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CAPITAL AND ITS
PRODUCTIVITY IN
FINLAND, 1975-2001
Pirkko Aulin-Ahmavaara & Jukka Jalava
Statistics Finland / Helsinki School of Economics
Capital’s role in growth



The fundamental role of capital known at least since
the physiocrat Turgot and Adam Smith
alternative explanations of economic growth, Crafts
(1992):
 exogenous growth
 endogenous growth
 institutions
 catching-up
K usually denotes both the value of capital and its
input into production, which both are assumed to
decline by the same depreciation rate δ
Capital in the national accounts


Gross Capital Stock, no adjustments for loss of
efficiency due to aging. Capital goods stay in the stock
until they are retired at the end of their service lives.
Gross capital stock at the end of year is estimated
using the perpetual inventory method pioneered by
Goldsmith (1951):
S 1
K  d I
G
t

s 0
G
s t s
where d is the surviving share of the cohort of capital
goods that are s years old in year t and S is the
maximum service life of the asset type.
Capital in the national accounts II

Net Capital Stock, depicts the market value of capital
and not its productive capacity. The net value of the
capital good equals the current purchaser’s price of a
new asset of the same type less the cumulated
consumption of fixed capital (SNA93, para.6.199).
Capital services


Jorgenson & Griliches (‘67) showed that it is important
to take into account the substitution between different
kinds of capital (and labour). Hence, capital services
should be used as capital input in growth accounting.
We calculate productive capital stocks for each
homogeneous asset type:
Productive capital stock

is (when we are assuming a geometric age-efficiency
profile):

K t  K t 1 (1  d )  I t   (1  d ) I t 

 0


i.e. if Kt-1 is 100, the rate of depreciation is 0,05 and the
new investment is 10, then Kt is 100*(1-0,05)+10 = 105
This was for a single capital asset type, and when we
aggregate several asset types into a measure of capital
services, their Hall-Jorgenson (‘67) user costs are used as
weights.
User cost of capital

e.g. the service lives of computers and buildings are
very different (capital theory tells us that the value of a
capital good equals the discounted value of the revenue
it is expected to accrue, e.g. Diewert, 2001), therefore
the software must generate revenue much faster than
the building. We cannot sum the productive stocks as is,
but must weigh them with their respective user costs:
the user cost is comprised of the rate of return, the rate
of depreciation and the holding gain/loss, i.e.
User cost of capital II
rt  p(t 1) qt  pt d t  ( pt  p(t 1) ),

r is user cost, p is the price index of a new investment
good and q is the rate of return. In the ex-ante method
some external rate of return is used, e.g. the base rate
of the central bank. In the residual or ex-post method
the internal rate of return is estimated by using the
information of the national account’s production and
generation of income account. Capital income is
defined as nominal value added less compensation of
employees (plus an imputed compensation of the selfemployed) and since we know the rate of depreciation
and the holding gain, the rate of return is
User cost of capital III
capital income  pt d t   pt  pt 1 K t 1
qt 
pt 1 K t 1

where K is real productive stock and pK nominal stock,
i.e. the market value of the capital stock.
Capital services

The aggregate volume index of capital services is:
vijt
 K ijt 
K it
 ,
cit 
 

j K
K i (t 1)
ij
(
t

1
)



The weights  are (i is industry and j is asset type):


 rijt K ijt
rij (t 1) K ij (t 1) 
vijt  

/2
  rijt K ijt  rij (t 1) K ij (t 1) 
i
 i

Rate of return and capital productivity

The rate of return:
Ex-ante
Ex-post

1975–1990
8.5
11.5
1990–1995
7.2
5.7
1995–2001
4.4
14.4
Compound average annual growth of capital
productivity:
1975–1990
Capital services (ex0.0
ante)
Capital services (ex0.1
post)
GCS
-0.3
NCS
0.3
1990–1995
-0.1
1995–2001
3.5
-0.1
3.7
-1.9
-0.4
3.5
4.1
Capital’s contribution to growth
1975–1990 1990–1995 1995–2001
GDP at basic prices (excl. dwellings), average
1
annual volume growth
2
Contribution
Capital services (ex-ante)
Capital quantity
Capital quality
Capital services (ex-post)
Capital quantity
Capital quality
GCS
NCS
1
Capital’s income share
2.9
-0.5
4.7
0.6
0.5
0.1
0.5
0.5
0.1
0.6
0.5
19.3
-0.1
-0.1
0.0
-0.1
-0.1
0.0
0.3
0.0
19.9
0.3
0.2
0.1
0.3
0.2
0.0
0.3
0.2
27.1
Alternative MFP measures
Capital services (ex-ante)
Capital services (ex-post)
GCS
NCS
1975–1990
1990–1995
1995–2001
2.4
2.5
2.4
2.5
2.6
2.6
2.2
2.5
2.9
2.9
2.9
3.0