Canadian net capital stock estimates and depreciation profiles:

Transcription

1 Working Paper Statistics Canada September, 1999 Investment and Capital Stock Division National Wealth and Capital Stock Section Canadian net capital stock estimates and depreciation profiles: A comparison between the existing series and a test series using the US (BEA) methodology

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3 Statistics Canada Investment and Capital Stock Division National Wealth and Capital Stock Section Canadian net capital stock estimates and depreciation profiles: A comparison between the existing series and a test series using the US (BEA) methodology This note was prepared by: P. Koumanakos, Director, Investment and Capital Stock Division R. Landry, Chief, National Wealth and Capital Stock Section K. Huang, National Wealth and Capital Stock Section S. Wood, National Wealth and Capital Stock Section September 1999

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5 Introduction 1 Capital stocks are reproducible tangible assets that are used as factors of production in combination with other factor inputs such as labour, energy and other natural resources or materials. The stock of capital consists of building construction (such as plants and offices), engineering construction (such as roads and dams) and machinery and equipment used in the production process. These are distinguished from non-reproducible assets such as land, mineral deposits and natural resources, which are not produced but are directly incorporated in the production of other commodities. Although capital stocks by industry can be measured in a variety of ways such as surveys of physical stock or book values, the method traditionally used by Statistics Canada is the perpetual inventory method. This method, which is a flexible way to develop time series of capital stocks, accumulates investment expenditures by industry to obtain estimates of capital stock in any particular year. It requires information on the value of investment, price indexes for capital goods, service lives, and methods of depreciation. The essence of the perpetual inventory method is to add each year s gross investment (gross fixed capital formation) to the capital stock of the previous year. If the value of assets which cease to exist each year is subtracted from this accumulated investment, then a gross measure of the capital stock is obtained. If yearly deductions for depreciation are made, then a net measure of the capital stock is the result. Section I, Current Methodology, describes the methodology underlying the current measures of capital stock. Section II, BEA-type Geometric Depreciation Methodology, describes another set of measures more in line with the latest measures of capital stock being produced in the United States Bureau of Economic Analysis (BEA). Section III compares the results of the two different geometric methodologies and Section IV gives some concluding remarks. Finally, a series of appendices compares the levels and rates of growth of the net stocks produced by the BEA-type methodology with the other non-geometric measures of capital stock produced by Statistics Canada: Appendix A compares the BEA-type with net stock using linear depreciation, Appendix B compares it with net stock using delayed depreciation and Appendix C compares it with gross stock. I Current methodology Statistics Canada provides estimates of gross and net capital stocks for broad categories of assets and industries. Gross stocks and retirements 1 For a complete explanation of the Statistics Canada methodology, see Statistics Canada, 199 Katz and Shelby, 1997 and Fraumeni,

6 The gross stock is an accumulation of past gross investment with yearly deductions (called retirements or discards) of the value of assets which cease to exist in that year. Thus this measure of the capital stock assumes that the efficiency of the capital asset remains the same over its entire service life.the retirement pattern is a bell-shaped distribution which has been truncated so that all retirements occur between 5% and 15% of mean useful life. The asset lives used are derived from the Capital and Repair Expenditures Survey. The assets which the investment of a given year represent are described as a cohort of assets. If the mean service life of a cohort of assets is 1 years, then when the truncated normal retirement distribution is applied, there are 11 sub-cohorts each with its own service life. The following table shows the division into sub-cohorts of a cohort of assets with a value of $1, when purchased and with a mean useful life of 1 years: Table 1. Truncated normal retirement distribution applied to a cohort of assets worth $1, with mean service life of 1 years: Sub-cohort Length of life of sub-cohort Fraction of cohort Value in dollars of sub-cohort , , , , , , , , , Total 1. 1, Net stocks and depreciation The net stock concept attempts to measure the productive capacity of the capital stock. This means that in addition to assembling data on investment flows, price indexes and asset lives, the analyst must make assumptions about the pattern of aging and loss of efficiency of the assets and The Capital and Repair Expenditures Survey was extensively revised in 1985 and 1987 to satisfy data requirements for the estimation of capital stocks. --

7 incorporate them into the perpetual inventory method in the form of depreciation. The estimates of net stocks are derived from the gross by making yearly deductions for depreciation. Various methods can be used to measure the deterioration of assets making up the capital stock. Three sets of depreciation and net stock estimates are produced by using the straight-line form, the double-declining balance form and the hyperbolic or delayed form of depreciation. Following is a brief comparison of the methods used to produce the current measures and the relationships between them. Probably the most familiar model of depreciation is the straight-line method in which equal dollar amounts are deducted from the stock every year. The amount of straight-line depreciation (SL) is given by d x,sl 1 L, x1,,,...,l where L is the number of years over which the asset is depreciated and x is the age of the asset. In the linear form, all of the asset s value has disappeared from the capital stock by the end of the asset s service life. When the truncated normal retirement pattern is applied to straight line depreciation, the effect is to produce an accelerated rate of depreciation (see table (a)). The geometric rate of depreciation is one type of accelerated depreciation. The term accelerated is used because the dollar amounts of depreciation deducted are highest in the earlier years of the asset s life and become progressively smaller with each year of the asset s life. With the geometric form (G), the declining-balance rate is the same every year: δ G R L where R is the rate relative to the straight-line rate of 1. Thus the double-declining-balance rate is /L. The higher the value of R, the more accelerated the rate i.e. the higher the dollar values deducted in the earlier years. --

8 The depreciation for 1 dollar of investment using the geometric pattern is: d x,g δ G (1δ G ) x1, x1,,,...l The current measures also include a pattern called hyperbolic or delayed depreciation which has the following form: d x,d L(x1) Lβ(x1) Lx Lβx, x1,,,...l where β is a curvature parameter. This form can help in understanding the relationships between the other forms. When the parameter β is equal to zero, the beta-decay form is reduced to straight-line depreciation. When β is equal to 1, the result is the gross stock concept where depreciation is zero for every year of the asset s life except the last when it is 1%. For values of β between and 1, the graphical representation of the depreciation is concave to the origin i.e. it is bowed outwards. This means that depreciation is lower in the early years of the asset s life and increases as the asset ages. This delay in the depreciation increases the closer β is to 1. When β is negative, the result is an accelerated form of depreciation. As β becomes a very large negative value, the curve approaches a pattern in which all the depreciation occurs in the first year of the asset s life and is zero for all other years i.e. it is the mirror image of the extreme when β is equal to 1. Chart 1 illustrates the effect of β on this pattern of depreciation on an asset with a service life of 1 years. In the current delayed depreciation measures, the value of β is equal to.75 for structures and.5 for machinery and equipment. --

9 Chart 1: Survival of capital stock using beta-decay depreciation: L-x/L-Ax Survival Percentage (Life=1 years) A=-1 A =-5 A =-1, A = 1 A =.75 A=.5 A= For all three of these depreciation patterns, to calculate the depreciation for an entire investment cohort, each sub-cohort must be depreciated according to its own rate. For example, if the straight-line form of depreciation is used, the first sub-cohort will be depreciated at a rate of 1/5 or % per year ($6 in the above example) for 5 years. Similarly, the second sub-cohort will be depreciated at a rate of 1/6 or 16.67% ($5) for 6 years and so on until the 11 th sub-cohort where the depreciation will be 1/15 or 6.67% ($1) for 15 years. The following tables illustrate the combined effects of the truncated normal retirement pattern with each of the three depreciation patterns: straight line (table (a)), geometric (table (b)) and delayed (table (c)). As before, the value of the cohort is assumed to be $1, and the average useful life to be 1 years. -5-

10 Table (a) Truncated normal retirement pattern and straight line depreciation pattern Sub cohort Percentage Reduction by Age Weight from Retirement Life fraction 1 5 Depreciation. Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Total weights 1. Total weighted percentages Total dollar value of depreciation for cohort of $1, 1, 1, 1, 1, 1, 1,7 9,8 8,76 7,16 5,8, 1, , -6-

11 Table (b) Truncated normal retirement pattern and geometric depreciation pattern -7- Subcohort Weight from Retirement fraction Percentage Reduction by Age Life Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Total weights 1. Total weighted percentages Total dollar value of depreciation for cohort of $1, 7,6,65 15,55 11,59 8,5 6,9,,76 1, ,

12 Table (c) Truncated normal retirement pattern and delayed depreciation pattern -8- Weight Sub- Percentage Reduction by Age from co- retirement hort Life fraction 1 5 Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Depreciation Weighted Total weights 1. Total weighted percentages Total dollar value of depreciation for cohort of $1, 1,16 1,5 1,88,57, 7,5 11,1 1,5 15,86 1,9 11,91 7,87,1 1, 1 1,

13 Geometric depreciation in the current measures Since the geometric pattern of depreciation is infinite, some further explanation is necessary in order to understand the geometric rates of depreciation appearing in table (b) above: Column in the table below shows the first years of the geometric distribution for a subcohort of assets with a service life of 1 years (i.e. the rate, δ, is /1). When the cutoff point is at age 1, the depreciation function is adjusted so that the area under the truncated distribution is 1 and so that the depreciation is zero from age 11 onwards (i.e. the assets in the sub-cohort are fully depreciated by the end of their service life). This is accomplished in two steps. First the original distribution is moved downwards by the amount of depreciation at age 11 (giving column in the table). The total value of this new distribution is then adjusted proportionally to give the values in column. For example, divided by gives.659. The accompanying graph shows the two distributions. The area redistributed is the area on the graph bounded by the heavy line. -9-

14 Table : Geometric depreciation of a sub-cohort of assets with service life L of 1 years and δ = /L Age (x) Value of depreciation function D = δ(1-δ) x-1 for asset of age x years Shifted D: values in column shifted down by depreciation at age 11 (i.e. column -.175) Proportional distribution of shifted D: individual values in column divided by the column total Sum = Sum =

15 Chart : Geometric decay function, life = 1 yr, Infinite vs with redistribution Infinite With redistribution Boundary of area redistributed II BEA-type geometric depreciation methodology As with the current measures, estimates of net stock and depreciation are derived using the perpetual inventory method: accumulated past gross investment is reduced by the cumulative value of depreciation. The initial calculations are performed in real terms and current dollar values are estimated by reflation. The asset lives and price indexes used are the same as those used in the current measures. The BEA-type methodology for estimating geometric depreciation and net stocks differs from that used to calculate the current measures in several important respects. The BEA-type methodology uses rates of depreciation derived from studies of actual price-age profiles of used assets. These studies showed that depreciation is close to geometric for most assets but whereas the current geometric measures use a double-declining-balance rate for all types of assets, the BEA-type geometric measures use a rate of 1.65 for machinery and equipment and.9 for structures. Also, as noted previously, the current methodology breaks a cohort of investments in to subcohorts based on an assumed retirement pattern, calculates the depreciation for each sub-cohort based on its own service life and redistributes the tail of the infinite distribution for each subcohort. Under the BEA-type methodology, the geometric pattern of depreciation is assumed to take retirements into account and hence the retirement pattern and the division of a cohort of investment into sub-cohorts in not necessary. The tail of the distribution is covered under the BEA-type methodology by allowing the calculation of the declining-balance to continue for a period of years equal to five times the service life of the asset. At this point, the remaining value -11-

16 of the asset is close enough to zero that it can be ignored. Since the BEA-type geometric methodology does not use the concept of a retirement pattern separate from depreciation and uses the same depreciation profile for all investment in a cohort, it is not possible to derive measures of gross stocks and discards corresponding to these BEAtype geometric measures. -1-

17 III Comparisons In summary, the difference between using the BEA-type methodology rather than the current is to dramatically reduce the amounts deducted as depreciation, thereby yielding very much higher levels of capital stock in existence. As can be seen from tables 5 and 6, the rates of depreciation are much lower with the BEA method than in the current geometric measures. Charts to 8, show the behaviour of the depreciation profiles according to the two methodologies. Table summarizes the resulting growth rates for the two methodologies. (See also charts 18 to 6.) As can be seen, the growth rate for all assets for the period 198 to 199 under the BEA methodology is over half as much again (15%) as the growth rate for the current methodology, and for the period 1991 to 1998, it is double. For structures, the differences are even more dramatic. For the period 198 to 1998, the rate of growth for structures using the BEA methodology is over twice what it is under the current methodology and for the period 1991 to 1998 it is over three times the current rate. Similarly, comparing the levels of capital stock produced by the two methodologies, the total for all assets under the current measures is 587 billion dollars in 1998 but under the BEA-type measures, it is 1,5 billion dollars - about.5 times as large. (See charts 9 to 17 for other comparisons of levels.) Table. Average growth rates of net capital stock (geometric depreciation), current measures and BEA-type Current measures BEA-type Period All assets Structures Equipment All assets Structures Equipment

18 Table 5. Depreciation rates with service life of 15 years Current Methodology BEA-type Methodology Age Straight-line Delayed Geometric Geometric Depreciation Depreciation Depreciation Depreciation Pattern Pattern Pattern Pattern

19 Table 6. Depreciation rates with service life of 6 years Current Methodology BEA-type Methodology Straight-line Delayed Geometric Geometric Depreciation Depreciation Depreciation Depreciation Age Pattern Pattern Pattern Pattern

20 Table 6. Depreciation rates with service life of 6 years Current Methodology BEA-type Methodology Straight-line Delayed Geometric Geometric Depreciation Depreciation Depreciation Depreciation Age Pattern Pattern Pattern Pattern

21 Chart : Typical depreciation profiles for equipment with 15-year service life 1 Percent of real value 1.65-Declining balance depreciation (BEA) Straight-line depreciation and normal distribution (STC) Years after initial investment Chart : Typical depreciation profiles for structures with 6-year service life 1 Percent of real value.9-declining balance depreciation (BEA) Straight-line depreciation and normal distribution (STC) Years after initial investment -17-

22 Chart 5: Typical depreciation profiles for equipment with 15-year service life 1 Percent of real value 1.65-Declining balance depreciation (BEA) Geometric depreciation and normal distribution (STC) Years after initial investment Chart 6: Typical depreciation profiles for structures with 6-year service life 1 Percent of real value.9-declining balance depreciation (BEA) Geometric depreciation and normal distribution (STC) Years after initial investment -18-

23 Chart 7: Typical depreciation profiles for equipment with 15-year service life 1 Percent of real value 1.65 Declining balance depreciation (BEA) Delayed (hyperbolic) and normal distribution (STC) Years after initial investment Chart 8: Typical depreciation profiles for structures with 6-year service life 1 8 Percent of real value.9-declining balance depreciation (BEA) Delayed (hyperbolic) and normal distribution (STC) Years after initial investment -19-

24 Chart 9: Net capital stocks, manufacturing, structures Current Chart 1: Net capital stocks, manufacturing, equipment Current Chart 11: Net capital stocks, manufacturing, all assets Current --

25 Chart 1: Net capital stocks, non-manufacturing, structures Current Chart 1: Net capital stocks, non-manufacturing, equipment Current Chart 1: Net capital stocks, non-manufacturing, all assets Current -1-

26 Chart 15: Net capital stocks, all industries, structures Current Chart 16: Net capital stock, all industries, equipment Current Chart 17: Net capital stocks, all industries, all assets Current --

27 Chart 18: Growth rates of net capital stocks, manufacturing, structures Growth rate average (198 to 1998): BEA-type =.9 Current =.95 Current Chart 19: Growth rates of net capital stocks, manufacturing, equipment Growth rate average (198 to 1998): BEA-type =.75 Current =.1 Current Chart : Growth rates of net capital stocks, manufacturing, all assets Growth rate average (198 to 1998): BEA-type = 1.8 Current =.8 Current --

28 Chart 1: Growth rates of net capital stocks, non-manufacturing, structures 1 Growth rate average (198 to 1998): BEA-type =.5 Current = 1. Current Chart : growth rates of net capital stocks, non-manufacturing, equipment Growth rate average (198 to 1998): BEA-type =.77 Current =.5 Current Chart : Growth rates of net capital stocks, non-manufacturing, all assets 1 Growth rate average (198 to 1998): BEA-type =.68 Current = 1.6 Current --

29 Chart : Growth rates of net capital stocks, all industries, structures 1-1 Growth rate average (198 to 1998): BEA-type =. Current = 1.6 Current Chart 5: Growth rates of net capital stocks, all industries, equipment Growth rate average (198 to 1998): BEA-type =.7 Current =.88 Current Chart 6: Growth rates of net capital stocks, all industries, all assets 1-1 Growth rate average (198 to 1998): BEA-type =.57 Current = 1.5 Current -5-

30 IV Conclusions Canadian empirical research used an econometric framework to study economic depreciation using survey data on the prices of used assets. Our analysis used the Box-Cox power transformation which enabled us to test whether depreciation is geometric, linear or rectangular in form. According to this research, it appears that depreciation patterns are close to geometric in form for both the manufacturing and non-manufacturing sector, although the degree of convexity is more pronounced in manufacturing. The rates of depreciation by industry as determined by this study (5% to 1% for building construction and % to % for machinery) are much higher than those obtained by the U.S. model. We are continuing to collect data on used asset prices and are continuing our research in this area. See Koumanakos and Hwang,

31 Bibliography Achour, Dominique. "Méthodes d'évaluation du stock immobilier dans les séries temporelles." L Actualité économique, 7, (197): Ackerman, Susan Rose. "Used Cars as Depreciating Assets," Western Econ. J. 11 (December 197): 6-7. Barna T. "Alternative Methods of Measuring Capital." Income and Wealth, Series 8, 1959: Chapter. Blades, Derek. "Service Lives of Fixed Assets." OECD, Economics and Statistics Department, (March 1 98). Canada, Department of Finance. Income Tax Reform. Ottawa, Statistics Canada. Evaluation Report for the Capital Stock Survey Project. Ottawa, June Chinloy, Peter. "The Estimation of Net Depreciation Rates in Housing." Journal of Urban Economics, 6 (1979):-. Christensen, L.R. and D.W. Jorgenson. "The Measurement of U.S. Red Capital Input, " The Review of Income and Wealth, Series 15, no., Coen, Robert. "Investment Behavior, the Measurement of Depreciation and Tax Policy." American Economic Review, 65 (March 1975): Denison, Edward. Accounting for United States Economic Growth, Washington, D.C.: The Brookings Institution, 197. Denny, Michael. Endogenous Capital Utilization in a Short-run Production Model. Toronto: Institute for Policy Analysis, University of Toronto, 198. Diewert, W. "Functional Forms for Profit and Transformation Functions." Journal of Economic Theory, 6 (197): Economic Council of Canada. Patterns of Growth: 7th Annual Review. Ottawa, Supply and Services Canada, 197, 9.. A Climate of Uncertainty: 17th Annual Review.Ottawa, Supply and Services Canada, 198, Fraumeni, Barbara M. "The Measurement of Depreciation in the U.S. National Income and Product Accounts."Survey of Current Business (U.S. Department of Commerce), July,

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33 Examining the Feasibility of a Capital Stock Survey In Canada. Statistics" Canada, working paper, Ottawa: October 198. Leigh, W. "Economic Depreciation of the Residential Housing Stock of the United States, " The Review of Economics and Statistics, 6, (May 198). Musgrave, J.C. "Fixed Non-residential Business and Residential Capital in the United States, " Survey of Current Business, 56, (April 1976). Rao, Someshwar. Inter-factor Substitution and Total Factor Productivity Growth, Evidence from Canadian Industries. Ottawa, Economic Council of Canada, 198. Redfem, P. "Net Investment in Fixed Assets in the United Kingdom, " Journal of the Royal Statistical Society, 11 8 (Series A), no. (1 955). Rymes, T. K. Fixed Capital Flows and Stocks, Manufacturing, Methodology, Canada, Statistics Canada, Catalogue No Hull: Queen's Printer, Solow, Robert. "Technology Change and the Aggregate Production Function." The Review of Economics and Statistics, 9 (August 1957): 1-. Statistics Canada 199. Fixed capital flows and stocks, , Historical (Statistics Canada Catalogue no Occasional). Ottawa: Minister responsible for Statistics Canada Tice, H.S. "Depreciation, Obsolescence, and the Measurement of the Aggregate Capital Stock of the United States, " The Review of Income and Wealth, Series 1, no. (June 1967). United States, Department of Labor. Capital Stock Estimates for Input-Output Industries: Methods and Data. Bureau of Labor Statistics, Bulletin, Washington, D.C.: GPO, Department of Labor. "Capital Input and Capital and Labor Shares." Trends In Multifactor Productivity, Bureau of Labor Statistics, Bulletin 178 (September 198): Varian, H. Microeconomic Analysis. New York: Norton, Ward, M. The Measurement of Capital. The Methodology of Capital Stock Estimates in OECD Countries. Paris: OECD, Young, A.H., J.C. Musgrave and C. Harkins. "Residential Capital in the United States, " Survey of Current Business (November 1971). -9-

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35 Appendix A: Comparison of net capital stocks: BEA-type vs Linear Chart A1: Net capital stocks, manufacturing, structures Linear Chart A: Net capital stocks, manufacturing, equipment Linear Chart A: Net capital stocks, manufacturing, all assets Linear -A1-

36 Appendix A: Comparison of net capital stocks: BEA-type vs Linear Chart A: Net capital stocks, non-manufacturing, structures Linear Chart A5: Net capital stocks, non-manufacturing, equipment Linear Chart A6: Net capital stocks, non-manufacturing, all assets Linear -A-

37 Appendix A: Comparison of net capital stocks: BEA-type vs Linear Chart A7: Net capital stocks, all industries, structures Linear Chart A8: Net capital stocks, all industries, equipment Linear Chart A9: Net capital stocks, all industries, all assets Linear -A-

38 Appendix A: Comparison of net capital stocks: BEA-type vs Linear Chart A1: Growth rates of net capital stocks, manufacturing, structures - - Growth rate average (198 to 1998): BEA-type =.9 Linear = -. Linear Chart A11: Growth rates of net capital stocks, manufacturing, equipment Growth rate average (198 to 1998): BEA-type =.75 Linear =. Linear Chart A1: Growth rates of net capital stocks, manufacturing, all assets 6 - Growth rate average (198 to 1998): BEA-type = 1.8 Linear = 1.7 Linear -A-

39 Appendix A: Comparison of net capital stocks: BEA-type vs Linear Chart A1: Growth rates of net capital stocks, non-manufacturing, structures 1 Growth rate average (198 to 1998): BEA-type =.5 Linear = 1.7 Linear Chart A1: Growth rates of net capital stocks, non-manufacturing, equipment Growth rate average (198 to 1998): BEA-type =.77 Linear =.65 Linear Chart A15: Growth rates of net capital stocks, non-manufacturing, all assets 1 Growth rate average (198 to 1998): BEA-type =.68 Linear =.1 Linear -A5-

40 Appendix A: Comparison of net capital stocks: BEA-type vs Linear Chart A16: Growth rates of net capital stocks, all industries, structures 1 Growth rate average (198 to 1998): BEA-type =. Linear = 1.58 Linear Chart A17: Growth rates of net capital stocks, all industries, equipment Growth rate average (198 to 1998): BEA-type =.7 Linear =.9 Linear Chart A18: Growth rates of net capital stocks, all industries, all assets 1 Growth rate average (198 to 1998): BEA-type =.57 Linear =. Linear -A6-

41 Appendix B: Comparison of net capital stocks: BEA-type vs Delayed Chart B1: Net capital stocks, manufacturing, structures Delayed Chart B: Net capital stocks, manufacturing, equipment Delayed Chart B: Net capital stocks, manufacturing, all assets Delayed -B1-

42 Appendix B: Comparison of net capital stocks: BEA-type vs Delayed Chart B: Net capital stocks, non-manufacturing, structures Delayed Chart B5: Net capital stocks, non-manufacturing, equipment Delayed Chart B6: Net capital stocks, non-manufacturing, all assets Delayed -B-

43 Appendix B: Comparison of net capital stocks: BEA-type vs Delayed Chart B7: Net capital stocks, all industries, structures Delayed Chart B8: Net capital stocks, all industries, equipment Delayed Chart B9: Net capital stocks, all industries, all assets Delayed -B-

44 Appendix B: Comparison of net capital stocks: BEA-type vs Delayed Chart B1: Growth rates of net capital stocks, manufacturing, structures Growth rate average (198 to 1998): BEA-type =.9 Delayed = -. Delayed Chart B11: Growth rates of net capital stocks, manufacturing, equipment Growth rate average (198 to 1998): BEA-type =.75 Delayed =.58 Delayed Chart B1: Growth rates of net capital stocks, manufacturing, all assets 6 - Growth rate average (198 to 1998): BEA-type = 1.8 Delayed = 1. Delayed -B-

45 Appendix B: Comparison of net capital stocks: BEA-type vs Delayed Chart B1: Growth rates of net capital stocks, non-manufacturing, structures 1 Growth rate average (198 to 1998): BEA-type =.5 Delayed =.7 Delayed Chart B1: Growth rates of net capital stocks, non-manufacturing, equipment Growth rate average (198 to 1998): BEA-type =.77 Delayed =.76 Delayed Chart B15: Growth rates of net capital stocks, non-manufacturing, all assets 1 Growth rate average (198 to 1998): BEA-type =.68 Delayed =.9 Delayed -B5-

46 Appendix B: Comparison of net capital stocks: BEA-type vs Delayed Chart B16: Growth rates of net capital stocks, all industries, structures 1 Growth rate average (198 to 1998): BEA-type =. Delayed = 1.9 Delayed Chart B17: Growth rates of net capital stocks, all industries, equipment Growth rate average (198 to 1998): BEA-type =.7 Delayed =.1 Delayed Chart B18: Growth rates of net capital stocks, all industries, all assets 1 Growth rate average (198 to 1998): BEA-type =.57 Delayed =.7 Delayed -B6-

47 Appendix C: Comparison of capital stocks: BEA-type (net) vs gross stocks Chart C1: Gross capital stocks, manufacturing, structures Gross Stock Chart C: Gross capital stocks, manufacturing, equipment Gross Stock Chart C: Gross capital stocks, manufacturing, all assets Gross Stock -C1-

48 Appendix C: Comparison of capital stocks: BEA-type (net) vs gross stocks Chart C: Gross capital stocks, non-manufacturing, structures Gross Stock Chart C5: Gross capital stocks, non-manufacturing, equipment Gross Stock Chart C6: Gross capital stocks, non-manufacturing, all assets Gross Stock -C-

49 Appendix C: Comparison of capital stocks: BEA-type (net) vs gross stocks Chart C7: Gross capital stocks, all industries, structures Gross Stock Chart C8: Gross capital stocks, all industries, equipment Gross Stock Chart C9: Gross capital stocks, all industries, all assets Gross Stock -C-

50 Appendix C: Comparison of capital stocks: BEA-type (net) vs gross stocks Chart C1: Growth rates of gross capital stocks, manufacturing, structures Growth rate average (198 to 1998): BEA-type =.9 Gross stock =.5 Gross Stock Chart C11: Growth rates of gross capital stocks, manufacturing, equipment Growth rate average (198 to 1998): BEA-type =.75 Gross stock =.95 Gross Stock Chart C1: Growth rates of gross capital stocks, manufacturing, all assets 6 - Growth rate average (198 to 1998): BEA-type = 1.8 Gross stock = 1.9 Gross Stock -C-

51 Appendix C: Comparison of capital stocks: BEA-type (net) vs gross stocks Chart C1: Growth rates of gross capital stocks, non-manufacturing, structures 1 Growth rate average (198 to 1998): BEA-type =.5 Gross stock =.9 Gross Stock Chart C1: Growth rates of gross capital stocks, non-manufacturing, equipment Growth rate average (198 to 1998): BEA-type =.77 Gross stock =.98 Gross Stock Chart C15: Growth rates of gross capital stocks, non-manufacturing, all assets 5 1 Growth rate average (198 to 1998): BEA-type =.68 Gross stock =.81 Gross Stock -C5-

52 Appendix C: Comparison of capital stocks: BEA-type (net) vs gross stocks Chart C16: Growth rates of gross capital stocks, all industries, structures 1 Growth rate average (198 to 1998): BEA-type =. Gross stock =. Gross Stock Chart C17: Growth rates of gross capital stocks, all industries, equipment Growth rate average (198 to 1998): BEA-type =.7 Gross stock =.67 Gross Stock Chart C18: Growth rates of gross capital stocks, all industries, all assets 5 1 Growth rate average (198 to 1998): BEA-type =.57 Gross stock =.69 Gross Stock -C6-