[Paper Review] Disaggregating Input-Output Tables by the Multidimensional RAS Method

Vladimír Holý, Karel Šafr|arXiv (Cornell University)|Apr 25, 2017

Monetary Policy and Economic Impact10 references4 citations

TL;DR

This paper proposes the multidimensional RAS method to improve the disaggregation of input-output tables by simultaneously preserving row, column, regional, quarterly, and domestic/imported totals. By extending the traditional RAS algorithm to handle multiple dimensions of constraints, the method enhances estimation accuracy for national, regional, and sectoral applications, particularly improving the reliability of Leontief inverse and value-added calculations in the Czech industry case study.

ABSTRACT

An unknown input-output table can be estimated by the RAS method when only its row and column sums are known and some initial structure is assumed. The RAS approach can also be utilized for disaggregation of an annual national table to more detailed tables such as regional, quarterly and domestic/imported tables. However, the regular RAS method does not ensure that the sums of disaggregated tables are equal to the total table. For this problem, we propose to use the multidimensional RAS method which besides input and output totals also ensures regional, quarterly and domestic/imported totals. Our analysis of the Czech industry shows that the multidimensional RAS method increases the accuracy of table estimation as well as accuracy of input-output applications such as the Leontief inverse, the regional Isard's model and the quarterly value added.

Motivation & Objective

• To address the limitation of the standard RAS method, which fails to preserve disaggregated totals such as regional, quarterly, and domestic/imported sums.
• To develop a method that ensures consistency across multiple dimensions of input-output table disaggregation.
• To improve the accuracy of input-output applications like the Leontief inverse and regional Isard’s model by maintaining structural integrity across disaggregated tables.
• To validate the method’s effectiveness using real-world data from the Czech national industry table.

Proposed method

• Extends the classical RAS algorithm to incorporate multiple constraint dimensions, including national totals, regional distributions, quarterly fluctuations, and domestic vs. imported input shares.
• Applies iterative scaling across multiple dimensions simultaneously, adjusting the initial input-output matrix to satisfy all specified marginal constraints.
• Uses a weighted iterative procedure that preserves the initial structure while converging toward all required row, column, regional, and domestic/imported totals.
• Implements a multidimensional balancing mechanism that ensures all disaggregated tables sum precisely to the original total table.
• Employs a convergence criterion based on relative deviations between successive iterations to ensure stability and accuracy.
• Validated using the Czech national input-output table with known regional, quarterly, and trade composition data.

Experimental results

Research questions

• RQ1 How can input-output tables be disaggregated into regional, quarterly, and domestic/imported components while preserving all marginal totals?
• RQ2 To what extent does the multidimensional RAS method improve estimation accuracy compared to the standard RAS method?
• RQ3 How does the method affect the reliability of downstream economic applications such as the Leontief inverse and value-added calculations?
• RQ4 What is the impact of multidimensional constraints on the stability and convergence of the disaggregation process?

Key findings

• The multidimensional RAS method successfully preserves all specified marginal totals, including regional, quarterly, and domestic/imported inputs, ensuring consistency across disaggregated tables.
• The method significantly improves the accuracy of input-output model applications, particularly for the Leontief inverse and regional Isard’s model.
• Estimates of quarterly value added are more accurate under the multidimensional RAS approach compared to the standard RAS method.
• The method converges reliably and maintains structural coherence across all disaggregated components, as demonstrated in the Czech industry case study.