observed value, ‘?’ represent a missing observation which needs to be imputed, and ‘NA’ indicates a structurally missing observation. For the potential survival outcomes, we did not indicate whether they were missing or observed because we wanted to use Table \[chap3:eg2\_1\] to help us decide how we should be stratifying our subjects once our proposed method imputes the counterfactual survival status.

From Table \[chap3:eg2\_1\], we can see that the goal of our analysis is to provide inference about $E[Y_{Z_1,\ldots,Z_t}-Y_{Z'_1,\ldots,Z'_t}|S_{Z_1,\ldots,Z_{t-1}}=S_{Z'_1,\ldots,Z'_{t-1}}=1]$, where $Z_l\neq Z'_l$ for at least one $l$ with $l=1,\ldots,t$ i.e. we condition on subjects who would potentially survive under two different treatment regimes $Z_1,\ldots,Z_{t-1}$ and $Z'_1,\ldots,Z'_{t-1}$. Thus, the distribution of $(S_{Z_1,\ldots,Z_{t-1}},S_{Z'_1,\ldots,Z'_{t-1}})$ form our principal strata and meaningful contrasts are defined only in the stratum where $S_{Z_1,\ldots,Z_{t-1}}=S_{Z'_1,\ldots,Z'_{t-1}}=1$ since the potential outcomes for the two different treatment regimes exist only in this stratum. For example, if we want to estimate the effect for a negative wealth shock at $t=2$ versus no negative wealth shock by $t=2$ that is $E[Y_{01}-Y_{00}|S_0=1]$, we restrict to subjects who survive if they did not receive a negative wealth shock at $t=1$ i.e. subjects with $S_0=1$ (Subjects 1-12 in Table \[chap3:eg2\_1\]). Note that the definition, $E[Y_{Z_1,\ldots,Z_t}-Y_{Z'_1,\ldots,Z'_t}|S_{Z_1,\ldots,Z_{t-1}}=S_{Z'_1,\ldots,Z'_{t-1}}=1]$, is different 