Updated Capital Asset Service Lives Susan Powers (BLS), Michael D. Giandrea (BLS), Robert Kornfeld (BEA), Peter B. Meyer (BLS), Steve Rosenthal (BLS), Randy Kinoshita (BLS), Michael Cusick (BEA) World KLEMS meetings June 4, 2018

Need for service life estimates Productive capital = structures, equipment, software Direct measures of capital stocks are not available Perpetual Inventory Method (PIM) makes estimates of capital stock by industry from past investment Service lives assumed to be distributed symmetrically around reported average age (haystack distribution) Adjust past investment for deterioration using an age-efficiency function (BLS-hyperbolic and BEA-geometric) Aggregate efficiency-adjusted investments over time into a productive capital stock in each period BEA measures of net investment and BLS measures of MFP growth and capital services Often cited – recently in relation to productivity slowdown and productivity / wage gap Measures are sensitive to estimates of service lives and depreciation Measurement of MFP requires information on output and multiple inputs: Capital Services Labor Energy Materials Purchased Business Services

Sources of current asset service lives Bureau of Economic Analysis provides BLS with depreciation rates for asset categories. Sources: Hulten and Wykoff (1979, 1981a, 1981b) U.S. Treasury Bulletin F (1942) IRS/Treasury Office of Industrial Economics (1970s) Treasury Office of Tax Analysis (1980s and 1990s)

Establishment survey by Statistics Canada Annual Capital and Repair Expenditures Survey Ongoing survey since 1980s Data includes Expenditures on 155 asset types Expected service lives of new assets Selling prices and ages of disposed assets / discards Used asset sales and discards Large sample of service lives and depreciation rates 1985-current Two sets of analyses, 1985-2001 and 2002 – 2010 No real change in structures Overall slightly larger depreciation rates in equipment but largely a compositional change moving towards more computerized equipment with higher depreciation rates. Asset compared to asset is similar. 155 asset types is more than in data from Italy or Netherlands We reviewed more recent data from other countries Italy’s Istat, Statistics Netherlands, Japan’s Economic and Social Research Institute, and Statistics Canada Italy and Netherlands have relatively few asset types Japan has over 600 asset classes Differences are primarily shorter, but they are in both directions depending on asset Goods incorporating semiconductors tend to have shorter lives in newer data

Canada’s Annual Capital and Repair Expenditures Survey

Canadian service lives and depreciation rates for construction Canadian categories include Industry building construction, commercial building construction, Institutional building construction, Marine engineering construction, Transportation engineering construction, Waterworks engineering construction, Sewage engineering construction, Electric power engineering construction, Communication engineering construction, Oil and gas engineering construction, Mining engineering construction, Other engineering construction.

Canadian service lives and depreciation rates for equipment

US – Canada concordance Needed a concordance between US and Canadian asset categories to map Canadian service lives to US asset categories BLS and BEA worked together to construct a concordance BEA documentation on the definitions of fixed investment expenditure categories used in developing concordance

US – Canada concordance

US – Canada concordance Statistics Canada asset categories more detailed than US typically. In some cases, multiple Canadian categories are combined into one U.S. category BEA nominal fixed investment data used to weight depreciation rates and develop single rate In one case, Nuclear Fuel (31), no comparable asset exits in the Canadian scheme so we continue to use the current BEA/BLS rate, provided by an expert

Comparison of US and Canadian lives Higher depreciation rate and shorter service life for computers: 3 years in Canada and 5 in US. Service lives could be reduced if there is rapid ongoing quality improvement or changes in technical standards. These kinds of changes would make it optimal to upgrade to the latest stuff more quickly. Devices with semiconductors such as computers and smartphone have these properties. We did not investigate whether such quality changes were correlated to the assets whose measured service lives were shorter than before.

US and Canadian lives - structures

Testing new service lives BLS re-computes depreciation through hyperbolic; BEA through geometric Challenging to compute stocks from an existing asset base whose lives changed 2 possible models of changing service life: Service lives change for all assets because new substitutes available or standards to be met Service lives changed for newly created assets Can lead off with: “Having applied the concordance to map service lives from the Canadian categories to the US ones . . . “ DMSP “recomputes depreciation” with ASUM program

Effects of revised service lives BEA and BLS evaluated capital stocks scenarios with the revised SC depreciation rates: The first adopted the new rates from the start of the investment time series – 1901 The second implemented the new rates beginning in 1985, assuming services lives had changed Steve points out that BEA has already updated some figures SINCE 1985. There are 1992 updates. How did we handle these? In conversation Steve had an interest in switching to the SC figures earlier Steve would like to see growth rates on the graph of “comparison of existing and revised capital stocks” and a year-by-year table of growth rates in the paper. The growth rates change with the adoption of the SC lives, right? That’s relevant for all the later computations. Levels are less relevant.

Comparison of existing and revised capital stocks – BEA

Comparison of existing and revised capital stocks – BLS

Comparison of existing and revised growth rates of the capital stock

Effects of revised service lives on MFP

Conclusions The revised depreciation rates have a substantial downward impact on capital stock levels and growth rate trends For most assets, the updated service life data has little impact on estimated capital services and MFP growth rates

BLS and BEA Future Plans Use Canadian depreciation rates as guidance for revising current US depreciation rates and related BEA and BLS service lives Develop and jointly propose a set of new U.S depreciation rates in the near future

Internal and External Rates of Return BLS Michael D. Giandrea Peter Meyer Susan Powers Steve Rosenthal Brian Chansky Randy Kinoshita June 4, 2018

Rate of return The rate of return, rit , represents how many dollars of income are generated per $100 of physical capital assets Effort underway to standardize methodology across major sector and industry studies divisions IRR = Internal Rate of Return ERR = External Rate of Return

Rate of return – Industry Division Uses a simplified version of the IRR formula 𝑟 𝑖,𝑡 = 𝐶𝐶 𝑖,𝑡 − 𝑘 𝑖,𝑡 𝑝 𝑡 𝑇 𝑡 𝑑 𝑡 − 𝑘 𝑖,𝑡 ∆ 𝑝 𝑡 𝑇 𝑡 𝑘 𝑖,𝑡 𝑝 𝑡 𝑇 𝑡 Capital compensation CCit Capital stock kit Asset price deflator pt Tax parameter 𝑇 𝑡 = 1− 𝑢 𝑡 𝑧 𝑡 1− 𝑢 𝑡 Asset depreciation dt Industry output is sectoral output ut corporate income tax rate zt p.v. of tax depreciation allowances

Rate of return – Industry Division Calculates IRR for 88 industries (primarily 4-digit) Must first generate estimates of capital income by detailed industry Capital income is industry output less value of labor and intermediate purchases

Major Sector and Industry Divisions Both calculate IRR at the industry level Major Sector: at the NIPA industry level Industry Division: 4-digit NAICS industry level Different measures of capital income Major Sector: uses BEA corporate capital income and proprietors’ income data Industry Division: estimates capital income as an industry residual

Industry Division – External rate of return Focus is not on whether IRR is negative Instead, look for negative detailed asset rental prices which can occur for many reasons Low capital income levels Negative IRRs High capital gains

Industry Division – Use of ERR If the rental price for an industry is negative, substitute an ERR of 3.5% If rental price for ANY asset calculated with an IRR is negative, the ERR is used for ALL assets in that industry in that year Industry Division also omits the capital gains term for the rental price calculation when using the ERR This change is only for the single year

Upcoming changes – Industry Division Calculate and use an ERR based on the Industry Division’s manufacturing sector IRR Requires evaluation of change to assess effect on rental prices and capital measures compared to current approach Adjust the new ERRs such that industry sectoral output equals value of capital, labor and intermediate inputs, by industry ERR for Air Transportation and Line-Haul Railroads will not be changed

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