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I am working on a paper that tests to see if banking competition has an impact on whether borrowers engage in relationships with multiple banks.

Number of relationships with various banks obtained from the survey :

Eg

firm (a) 1 relationship with a bank

firm (b)3 relationships with 3 different banks

firm (c)5 relationships 5 with 5 different banks

I made a small change to the number of relationship variable as I want to use counts models such as poisson, nbreg and ZIP on Stata :

Instead I am using a slightly transformed version, I am using firms with 1 relationship as having zero multiple relationship and firms with lets say 5 relationships as having 4 multiple relationships .

Is this a sensible approach to model counts?

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It sounds like all you're proposing to do is just subtract 1 from the number of bank relationships each company has.

The only effect this will have on your model is on its interpretation. For instance, if you're using linear regression, then the coefficients change from "the effect on the number of bank relationships" to "the effect on the number of additional bank relationships".

Statistically, there is nothing wrong with this procedure. I think it makes some intuitive sense as well.

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