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

<jats:p>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.</jats:p>