CAPITAL AND ITS PRODUCTIVITY IN FINLAND, Pirkko Aulin-Ahmavaara & Jukka Jalava Statistics Finland / Helsinki School of Economics

Capitals 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 growth exogenous growth endogenous growth endogenous growth institutions institutions catching-up 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 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, 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): Gross capital stock at the end of year is estimated using the perpetual inventory method pioneered by Goldsmith (1951): 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. 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 purchasers price of a new asset of the same type less the cumulated consumption of fixed capital (SNA93, para.6.199). Net Capital Stock, depicts the market value of capital and not its productive capacity. The net value of the capital good equals the current purchasers 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. 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: We calculate productive capital stocks for each homogeneous asset type:

Productive capital stock is (when we are assuming a geometric age-efficiency profile): is (when we are assuming a geometric age-efficiency profile): i.e. if K t-1 is 100, the rate of depreciation is 0,05 and the new investment is 10, then K t is 100*(1-0,05)+10 = 105 i.e. if K t-1 is 100, the rate of depreciation is 0,05 and the new investment is 10, then K t 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. 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. 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 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 accounts production and generation of income account. Capital income is defined as nominal value added less compensation of employees (plus an imputed compensation of the self- employed) and since we know the rate of depreciation and the holding gain, the rate of return is 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 accounts production and generation of income account. Capital income is defined as nominal value added less compensation of employees (plus an imputed compensation of the self- employed) and since we know the rate of depreciation and the holding gain, the rate of return is

User cost of capital III where K is real productive stock and pK nominal stock, i.e. the market value of the capital stock. 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: The weights are (i is industry and j is asset type):

Rate of return and capital productivity The rate of return: Compound average annual growth of capital productivity:

Capitals contribution to growth

Alternative MFP measures