Rubin (1987) has proposed multiple imputations as a general method for estimation ion the presence of missing data. Rubin's results only strictly apply to Bayesian models, but Schenker and Welsh (1988) directly prove the consistency of multiple imputations inferences when there are missing values of the dependent variable in linear regression models. This paper extends and modifies Schenker and Welsh's theorems to give conditions where multiple imputations yield consistent inferences for both ignorable and nonignorable missing data in exogenous variables. One key condition is that the imputed values must have the same conditional first and second moments as the true values. Monte Carlo studies show that the multiple imputation covariance estimates are accurate for realistic sample sizes. They also support the applications of multiple imputations in Brownstone and Valletta (1991), where the multiple imputations estimates substantially changed the qualitative conclusions implied by the model.
