Inference on outcome distribution and quantile functions with missing data, by quantile imputation, probability weighting, and doubly robust estimators

This study introduces a flexible imputation method to estimate the marginal outcome distribution and quantile functions in the presence of missing responses. The quantile imputation method is compared to inverse probability weighting (IPW) and doubly robust (DR) estimators. When a considerable portion of wage data is missing in survey responses, our proposed method serves to assess whether nonrespondents and respondents share the same marginal wage distribution function. We establish the uniform consistency of the estimators, their weak convergence, and the validity of the bootstrap procedure. Extensive simulation exercises are employed to investigate whether quantile imputation offers advantages over weighting-based methods. Using monthly income data from the Current Population Survey, we find that nonrespondents tend to have significantly lower wages than respondents. As a result, complete case (CC) analysis, which excludes missing and Census-allocated wages, tends to overestimate wages, especially at the middle and upper ends of the distribution. Moreover, CC analysis biases wage inequality measures, with a greater impact on men due to their higher rates of missing wage data.