  Imputation models sometimes use auxiliary variables that, though not part of
the planned analysis, can improve the accuracy of imputed values and the
efficiency of point estimates. A recent article, using evidence from
simulations, argued that the use of auxiliary variables in imputation did not
improve efficiency. We review the simulation results and find that the use of
auxiliary variables did improve efficiency; under some conditions the
efficiency gain was equivalent to increasing the sample size by a quarter. We
give an example from our own research where the efficiency gained from
auxiliary variables was equivalent to increasing the sample size by three
quarters, and pushed some estimates from statistical insignificance to
significance. For auxiliary variables to make a difference, there must be a lot
of missing data, some estimates must be near the border of significance, and
the auxiliary variables must be excellent predictors of the missing values.
