Affiliations: [a] Investment and Capital Stock Division, Statistics
Canada, 9th Floor, Section D-7, Jean Talon Building, Tunney's Pasture, Ottawa,
Ontario K1A 0T6, Canada
Note: [1]
The views presented here, of course, represent those of the author only, and
should not be interpreted as representing the views of Statistics Canada or
members of its staff.
Abstract: Economic depreciation has been studied extensively by many researchers, but there
are very few studies on physical depreciation. The voluminous empirical research
studies on economic depreciation in economic literature indicate that economic
depreciation is much easier to estimate than physical depreciation. There are
some differences in the measurement of physical depreciation between the
engineering and the economic point of view. An asset in its early age may have
to be retired because of economic reasons due to technological change. This
makes the empirical measurement of physical depreciation even more difficult. In
this paper, we derive a formula which can transform economic depreciation into
physical depreciation. The transformation will provide us a consistent
measurement of physical depreciation vis-a-vis economic depreciation. Two different parametric forms are also studied in this paper. The almost perfect
match between the Box–Cox power transformation form and the converted form of
physical depreciation further proves that the former is one of the most flexible
functional forms especially well suited to the problem of analyzing depreciation
patterns. The estimated curvature parameter of the Beta-decay form is negative
for all Canadian industry components. The convex form of physical depreciation
of the Canadian experience is contrary to the concave forms assumed by the
Bureaus of Labor Statistics of the US in its capital stock estimates for the
input-output industries.
Keywords: Age–date price matrix, economic depreciation, physical depreciation, transformation formula, Box–Cox power transformation parametric form, test for geometric form of depreciation, Beta-decay parametric form
