How is the "value added" of firms distributed 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.
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.