Munich Personal RePEc Archive

Accounting for variety

Winkler, Julian (2022): Accounting for variety.

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I introduce a general method to account for the distribution of underlying components (variety) in the growth of an aggregate quantity, using the notion of entropy. This accounting decomposition enables a number of insightful applications to index numbers in economics. The cross-entropy of GDP with respect to a benchmark captures the change in its distribution, and thus how well this benchmark matches data for price and volume indices across time. This ‘error’ changes demonstrably over time. Accounting of variety also lends itself to a decomposition of labour productivity growth by a technology component (how many more ‘average’ goods are produced per unit of labor?), and the allocation of labour (does the distribution of labour inputs converge to the distribution of outputs?) plus demand (does the distribution of expenditures diverge from the distribution of outputs?).

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