Statistical Approaches to Balancing National Accounts

1. Statistical Approaches to Balancing National Accounts Brent R. Moulton OECD, Working Party on National Accounts, Paris October 5, 2007

2. 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

3. 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.

4. Source Data Are Subject to Errors • Survey data are subject to sampling and non-sampling errors. • Administrative data may be more comprehensive, but are not designed to match national accounting concepts. • Mixture of enterprise and establishment-based data may require bridging. • Data from different sources may not use the same classifications. • Estimates for some components may be extrapolated from earlier periods.

5. Simple Methods • In an input-output table, the RAS method (bi-proportional adjustment) updates inter-industry multipliers to be consistent with given row and column totals. It is simple to compute and preserves zero and non-negative flows. • A number of related techniques have also been developed, based on linear or quadratic programming or Theil’s entropy approach.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. Adjustments to Source Data • A number of adjustments must made to source data: • Conceptual adjustments • Misreporting adjustments (for under-reporting or misreporting on tax returns) • Double counting adjustments • Current-cost accounting of inventories and consumption of fixed capital • Imputations

12. 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 expenditure-based estimate and adjust initial estimates of IC and GOS to be consistent. • Chen applied her approach to historical data (the 1997 benchmark industry accounts).

13. 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

14. 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.