1. Capital stocks, capital services, and depreciation: an integrated framework Nicholas Oulton London School of Economics Sylaja Srinivasan Bank of England Paper to be presented to the 1 st EUKLEMS Consortium Meeting, London, 26-27 October, 2004

2. 2 This paper Presents an integrated framework –Approach to measuring capital and depreciation is consistent –Common dataset Illustrates empirical differences in growth rates, levels of aggregate capital and depreciation when assumptions are changed on –Asset composition –Asset level depreciation rates –Asset prices –Method of aggregation

3. 3 Roadmap Theory capital services versus capital stocks rental prices versus asset prices Obsolescence and ICT: does the basic theory still apply? Some evidence for the UK

4. 4 In a production function, the measure of capital needed is one that captures the flow of capital services (Jorgenson and Griliches(1967)) This measure is called a Volume Index of Capital Services (OECD (2001)) or VICS Wealth or VICS?

5. 5 Aggregate Capital: Wealth Stock measure Growth of aggregate capital is weighted average of growth rates of individual assets where weights are shares of each asset in the value of wealth Since value of each asset is its price times quantity, we refer to these weights as asset price weights Asset price is the price you pay for the asset

6. 6 Aggregate Capital: VICS Flow measure : measures the flow of capital services derived from all capital assets Growth of aggregate capital is weighted average of growth rates of individual assets where weights are shares of each asset in the value of profits Since value of each asset in value of profits is its rental price times quantity, we refer to these weights as rental price weights Rental price is the (notional) price you pay to hire the asset

7. 7 Rental price/user cost of capital Definition: What a firm would have to pay to rent an asset for 1 period Why does it matter? If firms optimise, User cost = MR times Marginal Physical Product of the asset

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12. 12 Accounting relationship

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14. 14 Relationship between decay and depreciation If decay is geometric, then the depreciation rate equals the decay rate: The converse is also true

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16. 16 Empirical requirements Asset prices Investment (real) Aggregate profit (needed to derive the rate of return) Tax adjustment factors Depreciation rates

17. 17 Obsolescence: does it make a difference? The answer is no. 1. Scrapping is a form of decay (and its prospect causes depreciation). If an asset is scrapped because of obsolescence, then it cant deliver any services 2. It doesnt matter why an asset decays, just that it does decay

18. 18 Panel approach to estimating depreciation where p(i,s,t) is the transactions price (not quality adjusted) of the ith computer that is s years old in year t z(i) is some characteristic (say speed) which affects the perceived quality of computers YD: year dummy

19. 19 Panel approach to estimating depreciation Coefficient on age (beta2): measures depreciation Coefficient on year dummy (beta3): measures quality-adjusted price change

20. 20 UK national accounts Assets Traditional Buildings and other structures Other machinery and equipment (plant) Transport equipment (vehicles) Intangibles

21. 21 Assets TraditionalICT related Buildings and other structuresComputers Other machinery and equipment (plant) = rest + computers + part of software Software Transport equipment (vehicles) Intangibles = rest + part of software

22. 22 Average growth rates of UK asset stocks: 1979 Q1-2002 Q2 (per cent per quarter) VariantBuildingsPlantVehiclesIntangiblesComputersSoftware BEA (US dep. rates) 0.701.040.180.94-- ONS1 (UK dep. rates) 0.730.980.190.94-- ICT1 (UK prices) 0.700.470.180.945.21-- ICT3 (US prices) 0.700.450.180.917.255.89

23. 23 Aggregate Capital Growth: Does separating out ICT matter? Basic ----- Separate out computers and software -----

24. 24 Growth rates, per cent per quarter

25. 25 Guide: Basic Longer asset lives Separate out computers and software (US prices) US private non-residential

26. 26 Conclusions Separating out ICT matters to growth rate of capital; effect is larger for VICS measure Asset level depreciation rate assumptions matter for the level of wealth Aggregate depreciation rate rises a bit in the 1990s when ICT is treated separately (though not as much as in U.S.) However, depreciation to GDP ratio is almost flat except in the last few quarters (even when ICT is treated separately)

27. 27 THE END