A Data Generating Process Implying Homogeneous Individual Treatment Effects I want to find a data generating process implying homogeneous individual treatment effects.
Specifically, consider two potential outcomes $y_i^1$ and $y_i^0$.
The first one is the individual $i$'s (potential) outcome if she took a treatment.
and the second one is the individual $i$'s (potential) outcome if she did not take any treatment.
In this situation, I want to consider a data generating process under which the individual treatment effect, $y_i^1 - y_i^0$ is identical across all individual, that is $y_i^1 - y_i^0=y^1 - y^0$.
What data generating process yield the homogeneous individual treatment effects?

Your question sounds a bit vague to me. But this is what I understood:
$y_{i} \sim N(\mu_{i}, \sigma^2)$
$\mu_{i} = \alpha_{0} + \alpha_{1} * treatment$
where $y_{i}$ is the outcome for individual i which is normally distributed and we model its mean using $\alpha_{0}$ the general intercept and $\alpha_{1}$ is the effect of treatment where treatment takes 1 and 0. Note that $\alpha_{1}$ is fixed and doesn't change depending on the individual. Is that what you want?
