# Cost of capital services and the national accounts Anne Harrison (on behalf of Paul Schreyer and Erwin Diewert)

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Cost of capital services and the national accounts Anne Harrison (on behalf of Paul Schreyer and Erwin Diewert)

Why do we need capital stocks? 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? 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 11005% 27680 3545760 434363840 51617181920 Value2811901165920 Decline9074573920 Income10631

Table 2 Year 11005% 27680 3545760 434363840 51617181920 Value2811901165920 Decline9074573920 Price1.000.820.630.430.22 Income10631

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 1685% 28286 3757984 445485153 511 12 13 Value2812251466613 Decline5679805313 Price1.000.800.650.450.20 Income11731

Table 2 vs table 3 Earnings10080604020 Value2811901165920 Price1.000.820.630.430.22 Income9.515.82.951.050 Earnings6786845313 Value2812241466613 Price1.000.800.650.450.20 Income11.237.303.280.660

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 1100 280 360 440 520 Value2811901165920 CFC9074573920 10631 Capital services or GOS 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? 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?

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