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

We propose a quantile regression method which eectively 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 signicant 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 exible imputation method where missing values in response are drawn from the conditional quantile function of the response at given values of regressors. The rst- step quantile regression estimates the family of conditional quantile functions, from which missing values in the response are lled-in. Once data is completed by imputation, the second step-analysis is performed. We prove the consistency and the asymptotic normality of this two-step procedure and study its relative eciency compared to other possible methods.