A Multiple Imputation Approach To Address The Problem Of Nonignorable Nonresponse and Misreporting Patterns In Income Data

When people are asked to report their monthly income they are likely to refuse to answer. If they answer, they tend to round their income to the nearest fifty, hundred or thousand, or they even completely misreport the value of income. It is well known that the propensity to misreport or to refuse to answer income questions depends on individual characteristics. For example, people with migration background are normally more likely to refuse to answer. Thus, commonly income data collected by personal interviews show nonignorable nonresponse and abnormal concentrations of reported values at certain “heaping points”. Using such data to compute, e.g., distribution characteristics like sample quantiles or proportions usually causes severe bias. In order to allow to adequately modeling such kind of incomplete and heaped data, we introduce a general method that allows addressing both, the issue of incomplete data and the problem of rounding. To impute missing values, we suggest using the proven method of multiple imputation by chained equations. The method requires determining a univariate imputation model for each variable with missing values. We suggest specifying the imputation model for the income variable such that it describes the true distribution of the income variable simultaneously with the heaping pattern present in a data set. Monte Carlo simulations are used to validate the novel approach. To illustrate the capacity of the approach we conduct a case study using income data from the adult cohort of the German National Educational Panel Study.