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Measuring Capital

  • W. Erwin Diewert

The paper revisits Harper, Berndt and Wood (1989) and calculates Canadian reproducible capital services aggregates under alternative assumptions about the form of depreciation, the opportunity cost of capital and the treatment of capital gains. Five different models of depreciation are considered: (1) one hoss shay; (2) straight line depreciation; (3) declining balance or geometric depreciation; (4) linearly declining efficiency profiles and (5) linearly increasing maintenance profiles. The latter form of depreciation does not seem to have been considered in the literature before. This model assumes that there is a known time profile of maintenance expenditures that can be associated with each asset and the optimal time of retirement of the asset as well as the profile of used asset prices becomes endogenous under this specification. It turns out if the maintenance profile increases linearly, then the linearly declining efficiency profile model emerges; see (4) above. We consider 3 alternative assumptions about the interest rate and the treatment of capital gains so that we evaluate 15 models in all and compare their differences. Following Hill (2000), we also consider the differences between cross section and time series depreciation and anticipated time series depreciation (which adds anticipated obsolescence of the asset to normal cross section depreciation of the asset). Finally, we follow the suggestion made by Diewert and Lawrence (2000) that a superlative index number formula be used to aggregate up vintages of capital rather than the usual assumption of linear aggregation, which implicitly assumes that the capital services yielded by each vintage of a homogeneous type of capital are perfectly substitutable.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 9526.

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Date of creation: Mar 2003
Date of revision:
Handle: RePEc:nbr:nberwo:9526
Note: EFG PR
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  1. Diewert, W. Erwin, 1999. "Index Number Approaches To Seasonal Adjustment," Macroeconomic Dynamics, Cambridge University Press, vol. 3(01), pages 48-68, March.
  2. Jorgenson, Dale W, 1996. "Empirical Studies of Depreciation," Economic Inquiry, Western Economic Association International, vol. 34(1), pages 24-42, January.
  3. Hulten, Charles R & Wykoff, Frank C, 1996. "Issues in the Measurement of Economic Depreciation: Introductory Remarks," Economic Inquiry, Western Economic Association International, vol. 34(1), pages 10-23, January.
  4. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
  5. Triplett, Jack E, 1996. "Depreciation in Production Analysis and in Income and Wealth Accounts: Resolution of an Old Debate," Economic Inquiry, Western Economic Association International, vol. 34(1), pages 93-115, January.
  6. Kholi, U. & Fox, K., 1996. "GDP Growth, Terms-of-Trade Effects and Total Factor Productivity," Papers 96/28, New South Wales - School of Economics.
  7. Oulton, Nicholas, 1995. "Depreciation, Obsolescence and the Role of Capital in Growth Accounting," Bulletin of Economic Research, Wiley Blackwell, vol. 47(1), pages 21-33, January.
  8. Diewert, W E, 1974. "Intertemporal Consumer Theory and the Demand for Durables," Econometrica, Econometric Society, vol. 42(3), pages 497-516, May.
  9. repec:cup:macdyn:v:3:y:1999:i:1:p:48-68 is not listed on IDEAS
  10. Diewert, W Erwin, 1978. "Superlative Index Numbers and Consistency in Aggregation," Econometrica, Econometric Society, vol. 46(4), pages 883-900, July.
  11. Usher, Dan (ed.), 1980. "The Measurement of Capital," National Bureau of Economic Research Books, University of Chicago Press, edition 0, number 9780226843001.
  12. Paul Schreyer, 2001. "The OECD Productivity Manual: A Guide to the Measurement of Industry-Level and Aggregate Productivity," International Productivity Monitor, Centre for the Study of Living Standards, vol. 2, pages 37-51, Spring.
  13. Diewert, W E, 1992. "The Measurement of Productivity," Bulletin of Economic Research, Wiley Blackwell, vol. 44(3), pages 163-98, July.
  14. W. Erwin Diewert, 1980. "Aggregation Problems in the Measurement of Capital," NBER Chapters, in: The Measurement of Capital, pages 433-538 National Bureau of Economic Research, Inc.
  15. W. Erwin Diewert & Kevin J. Fox, 1999. "Can measurement error explain the productivity paradox?," Canadian Journal of Economics, Canadian Economics Association, vol. 32(2), pages 251-280, April.
  16. Hulten, Charles R. & Wykoff, Frank C., 1981. "The estimation of economic depreciation using vintage asset prices : An application of the Box-Cox power transformation," Journal of Econometrics, Elsevier, vol. 15(3), pages 367-396, April.
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