COST OF CAPITAL SERVICES IN THE PRODUCTION ACCOUNT
Erwin Diewert
Anne Harrison
Paul Schreyer
Draft 20-August 2004
1. Introduction
1.
At its meetings in October 2003 and April 2004, the Canberra Group discussed a paper
by Ahmad (2004), proposing the introduction of capital services measures into the SNA
production account. While the Group expressed a favourable view to this proposal, and agreed
that identifying capital services was useful from a national accounts perspective, it was also found
that specific advice as to the calculation of capital services measures was still missing, in current
and in constant prices. Furthermore, several other topics have been tackled by the Canberra
Group which cannot be seen in isolation from the treatment of capital services. These are the
question of depreciation and obsolescence, the treatment of public assets and the capitalisation of
R&D. The purpose of the present paper is to present a method of computing capital services that
is consistent with other decisions that have been/will be made by the Group and to provide
practical guidance for future implementation.
2.
At the present stage, this document draws up the issues that need settling and proposes
one or two strategic decisions without, however, working out every methodological detail. This
will be done in a future version of the document. To provide an indication about the quantitative
importance of one of the strategic issues – the choice of the rate of return - simulation results for
Canada are also provided in this paper. Again, a future version of the document will incorporate
results for other OECD economies.
3.
The proposals made in this paper imply no radical changes to the presentation of the
accounts or to the general meaning given to any of its aggregates; such as net operating surplus.
This prudence reflects the fact that the development and understanding of statistics in this area is
still relatively new; and the fact that the valuation of concepts, such as capital services, are, to
some extent, dependent on assumptions about the way the economy works. Generally, the
1
introduction of capital services into the accounts does not change the value of the aggregates as
capital services enter as ‘of which’ items. Only to the extent that a consistent framework that links
capital services, capital stocks, depreciation and balance sheets leads to modifications in the
existing practice of countries’ calculation procedures, may there be an effect on major aggregates
such as GDP or NDP.
One specific item, however, may change GDP and NDP estimates: the
introduction of cost of capital services for public assets. For further reference, see Harrison
(2004).
2. A brief reminder: what are capital services?
4.
In a production process, labour, capital and intermediate inputs are combined to
produce output. Conceptually, there are many facets of capital input that bear a direct analogy to
labour input. Capital goods are seen as carriers of capital services that constitute the actual input
in the production process. For purposes of productivity and production analysis, then, capital
services constitute the appropriate measure of capital input. At present, however, the national
accounts provide no measure of the value, price or volume of capital services.
5.
Consumption of fixed capital is sometimes thought of as reflecting the full benefits or
costs of using fixed assets. That this is a misconception1 can easily be shown by taking the case
where fixed assets are not owned by a firm but rented from another unit who owns the capital
good. The owner’s price charged for the rental will comprise depreciation (consumption of fixed
capital), a return reflecting either financing costs or the opportunity cost of holding capital and
there may be an item reflecting changes in the market price of the asset (when an asset loses
value quickly, this has to be factored into the rental).
6.
If all fixed assets were leased on the market, rental values would be directly observable
and national accountants could turn to this data to estimate the cost of capital services. In
practice, many fixed assets are owned by their users and no rental transactions can be observed.
To estimate the costs of capital services to owner-users, an imputation has to be made that brings
together the various elements of rentals as described above. As often, imputing unobserved
values raises conceptual and empirical issues and one objective of the present document is to
provide guidance on the choice of these elements.
7.
The idea that the production account does not explicitly identify the total values of
capital services from fixed assets but instead records them within value-added or operating
1
.
For a fuller discussion see Triplett (1996).
2
surplus is not, of course, new. The impetus to separately identify these capital services now
however, largely reflects the increased interest in growth accounting and productivity analysis
(OECD (2001), Harper et al (2003), Jorgenson and Landefeld (2004)).
Recommendation 1: the Group confirms its general support for introducing
measures of the cost of capital services into the national accounts. This
introduction should not change the basic structure of the accounts.
3. Components of the cost of capital services and their computation
General
8.
When rentals and the cost of capital services cannot be observed directly, its various
components have to be added up to approximate the costs of capital services. We use Diewert’s
(2001) notation and specify for a single asset the value of capital services per unit of fixed asset or
the user costs of an asset in period t. This discrete formulation is due to Christensen and
Jorgenson (1969):
(1) u nt  r t Pnt  Pnt  Pnt 11
9.
In (1), Pnt is the market price of an n-year old asset in period t and r t is the rate of return
that the owner-user expects from the asset in production, so that r t Pnt is the monetary return to
using the asset in period t. Pnt  Pnt 11 is the change in the value of the asset between the two
periods: it brings together two effects: the change in value due to ageing (the capital good is n+1
years old in the next period) and the change in the market price of the asset for a given age.
Whether the entire expression or only that part that relates to ageing is called depreciation or
consumption of fixed capital has been a matter of discussion and is debated further in Ahmad,
Aspden and Schreyer (2004). For the purpose at hand, the distinction is of secondary
importance.
10.
The user cost term is also the price per unit of capital service. Because it is common to
assume that the flow of capital services is a fixed proportion of the stock of assets, the total value
of capital services for a particular type of asset is obtained by multiplying the user cost terms for
n-year old assets by the stock of n-year old assets of a particular type. The stock of n-year old
assets corresponds to the quantity of new investment n years ago ( I t n ) and therefore:
(2) Cost of capital services for n-year old assets = u nt I t n
3
11.
Only brief mention is made here of aggregation across capital goods of different age. In
practice, statistical offices use the perpetual inventory method to construct a capital stock by
aggregating past investments. For this purpose, the latter have to be expressed in equivalent units
of new investment goods so that the overall stock of a particular type of asset is expressed in ‘new
equivalent units’. Then, user costs for new assets are applied to this stock to yield the overall cost
of capital services for a particular asset. For a discussion of aggregation issues in this context, see
Diewert (2001), Diewert and Lawrence (2000), Hulten (1990), and Annex C of this document.
Depreciation and expected asset price changes
12.
For the discussion about measuring the components needed to impute user costs, we
start by taking a look at the combined depreciation/asset price component Pnt  Pnt 11 . An
important point is that this term contains an element of price change over time ( Pnt 1  Pnt 11 or
Pnt  Pnt 1 ) and the question arises how such a price change should be measured empirically.
Moreover, this price change is an expected one, projecting the asset price movement to the next
period.
13.
Take the conceptual issue first: the System of National Accounts is based on ex-post
prices, observed in the context of actual transactions. Would the use of expected price changes
that govern user cost imputations be in contradiction with the principles of national accounts?
14.
In our view, the answer is ‘no’. Note that the presence of expectations does not make the
user cost term less ‘real’: transactions are concluded at this price, and economic decisions are
made at this price, even if with hindsight (ex post) the expectations underlying it may turn out to
be wrong. This is most apparent when one thinks of a case where capital goods are actually
rented: the observed rental price characterises the transaction and is the relevant market price,
typically dependent on expectations on the side of the lessor and the lessee. Nobody would
challenge using such observed prices in the national accounts. If rental prices are not observable,
values have to be imputed, and the expression above indicates how this can be done on the basis
of economic theory. Imputations are numerous in the national accounts, and in this sense, the
imputation of user costs would not constitute an exception. In other words, the introduction of
expected price changes does not imply a shift towards an ex-ante accounting framework.
15.
Once the principle of introducing expected price changes into the imputed measure is
accepted, the question remains how to actually go about measuring them. The economic
literature frequently makes an assumption of perfect foresight, assuming that the observed price
4
changes are exactly equal to expected price changes. Apart from the fact that this is a strong
assumption, this method is not feasible for statistical offices that have to produce data for the
current period and simply do not yet have information about price levels in the next period. Thus,
national accountants will have to use some simple mechanism to model expected price changes at
any given point in time. More details will be provided on specific options for projecting price
changes (Annex A).
Return to capital – exogenous and endogenous rates
16.
A key element in the approximation of the cost of capital services is the choice of the rate
of return. The issue was first evoked by Diewert2 (1980) and then more extensively examined by
Harper, Berndt and Wood (1989) have been followed in the economics literature. There are two
broad options:
17.

Use of an endogenous (internal) rate of return.

Use of an exogenous (external) rate of return.
Consider the endogenous option first. Frequently used in empirical research, it assumes
that gross operating surplus as measured in the national accounts exactly exhausts the costs of
capital services.
Given the value for gross operating surplus, for the capital stock and
depreciation, there is only one unknown variable, the rate of return and the equation can be
solved to yield an endogenous measure of the rate of return.
18.
This procedure brings with it several advantages: from a theoretical perspective, it is
consistent with a fully competitive economy and production processes under constant returns to
scale. From a practical viewpoint, computation is straightforward, and results can be of analytical
interest in themselves. For example, it would be interesting to compare internal rates of return
between industries or between countries. Finally, the fact that the costs of capital services exactly
exhaust gross operating surplus avoids interpreting any difference term between the value of
capital services and gross operating surplus that may show up otherwise. At the same time, the
choice of an endogenous rate raises a number of other questions.
2
.
“Which r should be used? If the firm is a net borrower, then r should be the marginal cost of
borrowing an additional dollar for one period, while if the firm is a net lender, then r should be
the one period interest rate it receives on its last loan. In practice, r is taken to be either (a) an
exogenous bond rate that may or may not apply to the firm under consideration, or (b) an
internal rate of return. I tend to use the first alternative, while Woodland and Jorgenson and his
co-workers use the second. As usual, neither alternative appears to be correct from a theoretical a
priori point of view, so, again, reasonable analysts could differ on which r to use in order to
construct a capital aggregate.” Diewert (1980; 476-477).
5
19.
First, the economic assumptions that are needed to justify the use of an internal rate are
stringent and it is not obvious that they hold empirically:

The set of assets has to be complete in the sense that all assets are observed by the
statistician who compiles the national accounts. This is far from obvious. The national
accounts provide no indication as to exactly which factor of production is remunerated
through gross operating surplus. Fixed assets are certainly among them but they are not
necessarily the only ones. The business literature offers a wealth of discussions about the
importance of intangible assets, and there are good reasons to argue that such assets
account at least for part of gross operating surplus. If an endogenous rate is computed
on the basis of those fixed assets that are measured in the accounts, but if there are
other, unmeasured assets that provide capital services, the resulting rate is liable to bias.

Perfect foresight has to prevail so that the ex-post rate of return on each asset (implicitly
observed by the national accountant as part of GOS) equals its ex-ante rate return, the
economically relevant part in the user costs of capital services.

There has to be absence of residual profits (or losses) that may arise in the presence of
market power, under non-constant returns to scale or with publicly available capital
assets.
20.
Second, the endogenous method is inapplicable when it comes to those institutional
units for which the national accounts do not generate an independent measure of gross operating
surplus, notably non-market producers.
21.
Third, the endogenous method is dependent on the estimated values of current-price
output or GDP and any errors present in these statistics, in particular at the industry and sector
level, affect the resulting rate of return.
22.
Next, turn to the option of selecting an exogenous rate of return. Its key advantages are
(i) that it does not rely on as restrictive a set of assumption as the endogenous method. Schreyer
(2004) has shown that exogenous rates are compatible with occurrences of non-observed assets,
imperfect competition and non-constant returns to scale; (ii) that it can deal with government
units for which there is no information on gross operating surplus; (iii) that it avoids importing
errors from output data. But there are some additional advantages.
6
23.
The first one is that the exogenous method permits modelling the rate as an expected or
required rate. There is thus no assumption of perfect foresight and this helps to deal with the
question of expectations: the level of capital services is what the entrepreneur expects when
making decisions about the use of assets in production. If the costs of capital services turn out to
be less than gross operating surplus, the entrepreneur has made some pure profit or some of the
gross operating surplus pertains to non-measured assets. Further, when the exogenous rate is an
expected rate, it reflects the conditions (in particular the implicit rental prices) that producers are
facing when deciding about production and investment. Also, from a purely practical perspective,
if there are implausibly large differences between the estimated cost of capital services and gross
operating surplus or if the latter is persistently lower than the former, this may be an indication
of data problems in the accounts and provide useful insights to statisticians. For example,
Diewert and Lawrence, in a recent paper, used industry-level data for Australia and found a
number of implausible results for industry-level endogenous rates of return. This may reflect
data issues rather than economic reality.
24.
The second additional advantage of an exogenous rate is that it may provide a handle to
advance on splitting mixed income between income to labour and income to capital. In principle,
if there are independent estimates for the cost of capital services of those institutional units
whose income is mixed, it is possible to sort out the share of labour and capital remuneration.
Such information could be compared against plausible estimates of the labour income of selfemployed. Obtaining the empirical information on capital stocks and capital services by
institutional unit may be difficult but at least there is a possibility of advancing on the analysis of
mixed income.
25.
There are related topics for which exogenous rates are advantageous. For example, in the
context of R&D capitalisation, Pitzer (2004) Diewert (2004) have suggested a cost matching
methodology, which cannot be implemented without using an exogenous rate of return. Along the
same vein, if one wanted to distinguish “non-productive” inventories from “productive” ones,
then accounting for the non-productive inventories will involve Pitzer’s (2004) and Diewert’s
(2004) cost matching and again, it would essential to have an exogenous rate available to do this
shifting.
26.
There are also several disadvantages to the exogenous model. First, and foremost, a
choice has to be made as to exactly which rate should be chosen – options are manifold with
potentially important impacts on results, as shown by the simulations in Annex B. A more
extensive conceptual discussion is needed here to select an appropriate rate of return. There is
7
also a question whether the rate should be allowed to vary between industries or sectors, and if
so, to which statistical source the national accountant should turn for this purpose.
27.
Second, there may be occurrences of economically meaningless negative user cost.
However, as explained by Harper, Berndt and Wood (1989) negative rental prices tend to occur
when ex-ante exogenous rates of return are combined with ex-post rates of asset price change. It
is thus important that the different components of the user cost term be treated consistently
either as ex-ante or as ex-post variables.
28.
Overall, though, it would appear that the advantages of using an exogenous, expected
rate of return would outweigh the disadvantages and this leads to
Recommendation 2:
It is recommended that user cost imputations in the
national accounts are based on exogenous rates of return. Further guidance has
to be provided on the computation of the appropriate rate, with particular regard
to how industry- and sector specific rates should be computed.
4. Capital services, depreciation and net capital stocks – a consistent entity
29.
Whereas the introduction of costs of capital services into the accounts is of interest in
itself, they should also be internally consistent with measures of the net capital stock so that the
volume and price measures of capital services, depreciation and net income aggregates in the
national accounts as well as balance sheets form a coherent entity. This will also allow
researchers and statistical offices to produce consistent indicators of multi-factor productivity
(see OECD (2001)) which are of significant analytical interest.
30.
An important statement of this interest in setting up integrated system of accounts,
capital measures and productivity has recently been for formulated for the United States.
Jorgenson and Landefeld (2004) outlined a “Blueprint for Expanded and Integrated U.S.
Accounts” where they state as their ‘first and foremost objective to make the NIPAs consistent
with the accounts for productivity compiled by the Bureau of Labor Statistics and the flow of
funds accounts constructed by the Federal Reserve Board. The boundaries of production,
income and expenditures, accumulation and wealth accounts must be identical throughout the
system in order to achieve consistency’. Similar statements may well be true for other countries.
Annex C will set out a description of such an integrated framework.
8
Recommendation 3:
cost of capital services measures should not be
introduced into the national accounts in an isolated manner. This introduction is
the opportunity for statistical offices to create a consistent and transparent set of
capital-related data that serves both the analysis of income and wealth (via NDP
and balance sheets) and the analysis of production and productivity (via prices
and quantities of capital services).
5. Scope of capital services
31.
There is no disagreement that fixed assets are sources of capital services. Together with
the fact that there is statistical coverage of investment flows into fixed assets, they will clearly
enter the scope of capital services measures. There are, however, several other assets that may
play a role in the provision of capital services but:

Some entities are at present not recognised as assets, such as research and development.
Although the Group is in favour of the possibility to consider R&D expenditure as
investment, a number of issues need resolving before the stock of R&D can be fully
integrated into the accounts (see discussion papers on R&D in the Canberra Group, such
as Pitzer (2004)).

Some entities are non-produced such as land. These give rise to income in the form of
operating surplus but in the account of the user of the asset, not of the owner (unless the
owner is also the user). There is thus an asymmetry with produced assets which always
provide income to the owner regardless of which unit is the user of the asset. The SNA
does not regard placing of non-produced assets at the disposal of a producer as
production in itself but an action giving rise to property income. In a previous meeting,
the Group decided to split land into two categories, produced land and non-produced
land. This has implications for the measurement of capital services because, for
produced land, capital services and consumption of fixed capital will be shown in the
accounts. Also, when land is rented from another unit, there should be rentals paid to
the landlord, and a productive activity ascribed to the landlord, so that these entries
appear in his production account and not in the production of the tenant. This treatment
of produced land should attenuate some of the asymmetries in conjunction with the
present treatment of land in the accounts. However, more specific guidance has to be
developed how to measure productive and non-productive land.
9

Conceptually, it is not entirely clear to which extent some assets provide capital services.
Inventories are a case in point. One issue at hand is whether un-wanted inventories
should be considered as delivering capital services and if not, how they can be separated
from other inventories. This separation would appear very difficult empirically, thus
raising the question whether all or none inventories should be considered. If all are
considered, some practical issues have to be settled such as how to choose the life length
of the stock .

Empirically, the measurement of some assets is very difficult – the example being
historical monuments.
6.
Price-volume splits of the cost of capital services
32.
New items in the production accounts cannot be introduced without discussing their
presentation at constant prices. Even though some more detailed questions about aggregation
across quantities of past investments may arise in the process of computation, the split of the
value of capital services into a price and a volume component does not pose specific difficulties.
By its very nature, user costs per unit of capital are the price measure of capital services.
33.
To illustrate with a simple example, take the case where the stock of a particular type of
asset is computed with the perpetual inventory method. The relevant capital stock is the
‘productive stock’ (see OECD (2001), Hulten (1990)) made up of past investments that are
weighted with an ‘age-efficiency profile’ of assets of different age3:
(3) K t  I t  h1I t 1  h 2 I t 2  ...  h T I t T
34.
Implicit in the above linear formulation is that investments of different age are perfectly
substitutable4 once their relative efficiency has been scaled by the factor h s . K is then expressed
in units of the most recently acquired investment good and the value of capital services at current
prices of period t is given by multiplying K by the user cost of a new asset:
(4) Cost of capital services in period t at period t prices  u 0t K t
3
To keep things simple, we ignore a retirement distribution.
4
For a more general aggregation method across investment goods of different age see Diewert and Lawrence (2000).
10
35.
It is now straight forward to express the cost of capital services at constant prices of a
base year, if this is the index number procedure applied in the national accounts. For example,
the value of capital services in year t at prices of the base year t 0 can be computed as:
t
(5) Cost of capital services in period t at period t 0 prices  u 00 K t .
36.
Volume indices of capital services – the relevant measure for capital input in
productivity calculations are easily established by aggregating across different types of assets.
Again, the specific index number formula applicable in this case depends on the index number
formula used elsewhere in the accounts and on the analytical purpose5.
37.
For implementation by national statistical offices, several additional issues have to be
considered, in particular valuation of flows at average prices of a period – this concerns the value
of capital services – and valuation of stocks in the balance sheets at prices at the beginning and at
the end of the period. How these valuation methods hang together in applied work, will be spelled
out in greater detail in Annex C to this document.
5
For example, a chained Laspeyres index of capital services, obtained by aggregation across different asset types i,
t / t 1
would read as L
 i u 0t ,i1K it
u
i
t 1
0 ,i
K it 1 .
11
ANNEX A: Measuring expected asset price changes
[To be developed]
ANNEX B: Alternative user cost specifications: simulations for Canada
This annex supplies some empirical estimates for the sensitivity of cost of capital services
estimates with regard to different specifications of the rate of return and asset price changes. The
basic data are taken from the OECD productivity database www.oecd.org/statistics/productivity
where additional information about data sources and methodology can be found. For the purpose
at hand, we compare results for the measures of the cost of capital shown below. For simplicity,
the precise specifications have been taken in line with approach in the OECD productivity
database. However, more discussion and elaboration will be needed concerning these points, and
the present computations are illustrative only. In particular, a future Annex A will develop
methods to measure expected asset price changes and expected rates of return and the
recommendations may well deviate from the specifications below.
User costs defined
For the purpose at hand, we start from the following expression for user costs:



u it,0  rkt  di  it,k  di it,k Pit,01
(B.1.)
In (B.1.), u it,0 is the user cost for a new asset (age zero) of type i. The OECD productivity
database distinguishes 7 types of assets: hardware, communications equipment, other
machinery, transport equipment, non-residential buildings, structures and software.
Pit,0 is the purchase price of a new asset of type i in period t.

rkt is the rate of return, common to all types of assets. The index k indicates three
different types of rates of return: (i) endogenous, ex-post rates; (ii) exogenous, ex-post
rates; and (iii) exogenous, ex-ante rates. How these rates are computed is spelled out
more precisely below.

d i is the rate of depreciation where again terminology follows current OECD practice. To
simplify, geometric rates of depreciation were used for the present simulations, based on
the double-declining balance method. We note, though, that the OECD productivity data
at present relies on hyperbolic specifications for the age-efficiency profile from which
consistent (and time-varying) rates of depreciation are derived. In terms of the
specification (1), the rate of depreciation is defined as d i 
Pit,0  Pit,1
Pit,0
, i.e., the relative
price difference between a one-year old and a new asset.


t
i ,k

Pit,1,1k  Pit,1,k
Pit,1,k

Pit,01,k  Pit,0,k
Pit,0,k
is the rate of price change of asset i where it is assumed
that this price movement is independent of age. A subscript k has also been introduced
to allow for two types of calculation: ex-post price changes and ex-ante price changes.
These are described further below.
12

di  it,k is an interaction term that arises from the specific discrete formulation of the user
cost equation.
Three measures of user costs
For purposes of simulation, three user cost measures are implemented empirically for
Canada. The three measures are:
(i) endogenous, ex-post rates of return and ex-post measures of asset price
changes. Their computation follows the standard
(ii) exogenous, ex-post rates of return and ex-post measures of asset price
changes. Ex-post rates of return are measured as an un-weighted average of interest rate with
different maturities. These are the average bank rate, the bank rate on prime loans, long-term
government bond yields, short-term government bond yields, the interest rate on a 90 day bank
fixed deposit and the treasury bill rate.
(iii) exogenous, expected rates of return and expected asset price changes. We
follow a suggestion by Diewert (2001) and use as a starting point a constant value for the
expected real interest rate rr. The constant real rate is computed by taking a series of annual
observed nominal rates, the un-weighted average of interest rate with different maturities and
deflating them by the consumer price index. The resulting series of real interest rates is averaged
over the period (1980-2000) to yield a constant value for rr. The expected nominal interest rate
for every year is then computed as rt  (rr  1)(1  p t )  1 where p is the expected value of an
overall deflator, the consumer price index.
To obtain a measure for p, the expected overall inflation, we construct a 5-year centred
moving average of the rate of change of the consumer price index p t 

2
s  2
CPIt s / 5 where
CPI t is the annual percentage change of the consumer price index. This yields the expected rate
of overall price change and, by implication, the nominal net rate of return.
Expected asset price changes are derived as a smoothed series of actual asset price change: a
simple 5-year centred moving average serves as a filter.
Results
Rates of return. We are now in a position to present the outcome of this simulation. All
results relate to Canada and concern the total economy for the period 1980-2001. The first, and
important result concerns the three different rates of return, as shown in Table 1 and Figure 1.
Differences between the three rates are apparent: one notes the greater volatility of the
endogenous rate compared with the exogenous rates. By construction, the ex-ante exogenous rate
is the least volatile. One also notes the significant divergence of exogenous and endogenous rates
in the second half of the 1990s. We do not have a ready interpretation for this difference at hand
but it is an observation that merits further investigation. Finally, and as would be expected (see
Schreyer 2004 for a discussion), the endogenous rate exceeds the exogenous ones in nearly all
periods.
13
Table 1 Alternative rates of return
Total economy, Canada
Endogenous ex- Exogenous ex- Exogenous
post RoR
post RoR
ex-ante RoR
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
14.6%
9.0%
18.5%
12.8%
15.8%
15.2%
12.9%
14.6%
15.8%
14.9%
12.7%
5.8%
8.6%
9.6%
12.8%
12.0%
12.4%
12.3%
11.7%
11.4%
14.2%
13.7%
16.8%
13.6%
10.1%
11.3%
9.9%
9.2%
8.9%
10.2%
11.7%
12.3%
9.0%
7.4%
5.7%
7.0%
7.4%
5.3%
4.7%
5.4%
5.4%
6.1%
4.4%
15.60%
14.95%
13.94%
12.64%
10.91%
9.56%
9.18%
9.32%
9.49%
9.79%
9.20%
8.73%
7.72%
7.18%
6.33%
6.36%
6.18%
6.50%
6.62%
6.82%
6.96%
7.23%
Figure 1 Alternative rates of return
Total economy, Canada
20.0%
18.0%
16.0%
14.0%
12.0%
10.0%
8.0%
6.0%
4.0%
2.0%
Endogenous, ex-post
Exogenous, ex-post
20
00
19
98
19
96
19
94
19
92
19
90
19
88
19
86
19
84
19
82
19
80
0.0%
Exogenous, ex-ante
14
Gross rates of return. A second simulation of interest is the impact on the gross rates of
return for various assets. Gross rates of return are defined as the above (net) rates of return plus
depreciation minus asset price changes, in other words as the term


(B.2.) GRR it,0,k  rkt  di   it,k  di  it,k .
Gross rates of return are asset-specific and to avoid presenting too much information, we
limit ourselves to showing alternative gross rates of returns for two types of assets: hardware and
transport equipment. Table 2 presents results for hardware, Table 3 for transport equipment.
There are marked differences between the three alternatives, mainly driven by the differences in
net rates of return, and to some extent by the different formulations of asset price changes.
Table 2: Alternative gross rates of return for hardware
Total economy, Canada
Gross rate of return
Endogenous
Ex-ante
Ex-post
ex-post RoR
Rate of
rate of
rate of
and ex-post
depreciation asset price asset price asset price
(geometric)
change
change
change
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
28.6%
-6.8%
-10.5%
-10.9%
-11.7%
-16.5%
-19.6%
-15.3%
-16.1%
-14.8%
-16.3%
-15.2%
-14.3%
-12.4%
-12.9%
-12.2%
-12.1%
-14.2%
-16.6%
-16.5%
-14.3%
-14.2%
-13.8%
-12.9%
6.3%
-2.9%
-30.4%
-14.5%
-16.9%
-17.9%
-18.2%
-9.3%
-18.0%
-10.6%
-25.2%
-12.8%
-5.1%
-8.2%
-13.4%
-21.5%
-12.2%
-15.7%
-20.3%
-13.0%
-10.4%
52.4%
33.1%
49.1%
63.0%
54.7%
55.9%
54.2%
56.2%
51.0%
56.3%
48.9%
52.3%
46.3%
41.8%
47.2%
50.2%
56.4%
49.6%
51.5%
54.4%
52.1%
Exogenous expost RoR and
ex-post asset
price change
Exogenous exante RoR and
ex-ante asset
price change
51.5%
40.9%
44.3%
60.4%
50.2%
50.6%
50.5%
50.4%
45.4%
53.1%
48.4%
55.5%
45.1%
37.9%
41.4%
45.6%
49.2%
41.9%
45.2%
48.5%
43.9%
40.4%
49.0%
51.0%
50.3%
49.6%
51.3%
52.1%
48.7%
49.4%
48.6%
50.0%
48.6%
47.5%
45.1%
45.0%
43.6%
43.5%
44.9%
46.9%
47.0%
45.6%
45.6%
45.6%
15
Table 3 Alternative gross rates of return for transport equipment
Total economy, Canada
Gross rate of return
Ex-ante
Ex-post
Rate of
rate of
rate of
depreciation asset price asset price
(geometric)
change
change
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
13.3%
1.9%
2.4%
2.9%
3.4%
5.1%
3.7%
2.5%
2.4%
1.9%
0.1%
0.7%
1.6%
1.7%
2.4%
4.2%
3.7%
3.7%
2.6%
1.7%
1.3%
1.7%
1.3%
2.7%
-5.3%
7.1%
5.0%
4.9%
5.3%
3.3%
0.1%
-1.1%
4.1%
2.9%
-5.8%
3.5%
3.1%
5.0%
6.3%
3.3%
1.0%
3.1%
-0.8%
2.1%
1.0%
Endogenous ex- Exogenous ex- Exogenous expost RoR and post RoR and ante RoR and
ex-post asset ex-post asset
ex-ante asset
price change
price change
price change
25.6%
26.9%
25.7%
21.8%
24.9%
23.9%
23.4%
27.8%
30.1%
24.6%
23.6%
24.1%
18.9%
20.2%
21.8%
19.8%
22.9%
24.8%
22.3%
25.3%
25.8%
24.7%
34.7%
20.8%
19.2%
20.4%
18.6%
19.6%
22.1%
24.5%
21.4%
23.1%
27.3%
17.7%
16.3%
16.0%
15.2%
15.8%
17.2%
16.0%
19.4%
17.6%
16.9%
27.3%
26.2%
24.8%
23.0%
19.8%
19.7%
20.3%
20.6%
21.2%
23.1%
21.9%
20.7%
19.5%
18.4%
16.0%
16.4%
16.3%
17.6%
18.4%
19.0%
18.8%
19.4%
Capital services. The third type of result worth presenting is the overall rates of change of
capital services flows that arise in conjunction with the three simulations. The overall rate of
change of capital services is a weighted average of the rates of change of each asset’s capital
service flow. Weights are user cost weights, i.e., each asset’s share in the total nominal value of
user costs. Because the rates of change of each asset’s capital service flow is unaffected by the user
cost specification, the differences in results presented in Table 4 is exclusively due to differences
in weights that attach to each asset.
It is apparent from Table 4 and from Figure 2 that these differences in weights only have
limited impact on the overall rate of change of capital services, and consequently, on the rate of
change of multi-factor productivity. However, this does not mean that differences are small in
terms of current-price levels of the value of capital services. Also, these results relate to a single
country and to the total economy, and in all probability, differences are more accentuated when it
16
comes to industry-level measures and may turn out differently for other countries even at the
level of the total economy. This remains to be explored.
Table 4 Capital services under alternative user costs
Annual rate of change, total economy, Canada
Endogenous
ex-post RoR Exogenous exand ex-post post RoR and
asset price
ex-post asset
change
price change
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
7.6%
8.2%
5.6%
5.0%
4.6%
4.8%
4.6%
5.0%
5.7%
5.6%
4.5%
3.6%
2.9%
2.4%
2.8%
2.7%
2.9%
4.2%
4.3%
4.5%
4.1%
7.6%
8.1%
5.6%
5.1%
4.7%
4.9%
4.8%
5.3%
6.2%
5.9%
4.6%
3.6%
2.9%
2.5%
3.0%
2.9%
3.4%
5.0%
5.2%
5.3%
4.7%
4.4%
Exogenous exante RoR and
ex-ante asset
price change
6.6%
8.1%
5.7%
4.9%
4.6%
5.0%
4.8%
5.3%
6.1%
5.9%
4.6%
3.7%
2.9%
2.5%
3.0%
2.9%
3.3%
4.7%
4.9%
5.1%
4.5%
4.1%
17
Figure 2 Capital services under alternative user costs
Annual rate of change, total economy, Canada
9.0%
8.0%
7.0%
6.0%
5.0%
4.0%
3.0%
2.0%
1.0%
Endogenous, ex-post
Exogenous, ex-post
20
00
19
98
19
96
19
94
19
92
19
90
19
88
19
86
19
84
19
82
19
80
0.0%
Exogenous, ex-ante
ANNEX C: Consistent measures of depreciation, capital services, and capital stocks
[To be developped]
18
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20