Using a Weighted Average of Base Period Price Indexes to Approximate a Superlative Index

Janice Lent, Alan H. Dorfman

Abstract:
The Lloyd–Moulton price index has been advocated as a timely approximation to a superlative price index. We show that a weighted average of the arithmetic and geometric base-weighted (Laspeyres) indexes can serve as a simple, robust alternative to the Lloyd–Moulton. The parameter needed for the weighted average can be readily and systematically estimated from past data and continuously updated as new data become available. Previous methods of estimating this parameter have entailed either a trial-and-error process, requiring human judgment, or the use of iterative numeric algorithms. An empirical study indicates that we may compute timely, close approximations to a superlative index using a weighted average of the arithmetic and geometric Laspeyres indexes with parameters estimated and systematically updated from prior data.

Keywords:
Taylor series, elasticity of substitution, Lloyd–Moulton Index, sample survey