The estimation of economic depreciation using vintage asset prices: An application of the Box-Cox power transformation

Abstract This paper applies the Box–Cox power transformation to the problem of estimating the rate and form of economic depreciation from data on used asset prices. The use of the Box–Cox model to statistically discriminate between geometric, linear and ‘one-hoss-shay’ depreciation patterns (which are special cases of the Box–Cox form) is analogous to the use of the CES production function to discriminate between Cobb–Douglas and fixed proportion technologies. We apply the Box–Cox model to a sample of used building prices, and find that the appropriate depreciation pattern is approximately geometric.

[1]  Dale W. Jorgenson,et al.  The Measurement of U.S. Real Capital Input, 1929-1967 , 1969 .

[2]  P. Zarembka.  Frontiers in econometrics , 1973 .

[3]  B. Lee,et al.  Measurement of Capital Depreciation within the Japanese Fishing Fleet , 1978 .

[4]  M. Rothschild,et al.  Towards an Economic Theory of Replacement Investment , 1974 .

[5]  Robert E. Hall,et al.  Investment, Interest Rates, and the Effects of Stabilization Policies , 1977 .

[6]  Dale W. Jorgenson,et al.  Tax Policy and Investment Behavior , 1967 .

[7]  J. Heckman.  The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models , 1976 .

[8]  Z. Griliches,et al.  The Explanation of Productivity Change , 1967 .

[9]  George A. Akerlof.  The Market for “Lemons”: Quality Uncertainty and the Market Mechanism , 1970 .

[10]  Paul A. Samuelson,et al.  Tax Deductibility of Economic Depreciation to Insure Invariant Valuations , 1964, Journal of Political Economy.

[11]  T. Wales.  Estimation of an Accelerated Depreciation Learning Function , 1966 .

[12]  R. Hall.  Technical Change and Capital from the Point of View of the Dual , 1968 .

[13]  P. Cagan.  7. Measuring Quality Changes and the Purchasing Power of Money: An Exploratory Study of Automobiles , 1971 .

[14]  H. Hotelling.  A General Mathematical Theory of Depreciation , 1925 .

[15]  Arnold C. Harberger.  The Demand For Durable Goods , 1960 .

[16]  Frank C. Wykoff.  CAPITAL DEPRECIATION IN THE POSTWAR PERIOD: AUTOMOBILES , 1970 .

[17]  Dale W. Jorgenson,et al.  Econometric Studies of Investment Behavior: A Survey , 1971 .

[18]  R. Coen,et al.  Investment Behavior, the Measurement of Depreciation, and Tax Policy , 1975 .

[19]  Dale W. Jorgenson,et al.  U.S. Real Product and Real Factor Input, 1929-1967 , 1970 .

[20]  R. Hall.  8. The Measurement of Quality Change from Vintage Price Data , 1971 .

[21]  Z. Griliches,et al.  Price Indexes And Quality Change , 1973 .

[22]  D. Jorgenson.  The Economic Theory of Replacement and Depreciation , 1974 .

[23]  S. Ackerman.  USED CARS AS A DEPRECIATING ASSET , 1973 .

[24]  Robley Winfrey,et al.  Statistical Analyses of Industrial Property Retirements. , 1937 .

[25]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[26]  Vernon L. Smith,et al.  Tax Depreciation Policy and Investment Theory , 1963 .

[27]  David K. Foot,et al.  The Other Half of Gross Investment: Replacement and Modernization Expenditures , 1971 .