A Recursive Framework for Consistent Sectoral Real Value-Added in Chain-Weighted National Accounts

Chain-weighted Fisher indexes are widely used in modern national accounts for their theoretical strengths and ability to capture changes in relative prices over time. However, the fundamental limitations of this approach are non-additivity and inconsistency - the sum of sectoral real value-added does not equal aggregate real GDP, and the sum of sectoral contributions to growth does not match the aggregate economic growth rate. This difference complicates empirical analysis and undermines the interpretability of sectoral dynamics. To resolve this issue, we extend the recursive method proposed by Choi and Pyo (2025), adapting it to the U.S. National Income and Product Accounts (NIPA), based on the Fisher Ideal Index. By constructing symmetric, Fisher-compatible growth contributions and embedding them in a recursive structure, we generate sectoral real value-added series, both level- and growth-additive. Empirical validation using U.S. BEA data confirms that our method fully restores internal consistency, offering a theoretically sound and operationally effective solution to the non-additivity problem in chain-weighted systems.