While it can be justified that the sales (or revenues) of firms in an industry follow a Pareto-distribution, I wonder how the value added (sales minus input costs minus taxes, excluding depreciation) can be summarized by a parametric distribution. Pareto seems not to work, since negative values are possible.

Is there an econometric theory that gives ground for a specific class of distributions? My dataset suggest something like Gumbel.

  • $\begingroup$ Why not to draw an empirical distribution of EBITDA from Compustat or open sources? $\endgroup$ Jun 2 '16 at 16:27
  • $\begingroup$ My data is incomplete and I like to use theoretical insights to fit a distribution that represents all data. $\endgroup$
    – Karsten W.
    Jun 2 '16 at 23:14

Interesting question.

Indeed, it's somewhat difficult to model value added because in many models firms don't make profits all the time. But therein lies your answer I think. Model VA as $Z$ in a distribution $g$ with two dimensions $(Z,Y)$, where Y is the size of the firm, Pareto distributed, and then for any given $Y$, $Z$ is distributed as $Z \sim Y \cdot (1+ X)$ with $X$ a normal variable or something like that, so that $Z$ can be negative, but it is still on average proportional to $Y$. You can maybe then solve for $f_Z=\int g(Z,Y)dY$ analytically or numerically otherwise.


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