Imputing Missing Covariate Values in Nonlinear Models

I propose a new imputation estimator for missing covariate values in nonlinear models. The estimator provides efficiency gains relative to just using the complete cases, and is consistent for any model that falls under M-estimation. This is unlike the commonly used dummy variable method and regression imputation, which I show to be generally inconsistent in nonlinear models. The proposed estimator is straightforward to implement and relies only on the commonly used assumptions on missingness. To test these assumptions, I provide a novel and simple variable addition test. I show how the framework applies to nonlinear models for fractional and nonnegative responses.