Interaction terms in non-linear model

[Simona Gamba]

Dear Statalist,
I am running a NB and a ZINB model with an interaction term.
In particular, I want to evaluate the effect of a given policy on the number of patents. Since I believe that the effect of the policy may be different for developed and developing countries, together with the dummy variable "policy" I added the interaction term "policy* developing country" (instead, I have no dummy for being a developing country since this country characteristic is time invariant, and it is dropped once I add the country FE).
Now, what I obtain, in terms of IRR, is a coefficient (not statistically significant) of 1.395 for "policy", and a coefficient of 0.494 (statistically significant at the 5% level) for "policy* developing country". If both coefficients were significant, I would have said that having a given policy causes an increase of 39.5% in the number of patents, while this effect reduces by 50.6% for developing countries (for which therefore the effect of the law is 0.395*0.494=19.5%).
But what can I say if the coefficient for "policy" is not statistically significant, while the one for "policy* developing country" is?
Thank's
Simona

[Dave Airey]

Just to be clear, are you saying you have an interaction term in the model without both main effects in the model?

[Simona Gamba]

Yes, because the main effect "being a developing country" is omitted because of country FE...

[Dave Airey]

I'm posting this just in case: http://www.ats.ucla.edu/stat/stata/f...ain_effect.htm. Sounds like you are already familiar with this kind of thing, about how standard interpretations can change when the model doesn't have main effects too.

[Simona Gamba]

Thank's for the link! This compicates things even more: I was erroneously thinking that loosing one main effect because of FE was like controlling for it...
May I ask you some help to interprete the results? I have understood I need to rescale them, but it's not clear to me how to do it with an exponential model.
Here are results I obtain for a simplified NB model, where country FE are not included (so that I can have both main effects- "least_developing" is the same as "poor"):

weightedp	IRR	Std. Err.	z	P>z	[95% Conf.	Interval]
law	1.745122	.3688159	2.63	0.008	1.153273	2.640704
least_developing	.0071902	.0012028	-29.50	0.000	.0051802	.0099801
law_poor	.7586166	.2447968	-0.86	0.392	.4030412	1.427892
_cons	353.8976	51.86221	40.05	0.000	265.5447	471.6476

while these are the results when one main effect is omitted (always without FE):

weightedp	IRR	Std. Err.	z	P>z	[95% Conf.	Interval]
law	7.66305	1.702895	9.16	0.000	4.957313	11.8456
law_poor	.0054546	.0019868	-14.31	0.000	.0026713	.011138
_cons	80.59382	7.400211	47.80	0.000	67.31991	96.48504

So, in the first table I see that the effect of the law causes an increase of 75% in the number of patents for developed countries, and (if I am not wrong) the effect for developing countries should be the same (given that "law_poor" is not significant).
But what about the second table?
Thank you very much for pointing this out!!

[Simona Gamba]

Ok, thank's (again) to the help of Statalist I have solved this last problem: although one of the main effect is omitted (because it is time invariant and I have country FE), I can still interprete my results and my coefficients as I was doing (so, no need to rescale them).

So, the previous question should still make some sense:
Using a NB model, I obtain a coefficient, in terms of IRR, of 1.395 for "policy", and a coefficient of 0.494 for "policy* developing country".
However, the coefficient for "policy" is not statistically significant, while the one for "policy* developing country" is statistically significant at the 5% level.
If both coefficients were significant, I would have said that having the given policy causes an increase of 39.5% in the number of patents, while this effect reduces by 50.6% for developing countries (for which therefore the effect of the law is 0.395*0.494=19.5%).
But what can I say if the coefficient for "policy" is not statistically significant, while the one for "policy* developing country" is?
Not having the dummy variable "developing country", I cannot even interprete the interation term as a variation in the effect of being a developing country when the policy is there.

Thank you again!
Simona