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REGIONAL ECONOMIC ISSUES
Working Paper Series

Census Content of Bureau of Economic
Analysis Input-Output Data
Philip R. Israilevich, Randall W. Jackson and Jon Comer

FEDERAL RESERVE BANK
OF CHICAGO




WP-1991/2

Census Content of Bureau of Economic Analysis
Input-Output Data
Introduction
Perspectives on the nature of input-output (I-O) frameworks can be
characterized by two schools of thought. One school views the input-output
data as a representation of empirical reality. The values are believed to
represent observations drawn from economic reality. The second school
views the input-output model essentially as a concept. An input-output table
is seen by this group as a qualitative representation of regional economic
structure. Qualitatively accurate tables can be based in large part on expert
opinion. Conversely, quantitatively accurate tables will be based strongly on
empirical observation.
The ex-ante input-output framework, originally developed by Battelle
Institute, is an example of the qualitative representation of economic
structure. 1 These tables, which are based on expert opinion instead of
observed data, can be constructed relatively quickly and inexpensively. The
reliability of these tables has not been established. Ex ante 10 tables have not
been tested, for example, against data from the U.S. Censuses.
The input-output accounts compiled and published by the U.S. Census,
Bureau of Economic Analysis (BEA), are treated widely as tables based on
observation. However, close examination of the BEA manufacturing data
reveals less than total consistency with the Census data on which they are
based. Hence, some degree of "expert opinion", either subjective or
mechanical, enters into the BEA process. Therefore, there may be no
examples of purely objective quantitative 10 tables. There is, more likely, a
continuum of positions between purely quantitative tables based solely on
observation, and tables based solely on expert opinion.

Philip R. Israilevich, Federal Reserve Bank, Chicago and University of Illinois. Randall W.
Jackson and Jon Comer, Ohio State University. The support of National Science Foundation
Grant SES-8822044, and of the Federal Reserve Bank of Chicago are gratefully acknowledged.

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In this paper, we compare the published BEA data with published Census data
to determine the degree of the bias introduced by "expert opinion" in the BEA
10 table construction process.2 If this bias is strong, then the distinction
between the ex ante type and BEA type tables is overemphasized, i.e. in the
process of 10 tables construction both BEA and ex ante approaches rely
heavily on the expert opinions. Conversely, a strong similarity between
primary Census data and BEA 10 data would suggest that BEA type tables
primarily relies on the observed data. This would make BEA IO approach
distinct from the ex ante approach.
More specifically, this paper presents the results of a preliminary analysis of
the relationship between Census of Manufacturing data and BEA data. The
tests reported here are part of a larger project in which the spatial variability
of input-output relationships is the primary focus. Broader long-run interests
include
1.

providing a stronger empirical basis for modifying national input-output
tables to reflect the structure of regional economies (referred to as
adaptation techniques)

2.

assessing variability in production within industries due to establishment
size, stage of production process, capital and labor intensity, etc., and

3.

providing an establishment scale basis for the development of
probabilistic input-output models.

These issues involve or influence the relationships among national and
regional input-output data and the production relationships of establishments.
Throughout the larger project, we focus on the empirical relationships
between disaggregated Bureau of Census data and aggregated Bureau of
Economic Analysis data. An appropriate starting point is therefore an
analysis of the relationship between aggregate national input-output data and
the aggregate primary data that are the foundation of the national input-output
accounts.
The following section begins by describing our understanding of the inputoutput tables construction process. This is a necessary basis from which to
elaborate our expectations. The third section describes the data preparation
and testing procedure, and the results of each step of the test. The final
section summarizes our findings and raises important issues for further
attention.
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Accounts Construction
The procedure

Constructing and publishing the national input-output accounts is one among
many responsibilities of the Bureau of Economic Analysis (BEA). The
quinquennial accounts represent the interindustry and inter-sectoral dollar
flows for years in which the Bureau of Census surveys manufacturers,
services, trade, etc. (i.e., 1967, 1972, 1977, 1982, etc.). Since 1972, the inputoutput accounts have been published on a commodity-industry basis.
The BEA table is based on data from the Manufacturing, Construction,
Wholesale and Retail Censuses, on data from regulatory agencies related to
financial institutions and utilities, and numerous other sources. To illustrate
some of the problems faced by the BEA, consider the example of the
Manufacturing Census. This Census reports expenditure shares on materials
(6 - digit) consumed by each industry. Some materials are not specified by
the questionnaire and fall into the "other" category. The BEA, using expert
opinion, has to reapportion this "other" category into specific products and
services. The Manufacturing Census does not collect any data on the
consumption of services or construction, or trade, or transportation
expenditures. All of these have to be estimated based on nonmanufacturing
Census reports and expert opinion. The BEA has the additional chores of
splitting expenditure shares into domestic and foreign, and reconciling
industry sales with industry purchases and with the national income and
product accounts.
As most input-output analysts are acutely aware, the process is extremely
time-consuming. The accounts for a given year may be published seven or
eight years later (e.g., the 1982 input-output structure is expected to be
publicly available in mid-1991). From an outside user's perspective, there
appear to be three main reasons for this delay. First is the sheer magnitude of
the task, which will be described more fully, below. Second, like most federal
agencies in the last decade, the funding for the BEA has not kept pace with
the increasing demands for data provision. The result of budget tightness has
led to reduction of full-time employees (primarily by attrition) devoted to the
task, during a period in which the changes in the underlying structure of the
U.S. economy have been complex and rapid. The third reason is due to the
delay in the transfer of data from the Bureau of the Census (BOC) to the BEA.
Based on a synthesis of various documents and conversations with staff of the

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two Bureaus, and focussing on manufacturing, our understanding of the
process is as follows.
During the Census year, the BOC gathers its survey data via questionnaire.
Great effort is taken to ensure that coverage is as complete as possible.
Follow-up questionnaires and contacts by phone or in person are frequently
undertaken. The data gathering process itself is time consuming. As the data
come in, they are encoded and tested for consistency, especially with respect
to reporting and coding errors. Once the data are encoded and checked, they
are evaluated with respect to disclosure rules. The data are then compiled in
various forms, such as that of Table 7 in the Census of Manufacturing, which
lists selected materials consumed by industry. This entire process can take as
long as four years.
During this time, the BEA will have been gathering primary data in other
formats, including canvassing trade association experts, industry leaders, and
key persons in targeted industries. At some point, perhaps four years after the
quinquennial census, the BOC makes its industry summaries available to the
BEA on a computer tape.
From this point on, the process becomes less clear. The input-output research
community generally has operated on the assumption that BEA uses BOC
data, in the form of Table 7 of Census of Manufacturing, for example, in
conjunction with its own primary data, to develop a prototype input and
output structure of the economy. Discrepancies among the various data
sources would be arbitraged and reconciled, and the entire accounting
structure would be reconciled with the national income and product accounts
(NIPA's) and gross national product (GNP) for the census year.
The whole procedure is much more intricate than here suggested. To trace
every procedure executed by the BEA is beyond the scope of this study.
However, the activities listed, form a skeletal view of the input-output account
construction process.
Expectations

Intuition suggests that inertia is characteristic of the accounts from period to
period. Sources of this inertia are varied. One source is the technological
inertia in the production system itself. The error and consistency checking
procedure may be a second source of inertia in the accounts. Values different
in the extreme from previous period values logically demand further scrutiny.
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The result might well be a temporal smoothing of the data. This intentional or
unintentional smoothing may, in fact, take place within both involved
agencies.
We expect a significant relationship between input-output coefficients based
on BOC estimates of materials consumed by industry and the final
coefficients based on the BEA Use table, which lists commodities consumed
by industry. We logically expect the direction, and to a significant extent the
magnitude of changes, in these coefficients to correspond. Trends in the BOC
data should be reflected by trends in the BEA data.

The Analysis
Generating comparable data for BEA and BOC industries is a task made more
difficult by the differences in agency practices. The BEA uses its own
sectoral classification, while the BOC uses the Standard Industrial
Classification (SIC) code system. To conduct the tests described below, we
limited the analysis to those sectors whose definitions were virtually identical.
Sectoral definitions vary temporally, which further restricted the number of
usable time periods. Also, because we had access only to the printed versions
of these data sources, it was necessary to limit the number of sectors analyzed.
The industrial sectors for the analysis were selected by assessing the
sensitivity of industries in the economy. The technique identifies sensitive
sectors based on West's (1982) measure of inverse sensitivity. An input
coefficient is defined to be inverse sensitive if a given change in value leads to
a greater than average change in the Leontief inverse. Quantitative estimates
of these sensitivities were combined on a column by column basis to
determine the relative sensitivity rankings of industries. For 1977, these are
BEA sectors:
14 Food and Kindred Products
17 Miscellaneous Textile Goods and Floor Coverings
59 Motor Vehicles and Equipment
These three sectors are comprised of 59 BEA sub-sectors. From these, we
compiled 109 observations on materials used, for consistently defined 1972
and 1977 BEA and BOC data. The variables used in the following analysis are

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B72, B77, denoting BEA 10 tables for 1972 and 1977, and C72 and C77
denoting BOC data for 1972 and 1977.
To assess the variability in each data source, we initially regressed 1977
values on 1972 counterparts. A constant term was not included, because a
zero base-level is expected.3 We were interested in variability within each
data set, and in the consistency between data sources within declining and
growing input-coefficients. Therefore, we also partitioned each agencies data
base. One partition corresponds to materials for which the BEA input
coefficients were increasing in magnitude, and the other subset is comprised
of materials for which the BEA input coefficients were decreasing. Because
we expect inertia to be dominant, we expect the coefficient on prior year
coefficient to be very near unity. Hence, the t-statistics and 2-tail probabilities
for the prior year variable have been adjusted to indicate statistical difference
of the regression coefficient from unity, rather than from zero. The results of
these regressions are shown in Table 1 for BEA and Table 2 for BOC.
By regressing B77 on B72 for all observations, the coefficient for B72 is not
significantly different from one. The R-squared indicates that nearly 95% of
the variation in B77 can be explained by the variation in B72 If we knew
beforehand which BEA coefficients would be increasing over the period, then
for these coefficients the results shown in Table lb indicate an average
increase of roughly 10 % in the input coefficient value over the period, with a
regression coefficient that is significantly different from one. Likewise, Table
lc suggests that for input coefficients whose values were decreasing over the
period, the new value, on average, would be roughly 85% of the old, with
nearly 96% of the variation in the new values explained. The results for the
BOC input coefficients are very similar in form. On average, however, the
observation pairs from the Census either increased more than, decreased less
than, or, in the extreme, changed in the opposite direction from their BEA
counterparts.
An important difference between the two data sources is that the BOC reports
values in purchaser's prices, while the BEA reports values in producers prices.
Ideally, we expect the foundation of the relationship to be that given in
equation 1 .
B11 m,1C71
B12 m12C12

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(1)

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where Bl = BEA reported commodity use for time t divided by BEA's
estimate for total output for the using industry for time t
C1 = Census reported material purchased for time t divided by the

Census estimate of total value of shipments for time t
and

ml = a downward adjustment factor to purge material purchased

estimates of trade and transport margins.
To simplify the expression, rewrite the equation as
(2)

B = mC

With the corresponding data, we can test to see how closely the equality holds
in practice. By using the logarithmic form:
ln(B) = In (m) +

ln(C)

(3)

we can test for a change in margin factors ln(m) as a constant, as well as for
ai = 1. Throughout the remainder of the paper, the following variable names
are used:
ocq

- constant term in the regression equation

LBRATIO - In (B77 / B72) as a proxy for In (B)
LCRATIO - In (C77 / C72) as a proxy for In (C)
The relationship shown in equation 3 was tested using OLS regression
methods. Again, the relationship was assessed for the whole set of 115
observations, and for partitions defined by increasing or decreasing BEA
input-coefficients. The results are presented in Table 3. The t-statistics refer
to difference from zero for the constant term and difference from unity for the
coefficient on the treatment variable.
Table 3a shows the regression results for the entire sample. The constant is
not statistically different from zero, so on average, the ratio of margins is not
different from one. The adjusted R2 of .15 shows that only 15% of the
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variation in the logged BEA ratios can be accounted for by corresponding
variation in the logged Census coefficient data. Influential variables must be
missing from the model specification. BEA’s decisions and other data
manipulations are responsible for the majority of the variation in published
input-output data.
The coefficient on the independent variable is the
elasticity of BEA coefficients to Census coefficients. On average, a 1%
change in Census coefficients changes the corresponding BEA coefficient by
.57%. However, this elasticity is not sufficiently informative, because it does
not separate coefficients increasing in time from those that are decreasing.
Had we had prior information on which BEA coefficients would increase and
which would decrease, Table 3b and Table 3c would provide the relevant
information. Partitioning the data set reveals the significance of the change in
margins in determining the change in BEA data. However, in both cases the
magnitude of the coefficient on the LCRATIO falls, which indicates an even
weaker relationship between the BEA data and the BOC data upon which they
are thought to be based.

Discussion
The results of this limited analysis might suggest cause for great alarm on first
reading. However, there are several points that should be noted, before any
call to arms. First among these is small sample size. The BEA’s use table
contains 534 x 537 transactions (286,758) values. Many of these are zero
values. Our analysis used only 109 observations from among the larger set.
This criticism is partially balanced by recalling our focus on coefficients from
industrial sectors with greater than average analytical significance. These
sectors are in one sense, key economic sectors. Hence, results for these
sectors alone are of interest.
There also are different views concerning the appropriate foundations of
input-output tables. There are those who believe that input-output tables must
be quantitatively precise. Many economists, for example, treat BEA IO
coefficients as unbiased, observed data, and attempt to ’’explain" these
coefficients with input prices or other variables (see Hudson and Jorgenson,
1975, for a well known example). There are others, however, who are
convinced that for the input-output framework to be useful, the structure must
only be qualitatively accurate.
For them, input-output tables are,
conceptually, qualitative representations.

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Based on the limited findings presented, herein, those who treat the BEA
input-output data as grounded on empirical observation might be tempted to
question the degree of confidence that can be placed on BEA's published
input-output data. However, if BEA 10 accurately reflect the qualitative
character of regional (national) economic structure, such input-output tables
should play a valuable role in economic analysis.
Lacking, however, is a more complete communication of the process by
which the BEA makes its final estimates of inter-industry and inter-sectoral
transactions. Input-output data increasingly provide the bases for estimates of
regional economic impacts of public capital expenditures, and for forecasts of
regional economic activity. The data are used in generating regional inputoutput models, and in integrated input-output econometric forecasting models.
The accounts at the national level are used by industry in assessing markets
and in forecasting demand. Researchers and analysts at all levels need to
know that the data on which they base their work is reliable. To this end, the
input-output table construction process must be more publicly available. This
effort may simply involve the disclosure of the extent to which there is heavy
reliance on expert opinion. Finally, if expert opinion is playing a significant
role in the BEA's table construction process, researchers may do well to re­
assess the merits of ex ante approaches to 10 table generation.

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Footnotes
^Kx ante IO was developed by the Battelle Memorial Institute and is based on the data developed
from experts testifying on the use of energy, materials and services by different industries, see
H.W. Fisher (1975).
9

Bias, in the content of IO table construction, should not be interpreted negatively. Problems of
primary data collection clearly may justify modification based on expert opinion.
There are no data pairs for which one element is zero. However, the use of a constant would
reflect an expected base-level use of an input in 1977 when that input was not used in 1972. The
number of new non-zero elements in a table is a very low percentage of all prior-year zero
elements. Separate regressions including a constant term produced a coefficient not statistically
different from zero.

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References
Fisher, H.W. (1975). E x A n te as a Supplement or Alternative to RAS in
Updating Input-Output Coefficients, in E stim a tin g a n d P ro je c tin g In putO u tpu t C o e ffic ien ts , edited by R. Allen and W. Gossling, Input-Output
Publishing Co., 1975.
Hudson, E., and D.W. Jorgenson (1974). US Energy Policy and Economic
Growth, 1975-2000, B e ll Jou rn a l o f E c o n o m ics a n d M a n a g em en t S c ie n c e ,
Volume 5, pp 461-514.
U.S. Department of the Census, C ensus o f M an u factu rin g, 1977.
U.S. Department of Commerce, Bureau of Economic Analysis,
1977.

D e ta ile d

In p u t-O u tp u t S tru ctu re o f the U.S. E c o n o m y ,

West, Guy R. "Approximating the Moments and Distributions of InputOutput Multipliers," Working Paper No. 6, University of Queensland,
Queensland, Australia, 1982.

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Table 1
Regression Results for Bureau of Economic Analysis’

a)
Dependent Variable is B77
N= 109 Sample includes all coefficients
STD. ERROR T-STAT.
VARIABLE COEFFICIENT
B72
0.9877550
0.0195678
.626
0.947483
Mean of dependent var
R-squared
Adjusted R-squared
0.947483
S.D. of dependentvar
b)
N= 53

Dependent Variable is B77
Increasing BEA input coefficient partition

STD. ERROR T-STAT.
VARIABLE COEFFICIENT
B72
1.0974697
0.0219744
4.436
0.971970
Mean of dependent var
R-squared
Adjusted R-squared
0.971970
S.D. of dependent var
c)
N= 56

2-TAIL SIG.
>0.35
0.067165
0.124958

2-TAIL SIG.
0.000
0.087723
0.145092

Dependent Variable is B77
Decreasing BEA input coefficient partition

STD. ERROR T-STAT.
VARIABLE COEFFICIENT
B72
0.8419614
0.0216109
7.313
0.956900
Mean of dependent var
R-squared
0.956900
Adjusted R-squared
S.D. of dependent var

2-TAIL SIG.
0.000
0.047708
0.099825

‘All T-statistics reported are absolute values.

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Table 2
Regression Results for Bureau of Census Data

a)
Dependent Variable is C77
N= 109 Sample includes all observations
STD. ERROR T-STAT.
VARIABLE COEFFICIENT
C72
0.9892841
0.0130227
.823
0.975604
Mean of dependent var
R-squared
Adjusted R-squared
0.975604
S.D. of dependent var
b)
N= 56

Dependent Variable is C77
Decreasing BEA input coefficient partition

STD. ERROR T-STAT.
VARIABLE COEFFICIENT
C72
0.9267161
0.0172175
4.256
0.976653
R-squared
Mean of dependent var
Adjusted R-squared
0.976653
S.D. of dependent var
c)
N= 53




2-TAIL SIG.
0.000
0.050503
0.101289

Dependent Variable is C77
Increasing BEA input coefficient partition

STD. ERROR T-STAT.
VARIABLE COEFFICIENT
C72
1.0204701
0.0177561
1.153
0.977768
Mean of dependent var
R-squared
0.977768
S.D. of dependent var
Adjusted R-squared

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2-TAIL SIG.
>0.3
0.074076
0.129948

2-TAIL SIG.
0.26
0.098984
0.151623

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Table 3
Inter-agency relationships

a)
Dependent Variable is LBRATIO
N= 109 Sample includes all observations
STD. ERROR T-STAT.
VARIABLE iCOEFFICIENT
-0.0526087
0.0642354 0.8189987
“0
0.6480273
0.1419332
2.479
LCRATIO
Mean of dependent var
0.163054
R-squared
0.155232
S.D. of dependent var
Adiusted R-squared
b)
N= 56

Dependent Variable is LBRATIO
Decreasing BEA coefficient partition

STD. ERROR T-STAT.
VARIABLE COEFFICIENT
0.1276762 3.5477574
-0.4529642
“0
0.1820999
0.2345767
3.487
LCRATIO
0.011037
Mean of dependent var
R-squared
-0.007278
S.D. of dependent var
Adiusted R-squared
c)
N= 53




2-TAIL SIG.
0.001
0.001
-0.509457
0.782208

Dependent Variable is LBRATIO
Increasing BEA coefficient partition

STD. ERROR T-STAT.
VARIABLE COEFFICIENT
0.2424457
0.0318115
7.6213158
«0
LCRATIO
0.4470740
0.0966971
5.718
0.295349
Mean of dependent var
R-squared
0.281532
Adiusted R-squared
S.D. of dependent var

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2-TAIL SIG.
0.415
0.001
-0.117065
0.711817

2-TAIL SIG.
0.000
0.000
0.297537
0.253333

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