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www.bea.gov
BEA’s Fixed Assets
Accounts:An Overview
Dave WasshausenThe First World KLEMS Conference
Harvard University
August 19-20, 2010
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Fixed Assets Accounts (FAAs)
▪ Net [Wealth] Stock
▪ Investment
▪ Depreciation
▪ Other Changes in Volume of Assets (OCVA)
▪ Average Age
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Net [Wealth] Stock vs BLS Productive Stock
▪ BEA calculates wealth stocks Depreciation rates generally derived from
market prices of used assets Corresponding depreciation reflected in the
NIPAs as a charge against income from current production
▪ BLS calculates productive stocks Deterioration rates reflect productive
capability of the asset Used to calculate multifactor productivity
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Wealth Stock vs Productive Stock
▪ Assets depreciate (BEA) quicker than they deteriorate (BLS)
▪ For example, an automobile provides similar level of productive service after 1-year of use; however its value has declined significantly
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Wealth Stock vs Productive Stock
0
200
400
600
800
1000
tt+
4t+
8t+
12t+
16t+
20t+
24t+
28t+
32t+
36t+
40
Year
Mill
ion
s o
f d
olla
rs
BLS Productive Stock BEA Wealth Stock
`
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Valuations
▪ Historical-cost Book value measure
▪ Real-cost Quantity measure
▪ Current-cost Replacement-cost measure Current-cost depreciation is the featured
NIPA depreciation (aka consumption of fixed capital or CFC)
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Perpetual Inventory Method (PIM)
Used for all asset-types except autos to indirectly derive net stock:
Kjt = Kj(t-1)*(1-rj) + Ijt*(1-rj/2) - Ojt
Where:Kjt = net stock for year t for type of asset j
rj = depreciation rate for type of asset j
Ijt = investment for year t for type of asset j
Ojt = other changes in volume of assets for year t for type of asset j
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Physical Inventory Method
▪ Applies independently estimated prices to a direct count of the number of physical units of each type of asset.
▪ More direct than PIM but is used only for autos because they are the only type of asset with sufficient source data.
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Estimating Methodologies
▪ PIM can be rewritten as follows:Kjt = Kj(t-1) + Ijt - Ojt - Mjt
Where:Mjt = depreciation for year t for type of asset j
▪ Depreciation is estimated as a residual as follows:
Mjt = Ijt – Ojt - (Kjt - Kj(t-1))
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Estimating Methodologies
▪ Historical- and real-cost net stock and depreciation are calculated using the perpetual (or physical) inventory method.
▪ Current-cost net stock and depreciation are calculated by reflating real-cost estimates.
Price indexes taken from NIPA fixed investment estimates.
Current-cost estimates can be sensitive to price changes (i.e., CFC for housing in recent periods).
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Current-cost vs. Historical-cost
Depreciation for Owner-Occupied Housing
0
50,000
100,000
150,000
200,000
250,000
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Mil
lio
ns
of
do
llar
s
0.020.040.060.080.0100.0120.0
Ind
ex l
evel
Current-cost Historical-cost Price Index
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Investment
▪ Investment (nominal and real) by asset-type comes from NIPAs for most assets.
Handful of asset-types that differ for the FAAs -- private fixed investment reconciliation tables can be found here (www.bea.gov/national/FA2004/index.asp)
▪ Investment by industry and by legal form of organization (LFO) are derived using Census data on:
Capital expenditures by industry
Payroll and revenue by legal form of organization.
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Depreciation
▪ Depreciation profiles are based on empirical evidence of used asset prices in resale markets wherever possible.
▪ Geometric patterns are used for most asset types because they more closely approximate actual profiles of price declines than straight-line patterns.
▪ Based on empirical studies, BEA data, or technological factors, some assets (autos, computers, missiles, and nuclear fuel) justify the use of a nongeometric pattern of depreciation by BEA.
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Depreciation
▪ Rates are calculated by dividing the declining-balance rate (DBR) by the asset’s assumed service life.
▪ DBRs primarily derived from estimates made by Hulten and Wykoff under the auspices of the U.S. Department of the Treasury.
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Service Lives
▪ Service lives for nonresidential fixed assets based primarily on studies conducted by the Department of the Treasury.
▪ Service lives for most types of residential structures are taken from a study by Goldsmith and Lipsey.
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Service Lives
▪ Ideally, service lives would be calculated by industry and varied over time to account for changes in business conditions and technology; however, data limitations prevent this.
Service lives for the following assets vary by industry: Communications equipment, metalworking machinery, special industry machinery, general industry machinery, heavy trucks, aircraft and service industry machinery.
Service lives for the following assets vary over time: Computers, office and accounting machinery, light and heavy trucks, autos, aircraft, electric power structures, and mining exploration, shafts, and wells for petroleum and natural gas.
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Published Depreciation Rates
Rate of Service Declining Type of Asset depreciation life balance rate
Photocopy and related equipment 0.1800 9 1.6203
Office and accounting equipment:
Years before 1978 0.2729 8 2.1832
1978 and later years 0.3119 7 2.1832
Other fabricated metal products 0.0917 18 1.65
Steam engines and turbines 0.0516 32 1.65
Internal combustion engines 0.2063 8 1.65
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OCVA
War losses (begin with 1940)
Estimated from a variety of sources, including newspapers and other media sources.
Disaster losses (begin with 1971)
Generally defined as catastrophic events with property losses exceeding 0.1 percent of GDP (or about $15 billion).
Also estimated from a variety of sources, including insurance-related trade data, risk management firms, and official government reports.
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Disaster Losses
020,00040,00060,00080,000
100,000120,000
1992
1994
1996
1998
2000
2002
2004
2006
2008
Mil
lio
ns
of
do
llar
s
Disaster Losses
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Average Age
▪ Weighted average of the ages of all depreciated investment in the net stock as of yearend.
▪ Net stock expressed as a function of investment only:
Kjt = Ijt*(1-rj/2) + Ijt-1*(1-rj/2)(1-r)1 + … + Ijt-n*(1-rj/2)(1-r)n
▪ Net “age” stock calculated by “aging” each vintage of investment as follows:
= (0.5)*Ijt*(1-rj/2) + (1.5)*Ijt-1*(1-rj/2)(1-r)1 + … + (n+.5)Ijt-n*(1-rj/2)(1-r)n
▪ Age equals net “age” stock divided by net stock
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Average Age Example
Year Ijt Kjt Age_Kjt Age_Kjt derived as a function of investment, Ijt Age
t 5 4.9 2.4 = 0.5 * (5 * 0.975) 0.5
t+1 10 14.4 11.8 = (0.5 * (10 * 0.975)) + (1.5 * (5 * 0.975 * 0.95)) 0.8
t+2 20 33.2 34.6 = (0.5 * (20 * 0.975)) + (1.5 * (10 * 0.975 * 0.95)) + (2.5 * (5 * 0.975 * 0.952)) 1.0
t+3 40 70.5 83.9 = (0.5 * (40 * 0.975)) + (1.5 * (20 * 0.975 * 0.95)) + (2.5 * (10 * 0.975 * 0.952))… 1.2
Where: Ijt = investment
Kjt = net stock
Age_Kjt = "age" stock
Age = Age_Kjt ÷ Kjt
* The depreciation rate is assumed to be 0.05 in this example
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Published Estimates
Standard FAA tables presented by: Asset-type Industry Legal form of organization
Detailed FAA Tables presented by: Detailed asset-type and industry
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BEA Fixed Assets Accounts
www.bea.gov/national/FA2004/Index.asp
Email questions to:FANIWD@bea.gov
OrDavid.Wasshausen@bea.gov
(202) 606-9752
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