BEA’s
Fixed Assets Accounts:
An Overview
Dave Wasshausen
The First World KLEMS Conference
Harvard University
August 19-20, 2010
www.bea.gov
Fixed Assets Accounts (FAAs)
▪ Net [Wealth] Stock
▪ Investment
▪ Depreciation
▪ Other Changes in Volume of Assets (OCVA)
▪ Average Age
www.bea.gov
2
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
www.bea.gov
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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
www.bea.gov
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Wealth Stock vs Productive Stock
Millions of dollars
1000
800
600
400
`
200
t+
12
t+
16
t+
20
t+
24
t+
28
t+
32
t+
36
t+
40
t+
8
t+
4
t
0
Year
BLS Productive Stock
www.bea.gov
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)
www.bea.gov
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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
www.bea.gov
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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.
www.bea.gov
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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))
www.bea.gov
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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).
www.bea.gov
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Current-cost vs. Historical-cost
120.0
100.0
80.0
60.0
40.0
20.0
0.0
200,000
150,000
100,000
50,000
0
Index level
250,000
19
99
20
00
20
01
20
02
20
03
20
04
20
05
20
06
20
07
20
08
20
09
Millions of dollars
Depreciation for Owner-Occupied Housing
Current-cost
www.bea.gov
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.
www.bea.gov
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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.
www.bea.gov
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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.
www.bea.gov
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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.
www.bea.gov
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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.
www.bea.gov
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Published Depreciation Rates
Type of Asset
Photocopy and related equipment
Rate of
Service
depreciation
life
Declining
balance rate
0.1800
9
1.6203
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
Office and accounting equipment:
www.bea.gov
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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.
www.bea.gov
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20
08
20
02
20
04
20
06
19
96
19
98
20
00
120,000
100,000
80,000
60,000
40,000
20,000
0
19
92
19
94
Millions of dollars
Disaster Losses
Disaster Losses
www.bea.gov
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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
www.bea.gov
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Average Age Example
Year
Ijt
Kjt
Age_Kjt
Age_Kjt derived as a function of investment, Ijt
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
2
= (0.5 * (20 * 0.975)) + (1.5 * (10 * 0.975 * 0.95)) + (2.5 * (5 * 0.975 * 0.95 ))
1.0
t+3
40
70.5
83.9
2
= (0.5 * (40 * 0.975)) + (1.5 * (20 * 0.975 * 0.95)) + (2.5 * (10 * 0.975 * 0.95 ))…
1.2
Age
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
www.bea.gov
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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
www.bea.gov
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BEA Fixed Assets Accounts
www.bea.gov/national/FA2004/Index.asp
Email questions to:
FANIWD@bea.gov
Or
David.Wasshausen@bea.gov
(202) 606-9752
www.bea.gov
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