When would Listwise Deletion be preferable to Emis?

The following four conditions must all hold.

1. The analysis model is conditional on the explanatory variables $X$ (such as a regression model) and the functional form is known to be correctly specified (so that listwise deletion is consistent and robustness is not lost when applying listwise deletion to data with slight problems of measurement error, endogeneity, nonlinearity, etc.).

2. There is nonignorable selection on $X$, so that multiple imputation can give incorrect answers, and no $Z$ variables are available that could be used in an imputation stage to fix the problem.

3. Missingness in $X$ is not a function of $Y$, and similarly unobserved omitted variables $Z$ that affect $Y$ do not exist.

4. The number of observations left after listwise deletion is large so that the efficiency lost does not counter balance (in a mean square error sense, for example) the biases induced by the other conditions.

To prefer listwise deletion to EMis, you must then have enough information about problems with the variables in your analysis that you do not trust them to impute the missing values in your $X$'s -- or you worry more about using available information to impute the $X$'s than the existence of selection on $X$ as a function of $Y$ in 3, which our approach would correct. Despite all this, you still trust your data enough to want to use them in an analysis model. If all these conditions hold, listwise deletion can outperform EMis, and researchers should obviously consider whether they might hold in their data. However, this situation -- where using more information is worse and we know about it -- is likely to be rare.