Industrial Production and Capacity Utilization – G.17

FRB Estimates of Manufacturing Investment, Capital Stock, and Capital Services

June 13, 2019

In order to estimate industrial capacity for the G.17 statistical release on Industrial 

Production and Capacity Utilization, the Federal Reserve Board (FRB) produces annual 

estimates of investment, capital stocks, and capital services in chain-weighted real dollars for 

detailed industries within the manufacturing sector. In 2016, the FRB began publishing data on 

investment and capital stocks by broad asset type at the four-digit North American Industry 

Classification System (NAICS) level.1 The 2019 release expands the level of industry detail and 

now includes capital services (capital input). In particular, the new data include estimates at the 

six-digit NAICS level for investment, capital stocks, and capital services, and also include the 

portions of investment and capital related to software.2 The following note briefly describes the 

methodology underlying the construction of these data series.

Industry-Level Investment

Historical time series of annual industry-level estimates of current-dollar spending on 

new equipment and new structures are derived from multiple sources. For 1972 and forward, the 

principal sources of industry-level investment data are the Annual Survey of Manufactures 

(ASM) and the quinqennial Census of Manufactures (COM), both from the U.S. Census Bureau. 

Because it typically takes one to two years to go from collecting the data for an ASM or COM to 

publication, the FRB forecasts investment for the most recent years using indicators of 

manufacturing capital spending plans, lagged utilization rates, and internal staff estimates of 

broad investment categories. 

For years prior to 1972, the FRB employs investment estimates from the Office of 

Business Analysis (OBA) at the Department of Commerce, which are available at a three-digit 

Standard Industrial Classification (SIC) basis. To share out these three-digit SIC investment 

figures to the four-digit level, the FRB uses information from Jack Faucett Associates, an 

 1 These data have been used for some time in the NBER-CES Manufacturing Industry Database jointly published by 

the National Bureau of Economic Research and the U.S. Census Bureau’s Center for Economic Studies.

2 Capital stock and investment data are available beginning in 1952, with capital services for individual industries 

available beginning in 1953. For the portions of investment and capital related to software, data begin in 1959 for 

investment and capital stock and in 1960 for capital services.
economic consultancy. The four-digit SIC level investment data are subsequently converted to 

NAICS using industry-level concordances.

Asset-Level Investment

The FRB divides investment into thirty-six asset categories (thirty for equipment, five for 

structures, and one for software) based on data from the Bureau of Economic Analysis (BEA) on 

aggregate U.S. capital spending. For recent years, estimates are based on asset-level investment 

from the BEA’s national income and product accounts (NIPA). Some published NIPA 

categories, however, are less detailed than the corresponding Federal Reserve asset categories; 

their data are allocated to the more detailed FRB categories based on historical shares in the 

BEA’s Fixed Assets and Consumer Durable Goods in the United States (FACDG).

3

 For years 

prior to 1992, the estimates are based on the BEA’s wealth stock models published in FACDG or 

on the earlier models published in Fixed Reproducible Tangible Wealth in the United States, 

1925-89 (FRTW).4 For years for which NIPA data are not yet available, the FRB forecasts 

asset-level investment.

Combining the Industry-Level and Asset-Level Estimates

Because detailed data for asset-by-industry investment are available for only select years, 

the Federal Reserve estimates annual time series for asset-by-industry investment by combining 

the annual industry spending totals on new equipment and on new structures with the annual 

economy-wide capital spending by detailed asset categories, along with their corresponding price 

deflators. This asset decomposition of industry-level investment is estimated separately for 

equipment and for structures. 

Data on asset-by-industry investment were previously available in the BEA capital flow 

tables (CFTs), which contained detailed parsing of hundreds of asset types across manufacturing 

and non-manufacturing sectors. Because the CFTs are only available for select years—and 

notably ceased to be published in 1997—the FRB creates an initial estimate of asset-by-industry 

investment for non-CFT years by interpolating between adjacent CFT shares; more recent years 

 3 “Fixed Assets and Consumer Durable Goods for 1995–2005,” Survey of Current Business, September 2006, pp.22-

33. In addition, the most up-to-date data may be found at http://www.bea.gov/national/FA2004/Index.asp. 4 Fixed Reproducible Tangible Wealth in the United States, 1925–89. Bureau of Economic Analysis (Washington: 

U.S. Government Printing Office).
use the 1997 CFT’s distribution as an initial estimate. The FRB also makes use of the annual 

data on investment in certain asset classes published in the ASM and COM.

For years when the CFT is unavailable, the final FRB estimates for the asset composition 

of industry investment results from using a biproportional matrix-balancing technique, more 

commonly called RASing.5

 In brief, if one considers the by-asset, by-industry composition of 

investment for a specific year as a matrix in which the i,jth element is the amount of investment 

by industry j made in asset i, then RASing will yield a unique final non-negative matrix of 

industry-by-asset investment flows such that the components of the matrix sum to appropriate 

industry- and asset-level totals.6

 

FRB-PIMS Estimates of Capital Stocks 

The FRB uses the investment data outlined above to construct industry-by-asset net 

capital stocks, defined as the accumulation of past gross investment less the accumulation of past 

depreciation. These capital stock estimates are based on the FRB’s perpetual inventory model 

(FRB-PIMS). FRB-PIMS is similar to a standard PIMS model, but does not use a constant rate 

of decline in productive capability. Rather, the FRB-PIMS assumes that efficiency declines less 

for a relatively new asset than it does for an asset nearer the end of its expected useful life. The 

non-constant decline rate combines two separate effects: discards and decay. The discards effect

is a probability-based estimate of the actual service life of an asset, conditional on a mean service 

life and a distribution around the asset’s expected service life. The decay effect is the relative 

loss of economic efficiency of the asset as it ages. The joint effects of discard and decay are 

combined into the age-efficiency function used in the FRB-PIMS.7

As described in Gilbert and Mohr (1996), the FRB-PIMS formula for the net capital stock 

at time t for asset j that allows for non-constant rates of efficiency decline is

(1) ∑= = −

j S

i

G

j i j t i

N

j t K I

0 , φ , , ,

 5 Michael Bacharach (1965), “Estimating Nonnegative Matrices from Marginal Data,” International Economic 

Review, vol. 6 (3), pp. 294-310. 6 More detail on the RASing procedure can be found in Gilbert, Charles and Mike Mohr (1996), "Capital Stock 

Estimates for Manufacturing Industries: Methods and Data," Working Paper. Available online at 

https://www.federalreserve.gov/releases/g17/CapitalStockDocLatest.pdf. 7 The expected efficiency of an a-year-old asset as a share of the efficiency of a brand new asset—that is, the 

proportion of economic efficiency remaining in an a-year-old asset is given by ( ) ( ) .5

.5 |, |, S

a D S φ κβ σ a S P S S dS − = ∫ .
where represents the proportion of economic efficiency remaining in an i-year-old asset and 

accounts for the combined effects of discard and decay, and Sj is the maximum service life of 

asset of type j. Equation (1) can be rewritten in terms of increments to the net capital stock from 

net investment flows:

(2) N

j t

N

j t

N

j t K K I , = , −1 + , ,

where net investment is the difference between gross investment flows and replacement 

investment,

(3) R

j t

G

j t

N

j t I I I , = , − , ,

so

(4) R

j t

G

j t

N

j t

N

j t K K I I , = , −1 + , − , .

Defining ω j,i as the amount by which the economic efficiency of an asset is reduced between 

ages i-1 and i—the combined effects of discard and decay—replacement investment is the sum 

of the incremental loss of economic efficiency between years t-1 and t in each investment 

vintage: 8

(5) ∑= = −

j S

i

G

j i j t i

R

j t I I

0 , ω , , .

Operationally, given a time series of gross investment flows in the j

th asset type, { }

T

t

G

j t I

0 , = , 

and given the assumptions for the stochastic mean service life and beta decay that yield the 

sequence of increments to economic efficiency loss over the life of an asset, { }S j

i j i 0 , = ω , 

replacement investment is calculated according to equation (5). Given equation (5) and 

assuming N

j

N

j K I ,0 = ,0 , the time series of net capital stocks is constructed according to

equation (4).

9

 

The service lives for the various assets are chosen from the BLS multifactor productivity 

system. For some assets, the service life varies by three-digit NAICS industry. For a few assets, 

a discrete change in the service life occurs at some calendar date (such as aircraft, which have a 

mean service life of 15 years before 1960 and 19 years thereafter). 

 

8 Therefore, , , 1 1 i

j i k j k φ ω= = −∑ in equation (1).

9 The time series of investment flows begins far enough in the past so that by the early 1950s, the level of the capital 

stock does not depend on the initial investment flows for any asset category.

φ j,i
An industry-level capital stock is obtained by aggregating asset-level stocks using chainweighting procedure with BEA investment prices.

Construction of Capital Services 

Capital services (also known as capital input) reflect the flow of services derived from the 

net stocks of productive assets. To create capital services for a given industry, the FRB 

aggregates asset-level capital stocks using a Tornqvist index method with implicit rental prices 

as weights. As stated in the primary source for the BLS method of constructing measures of 

capital, “The ‘implicit rental price’ or ‘user cost’ of capital is based on the neoclassical principle 

that inputs should be aggregated using weights that reflect their marginal products.”10 Indeed, 

because capital services more closely reflect the concept of the marginal product of capital than 

the total capital stock, a measure of capital services is a key independent variable in the FRB’s 

models of industrial capacity. For this reason, the FRB began publishing its estimates of capital 

services in 2019.

The rental price formula for a particular asset is derived from a simple neoclassical model 

in which the price of an asset is assumed to be the present discounted value of the expected flow 

of services from that asset over its lifetime.11 It is equivalent to the rent one would be willing to 

pay to get the same flow of services as would be obtained by purchasing the asset. The rental 

price takes into account asset-specific depreciation, expected price declines, and tax treatment of 

capital. The rental price formula is

(6) , , ( , ,, ) R rel rel

jt jt j jt jt jt p pr p p = +− δ τ  ,

where p is the deflator for the asset, r is a rate of return, δ is a deprecation rate, , ,

rel rel

jt jt p p  is a 

real capital gains-capital loss term (based on the asset deflator relative to the GDP deflator), and 

τ captures the effects of various tax considerations. 

 10 U.S. Department of Labor (1983), “Trends in Multifactor Productivity, 1948-1981,” Bulletin 2178. 11 Hall, Robert, and Dale Jorgenson (1967), “Tax Policy and Investment Behavior,” American Economic Review, 

vol. 57 (3), pp. 391-414.