NBS-OECD Workshop on National Accounts
6-10 November 2006
Measuring Capital and Capital Services:
An Overview
Paul Schreyer
OECD
1
Purpose of capital measurement
2 main purposes:
•
Capital as a storage of wealth
•
Capital as a source of productive services
The two purposes correspond more or less to
•
Capital in the balance sheets and in the income side of the
national accounts, e.g., value of fixed assets, depreciation,
net and gross income…
 Relevant questions: what is the value of wealth in the
economy? Is current income sustainable?
2
Purpose of capital measurement
•
Capital in the production side of the national accounts
 Relevant questions: capital and multi-factor
productivity, growth accounting, competitiveness
•
In the SNA93, no explicit recognition of capital in the
production account
•
In revision to SNA 93, explicit recognition of capital
income and capital services in the production account
3
Stocks and flows – an integrated approach
•
Key objective of new capital manual: present integrated
and consistent approach towards capital measurement
to link relevant flows and relevant stocks:
•
Investment
•
Depreciation
•
Capital services
•
Net stock
•
Gross stock
•
Productive stock
4
System of capital in the SNA93
Age-price
Net value added
function
Net
stock
CFC
Gross
stock
Investment
Retirement
function
5
System of capital in the new SNA
Age-price
Net value added
function
Net
stock
CFC
Return on capital
User costs
Gross
stock
Investment
Retirement
function
Age-efficiency
Productive
stock
Capital services
function
6
Stocks and flows – an overview
Income and wealth perspective
Basic flow
Aggregation across assets
different age based on
Investment
Production and productivity
perspective
Investment
of Depreciation profile (Age-price Age-efficiency profile
profile)
Resulting stock for each class of Net capital stock by asset type
assets
Productive stock by asset type
Derived flow
Capital services by type of asset
Depreciation
Aggregation across different Market prices
classes of assets based on
Rental prices or user costs
Resulting stocks
Total net capital stock
Total productive stock
Derived measure
Balance sheet entry, national Total capital services, multiwealth, net measures of income
factor productivity
7
Asset market equilibrium condition
Central economic relationship that links income and
production perspective Walras (1874); Boehm-Bawerk
(1888)
•
Stock value of an asset = discounted stream of future rental
payments that the asset is expected to yield
P0t: price of new asset purchased at the beginning of period t
fnt: nominal rental payable at beginning of period t
(1+rt): nominal discount factor
P0t=f0t+1/(1+rt) + f1t+2/(1+rt)2 + f2t+3/(1+rt)3+…
8
Asset market equilibrium condition (2)
In a functioning market, purchase price of an asset equals the
discounted stream of expected rentals
Purchasers will buy asset of flow of rental implies at least a
rate of return that is as large as rt  rt can also be
considered the opportunity cost of investing in the asset =
the return that the market would pay for investment of
similar risk
Central equation for integrated system of stocks and flows of
capital
9
Rentals and asset prices – numerical example (1)
Assume: asset with
•
Service life of 8 years
•
Discount rate 5 %
•
Rental for a new asset is 10$
•
For simplicity, no general inflation
•
Price of new asset and price of rentals are expected to rise
by 2% per year: fnt+1=fnt*1.02
•
Productive services of the asset decline by a constant
amount over its service life:  linear age-efficiency pattern
10
Rentals and asset prices – numerical example (2)
10*0.88*1.02 =8.93
Year (t)
Rental
Rental
price
Ageprice
discounted
efficiency beginning
to
of period beginning
of year 1
1
100%
2
88%
10.00
3
75%
8.93
4
63%
7.80
5
50%
6.63
6
38%
5.41
7
25%
4.14
8
13%
2.82
9
0%
1.44
10
0.00
Price of asset beginning of year
9.52
8.10
6.74
5.46
4.24
3.09
2.00
0.97
0.00
40.12
10.0/1.05=9.52
11
Rentals and asset prices – numerical example (3)
Rental price discounted to beginning of year
Year (t)
Rental
price
Ageefficiency beginning
of period
100%
1
10.00
88%
2
8.93
75%
3
7.80
63%
4
6.63
50%
5
5.41
38%
6
4.14
25%
7
2.82
13%
8
1.44
0%
9
0.00
10
Price of asset beginning of year
1
9.52
8.10
6.74
5.46
4.24
3.09
2.00
0.97
0.00
40.12
2
8.50
7.08
5.73
4.45
3.24
2.10
1.02
0.00
32.12
3
4
5
7.43
6.02
4.68
3.41
2.21
1.07
0.00
24.81
6.32
4.91
3.58
2.32
1.13
0.00
18.24
5.15
3.76
2.43
1.18
0.00
12.52
8
7
6
3.94
2.55
1.24
0.00
7.74
2.68
1.30
0.00
3.98
7.80/1.052 =7.08
12
1.37
0.00
1.37
Rentals and asset prices – numerical example (4)
This example also shows a very important link between ageefficiency profile and the age-price profile
For a given rate of interest, a given rate of price change of new
assets, there will be exactly one sequence of asset prices for
each age-efficiency profile
Consider the following price history of an asset
13
Rentals and asset prices – numerical example (5),
Price history of asset
Year (t)
1
2
3
4
5
6
7
8
9
0
1
2
40.12
40.92
41.74
42.57
43.43
44.29
45.18
46.08
47.01
32.12
32.77
33.42
34.09
34.77
35.47
36.18
36.90
24.81
25.30
25.81
26.32
26.85
27.39
27.94
Age of asset
3
4
18.24
18.61
18.98
19.36
19.75
20.14
12.52
12.77
13.03
13.29
13.56
5
6
7
8
7.74
7.89
8.05
8.21
3.98
4.06
4.14
1.37
1.39
0.00
Diagonal price movement: total change in value of asset between two years
e.g. 40.12-32.12 = 8
•Vertical movement: price change of new asset (2%) = 40.92-40.12=0.80
•Horizontal movement: price difference due to age = 40.92-32.12=8.80
14
Rentals and asset prices – numerical example (6),
Age-price profile
Year (t)
1
2
3
4
5
6
7
8
9
2
Age of asset
3
4
0
1
5
6
7
8
40.12
40.92
41.74
42.57
43.43
44.29
45.18
46.08
47.01
32.12
32.77
33.42
34.09
34.77
35.47
36.18
36.90
24.81
25.30
25.81
26.32
26.85
27.39
27.94
18.24
18.61
18.98
19.36
19.75
20.14
12.52
12.77
13.03
13.29
13.56
7.74
7.89
8.05
8.21
3.98
4.06
4.14
1.37
1.39
0.00
78.50%
78.50%
78.50%
78.50%
78.50%
78.50%
78.50%
78.50%
59.43%
59.43%
59.43%
59.43%
59.43%
59.43%
59.43%
42.85%
42.85%
42.85%
42.85%
42.85%
42.85%
28.84%
28.84%
28.84%
28.84%
28.84%
17.47%
17.47%
17.47%
17.47%
8.82%
8.82%
8.82%
2.97%
2.97%
0.00%
32.12/40.92=0.785
15
Rentals and asset prices – numerical example (7)
Note: Age-price profile does not depend on time here because
age-efficiency profile is not time-dependent and because
the expected rates of asset price change and discount
factors are given for any point in time
However, as historical time moves on, it may well be that
discount factors or price expectations change, in which
case the age-price profiles of all assets would be affected.
16
Rentals and asset prices – numerical example (8),
linear age-efficiency profile
Age
Age-efficiency profile
0
1.00
1
0.88
2
0.75
3
0.63
4
0.50
5
0.38
6
0.25
7
0.13
8
0.00
Age-price profile
1.00
0.79
0.59
0.43
0.29
0.17
0.09
0.03
0.00
1
0.8
0.6
0.4
0.2
0
1
2
3
4
5
Age-efficiency profile
6
7
8
9
10
Age-price profile
17
Rentals and asset prices – numerical example (9),
constant age-efficiency profile
Age
Age-efficiency profile
0
1.00
1
1.00
2
1.00
3
1.00
4
1.00
5
1.00
6
1.00
7
1.00
8
1.00
Age-price profile
1.00
1.00
0.89
0.77
0.65
0.53
0.40
0.27
0.14
1
0.8
0.6
0.4
0.2
0
1
2
3
4
5
Age-efficiency profile
6
7
8
9
10
Age-price profile
18
Rentals and asset prices – numerical example (10),
geometric age-efficiency profile
Age
Age-efficiency profile
0
1.00
1
0.78
2
0.60
3
0.47
4
0.37
5
0.28
6
0.22
7
0.17
8
0.13
Age-price profile
1.00
0.78
0.60
0.47
0.37
0.28
0.22
0.17
0.13
1
0.8
0.6
0.4
0.2
0
1
2
3
4
5
Age-efficiency profile
6
7
8
9
10
Age-price profile
19
Rentals and asset prices – numerical example (11),
hyperbolic age-efficiency profile
Age
Age-efficiency profile
0
1.00
1
0.93
2
0.86
3
0.77
4
0.67
5
0.55
6
0.40
7
0.22
8
0.00
Age-price profile
1.00
0.82
0.66
0.50
0.36
0.23
0.12
0.04
0.00
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0
1
2
3
4
Age-efficiency profile
5
6
7
8
Age-price profile
20
Retirement and survival functions (1)
•
Assets in a cohort are unlikely to retire all at the same
moment
•
Typically, there is a retirement distribution around an
average retirement age
•
To construct the age-efficiency function of a cohort, the
age-efficiency function for a single asset has to be
combined with a retirement distribution
•
This is shown in the following slides
21
Retirement and survival functions (2)
•
Probability density function of retirement: shows the
(marginal) probability for an asset to retire at age T
•
For simplicity, log-normal distribution
Normal distribution, average service life = 8 years
0.25
0.20
0.15
0.10
0.05
0.00
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
22
Retirement and survival functions (3)
•
Call the probability that an asset retires at age T, FT
•
In our example with a linear age-efficiency function gs, we
had gs=1-s/T.
•
For a single asset, the service life was assumed T=8
•
With a retirement distribution, for each age s, there is a
possibility that the asset retires at age s, or at age s+1 etc.
•
Calculate an average, with probability weighting where Tm
is the maximum service life:
hs= ∑T=sTm[1-s/T]*FT
•
This creates a new age-efficiency profile for the cohort that
reflects both efficiency loss and retirement {hs}
23
Retirement and survival functions (4), ageefficiency profiles
gs 
0.938
0.875
0.813
0.750
0.688
0.625
0.563
0.500
0.438
0.375
hs 
0.889
0.778
0.667
0.557
0.448
0.342
0.243
0.158
0.091
0.046
1
2
3
4
5
6
7
8
9
10
s-->
1.000
0.800
0.600
0.400
0.200
0.000
1
2
3
4
5
6
Single asset
•
7
8
9
10 11 12 13 14 15 16
Cohort with retirement distribution
hs is non-linear even with linear gs!
24
Retirement and survival functions (5)
A special case: one-hoss shay
•
Suppose a class of assets follows a one-hoss shay pattern of
efficiency loss: efficiency is constant until the asset retires
•
Then, the combined age-efficiency/retirement pattern {hsG}
becomes hsG= ∑T=sTmFT, i.e., only a retirement pattern.
•
More precisely, hsG is the cumulative probability density
function that varies from h0G=1 for a new asset to hTmG=0
•
It is now possible to construct the gross capital stock on the
basis of the perpetual inventory method:
•
Gross capital stock = sum of past investments of a class of
assets, with cohorts weighted by the retirement pattern
{hsG}
25
Retirement and survival functions (6)
A special case: one-hoss shay
1.200
1.000
0.800
0.600
0.400
0.200
0.000
1
2
3
4
5
6
Single asset
7
8
9
10 11 12 13 14 15 16
Cohort with retirement distribution
26
Retirement and survival functions (7)
Gross capital stock
•
Gross capital stock = sum of past investments of a class of assets, with
cohorts weighted by the retirement pattern {hsG}
•
Gross capital stock = stock of assets surviving from past investments
that ignores deterioration of assets and considers past investment ‘as
new’ - only retirement is taken into account
•
Although the gross capital stock is often calculated in practice, it serves
mainly as an intermediate step towards measuring depreciation and net
stocks rather than as an analytical measure in itself.
•
Note: net stocks and depreciation can but do not have to be calculated
via the gross stock. In fact, the usefulness of the gross stock is
relatively limited.
•
Some countries (eg United States) do not publish gross stocks any
more – they restrict themselves to net stocks and productive stocks (see
later)
27
Retirement and survival functions (8)
Gross capital stock
Year (t)
Investment
at historical
prices
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
500
800
1000
600
500
700
750
900
1200
1000
1100
1200
1100
1000
900
800
Price
index
(new)
capital
goods
1.000
1.020
1.040
1.061
1.082
1.104
1.126
1.149
1.172
1.195
1.219
1.243
1.268
1.294
1.319
1.346
Investment in
prices of year
16, weighted
Investment
with
in prices of Retirement
retirement
year 16
pattern
pattern
672.9
1055.6
1293.6
760.9
621.7
853.3
896.3
1054.5
1378.4
1126.2
1214.5
1298.9
1167.3
1040.4
918.0
800.0
0.0060
0.0225
0.0666
0.1584
0.3083
0.4998
0.6912
0.8411
0.9330
0.9770
0.9936
0.9984
0.9995
0.9997
0.9998
1.0000
4.0
23.8
86.1
120.6
191.7
426.4
619.6
886.9
1286.0
1100.3
1206.7
1296.9
1166.8
1040.1
917.8
800.0
Note three types of
valuation of stocks:
•Historical prices =
valuation in terms of
prices of the year of
acquisition
•Constant prices =
valuation in terms of
a base year
•Current prices =
special case of
constant prices =
valuation in terms of
the current (typically
latest) year
28
Gross stock at (current) prices of year 16
11173.6
Net or wealth stocks (1)
•
Net capital stock or wealth stock = market value of assets
•
Net capital stock = stock of assets surviving from past
investments that has been corrected for retirement and for
loss in value due to ageing
•
Net capital stock offers a wealth perspective. It is the
capital stock that shows up in the balance sheets of the
national accounts.
•
Calculation of net stocks: 2 possibilities:
•
Directly, as sum of past investments, weighted by ageprice profile
•
Derived from gross stock and depreciation
29
Net or wealth stocks (2)
•
Starting point: age-price profile, derived from combined
age-efficiency & retirement profile
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0
1
2
3
4
5
6
7
8
Age-efficiency & retirement profile
9
10 11 12 13 14 15 16
Age-price & retirement profile
30
Net or wealth stocks (3)
Year (t)
Investment
at historical
prices
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
500
800
1000
600
500
700
750
900
1200
1000
1100
1200
1100
1000
900
800
Price
index
(new)
capital
goods
1.000
1.020
1.040
1.061
1.082
1.104
1.126
1.149
1.172
1.195
1.219
1.243
1.268
1.294
1.319
1.346
Investment in
prices of year
Combined 16, weighted
Investment Age-price +
with
in prices of retirement
retirement
year 16
pattern
pattern
672.9
1055.6
1293.6
760.9
621.7
853.3
896.3
1054.5
1378.4
1126.2
1214.5
1298.9
1167.3
1040.4
918.0
800.0
0.0000
0.0001
0.0006
0.0020
0.0060
0.0154
0.0338
0.0656
0.1141
0.1816
0.2691
0.3768
0.5042
0.6509
0.8163
1.0000
Net stock 31/Dec/year 16 at (current) prices of year 16
0.0
0.1
0.7
1.5
3.7
13.1
30.3
69.2
157.3
204.5
326.9
489.4
588.5
677.2
749.4
800.0
4111.9
31
Depreciation (Consumption of fixed capital) (1)
•Depreciation is the loss in value of an asset or a group of assets
as they age
•A flow concept
•Economic meaning: deduction from gross income to account for
the loss in capital value owing to the use of capital goods in
production
•SNA definition: « 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. »
•Excluded: value losses due to acts of war or as a consequence of
32
exceptional events such as major natural disasters
Depreciation (Consumption of fixed capital) (2)
Note:
•Depreciation must be measured with reference to a given set of
prices, ie the average prices of the period
•“Used by producer” includes assets that are kept idle for
whatever reasons
•“Normal obsolescence” is included in depreciation but not
“abnormal obsolescence”. Example: scrapping of energyintensive machines following an oil-price shock
33
Computing depreciation (1)
Two avenues: directly and indirectly via net stock
Direct computation: main tool: age-price profile and investment
series
•Rate of depreciation of an s-year old asset = price difference
between an s-year old asset and an s+1 year old asset divided by
price of an s-year old asset:
t
t
P

P
d st  s t s 1
Ps
{P0t, P1t, P2t,…} is the age-price profile, so dst can be derived
directly
34
Computing depreciation (2)
•When applied to past investment, depreciation rates apply in a
cumulative way:
•Depreciation for a new capital good: d0It
•Depreciation for a one-year old capital good: d1(1-d0)It-1
•Depreciation for a one-year old capital good: d2(1-d1)(1-d0)It-2
•Etc.
Total depreciation = d0It + d1(1-d0)It-1 + d2(1-d1)(1-d0)It-2 + …
Note: investment {It, It-1,…} is expressed in constant prices of a
particular base year, therefore total depreciation is also in prices
of this base year.
35
Computing depreciation (3)
Age-price profile
Age
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Depreciation rates
Pst  Pst1
ds 
Pst
46.01
37.56
29.94
23.19
17.33
12.38
8.36
5.25
3.02
1.56
0.71
0.28
0.09
0.03
0.01
0.00
0.00
1.00
0.82
0.65
0.50
0.38
0.27
0.18
0.11
0.07
0.03
0.02
0.01
0.00
0.00
0.00
0.00
0.00
0.18369
0.20268
0.22538
0.25269
0.28564
0.32517
0.37181
0.42526
0.48412
0.54602
0.60813
0.66786
0.72348
0.77489
0.82538
0.88736
1.00000
Depreciation profile
D s  d s (1  d s 1 )(1  d s  2 )...(1  d 0 )
0.1837
0.1655
0.1467
0.1274
0.1076
0.0875
0.0675
0.0485
0.0317
0.0185
0.0093
0.0040
0.0014
0.0004
0.0001
0.0000
0.0000
(46.0137.56)/46.01=0.184
36
Computing depreciation (4)
Year (t)
Investment at
historical
prices
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
500
800
1000
600
500
700
750
900
1200
1000
1100
1200
1100
1000
900
800
Price
index
(new)
capital
goods
1.000
1.020
1.040
1.061
1.082
1.104
1.126
1.149
1.172
1.195
1.219
1.243
1.268
1.294
1.319
1.346
Investment
in prices of
year 16
672.9
1055.6
1293.6
760.9
621.7
853.3
896.3
1054.5
1378.4
1126.2
1214.5
1298.9
1167.3
1040.4
918.0
800.0
Investment in
prices of year
16, weighted
with
Depreciation depreciation
profile
profile
0.0000
0.0001
0.0004
0.0014
0.0040
0.0093
0.0185
0.0317
0.0485
0.0675
0.0875
0.1076
0.1274
0.1467
0.1655
0.1837
Depreciation during period 16 at (current) prices of year 16
0.0
0.1
0.6
1.1
2.5
8.0
16.6
33.5
66.9
76.1
106.3
139.8
148.7
152.6
151.9
147.0
1051.5
37
Computing depreciation (5)
Net capital stock for period 17 at prices of period 16
Year (t)
Investment
at historical
prices
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
500
800
1000
600
500
700
750
900
1200
1000
1100
1200
1100
1000
900
800
1000
Price
index
(new)
capital
goods
1.000
1.020
1.040
1.061
1.082
1.104
1.126
1.149
1.172
1.195
1.219
1.243
1.268
1.294
1.319
1.346
1.373
Investment in
prices of year
Combined 16, weighted
Investment Age-price +
with
in prices of retirement
retirement
year 16
pattern
pattern
672.9
1055.6
1293.6
760.9
621.7
853.3
896.3
1054.5
1378.4
1126.2
1214.5
1298.9
1167.3
1040.4
918.0
800.0
980.4
Net stock 31/Dec/year 17 at prices of year 16
0.0000
0.0001
0.0006
0.0020
0.0060
0.0154
0.0338
0.0656
0.1141
0.1816
0.2691
0.3768
0.5042
0.6509
0.8163
1.0000
0.0
0.2
0.4
1.2
5.1
13.8
35.7
90.4
128.5
220.6
349.6
439.8
524.5
597.5
653.0
980.4
4040.8
38
Computing depreciation (6)
Indirect way of computing depreciation via net stocks and the
following identity:
Net stock 31/Dec/year 16
+ Gross investment during year 17
- Depreciation during year 16
Net stock 31/Dec/year 17
4111.9
980.4
1051.5
4040.8
Note: specific lags in this identity (depreciation year 16)
disappear when everything is formulated in mid-year
valuations
39
Computing depreciation (7)
Note: depreciation is in prices of period 16
•To obtain depreciation at current prices, apply investment
goods deflator between years 16 and 17
• This is also an easy solution to split depreciation into price
and volume components – the deflator for depreciation always
equals the asset price deflator
40
Computing depreciation (8)
Empirical basis for depreciation rates
1. Derived from age-efficiency functions. This raises the issue
of how age-efficiency parameters are constructed. Needed:
average service lives and retirement distributions 
surveys or assumptions
2. Measured directly.
•
Service lives and retirement distributions from surveys,
combined with some assumptions about the functional
form of age-price functions
•
Most frequent assumption: linear profile (constant
amount of depreciation)
Ps/P0=1-s/T
41
Computing depreciation (9)
•
Geometric profile (constant rate of depreciation):
Ps/P0 = (1-)s where  = DBR/T
DBR: declining balance parameter, often set to equal 2
(“double declining balance”)
For example, BEA uses DBR=2.2 for computers,
DBR=1.65 for machinery and equipment, DBR=0.9 for
structures
T: expected mean service life
•
Econometric estimates based on used asset prices
(Hulten Wykoff 1981)
42
Productive stocks and capital services (1)
Net stock and depreciation have to do with the value side of
capital and income
Productive stocks and capital services have to do with the
quantity side of capital and its role in production, i.e. as
capital input
The flow of capital services is normally assumed to be a
constant proportion of the productive capital stock
The productive stock is the stock of cumulative investment of a
particular type, corrected for retirement and efficiency
losses, as captured by the age-efficiency and retirement
function
43
Productive stocks and capital services (3)
Productive stock of asset type i at the beginning of period t+1,
and in constant prices of period t:
K
i , t 1
 h 0 I  h 1I
t
t 1
 h 2I
t 2
 h 3I
t 3
 ...
{hs} s=0,1,2,… is the combined age-efficiency/retirement
profile
By way of the numerical example used earlier, the productive
stock is computed as follows:
44
Productive stocks and capital services (4)
Year (t)
Investment
at historical
prices
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
500
800
1000
600
500
700
750
900
1200
1000
1100
1200
1100
1000
900
800
Price
index
(new)
capital
goods
1.000
1.020
1.040
1.061
1.082
1.104
1.126
1.149
1.172
1.195
1.219
1.243
1.268
1.294
1.319
1.346
Investment in
prices of
Combined
year 16,
Ageweighted
Investment efficiency +
with
in prices of retirement retirement
year 16
pattern
pattern
672.9
1055.6
1293.6
760.9
621.7
853.3
896.3
1054.5
1378.4
1126.2
1214.5
1298.9
1167.3
1040.4
918.0
800.0
0.0001
0.0005
0.0021
0.0071
0.0197
0.0459
0.0914
0.1580
0.2434
0.3420
0.4478
0.5570
0.6674
0.7782
0.8891
1.0000
0.1
0.5
2.7
5.4
12.2
39.2
81.9
166.6
335.6
385.1
543.9
723.5
779.1
809.6
816.2
800.0
45
Productive stock 31/Dec/year 16 at (current) prices of year 16
5501.6
Productive stocks and capital services (5)
Example from Australia
180
170
Capital
services
160
150
140
130
Net (wealth)
capital stock
120
110
100
1986
1988
1990
1992
1994
1996
1998
46
User costs and its elements (1)
Price of capital services
Productive stock and capital services are the quantity/volume of capital
input to production
What is the price of capital services?
Price of capital services = user costs or rental price
Basic idea: how much would an owner of a capital good charge if he rented
out the capital good for one period under competitive conditions?
The rental price/user cost should cover:
•
A ‘normal’ net return to the capital owner to account for opportunity
costs
•
Depreciation
•
Expected revaluation
47
User costs and its elements (10)
A reasonable approximation is:
u0t = [r*t + d0] P0t.
where the user cost is the sum of a real rate of return and
depreciation
This user cost formula, due essentially to Walras says that the
user cost of capital is equal to the anticipated real interest
rate plus the anticipated depreciation rate times the
beginning of the period stock price of the asset.
48
User costs and its elements (11)
There are two broad options (Diewert 1980 and Harper, Berndt
and Wood 1989):
•
Use of an endogenous (internal) rate of return (estimated
capital services exactly corresponds to gross operating
surplus and the capital element of gross mixed income)
•
Use of an exogenous (external) rate of return (estimated
capital services is unlikely to be exactly equal to gross
operating surplus and the capital element of gross mixed
income)
49
Scope of assets and capital services
•
Note: new asset classification proposed in revised SNA
•
All fixed assets are within the scope of capital services
•
Some special cases:
1. Research and development – not presently recognised as
fixed assets, but SNA revision will bring them into asset
scope  statistical issues of how to measure R&D stocks,
how to deflate them, how to depreciate them
2. Some assets are non-produced but sources of capital
services, in particular land (see below for more extensive
discussion)
3. Some assets are produced but not fixed  inventories
should they be part of the scope of capital services?
4; Government assets
50
Valuation (1)
Valuation – an issue of practical importance
•SNA: flows should be valued at average prices of the
period to which they relate
•SNA: stocks in the balance sheets should be valued at the
prices of the point in time to which they relate
•The various flow measures (depreciation, value of capital
services) should thus be measured at average prices of the
period
•When there is a link to stock measures, stock measures
should also be valued at average prices of the period for
the purposes of carrying out calculations and preserving
the link, but not as an entry into the balance sheet
51
Valuation (2)
Example:
Net stock at the end of year t and at average prices of the
year t =
Net stock at the beginning of year t, valued at average
prices of year t
Plus
Gross investment during year t at average prices of year t
Minus
Depreciation during year t at average prices of year t
52
Data requirements
Summary of data requirement:
•Benchmark estimate for capital stock, eg from capital
survey
•Time series of investment expenditure by type of asset
and by industry
•Deflators for investment goods, possibly separate
deflators for new and for used assets
•Estimates of retirement or survival patterns
•Estimates of depreciation rates or age-efficiency rates
•Gross operating surplus (by industry)
•Split of mixed income into labour and capital part
53
Overall conclusions on capital measurement
•Measurement and interpretation of capital has long
occupied economists and statisticians
•Revision of SNA marks an important step forward in
the harmonised treatment of assets and the associated
flows in the national accounts
•Objective: consistent set of asset-related data with
flows and stocks that fit together and that are
analytically useful
•Capital measurement requires still many assumptions,
and national accountants rightly try to minimise
assumptions in measurement
54
Overall conclusions on capital measurement (2)
•Additional empirical information concerning capital is key to
improve quality of estimates and to reduce the number of
assumptions
studies on depreciation or asset lives
Investment in investment goods deflators
Capital flow matrices for the economy
•Significant movement and willingness to move forward in this
domain
55