Test significance of combined interaction coefficients

Question

Is there a way to test the significance of combined (interaction) coefficients in R?

I have a panel regression model of the following (simplified) form:

y_i,t = b₀ + b₁x_i,t + b₂x_i,t*phase_1_t+ b₃x_i,t*phase_2_t + l_i + k_t + e_i,t

where phase_1_t and phase_2_t are dummy variables equal to 1 in a non-overlapping subset of T. Hence, b₁ captures the effect of x in Phase 0, b₁ + b₂ the effect in Phase 1 and b₁ + b₃ the effect in Phase 2.

The results are a weakly significant positive effect of b₁ and a significant negative effect of b₂. b₃ is negative but insignificant. How can I know if the combined effect of b₁ + b₃ is significantly positive (or negative)? (i.e. does x have a significant positive/ negative effect in Phase 2?) I guess estimating the model without the b₃ would be problematic, as b₁ would then capture the effect of x in Phase 0 and Phase 2.

I currently estimate the model using the plm function with time (t) and country (i) fixed effects and interpret coefficients clustered at the country level.

Answer 1

I have solved the issue by just changing the coding of the dummy variables. That is, I code a dummy phase_0 instead of phase_2. The baseline coefficient now captures the total effect of x in Phase 2. The same approach would work for Phase 1.