Recovering income distribution in the presence of interval-censored data

We propose a method to analyze interval-censored data using a multiple imputation based on a Heteroskedastic Interval regression approach. The proposed model aims to obtain a synthetic dataset that can be used for standard analysis, including standard linear regression, quantile regression, or poverty and inequality estimation. We present two applications to show the performance of our method. First, we run a Monte Carlo simulation to show the method's performance under the assumption of multiplicative heteroskedasticity, with and without conditional normality. Second, we use the proposed methodology to analyze labor income data in Grenada for 2013-2020, where the salary data are interval-censored according to the salary intervals prespecified in the survey questionnaire. The results obtained are consistent across both exercises.