Suppose I have a set of units $n_i, i = 1,...,N$. One unit was receiving a treatment $n_j = 1$ at times $t=1$ to $t=\tau$. All other units never received the treatment so $\forall t, n_i=0,i\neq j$. At $\tau+1$ to $T=t,T>>\tau+1$, $n_j=0$.
Suppose the shock to $n_j$ is totally exogenous for simplicity.
Is there a causal framework that allows me to estimate the impact of $n_j=1$?