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

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tt+

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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

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0.020.040.060.080.0100.0120.0

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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

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2008

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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