Augmenting input-output system under the curse of dimensionality: AHP-RAS integration and algorithm simulation

Abstract

ABSTRACT In the estimation of input-output tables, one frequently encountered challenge is the aggregation of sectors in initial tables, which complicates the estimation of more detailed tables due to missing data—a phenomenon referred to as the “curse of dimensionality” when augmenting from lower to higher dimensions. We propose an AHP-RAS method to address the substantial data deficiencies encountered in the expansion of input-output tables. The method applies the Analytical Hierarchy Process (AHP) to transform the subjective relative importance of sectors into input coefficients using Pairwise Comparison Matrices (PCM) and eigenvector methods. Subsequently, it incorporates the RAS approach to supplement objective data, thereby integrating subjective judgement and objective information to tackle the curse of dimensionality. Unlike traditional AHP methods, this study employs binary integer programming to decompose large-scale matrices into subsets, making the AHP technique applicable to input-output tables with a broader range of sectors. We employ Monte Carlo simulation techniques to evaluate the robustness of the proposed methodology, specifically assessing the impacts of subjective judgement, objective data utilization, and the variation in sector numbers. Overall, the method overcomes the curse of dimensionality, yielding coefficients within an acceptable error margin, thereby demonstrating a significant advancement in the field of input-output analysis.