Cost of capital services and
the national accounts
Anne Harrison (on behalf of Paul
Schreyer and Erwin Diewert)
Why do we need capital stocks?
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Accounting
Balance sheets
Consumption of fixed capital
Analysis
Productivity
How do we estimate capital
stocks?
• Not simple aggregation like fixed capital
formation
• Must estimate value of assets bought in
earlier periods for which market values do
not always exist
What do we want?
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Two questions
What would you pay for it?
Traditional NA valuation
How much can it contribute to production?
Basic productivity question
Two concepts of capital stock but these
are not independent
Very simple example
• Numbers not algebra
• Simplifying assumptions
• Asset prices and general price level are
the same and move in line( see later)
Table 1
Year 1
100
5%
2
76
80
3
54
57
60
4
34
36
38
40
5
16
17
18
19
20
281
190
116
59
20
Decline
90
74
57
39
20
Income
10
6
3
1
Value
Table 2
Year 1
2
3
4
5
Value
Decline
Price
Income
100
76
54
34
16
281
90
1.00
10
5%
80
57
36
17
190
74
0.82
6
60
38
18
116
57
0.63
3
40
19
59
39
0.43
1
20
20
20
0.22
Table 1 vs Table 2
• Exactly the same values
• Table 1 starts with contribution to output,
derives prices (and depreciation)
• Table 2 starts with price decline, derives
contribution to output (and depreciation)
• Both tables give value for balance sheets
and for consumption of fixed capital
Table 3
Year 1
2
3
4
5
Value
Decline
Price
Income
68
82
75
45
11
281
56
1.00
11
5%
86
79
48
11
225
79
0.80
7
84
51
12
146
80
0.65
3
53
12
66
53
0.45
1
13
13
13
0.20
Table 2 vs table 3
Earnings
100
80
60
40
20
Value
281
190
116
59
20
Price
1.00
0.82
0.63
0.43
0.22
Income
9.51
5.8
2.95
1.05
0
67
86
84
53
13
Value
281
224
146
66
13
Price
1.00
0.80
0.65
0.45
0.20
11.23
7.30
3.28
0.66
0
Earnings
Income
Table 2 vs table 3
• Although theoretically starting from price
gives the same as starting from
contribution to output, using existing price
declines may give implausible results
• Achieving more plausible contributions to
output may well change price decline and
consumption of fixed capital
• But better
Question 2
• Should capital services, depreciation and
capital stock measures be compiled in an
integrated and consistent manner?
• Should a comprehensive description be
included in the SNA?
Table 4
Year 1
100
2
80
3
60
4
40
5
20
Value
281
190
116
59
20
CFC
90
74
57
39
20
10
6
3
1
Return to capital or NOS
Problem
• How to reconcile estimated figure for
capital services with GOS as a balancing
item determined residually?
• Answer lies in the discount rate
• Either determine this endogenously
• Or show residual (eg wrongly estimated or
omitted capital)
Constant prices
• The “user cost” is a price index associated
with capital services which gives a volume
estimate
• It depends on
– A rate of return to capital (exog or endog)
– Depreciation rate
– Discount factor
– Expected real asset price relative to general
price level
Question 3
• Do you agree with the proposed formulae
for the estimation of capital services and
the options given for the rate of return?
What else do we get?
• If we accept the general principle it gives a
handle on:
• Mixed income
• Land
• Imputed rent of owner occupied housing
• Non-market production
• Natural resources
Question 4
• Do you agree that all non-financial assets,
except valuables produce capital services
and should be included where feasible?
Capital services in an SNA
account?
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Arguments against
Modelling – but so is PIM
Rate of return – options given
Cambridge?
Resource cost
Question 1
• Should capital services be introduced into
the SNA?
• Should they appear in the main accounts
or in supplementary accounts?