Modelling profit-rate distributions: A case-study in the use of L-moments

L-moments are used to model distributions with long tails. We adapt them for company profit rates in economics.

Company profit rates are variables whose distributional properties have excited little interest among economists -- in contrast, say, to that which they have devoted to firm size.

Such discussion as there has been normally gets little further than consideration of measures of dispersion, never mind distributional models.

By contrast the hydrology literature has a pressing need to discriminate accurately between models whose principal differences are in the behaviour of the tails – a need that the method of L-moments has been developed to answer.

It turns out that profit rate distributions are not only skewed, but have very long tails, on the left as well as the right. If one believes that an appropriate model for their distribution is one with a lower bound (the gamma, for example) there is thus a need to estimate a threshold parameter, in addition to that for robust methods to take account of the right tails.

It turns out that L-moments answer both requirements -- but only after weighted sampling of profit rates by company size, such is the extreme character of the basic data.

Once this is done, the method can, among other things, show that different profit rate definitions imply widely varying distributional models, and, for some measures, discriminate clearly between different industries on the basis of their profit rate distributions.

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