1. Simultaneous Reconciliation of a Large Disaggregated Time Series of Accounts with an Application to the U.S. Input-Output Accounts
Baoline Chen1 Tommaso Di Fonzo2 Thomas Howells1 Marco Marini3
1BEA – Bureau of Economic Analysis
2University of Padova, Department of Statistical Sciences
3International Monetary Fund
Statistics Department   
2nd Conference of the Society of Economic Measurement
July 22~24, Paris, France

2. Outline of the Presentation

3. Motivation: A Practical Problem at National Accounts

4. Reconciliation Problems Preliminary Values, Linear Constraints in a System of Time Series

5. Statistical Reconciliation Minimize a Quadratic Constrained Minimization Function

6. Movement Preservation Principle Denton (1971), Cholette (1979), and Helfand, et al. (1977)

7. Simultaneous Solution Adjusting All Periods and All Variables at the Same Time

8. Reliability of Data, Alterability Coefficients Considering the Reliability of Variables in the Adjustment

9. Reconciliation of the U.S. Annual IO Accounts

10. BEA’s Solution for Reconciling Input-output Accounts Multi-step Procedure

11. Our Approach

12. The Reconciliation Problem Some Details and Dimensions of the Problem

13. Notation: Benchmark and Annual IO Accounts

14. Notation: Input vector and constraints

15. The Reconciliation Problem Aggregation Matrix, Exogenous and Endogenous Constraints

16. Adjustment Criterion: PFD and PROP Multivariate Denton PFD and proportional adjustment procedure

17. A Combined Criterion: PFD-PROP Bikker et al (2013)

18. Analysis of Discrepancies Temporal and Contemporaneous Constraints

19. Discrepancies by industry Aggregated from 830 industries at 6-digit NAICS to 65 industries at 3-digit NAICS level of detail

20. Discrepancies of 12 Major Industries and 13 Major Commodities Aggregated from disaggregated preliminary data (in $)

21. Exercise in This Study

22. Main Results Focus on 43 Major Aggregates

23. Assessment of Results Levels

24. Assessment of Results Growth Rates

25. Main Results: Performance of PFD, PROP and PFD-PROP

26. Comparison of PFD, PROP and PFD-PROP Summary Measure of Adjustment

27. Comparison of PFD, PROP and PFD-PROP Reconciliation at Disaggregated and Aggregated levels using PROP

28. Comparison of PFD, PROP and PFD-PROP Reconciliation at Disaggregated and Aggregated levels using PFD

29. Comparison of PFD, PROP and PFD-PROP Reconciliation at Disaggregated and Aggregated levels using PFD-PROP

30. Comparison of PFD, PROP and PFD-PROP Reconciliation at Disaggregated and Aggregated Levels

31. Conclusion and Further Development

32. Thank you for your attention!