Organisation for Economic Co-operation and Development Organisation de Coopération et de Développement Economiques

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1 OECD OCDE Organisation for Economic Co-operation and Development Organisation de Coopération et de Développement Economiques STATISTICS DIRECTORATE National Accounts Division SECOND MEETING OF THE CANBERRA GROUP ON CAPITAL STOCK STATISTICS Château de la Muette, Paris 29 September - 1 October 1998 Beginning at 10 a.m. on the first day Agenda item : 10c Document number : 16 Title : Age-Efficiency Profiles: Evidence from Recent Studies Author(s) : Derek Blades - OECD

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3 Introduction 1. This brief note summarises information from two kinds of studies on age-efficiency profiles - i.e. on the way in which incomes earned by fixed assets change. as they become older. 2. The first kind of study attempts to directly observe age-efficiency profiles; there are only two of these. There are many more of the second kind which describe age-profiles of assets, i.e. how asset prices decline as they get older; this information is used below to infer the age-efficiency profiles that could explain the observed age-price profiles. Two studies of age-efficiency profiles 3. In 1975 Robert Coen published a study of capacity depreciation patterns (i.e. age-efficiency profiles) for structures and equipment in 21 industries for the United States. The study was based on the assumption that capital formation in a given year is a function of the need to replace capacity lost during the year through scrapping and losses in productive efficiency of assets and the desire to hold an optimal stock of assets with a view to profit maximisation. The study then sought to identify the patterns of efficiency loss and service lives that would be consistent with observed levels of capital formation over the period 1950 to Table 1 below shows the distribution of capacity depreciation patterns estimated by Coen for equipment and structures in the 21 industries. Table 1: Capacity Depreciation Patterns in 21 Industries Equipment Structures SYD 2 1 SL 8 5 GD-FIN 8 4 GD-INF 1 - OHS 2 11 Total SYD: SL: GD-FIN GD-INF OHS Sum of Year s digits; Straight Line; Geometric with cut-off; Geometric with no cut off; One-Hoss-Shay The SYD and GD-INF patterns are rare. For equipment, straight line and geometric decline with a cut-off are equally common. Half of the structures suffered no decline in efficiency throughout their services lives (one-hoss-shay pattern). 5. John Penson and colleagues used engineering data on annual repair and maintenance costs and annual usage to estimate capacity depreciation for farm tractors. They concluded that the productive capacity of tractors deteriorates in a concave pattern. This is consistent with the hyperbolic function used by BLS to measure efficiency loss. 1

4 Studies of age-price profiles 6. Table 2 summarises information from 7 articles showing how the prices of assets decline as they get older. The studies use several different sources and cover quite a wide range of asset types - commercial and industrial buildings, farm equipment, industrial machinery, motor vehicles and fishing boats. The overwhelming conclusion is that there is no simple way to describe the way in which the prices of assets change with age. Except for skid steer loaders (a piece of farm equipment), every type of asset covered in these studies declined in value with age. (Skid steer loaders suffered no decline in value from age 2 to 20 years in the Cross and Perry study). In virtually every case, the age-price profiles were convex to the origin. In some cases, the rate of decline was constant - i.e. geometric - but usually the rate increased with age although in some instances it decreased. In a few cases asset prices fell linearly. Assuming that markets for capital assets are competitive, the relationship between the changes in the efficiency of an asset (i.e. changes in the income it earns) and the price of the asset is described as follows: K t L Yt = ( 1 + r ) t t Where, K t is the asset price in year t, Yt is the income earned in year t, r is a discount rate, and L is the expected lifetime of the asset. 8. When asset prices (K) are plotted over their lifetimes from 1 to L, they will produce an infinite number of age-price curves depending on the assumptions made about how Y changes between periods t and L. However, there are only a few Y-patterns (age-efficiency profiles) that will produce a convex age-price curve which the studies cited in Table 2 show to be the almost universal rule. 9. Age-efficiency profiles that will produce a convex decline price age curve include: income falls at a constant rate provided that the rate of decline is sufficiently large - e.g. over 3 % per annum income falls by a constant amount provided that the amount is sufficiently large - e.g. by an amount exceeding 4% of the original value of the asset income falls according to the hyperbolic function used by BLS provided that the B parameter is 0.5 or less. 2

5 Table 2: Seven Studies of Price - Age Curves for Fixed Assets Author Country Date Asset type Data source Scrapping adjustment Conclusions on shape of price - age curve Stephen Oliner USA 1996 Machine tools (not numerically controlled) Mail survey of second hand dealers Yes Depreciation rate increases with age - i.e. priceage curve is between convex and linear. Roger McNeill Canada 1979 Farm tractors Sales prices of new and second hand tractors obtained from dealers Prices fall by around 30% the first year and thereafter they decline at a constant rate - i.e. the price-age curve is convex. Carl Beidleman USA 1973 Industrial equipment: lathes, milling machines, fork-lift trucks, hopper and gondola cars Sales prices from second hand dealers After initial large falls in value, a constant rate of depreciation for some assets and a linear decline for others - i.e. the price age curve is convex for some assets and linear for others. Timoty Cross and Gregory Perry Combines and other harvesting machinery, farm tractors, ploughs, planters, manure spreaders and disk harrows Auction prices for used machinery The depreciation patterns for various types of farm equipment are quite different from one another. Planters exhibited straight line depreciation; for all other equipment second hand prices follow a curve that is convex to the origin but the rate of decline is not constant. Sometimes the rate of depreciation increases over time; for other equipment it decreased. The price-age curve is almost always convex. Yoram C. Peles USA 1988 Automobiles List prices of second hand vehicles The price-age curve is between convex and linear. Charles R. Hulten and Frank C. Wykoff USA 1981 Factory buildings, shops, warehouses and office buildings Survey data on prices paid by owners of buildings Yes Depreciation rates are constant or increasing - i.e. price-age curves are convex. Bun Song Lee Japan 1977 Six tonnage - categories of wood and steel fishing boats Valuation of new and used fishing boats for insurance against total loss For some types of fishing boats depreciation is geometric and for others the rate of depreciation slows with age. Price-age curves are convex 3

6 References Stephen Oliner Roger C. McNeill Carl R. Beidleman Thomas L. Cross and Gregory M. Perry Yoram C. Peles Charles R. Hulten and Frank C. Wykoff Bun Song Lee John B. Penson, Dean W. Hughes and Glenn L. Nelson Robert M. Coen New Evidence on the Retirement and Depreciation of Machine Tools in Economic Inquiry, January 1996 Depreciation of Farmer Tractors in British Columbia in Canadian Journal of Agricultural Economics, February 1979 Fixed Asset Depreciation Pattern: Market Based evidence in Journal of Institutional and Theoretical Economics, March 1991 Depreciation Patterns for Agricultural Machinery in American Journal of Agricultural Economics, February 1995 On the Depreciation of Automobiles in the International Journal of Transport Economics, February 1988 The Estimation of Economic Depreciation Using Vintage Asset Prices in Journal of Econometrics, 15, 1981 Measurement of Capital Depreciation Within the Japanese Fishing Fleet in the Review of Economics and Statistics, June 1978 Measurement of Capacity Depreciation Based on Engineering Data in American Journal of Agricultural Economics, May 1977 Investment Behaviour, The Measurement of Depreciation, and Tax Policy in American Economic Review, March