# Difference-in-difference estimator: structural break

Consider the following model:

$Y_{it} = \alpha + \alpha_1 T_{it} + \alpha_2 Post_{it} + \alpha_3 Post_{it} \times T_{it} + u_{it}$

where $i$ refers to individuals and $t=1,2$ to the first (pre treatment) or second (post treatment) period. Furthermore, $Post$ is an indicator variable that is 1 for a single post-treatment period, and $T$ is an indicator variable that is 1 if a specific observation is part of the control group.

Further assume that the measurement of my outcome variable changes between the two periods (for both, the treatment and control group). For example, because a reform also changes how the outcome variable is measured. I am wondering under which conditions I still can estimate a difference-in-difference model.