Quantile Regression Analysis with Missing Response, with Applications to Inequality Measures and Data Combination

Abstract

We propose a quantile regression method which effectively handles missing values due to non-response. We illustrate the usefulness of our method by two examples. First example is the estimation of income inequality measures when a significant proportion of earnings are missing in survey data. Second example is when we need to combine more than two samples because no single data contains all the relevant variables. We propose a flexible imputation method where missing values in response are drawn from the conditional quantile function of the response at given values of regressors. Once missing values are imputed, a second-step quantile regression is performed, if needed, by using the filled-in, completed sample. We establish the consistency and the asymptotic normality of this two-step procedure and compare its performance with matching estimators.

Keywords: Quantile Regression, Missing Data