all the remaining periods of the
capital good’s lifetime, from the combined influences of output decay, input decay and exhaustion that
occurs when the capital good is employed in the current period. This concept arises out of the
historical concern in the national accounts literature with defining situations where capital is kept
“intact” in the Hicksian sense. If capital used up in production is just replaced by new investment,
then the capital stock is maintained intact, in the sense that it will be consistent with long-run
sustainability of the current consumption or income flow.
Decay--the decline in capital services yielded by an individual capital good as it ages. A light bulb that
lasts for 10 periods with no loss in brightness or increases in energy consumption is an example of
zero decay. Most capital goods, however, lose productiveness as they age, and so exhibit some form of
decay. The concept is also termed “efficiency decline”, “efficiency decay,” or “loss of efficiency” in
the literature. Decay can be decomposed into “input decay” and “output decay”. (See below)
Deterioration--the loss in potential capital services from the combination of “output decay”, “input
decay” and “retirements” for a group of assets, from one period to the next. When deterioration is just
offset by new investment, the current-period productiveness of the capital stock remains intact in the
following period, in the sense that it yields an unchanged volume of capital services. Note that
deterioration is usually defined with respect to a single period (that is, one period to the next), or as a
rate of decline per unit of time.
Discards--synonym for “retirements”.
Efficiency decline--synonym for “decay”
78
Exhaustion--the capital services lost because of decline in the life expectancy of an asset. Each
period’s use of an asset shortens its remaining service lifetime. This physical capital concept appears
somewhat less frequently in the capital literature. Consider a group of light bulbs, all purchased in one
period. Suppose the light bulbs exhibit no decay, last for 10 periods, and all expire at the same
moment. After one period, no decline in productive services is experienced, but the asset owner now
has a stock of bulbs with 9 periods of use remaining, instead of a stock of 10-periods’ use.
Input decay--input decay occurs when an asset requires increased usage of other inputs as it ages. A
car, for example, might use more oil as it gets older, though everything else about its performance
remains "good as new." An older machine tool may need more maintenance and repair, which implies
that more labor must be used with it to obtain the same output.
Lemons--the idea that, owing to asymmetric information among buyers and sellers, used capital goods
prices estimated from resale markets understate the value of similar capital goods that do not change
hands. This might occur because the defective capital goods are more likely to appear on resale
markets, or because buyers think or fear this is so and lack the information to determine whether the
used capital good is a “lemon.”
Obsolescence--loss in value on an old asset because a newly introduced asset of the same class
contains improvements in productiveness or efficiency or suitability in production.
Obsolescence in an old capital good is closely linked to quality change in newer capital goods of the
same class, though there are some types of obsolescence that are not properly associated with technical
improvements in new goods. Suppose one found a new, unsold 1980 vintage computer, overlooked for
nearly 20 years in some corner of a warehouse. The 1980 computer experienced neither decay nor (by
definition) exhaustion. Because of the rapid pace of technological change in computers, the 1980-era
computer (state of the art in its day) is substantially inferior to a computer of the present vintage, and
so the 1980 computer would likely sell at a substantial discount relative to a 1998-vintage computer
(we ignore the possibility of curiosity or antique value that affects some obsolete goods).
Obsolescence affects only the value of a capital good: It does not affect the physical services provided
by the capital good.
"One hoss shay"--a colorful term, taken from the once famous poem, "The Deacon's Masterpiece,"
by Oliver Wendell Holmes (both the second and third words are rendered in nineteenth century
American dialect), to designate a capital good that exhibits neither input decay nor output decay
during its lifetime. In economic literature, the one hoss shay asset is usually taken as a polar case in
empirical analysis, or sometimes is introduced as a simplifying assumption in theoretical work.
Output decay--the decline in services rendered by the capital good as it ages. Suppose, for example,
one measures the services of a light bulb in terms of its brightness, perhaps in "lumens per period," or
a truck (lorry) in terms of “ton miles of hauling capacity per period.”
Output decay is the decline in lumens per period as the light bulb ages, or in ton-miles as the truck
ages.
Productive capital stock--This concept is best defined by an example. Consider a cohort of new
capital goods, not all of which necessarily survive to the subsequent period. After one period’s use,
their productiveness will have declined by one period’s deterioration (input and output decay and
retirements. The productive capital stock thus consists of all the capital goods that exist, each one
reduced by the proportionate deterioration that has occurred since it was new.
79
Retirements--also known in the literature as "discards" or "scrapping." All of these terms designate
assets withdrawn from service. Note that retirements, discards and scrapping are not synonymous
with “disposals”; this latter term includes sales of assets to other producers for continued use in
production.
Scrapping – synonym for “retirements”.
User cost of capital--a synonym for the capital service price.
Wealth capital stock—This is synonym for the “net capital stock”. The term is widely used in North
America. Elsewhere the SNA term “net capital stock” seems to be preferred.
80
Annex 3. Service lives of assets used in four countries
The service lives shown for these four countries – United States, Canada, Czech Republic and the
Netherlands – appear to be based on information that is generally more reliable than is usually
available in other countries.
81
United States
The table on the following page shows the service lives and “declining balance rates” used by the
US Bureau of Economic Analysis for its capital stock estimates. This rate is set at 2 for the commonly
used method of geometric depreciation known as “double declining” balance. See Chapter 5 for
further explanation.
82
Part (a) Private nonresidential
equipment and structures
Service Declininglife
balance
(years)
rates
Private nonresidential equipment
Office, computing, and accounting
machinery (1):
Years before 1978
Construction machinery, except
tractors
Mining and oil field machinery
Service
life
(years)
Decliningbalance
rates
10
1.5498
11
1.6500
8
2.1832
Service industry machinery:
7
2.1832
Wholesale and retail trade
10
1.6500
Other industries
11
1.6500
Business services
11
1.6500
Household appliances
10
1.6500
Other industries
15
1.6500
Other electrical equipment
9
1.6500
Instruments
12
1.6203
Other
11
1.6230
Photocopy and related equipment
9
1.6203
Private
nonresidential
structures
Industrial buildings
1978 and later years
Communications equipment:
Nuclear fuel (2)
4
..
31
0.9747
Other fabricated metal products
18
1.6500
Mobiles offices
16
0.8892
Steam engines and turbines
32
1.6500
Office buildings
36
0.8892
Internal combustion engines
8
1.6500
Commercial warehouses
40
0.8892
Metalworking machinery (3)
16
1.9600
Other commercial buildings
34
0.8892
Special industrial machinery, n.e.c
16
1.6500
Religious buildings
48
0.9024
General industrial, including materials
handling equipment
Electrical transmission, distribution,
and industrial apparatus
Trucks, buses, and truck trailers:
16
1.7150
Educational buildings
48
0.9024
33
1.6500
Hospital and institutional buildings
48
0.9024
Hotels and motels
32
0.8990
Local and interurban passenger
transit
Trucking and warehousing; and auto
repair, services, and parking
Other industries
14
1.7252
30
0.8990
10
1.7252
Amusement
and
recreational
buildings
All other nonfarm buildings
38
0.9480
9
1.7252
Railroad replacement track
38
0.9480
Autos (4)
..
..
Other railroad structures
54
0.9480
Aircraft:
Telecommunications
40
0.9480
Transportation by air,
Depository institutions, and business
services
Years before 1960
Electric light and power
16
1.6500
Years before 1946
40
0.9480
20
1.6500
1946 and over
45
0.9480
Gas
40
0.9480
Years before 1960
12
1.6500
Petroleum pipelines
40
0.9480
1960 and later years
38
0.9100
Years before 1973
16
0.9008
1973 and later years
12
0.9008
20
0.9008
1960 and later years
Other industries
15
1.6500
Farm
Ships and boats
27
1.6500
Railroad equipment
28
1.6500
Mining exploration, shafts, and
wells:
Petroleum and natural gas:
Household furniture and fixtures
12
1.6500
Other furniture
14
1.6500
Farm tractors
9
1.3064
Construction tractors
8
1.3064
Local transit
38
0.8990
Agricultural machinery, except tractors
14
1.6500
Other
40
0.8990
Other
83
Part (b) Government nonresidential
equipment
Service
life
(years)
Decliningbalance
rates
Federal:
Service
life
(years)
Decliningbalance
rates
..
..
7
1.6500
10
1.6500
Electronic equipment:
National defense:
Computers and peripheral
equipment (7)
Electronic countermeasures
Aircraft:
Airframes:
Other
Bombers
25
1.6500
F-14 type
19
1.6500
Medical
9
1.6500
Attack, F-15 and F-16 types
20
1.6500
Construction
10
1.5498
F-18 type
15
1.6500
Industrial
18
1.6500
Electronic warfare
23
1.6500
Ammunition plant
19
1.6500
Cargo and trainers
25
1.6500
Atomic energy
12
1.6500
Helicopters
20
1.6500
Weapons and fire control
12
1.6500
6
1.6500
General
10
1.6500
Other
12
1.6500
Years before 1982
14
1.6500
Nondefense:
1982 and later years
10
1.6500
Engines
Other:
Missiles: (5)
Other equipment:
General government:
Strategic
20
..
Computers and peripheral
equipment (7)
Aerospace equipment
..
..
15
1.6500
Tactical
15
..
Vehicles
5
2.2664
Torpedoes
15
..
Others
10
1.6500
Fire control equipment
10
..
Space programs
20
..
..
..
7
2.2664
15
1.6500
33
1.6500
33
1.6500
25
1.6500
Enterprises:
U.S. Postal Service:
Ships:
Surface ships
30
1.6500
Computers and peripheral
equipment (7)
Vehicles
Submarines
25
1.6500
Other
Government furnished equipment:
Tennessee Valley Power
Authority
Bonneville Power Authority
Electrical
9
1.6500
Propulsion
20
1.6500
Hull, mechanical
25
1.6500
Ordnance
10
1.6500
Other
10
1.6500
Power tools, lawn and garden
equipment
Miscellaneous metal products
10
1.6500
18
1.6500
20
1.6500
Agricultural machinery and
equipment
Construction machinery and
equipment
Metalworking machinery and
equipment
General purpose machinery and
equipment
Special industry machinery and
equipment
Integrating and measuring
instruments
9
1.6500
10
1.6500
16
1.6500
11
1.6500
11
1.6500
12
1.6500
Vehicles:
Tanks, armored personnel carriers,
and other combat vehicles
Noncombat vehicles:
Trucks
6
1.7252
Autos (6)
..
..
Other
7
1.7252
84
Other
State and local:
Service
life
(years)
Part (b) (continued) Government nonresidential
equipment
Motors, generators, motor generator
32
sets
Switchgear and switchboard equipment
33
Decliningbalance
rates
Service
life
(years)
Decliningbalance
rates
Household appliances
11
1.6500
1.6500
Home electronic equipment
11
1.6500
1.6500
Motor vehicles
10
1.6500
Electronic components and
accessories
Miscellaneous electrical machinery
9
1.6500
Motorcycles
10
1.6500
12
1.6500
Aircraft
15
1.6500
Calculating and accounting machines
7
1.6500
Railroad equipment
28
1.6500
Typewriters
7
1.6500
Sporting and athletic goods
10
1.6500
..
..
10
1.6500
10
1.6500
Computers and peripheral equipment
(7)
Machine shop products
8
1.6500
Wood commercial furniture
14
1.6500
Metal commercial furniture
14
1.6500
Part (c) Government nonresidential
structures
Federal, State and Local:
Photographic and photocopying
equipment
Mobile classrooms, mobile
offices, etc.
Musical instruments
9
1.6500
12
1.6500
Highways and streets
60
0.9100
60
0.9100
60
0.9100
Other equipment
Nonbuildings:
National defense:
Buildings:
Industrial
32
0.9100
Conservation and
development
Sewer systems
Educational
50
0.9100
Water systems
60
0.9100
Hospital
50
0.9100
Other
60
0.9100
Other
50
0.9100
80
0.9100
Mobile homes
20
0.9100
1-to-4-unit structures-additions and
alterations
1-to-4-unit structures-major replacements
40
0.9100
Other structures
40
0.9100
25
0.9100
Equipment
11
1.6500
5-or-more-unit structures-new
65
0.9100
5-or-more-unit structures-additions and
alterations
5-or-more-unit structures-major
replacements
32
0.9100
20
0.9100
Part (d) Residential capital (private
and government)
1-to-4-unit structures-new
(1 ) Depreciation rates for these assets are taken from Oliner. See The Measurement of Depreciation in the U.S. National
Income and Product Accounts, Barbara M. Fraumeni, Survey of Current Business, BEA, July 1997.
(2) The depreciation rates for nuclear fuel are based on a straight-line rate pattern and a Winfrey
retirement pattern.
(3) The service life listed is the average for nonmanufacturing industries; the service lives used for manufacturing
industries differ by industry.
(4) The depreciation rates for autos are derived from data on new and used auto prices.
(5) Depreciation rates for missiles are based on straight-line patterns of depreciation and Winfrey
retirement patterns.
(6) Depreciation rates for government-owned autos are derived from data on autos that are privately
owned.
(7) Depreciation rates for these assets are taken from Oliner. See The Measurement of Depreciation in the U.S. National
Income and Product Accounts, Barbara M. Fraumeni, Survey of Current Business, BEA, July 1997.
85
Canada
This table shows the service lives used by Statistics Canada. The lives for the recent period are based
on information regularly supplied by enterprises on the service lives of discarded assets. The lives for
the earlier period were based on a number of less reliable sources. The declines in service lives over
the period are based on assumption rather than observation.
Building construction
Engineering construction
Machinery and equipment
1961-65
1961-65
1991-94
1961-65
Activity/Sector
1991-94
1991-94
Agriculture, forestry and fishing
Agriculture and related services
29
24
29
24
10
8
Fishing and trapping
25
25
25
25
12
11
Logging and forestry
19
19
17
12
9
8
Mining (metal, non-netal, coal, petroleum)
20
17
20
15
12
9
Quarry, sand-pit and service industries
28
35
20
15
12
8
food and beverages
35
30
33
27
16
11
tobacco
35
30
31
24
12
11
rubber products
38
33
27
20
12
11
plastic products
37
32
28
21
13
12
leather
39
34
28
21
12
11
Mining and quarrying
Manufacturing:
textiles
34
29
35
29
14
9
clothing
29
28
35
29
14
10
wood
25
22
20
14
15
12
furniture and fixtures
37
37
paper and allied products
31
25
31
primary metal industries
36
35
fabricated metal products
33
28
machinery industries
34
transport equipment
13
8
24
19
18
32
26
18
17
32
26
13
10
29
33
28
11
8
33
30
32
27
14
9
electrical and electronic products
31
28
27
21
12
8
non-metal mineral products
26
22
27
22
16
13
Refined petroleum and coal
products
chemicals and chemical products
26
21
26
20
18
16
33
27
24
17
16
13
other manufacturing industries
34
34
23
18
10
9
25
25
30
30
10
10
Construction industries
86
Building construction
Engineering construction
Machinery and equipment
1961-65
1961-65
1991-94
1961-65
1991-94
Activity/Sector
1991-94
Transport and storage
Air transport and related services
31
28
43
40
16
16
Rail transport and related services
38
33
53
52
21
18
Water transport and related services
36
31
40
37
23
18
Truck transport
39
33
45
39
9
8
Public passenger transit systems
37
32
32
26
11
10
Other transport and related systems
39
33
45
39
9
8
Pipeline transport
35
30
35
30
14
14
Grain elevator industry
36
28
..
..
19
15
Other storage and warehousing
38
33
..
..
12
7
Broadcasting industries
37
32
18
13
11
9
Telecommunication carriers
39
35
37
31
17
14
Postal and courrier services
42
38
45
39
8
6
Electric power and gas distribution
49
48
49
47
32
31
Water systems
31
25
54
49
12
7
Wholesale trade and retail trade
33
27
25
18
11
8
Finance, insurance, real estate and
business services
Deposit accepting intermediary industries
45
43
..
..
19
7
Consumer and business financing
43
40
..
..
8
6
Insurance industry
45
43
..
..
10
7
Real estate and insurance agents
45
43
..
..
10
7
Business service industries
42
39
..
..
8
6
Government service industries
39
35
39
33
12
9
Federal government
39
35
39
34
12
9
Provincial and territorial
39
34
39
33
11
8
Local government
39
35
39
33
13
10
Elementary and secondary
44
42
..
..
13
10
Post secondary, non-university
44
42
..
..
13
10
University
53
53
..
..
13
10
Museums and archives
42
39
..
..
8
6
Hospitals
45
43
..
..
13
11
Other health and social services
43
40
..
..
16
14
Communications
Electricity, gas and water
Education and museums
Health and social services
87
Building construction
Engineering construction
Machinery and equipment
1961-65
1961-65
1961-65
Activity/Sector
1991-94
1991-94
1991-94
Accommodation, food and beverage
services
Accommodation services
42
39
..
..
8
6
Food and beverage services
42
39
..
..
8
6
Other
52
42
..
..
9
6
Amusement and recreation services
42
39
..
..
8
6
Membership organization industries
56
51
..
..
19
16
88
Czech Republic
These service lives are based on an annual survey of ages of assets when discarded.
Transport
Equipment
Activity
Other Machinery
and Equipment
of which
Computers
Agriculture
Forestry
Mining – coal
– other
Manufacturing
-
Food, beverages, tabacco
Textiles and clothing
Wooden products, paper and
pulp
Chemicals, rubber and plastic
Metal products, including
vehicles, office machinery, etc,
Electricity, gas, water
Construction
Sale and repair of motor vehicles
Wholesale and retail trade
Hotels and restaurants
Air Transport
Post and telecommunications
Financial and insurance services
Public administration and defence
Education
Health and welfare services
13
12
19
13
15
13
15
16
9
6
9
8
13
16
7
11
15
18
16
10
10
14
18
9
11
12
11
11
9
7
13
11
...
13
13
12
18
18
15
15
12
11
14
16
9
15
15
15
11
11
9
9
8
7
11
16
7
7
12
8
89
Netherlands
These service lives, used in the Netherlands, are “best source” estimates. For mining and
manufacturing they are mainly based on a survey of discards and on other indirect sources for other
assets.
dwellings
Buildings
other
construction
external
transport
machinery
computers
other
assets
Agriculture/forestry
45
35
12
15
5
10
Fishing
50
35
25
15
5
10
Mining and quarrying
40
35
10
20
12
25
Food and beverages
43
35
10
28
13
27
Textile/leather
47
35
10
28
15
40
Paper/paper products
55
35
10
29
10
36
Petroleum + products
46
35
10
37
10
38
Chemical industry
39
35
10
32
13
38
Basic metal + products
47
35
10
49
16
19
Other manufacturing
47
35
10
32
12
34
Publ. Utilities
47
35
10
32
12
34
Construction
47
35
10
20
12
34
Trade
60
35
8
15
5
10
Hotel restaurants etc.
60
35
8
15
5
10
Water
60
35
25
15
5
10
Air
60
35
25
15
5
10
Rail
60
35
25
15
5
10
Other
60
35
10
15
5
10
Banking and insurance
60
35
8
15
5
10
60
35
8
15
5
10
Rented buildings
60
35
8
15
5
10
Commercial services
60
35
8
15
5
10
Government
60
35
8
15
5
10
Health care
60
35
8
15
5
10
Transport
Rented dwellings
75
90
Annex 4. Questionnaire forms used by New Zealand and the Netherlands
These four PDF files comprise four pages (Page 1, Page 2, Page 3, Page 4) of a questionnaire used by
the Department of Statistics, New Zealand for measuring the ages of assets at time of discard.
The following three PDF files contain forms and questionnaires used by interviewers from Statistics
Netherlands :
The first form is used to collect information on the stock of company's assets ;
The second PDF file comprises a questionnaire used by Statistics Netherlands for its survey
of asset discards ; and
The third file contains a survey of capital investment.
Annex 5. Graph Showing Impact of Different Service Lives and Interest Rates on Asset Values
Implied by Five Capital Service Value Profiles. (Service Lives 15 and 50 Years; Interest rate 5%
and 10%)
This PDF file contains 20 graphs that illustrate the impact of 15 and 50 year service lives and interest
rates (at five and ten per cent) on asset values implied by five capital service value profiles: constant
service value, a service value fall by 10 per cent per year, a service value fall by five units per year,
hyperbolic fall of service value, and a constant then falling two step income.
Annex 6. Asset prices and depreciation implied by four capital service value profiles.
The attached PDF file contains capital service value, asset value and depreciation for four capital
service value profiles: capital service values fall by ten per cent each year; capital service fall by five
units per year, capital service fall hyperbolically (b = 0.5) and two step fall in capital service values
(constant then linear decline).
91