Difference in Difference econometric specification for multiple treatment(no treatment(control group), low treatment, high treatment)

My treatment variable (Di) includes three groups. Group 1 with no treatment(control group); and, Group 2 and Group 3 with different level (intensity) of treatment.like technology adoption: partially adopting and fully adopting. Group 2 low level of treatment (consumption) and Group 3 with high level of treatment (consumption of …) or like that. I have two period panel data set. I want to see the program effect (impact) through difference-in-difference method. This deviate from the common binary treatment case of group having the treatment and group having no treatment. How then I could specify the regression framework for such case? Any helpful material. I have been browsing in google but can't find one.

• Nov 11 '15 at 11:54

If your measure of treatment is continuous, you could estimate

$Y_{it} = \alpha + \beta_1 D_i + \beta_2 Post_t + \delta (D_i*Post_t) + \epsilon_{it}$

Then the effect of moving up the treatment intensity is $\beta_1 + \delta$.

If the measure of treatment is discrete, just include indicator variables for each level of treatment, a period indicator, and all interactions.

$Y_{it} = \alpha + \beta_1 D_{i2} + \beta_2 D_{i3} + \beta_3 Post_t + \delta_1 D_{i2}*Post_t + \delta_2 D_{i3}*Post_t + \delta_3 D_{i2}*D_{i3}*Post_t + \epsilon_{it}$

Now, $\delta_3$ gives the effect of any treatment relative to the control group, $\delta_2$ gives the effect of treatment group 3 relative to the control group, and $\delta_1$ gives the effect of treatment group 2 relative to the control group.

• gannawag, thank you so much! any recommendation for further reading..? Any one else who can recommend documents worked on this type of approach?
– MTW
Nov 12 '15 at 13:08
• Great appreciation so far. Suppose my outcome variable (Yi) is milk yield (continuous) and treatment variable (Di) is categorical (dairy technology adoption= no adoption, partial and full). • In δ3Di2∗Di3∗Postt, what do you mean by any treatment? • What can be said about group 1(the control group)? • Can I find any reference for such kind of work at least to refer to and for better understanding? • Can I get any STATA commands or do files? • Email: melkamtw@gmail.com Stay Blessed!
– MTW
Nov 23 '15 at 5:59
• This answer doesn't make sense. If the treatment is of varying intensity, we expect people in group 3 to also be in group 2, and hence the interaction term is exactly the same as the delta_3 term. Nov 3 '20 at 2:36
• @hrrrrrr5602 You're referring to the second equation, correct? Agreed, something appears to be off if we include every level of treatment and all pairwise interactions. You could run this y ~ post*low + post*high, where the "no treatment group" is the reference group. However, I'm sure if we tried this y ~ post*low + post*high + post*low*high, then we would find singularities; the triple interaction should be dropped if I am not mistaken, and even the interaction between the two treatments. Any recommendations on how this could be improved? Nov 15 '20 at 16:02