I'm conducting a difference-in-difference analysis, where I believe that my treatment effect is driven by a specific set of treatments (e.g., treated by a higher qualified teacher, compared to treated by a low qualified teacher (both groups are mutually exclusive)). To test this, I implemented the analysis by splitting my original treatment group in two parts and including both dummies into the equation: $$ Y=\alpha+b_1*Post + b_2*TreatLow+b_3*TreatHigh+b_4*Post*TreatLow+b_5*Post*TreatHigh $$ I get reasonable results, meaning that the coefficients and standard error look sensible. However, after reading more on the matter (incl. this post Difference in difference with interaction), I'm wondering whether this is the correct approach or I should rather use Triple-DiD instead.
Edit: I have an unabalanced panel dataset, where I can observe students over time. Students are nested within teachers and teachers can be either high or low qualified. The treatment is at the teachers' level.