Statistical Approaches to
Balancing National Accounts
Brent R. Moulton
OECD, Working Party on National Accounts, Paris
October 5, 2007
Initial Estimates Need to Be Adjusted
“It is impossible to establish by direct estimation a
system of national accounts free of statistical
discrepancies, residual errors, unidentified items,
balancing entries and the like since the information
available is in some degree incomplete, inconsistent
and unreliable. Accordingly, the task of
measurement is not finished when the initial
estimates have been made and remains incomplete
until final estimates have been obtained which
satisfy the constraints that hold between their true
values.”
—Richard Stone
Journal of the Royal Statistical Society, 1982
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Initial Estimates not Sufficient
 Source data may not be available for all
components of the accounts—some estimates
are derived residually or by assumption.
 In other cases, more than one estimate may
be available, based on national accounting
identities. Examples:
 Total commodity supply = total commodity use;
 GDP via production, expenditure, and income
approaches;
 Net lending or borrowing from capital account
versus financial account.
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Source Data Are Subject to Errors
 Survey data are subject to sampling and nonsampling errors.
 Administrative data may be more
comprehensive, but are not designed to
match national accounting concepts.
 Mixture of enterprise and establishmentbased data may require bridging.
 Data from different sources may not use the
same classifications.
 Estimates for some components may be
extrapolated from earlier periods.
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Simple Methods
 In an input-output table, the RAS method
(bi-proportional adjustment) updates interindustry multipliers to be consistent with
given row and column totals. It is simple to
compute and preserves zero and nonnegative flows.
 A number of related techniques have also
been developed, based on linear or
quadratic programming or Theil’s entropy
approach.
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Stone, Champernowne, and Meade
 In 1942 (Review of Economic Studies), Stone,
Champernowne, and Meade recognized that
measures of reliability could be used to determine
which flows should be adjusted.
 Explicitly recognizes errors in measurement.
 Larger adjustments made to flows with largest errors; little
adjustment to flows with reliable initial estimates.
 In absence of standard errors, margins of error may be set
judgmentally.
 Flexible approach; allows some constraints to hold exactly,
others to be subject to error.
 Least squares method for solution.
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Byron Method
 Method proposed by Stone et al. required a
large amount of computation.
 In 1978 (Journal of the Royal Statistical
Society, A), Byron proposed a conjugate
gradient algorithm that is computationally
efficient, even for very large matrices.
 Byron’s method led to applications, for
example:
 van der Ploeg, J. Royal Stat. Soc., 1982;
 Barker, van der Pleog, and Weale, Rev. Income
and Wealth, 1984.
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Balancing U.S. Industry Accounts
 Most important obstacle to implementation
of approaches of Stone, et al., was lack of
objective information on reliability of initial
data.
 Research by Baoline Chen of BEA:
“A Balanced System of Industry Accounts for the U.S. and
Structural Distribution of Statistical Discrepancy,” 2006.
 Proposed an efficient generalized least
squares (GLS) method.
 Systematically gathered information on
coefficients of variation.
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Data Problems to Be Addressed
 For benchmark input-output accounts, gross output
(GO) compiled mostly from economic census.
 Initial estimate of intermediate consumption (IC)
generally based on a business expense survey.
 Initial estimate of gross operating surplus/mixed
income (GOS) largely based on administrative (tax
return) data.
 Inconsistencies between gross value added
calculated using:
 Production approach (GVA = GO — IC) and
 Income approach (GVA = Compensation + Taxes less
subsidies on production and imports + GOS).
 Least reliable initial estimates were IC and GOS.
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Sampling and Non-Sampling Errors
 Census Bureau and Statistics of Income
Division of the Internal Revenue Service
provided coefficients of variation for
published estimates.
 Surveys are subject to non-sampling error.
BEA analysts make adjustments for
identifiable non-sampling errors in order to
reduce bias. However, these adjustments
may be subject to misallocation errors.
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Adjustments to Source Data
 A number of adjustments must made
to source data:
 Conceptual adjustments
 Misreporting adjustments (for underreporting or misreporting on tax returns)
 Double counting adjustments
 Current-cost accounting of inventories and
consumption of fixed capital
 Imputations
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Statistical Discrepancy
 The estimates based on the expenditure
approach and the income approach differ.
The difference is shown in the U.S. national
income and product accounts as a statistical
discrepancy.
 The balanced industry accounts are
consistent with the reconciled expenditurebased estimate and adjust initial estimates
of IC and GOS to be consistent.
 Chen applied her approach to historical data
(the 1997 benchmark industry accounts).
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Implementation
 As part of BEA’s integration efforts,
the GLS method was applied to the
reconciliation of the 2002 benchmark
use table.
 Paper by Howells, Morgan, Rassier, and
Roesch of BEA:
“Implementing a Reconciliation and Balancing Model
in the U.S. Industry Accounts,” 16th International
Conference on Input-Output Techniques, 2007,
http://www.iioa.at/conferences-IO.html
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Results and Next Steps
 Input-output tables were released on
September 21, 2007.
 Method was computationally efficient.
 Allowed less experienced staff to do
balancing work.
 Didn’t eliminate need for judgmental
adjustments, but allowed quick
identification of the most important
discrepancies.
 BEA plans to refine the model and
potentially expand its use.
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