<p>Interesting question.</p>

<p>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.</p>

CC BY-SA 3.0
2016-06-03T04:08:11.353Z
2016-06-07T20:41:11.410Z
2016-06-07T20:41:11.410Z
Fix.B.
<p>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.</p>

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

CC BY-SA 3.0
2016-06-02T16:27:49.300Z
Why not to draw an empirical distribution of EBITDA from Compustat or open sources?
Anton Tarasenko
CC BY-SA 3.0
2016-06-02T23:14:10.127Z
My data is incomplete and I like to use theoretical insights to fit a distribution that represents all data.
Karsten W.
<econometrics><reference-request><theory-of-the-firm>
How is the "value added" of firms distributed
Karsten W.
# How is the "value added" of firms distributed

(Asked by: username_0 on 2016-05-30)

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.

**Tags:** econometrics, reference-request, theory-of-the-firm
> **Comments:**
> **username_1**: Why not to draw an empirical distribution of EBITDA from Compustat or open sources?  
> **username_0**: My data is incomplete and I like to use theoretical insights to fit a distribution that represents all data.  

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## 1 answers

### Answer by username_2 on 2016-06-03. Score: 1 | Accepted answer

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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