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Chained Indices Unchained: Structural Transformation and the Welfare Foundations of Income Growth Measurement

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  • Omar Licandro
  • Juan Ignacio Vizcaino

Abstract

This paper examines how to measure welfare-relevant growth in economies undergoing structural transformation, where persistent changes in relative prices and expenditure patterns can lead to aggregation biases in standard output measures. We address this issue within a continuous-time dynamic general equilibrium model featuring non-homothetic preferences, sector-specific productivity trends, and investment-specific technical change. We compare two welfare-based measures of real income growth: a current-base equivalent variation measure and a chained Fisher-Shell index. The chained Fisher-Shell index coincides with the chained Divisia index, providing strong theoretical foundations for national accounting methodology and requiring the growth rates and nominal expenditure shares of major expenditure components as sufficient statistics for a welfare-based output index. In contrast, the current-base index is more informationally demanding, requires systematic revisions, and introduces base-dependent biases that distort the evaluation of past growth. Our quantitative analysis reveals that these biases are substantial, increase over time, and conflict with key stylized facts in the structural transformation literature.

Suggested Citation

  • Omar Licandro & Juan Ignacio Vizcaino, 2026. "Chained Indices Unchained: Structural Transformation and the Welfare Foundations of Income Growth Measurement," CESifo Working Paper Series 12946, CESifo.
    • Handle: RePEc:ces:ceswps:_12946
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    Keywords

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    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • E01 - Macroeconomics and Monetary Economics - - General - - - Measurement and Data on National Income and Product Accounts and Wealth; Environmental Accounts
    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • O11 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Macroeconomic Analyses of Economic Development
    • O14 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Industrialization; Manufacturing and Service Industries; Choice of Technology
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

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