Index Numbers: An Info-Gap Analysis of Uncertainty

Abstract

An index number is a scalar-valued function of price and perhaps quantity data that supports the assessment of the state or trend of an economy. Many researchers over the past 250 years have proposed diverse mathematical forms for index numbers, and discussed criteria for their validity. In this paper we propose an additional criterion for evaluating an index number and for interpreting its numerical value in practice: its robustness to uncertainty in the price data upon which it is based. High robustness implies reliable assessment by the index; low robustness implies unreliable assessment. We analyze the robustness to price uncertainty of four standard index numbers (Dutot, Carli, Jevons and Young), and suggest two additional index numbers. We consider two numerical examples based on observed global commodity prices. In both examples the estimated price indices all indicate price increase. In one example, the robustness to price-uncertainty is low, impugning the reliability of the estimates. In the other example, large robustness supports the implication of the indices. We establish three analytical relations between the robustnesses of the various indices.

Keywords: data uncertainty, index number, price index, info-gap theory, robustness to uncertainty, satisficing

JEL Classification: C43