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 baoline.chen@bea.gov thomas.howells@bea.gov 2University of Padova, Department of Statistical Sciences difonzo@stat.unipd.it 3International Monetary Fund Statistics Department mmarini@imf.org    2nd Conference of the Society of Economic Measurement July 22~24, 2015 Paris, France

Outline of the Presentation

Motivation: A Practical Problem at National Accounts

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

Statistical Reconciliation Minimize a Quadratic Constrained Minimization Function

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

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

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

Reconciliation of the U.S. Annual IO Accounts

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

Our Approach

The Reconciliation Problem Some Details and Dimensions of the Problem

Notation: Benchmark and Annual IO Accounts

Notation: Input vector and constraints

The Reconciliation Problem Aggregation Matrix, Exogenous and Endogenous Constraints

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

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

Analysis of Discrepancies Temporal and Contemporaneous Constraints

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

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

Exercise in This Study

Main Results Focus on 43 Major Aggregates

Assessment of Results Levels

Assessment of Results Growth Rates

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

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

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

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

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

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

Conclusion and Further Development

Thank you for your attention!