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:
yi,t = b0 + b1xi,t + b2xi,t*phase_1t+ b3xi,t*phase_2t + li + kt + ei,t
where phase_1t and phase_2t 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.