Interpreting negative interaction term

[Ama Perera]

Hi All,

I have a panel data set and I'm trying to find if the effect of my IV on DV differs as per the level of development of countries. Therefore, I create a dummy variable (dev_dummy) where the dummy is assigned 1 if the country is developed and 0 if the country is emerging and interact it with my IV. Then, I perform a base-line regression with the interaction term. Following are the used commands and the associated outputs. Please note that DV= Y, IV=X and "dev" represents the level of development.

//code

gen dev_dummy = 0

replace dev_dummy=1 if dev=="Developed"

xtreg Y X dev_dummy (c.X)#dev_dummy, fe vce(cluster firmid)

//output


. xtreg Y X dev_dummy (c.X)#dev_dummy, fe vce(cluster firmid)
note: dev_dummy omitted because of collinearity

Fixed-effects (within) regression Number of obs = 7559
Group variable: firmid Number of groups = 350

R-sq: Obs per group:
within = 0.0481 min = 1
between = 0.1117 avg = 12.7
overall = 0.0256 max = 16

F(17,7130) = 42.52
corr(u_i, Xb) = -0.2786 Prob > F = 0.0000

(Std. Err. adjusted for 350 clusters in firmid)


-------------------------------------------------------------------------------------
| Robust
Y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
X | -.0082551 .0023226 -3.55 0.000 -.0128082 -.0037021
dev_dummy | 0 (omitted)
|

|
dev_dummy#c.X |
1 | -.1097093 .0360816 -3.04 0.002 -.1804399 -.0389788
|
_cons | .0863293 .0013789 62.61 0.000 .0836263 .0890324
--------------------+----------------------------------------------------------------

Please also note that the individual coefficient of X (without interaction) in developed countries is -0.117 and in emerging countries is -0.0082.


//
As you can see, the coefficient for interaction term is negative (-0.1097). I understand that since the interaction term is significant, this means that there is a significant difference of the impact of X on Y between the two groups. But I have trouble in identifying in which group the effect of X on Y is stronger.

Does the negative coefficient for the interaction term mean that the impact of X on Y is more pronounced for developed countries? (where dev_dummy=1 if dev=="Developed")? or does the negative coefficient is simply since the negative coefficient of emerging countries is lower than the negative coefficient of developed countries?

Thank You.

[Clyde Schechter]

Well, for the emerging countries, dev_dummy == 0, so the effect of X on Y there is given by the coefficient of X, namely -0.0082... That is already a negative number. In the developed countries, the effect is the sum of the coefficient of X and the coefficient of the interaction term. That interaction term is negative, so the result is going to be an even more negative number, a negative number of larger magnitude. So the finding is that in emerging countries, increasing X is associated with decreasing values of Y. In the developed countries, increasing X is associated with even steeper decreases in Y.

[Ama Perera]

Thanks a lot Clyde Schechter . Appreciate your help.