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.

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#### Best Answer

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.

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