Allyn Young and the Theory of Index Numbers

This paper gives a fuller account of Allyn Young’s contribution to index numbers than given by Charles Blitch. It also examines Young’s claim in strengthening the logical foundations of Fisher’s ideal index number. Young entered into a lengthy correspondence with Wesley Mitchell and Irving Fisher on the subject and helped shape their works. His position on index numbers evolved over the years. Initially, he was fascinated by Fisher’s ideal index number because it was both an average of ratios and a ratio of averages, but he later gave up his predilection for the geometric average. He stated that any properly weighted and constructed index number was just as good. Although the harmonic mean gave results smaller than the geometric, and the geometric smaller than the arithmetic, for comparison purposes it made little difference which average was used. His conclusion was that a theoretically perfect index number was an impossibility, and the choice of the index depended on the problem at hand.