CAPITAL AND ITS CAPITAL AND ITS PRODUCTIVITY IN PRODUCTIVITY IN

FINLAND, 1975-FINLAND, 1975-20012001

Pirkko Aulin-Ahmavaara & Jukka Pirkko Aulin-Ahmavaara & Jukka JalavaJalava

Statistics Finland / Helsinki School of Statistics Finland / Helsinki School of EconomicsEconomics

Capital’s role in growthCapital’s role in growth

The fundamental role of capital known at least since the physiocrat Turgot and Adam Smith The fundamental role of capital known at least since the physiocrat Turgot and Adam Smith alternative explanations of economic growth, Crafts (1992):alternative explanations of economic growth, Crafts (1992):

exogenous growthexogenous growth endogenous growthendogenous growth institutionsinstitutions catching-upcatching-up

KK usually denotes both the value of capital and its input into production, which both are assumed to decline by the same depreciation rate usually denotes both the value of capital and its input into production, which both are assumed to decline by the same depreciation rate δδ

Capital in the national Capital in the national accountsaccounts Gross Capital Stock, no adjustments for loss of efficiency due to aging. Capital 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.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 Gross capital stock at the end of year is estimated using the perpetual inventory

method pioneered by Goldsmith (1951):method pioneered by Goldsmith (1951):

where where dd is the surviving share of the cohort of capital goods that are is the surviving share of the cohort of capital goods that are ss years old years old in year in year tt and and SS is the maximum service life of the asset type. is the maximum service life of the asset type.

1

0

S

sst

Gs

Gt IdK

Capital in the national Capital in the national accounts IIaccounts II

Net Capital Stock, depicts the market Net Capital Stock, depicts the market value of capital and not its productive value of capital and not its productive capacity. The net value of the capital good capacity. The net value of the capital good equals the current purchaser’s price of a equals the current purchaser’s price of a new asset of the same type less the new asset of the same type less the cumulated consumption of fixed capital cumulated consumption of fixed capital (SNA93, para.6.199). (SNA93, para.6.199).

Capital servicesCapital services

Jorgenson & Griliches (‘67) showed that it Jorgenson & Griliches (‘67) showed that it is important to take into account the is important to take into account the substitution between different kinds of substitution between different kinds of capital (and labour). Hence, capital capital (and labour). Hence, capital services should be used as capital input in services should be used as capital input in growth accounting. growth accounting.

We calculate productive capital stocks for We calculate productive capital stocks for each homogeneous asset type: each homogeneous asset type:

Productive capital stockProductive capital stock

is (when we are assuming a geometric age-efficiency is (when we are assuming a geometric age-efficiency profile):profile):

i.e. if i.e. if KKt-1t-1 is 100, the rate of depreciation is 0,05 and the is 100, the rate of depreciation is 0,05 and the new investment is 10, then new investment is 10, then KKtt is 100*(1-0,05)+10 = 105is 100*(1-0,05)+10 = 105

This was for a single capital asset type, and when we This was for a single capital asset type, and when we aggregate several asset types into a measure of capital aggregate several asset types into a measure of capital services, their Hall-Jorgenson (‘67) user costs are used as services, their Hall-Jorgenson (‘67) user costs are used as weights.weights.

01 )1()1(

tttt IdIdKK

User cost of capitalUser cost of capital

e.g. the service lives of computers and e.g. the service lives of computers and buildings are very different (capital theory buildings are very different (capital theory tells us that the value of a capital good tells us that the value of a capital good equals the discounted value of the revenue equals the discounted value of the revenue it is expected to accrue, e.g. Diewert, 2001), it is expected to accrue, e.g. Diewert, 2001), therefore the software must generate therefore the software must generate revenue much faster than the building. We revenue much faster than the building. We cannot sum the productive stocks as is, but cannot sum the productive stocks as is, but must weigh them with their respective user must weigh them with their respective user costs: the user cost is comprised of the rate costs: the user cost is comprised of the rate of return, the rate of depreciation and the of return, the rate of depreciation and the holding gain/loss, i.e.holding gain/loss, i.e.

User cost of capitalUser cost of capital II II

r is user cost, p is the price index of a new r is user cost, p is the price index of a new investment good and q is the rate of return. In the investment good and q is the rate of return. In the ex-ante method some external rate of return is ex-ante method some external rate of return is used, e.g. the base rate of the central bank. In the used, e.g. the base rate of the central bank. In the residual or ex-post method the internal rate of residual or ex-post method the internal rate of return is estimated by using the information of the return is estimated by using the information of the national account’s production and generation of national account’s production and generation of income account. Capital income is defined as income account. Capital income is defined as nominal value added less compensation of nominal value added less compensation of employees (plus an imputed compensation of the employees (plus an imputed compensation of the self-employed) and since we know the rate of self-employed) and since we know the rate of depreciation and the holding gain, the rate of depreciation and the holding gain, the rate of return isreturn is

),( )1()1( ttttttt ppdpqpr

User cost of capitalUser cost of capital III III

where where KK is real productive stock and is real productive stock and pKpK nominal stock, i.e. the market value of the nominal stock, i.e. the market value of the capital stockcapital stock. .

11

11

tt

tttttt Kp

Kppdpincomecapitalq

Capital servicesCapital services

The aggregate volume index of capital services is:

The weights are (i is industry and j is asset type):

,)1()1(

ijtv

tij

ijt

jti

itit K

K

K

Kc

2/)1()1(

)1()1(

itijtij

tijtij

iijtijt

ijtijtijt Kr

Kr

Kr

Krv

Rate of return and capital Rate of return and capital productivityproductivity The rate of return:

Compound average annual growth of capital productivity:

1975–1990 1990–1995 1995–2001Ex-ante 8.5 7.2 4.4Ex-post 11.5 5.7 14.4

1975–1990 1990–1995 1995–2001Capital services (ex-ante)

0.0 -0.1 3.5

Capital services (ex-post)

0.1 -0.1 3.7

GCS -0.3 -1.9 3.5NCS 0.3 -0.4 4.1

Capital’s contribution to Capital’s contribution to growthgrowth

1975–1990 1990–1995 1995–2001

GDP at basic prices (excl. dwellings), average annual volume growth

1

2.9 -0.5 4.7

Contribution2

Capital services (ex-ante) 0.6 -0.1 0.3 Capital quantity 0.5 -0.1 0.2 Capital quality 0.1 0.0 0.1 Capital services (ex-post) 0.5 -0.1 0.3 Capital quantity 0.5 -0.1 0.2 Capital quality 0.1 0.0 0.0 GCS 0.6 0.3 0.3 NCS 0.5 0.0 0.2 Capital’s income share

1 19.3 19.9 27.1

Alternative MFP measuresAlternative MFP measures

1975–1990 1990–1995 1995–2001

Capital services (ex-ante) 2.4 2.6 2.9 Capital services (ex-post) 2.5 2.6 2.9 GCS 2.4 2.2 2.9 NCS 2.5 2.5 3.0