Hi, does your academic discipline typically use logit (or probit)
regressions with interaction terms? If so, then you may be able to help
me.
I am an academic in finance. There is a branch of research on
management turnover in the finance literature that analyzes the
sensitivity of turnover to performance, i.e. how badly does a firm need
to perform before the CEO is asked to leave (a particularly timely
question these days!) Often, the emphasis is on comparing two
"types" of firms to see when turnover is most sensitive to performance.
For example, firms might be sorted into two groups based on
characteristics of the board of directors, the people responsible for
supervising the CEO.
In general, participants in this literature estimate logit regressions
where turnover=f(performance, type, type*performance, controls). In
general, researchers focus on the estimated coefficient for the
interaction term of type*performance. Unfortunately, the estimated
coefficient for the interaction term (and its statistical significance)
depends not just on the true underlying sensitivity of turnover to
performance, but on the difference in the average likelihood of
turnover between the two types of firms. In general terms, this is
because the estimate coefficient is the log of the odds ratio which
depends on the underlying level of the odds.
In any event, I have written a short note which uses simulations to
illustrate this problem. While it is a subtle point, it is really a very basic
point. I would be incredibly surprised if it has not been addressed in
the literature of a different field. That is where you can come in:
1) Is that particular form of logit or probit regression typical in your
field? If so, can you give me some references?
2) Have you seen this statistical issue addressed in a paper, textbook,
etc? If so, can you give me some references.
Thanks for any help that you can offer.
Sincerely
Eric A. Powers
Assistant Professor of Finance
The Moore School of Business
University of South Carolina
Columbia SC, 29208
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