At what threshold of a variable of interest does the interaction between two variables become negative?

[Loic DUBOIS]

Hello everyone,

I hope you're all well?

Here's my problem:

Dependent variable: vote "for" by institutional investors (forpourcent)

variables of interest :
nominee gender: dummy which takes 1 if female and 0 otherwise (GEND)
board gender diversity: proportion of women on boards (Boarddiversity)

Here is my regression:
regress forpourcent GEND centBoarddiversity i.GEND#c.centBoarddiversity controlvariables i.Year i.company


(centBoarddiversity is the Boarddiversity variable centred at the mean)

Here are the results:

(if the image is not displayed, here are the coefficients:
- GEND : 0,0355 (1% threshold)
- centBoarddiversity : 0,4398 (1% threshold)
- GEND * cenBoarddiversity : -0,4275 (1% threshold))


It turns out that when a woman is nominated, the percentage of "for" votes from investors is higher. The higher the proportion of women on boards, the higher the percentage of "for" votes from investors. On the other hand, the interaction has a negative and significant coefficient, indicating that when a woman is nominated to a diversified board, investors tend to vote less in favour.

So these are very interesting results, but now I'd like to know at what threshold of gender diversity on boards the proportion of investors voting 'for' decreases when a woman is proposed.

Do you have a way of finding out this threshold?

Thanks in advance.

[Clyde Schechter]

So, the marginal effect of GEND conditional on centBoarddiversity is 0.0355 - 0.4275*centBoarddiversity. To find the range of centBoarddiversity over which this would be negative, we can first observe that it is a monotone decreasing function of centBoarddiversity. Therefore, it suffices to find the upper boundary of that region--which would be the point at which the marginal effect is zero.

0.0355 - 0.4275*centBoarddiversity = 0
0.0355 = 0.4275*centBoarddiversity
0.0355/0.4275 = centBoarddiversity
0.083 = centBoarddiversity (rounded to 3 decimal places)

So, whenever centBoarddiversity exceeds 0.083, the marginal effect of GEND on forpourcent will be negative.

[Loic DUBOIS]

Thank you very much Clyde for your reply.