Machine Learning Predictions as Regression Covariates

In text, images, merged surveys, voter files, and elsewhere, data sets are often missing important covariates, either because they are latent features of observations (such as sentiment in text) or because they are not collected (such as race in voter files). One promising approach for coping with this missing data is to find the true values of the missing covariates for a subset of the observations and then train a machine learning algorithm to predict the values of those covariates for the rest. However, plugging in these predictions without regard for prediction error renders regression analyses biased, inconsistent, and overconfident. We characterize the severity of the problem posed by prediction error, describe a procedure to avoid these inconsistencies under comparatively general assumptions, and demonstrate the performance of our estimators through simulations and a study of hostile political dialogue on the Internet. We provide software implementing our approach.