Although applied economists often estimate interaction terms to infer how the effect of one
independent variable on the dependent variable depends on the magnitude of another independent
variable, most researchers misinterpret the coefficient in nonlinear models. The magnitude of the
interaction effect does not equal the marginal effect of the interaction term, can be of opposite
sign, and its statistical significance is not calculated by standard software. I have written a
paper with Chunrong Ai called "Interaction terms in nonlinear models" in which we present the correct
way to estimate the magnitude and standard errors of the interaction effect in nonlinear models,
including the widely used log transformation model with unknown error distribution.
You can find a copy of this working paper at www.unc.edu/the/THE_WPS.htm
Edward Norton
Associate Professor
UNC at Chapel Hill
> ------------------------------
>
> Date: Fri, 16 Aug 2002 15:11:57 -0400
> From: [email protected]
> Subject: st: Does your academic discipline use logit regressions with interaction terms?
>
> 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
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
