Accounting for variety

Abstract:

I introduce a general method to account for the distribution of underlying components (variety) of an aggregate quantity, using the notion of entropy. This accounting decomposition enables a number of insightful applications for 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 an decomposition of labour productivity growth by a technology component (how many more `average' goods are produced per unit of labor?), an allocation component (does the distribution of labor inputs converge to the distribution of outputs?), and cost disease (does the distribution of expenditures diverge from the distribution of outputs?).