Harmony, Statistical Inference with the Herfindahl H Index and C Index

Abstract

The Herfindahl H index and C index provide measures of harmony of accounting measurement practices by summarizing the extent to which companies use the same accounting practice. While the values of these indices are compared to obtain some idea concerning the relative harmony of accounting practice, standard errors for these estimates are not generally provided. That is, an index is calculated from a sample but no guidance is provided concerning likely values of the index in the population from which the sample was drawn. The present article fills this gap in the literature by providing formulae to estimate the standard error of the H and C indices calculated from a sample. The formulae are illustrated with several examples from the literature to show how conclusions are either enhanced or modified by the addition of these standard errors. It is shown that while both indices are biased, this bias is generally negligible. It is hoped that in future authors will quote not only the value of the index itself but also the standard error so differences between index values (both within and between studies) can be judged as being either significantly different or explainable by sampling variation alone.

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