# #StackBounty: #interaction Interpretation of interaction coefficient in PPML with fixed effects

### Bounty: 50

I am estimating a gravity model aiming at evaluating how environmental policies can affect trade patterns. I am using a ppml model using the ppmlhdfe command in Stata.

As identification strategy, I am using dyadic fixed effects. The model that I am estimating is the following:

$$ex_{ij,t} = exp[alpha_{i,t}+ alpha_{j,t}+ alpha_{ij}+ boldsymbol{beta_1 D_{eu,j} times Policy_{i,t}}] times varepsilon_{ij,t}$$

Where export between countries i and j ($$ex_{ij,t}$$) is a function of exporter-year ($$alpha_{i,t}$$), importer-year ($$alpha_{j,t}$$), and dyadic fixed effects ($$alpha_{ij}$$). My main variable of interest is an interaction between $$D_{eu,j}$$ that is a dummy variable that indicating whether the importer country $$j$$ is part of the EU(1=EU, 0= otherwise). $$Policy_{i,t}$$ is the log of a continuous variable that indicates stringency in environmental policies in the exporter country i. My aim is to assess whether having stringent environmental policies favours exports towards the EU affecting trade patterns. The interaction is identified because it varies for every dyad-year. The problem is how to interpret the coefficient of the interaction ($$beta_1$$).
The issue is that because of collinearity with the fixed effects I cannot estimate the individual coefficients for $$D_{eu,j}$$ and $$Policy_{i,t}$$. Hence I cannot do plots not I can say what is the reference level.

For instance, what would a significant coefficient of 0.4 mean?
Would it be correct to say that to a 1% increase in the policy score, exports towards the EU increase by 49% ($$[e^{0.4}-1]*100=49%$$) relative to exports to non-EU members?
Is there any way to estimate the significance level of these coefficients? I am not sure how I could estimate margin plots.

If anyone can help to understand the coefficient it would be very much appreciated.

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