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I have the following unbalanced dataset. In this, HHI is the Hirschman-Herfindahl-Index, a measure between 1/n and 1, and my sample is a large number of worldwide firms.

I am trying to investigate effects of market diversification (measured through HHI) and firm performance onto each other, (measured through ROA, profit margin, etc.) with some controls (firm size, industry category). All the other variables are distributed in a normal way (although not normally distributed), but I cannot think of what to do with this variable.

When this variable HHI is one of several independent variables, I do not see a problem with this skewed distribution. However, when it is the explained variable (i.e. I want to find out what are reasons for firms to diversify), I cannot seem tow ork with this. I thought about logit and probit, because I am regressing on something below 0 and 1, after all; but they actually require zero-values, and my HHI is never zero. Stata says to this:

outcome does not vary; remember:
                                  0 = negative outcome,
        all other nonmissing values = positive outcome

A very brute thing to do would be to categorize all data with a HHI<0.9 as "low_HHI" and above as "high_HHI", but that seems like a very unnecessary loss of information.

Do you have an idea?

unbalanced data

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    $\begingroup$ There are techniques for dealing with what I believe is called clumping. This is usually clumping at zero but in your case is at one. It is not an area in which I am expert so I leave it to others to offer a proper answer. $\endgroup$ – mdewey Nov 8 '16 at 10:14

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