st: What statistical method to use? Private equity in Scandinavia

[Christoffer Norman <21758@student.hhs.se>]

Dear Statalists,

I am currently writing my bachelor thesis about differences in operational performance between domestic and international investors. We use Scandinavian data to find out if Scandinavian private equity companies are better at improving the operational performance of its portfolio companies than international firms.

Here's the setup:

- Two time periods (before and after acqusition)
- Three groups (Scandinavian private equity companies, international without Scandinavian office and international with Scandinavian office

Now to the question:

Which statistical method would be most appropriate to use?

We are thinking about a diff-in-diff-in-diff estimation that would look as follows:

y = b0 + b1*dInt + b2*dInt*dOff + b3*d2 + b4*dInt*d2 + b5*dInt*dOff*d2 + controls + e 

dInt = international private equity company (non-Scandinavian)
dO = Scandinavian office
d2 = Owned by PE-company

Our dependent variables are (mainly) operational measures such as sales, EBIT-margin, change in EBIT-margin, etc.

Our worry with using the diff-in-diff(-in-diff) method is that this is not really a natural experiment. Furthermore, our contol group (companies owned by Scandinavian private equity firms) are affected by the "treatment" as well. However, one could say that the two groups get two different treatments, and we are only interested in the differences in the effects of the treatments (b4 and b5 in the equation above).

Is this an appropriate method to use given our setup? If no, what would be the alternative?

Thank you in advance!

Best regards,

Christoffer
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