# interaction variable in a fixed effect model

#### ducmil

##### New Member
Hello, everyone,

I struggle to interpret the variable interaction between a treatment dummy and a continuous covariate in a fixed-effect model. When I run the regression, the results come back counterintuitively negative, and I wonder if I'm misinterpreting them. So how do you interpret the coefficient of an interaction variable between a dummy and continuos in a fixed-effect model?

I know the question is a bit general, if necessary, I will give more details.

Thanks!

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Why is it counterintuitive, were you expecting it to have the other sign and do you have sufficient content knowledge to support that hypothesis? Or was this exploratory - which can't necessarily be generalized. Post your code and output please.

The best thing you can do is plot your data and results. You should have crossing lines.

#### fed2

##### Active Member
standard interpretation is difference in slopes. hope that helps

#### ducmil

##### New Member
Thank you both for your answers. So, I don't have any firm evidence to tell me that the results of the fixed effect regressions are wrong and that the value of the coefficients cannot be negative. However, the fact is that with pooled OLS the values are positive and statistically significant, which puzzled me a bit. I am aware that the fixed effect can correct the variable's endogeneity and change sign. Still, as I struggle to interpret the interaction variable in a fixed effect, that's why I asked.

I use STATA as my software and these are the two pooled and fixed effect regressions. I'm not sure how to post the results of the regressions as I haven't found any suggestions for them on the forum. I hope attaching two images is the right way.

Code:
reg AR GDP_dev ceqi T TxGDP Txceqi, vce(cluster NUTS2)
Code:
xtreg AR GDP_dev ceqi T TxGDP Txceqi, fe
T it's the treatment dummy, Txceqi is the interaction term I am concerned about.

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#### hlsmith

##### Less is more. Stay pure. Stay poor.
So this is a multilevel model and these interaction is at the fixed level? Is the only difference between the models, that one controls for cluster or groups. What is the group variable in particular? Also the TxGDP isn't an interaction as well, right?

#### ducmil

##### New Member
I don't think it is a multilevel model. I try to be more explicit in defining the variables.
The reference units are the European regions.
The variable of interest (AR) is the absorption rate of the funds allocated by the EU.
The treatment (T) corresponds to being eligible for a particular funding programme that should favour the absorption of the funds made available.
GDP_dev is the deviation from the threshold for eligibility for treatment, i.e. having GDP below 75% of the EU average.

Following the empirical strategy used in another paper, I'm also trying to analyse the impact that the quality of institutions (ceqi) has on treatment using what Becker et al., 2012 call HLATE (heterogenous local average treatment effect).

The remaining are control variables.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
The output says "clusters" and uses robust SE, that seems like you have observations nested in groups - correct?

What is TxGDP?

#### ducmil

##### New Member
Since I am analysing two funding periods (2000-2006 and 2007-2013), some regions are present twice in the pooled analysis while others only once since they entered only in the second funding period, so I clustered the standard errors by NUTS2 (which is the id of the Regions).

The variable TxGDP is the interaction between the treatment and the running variable, allowing for a different slope on either side of the cut-off point.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
So you are trying to figure out the effect of an interaction in a model with one of its base terms in another interaction as well. Seems pretty conditional to me, gonna have to tap out.

#### ducmil

##### New Member
This is the model I'm using: x is the vector of the running variables, z is the vector of interaction variables that render the treatment more or less effective, T is the treatment indicator.