Beat the heap: An imputation strategy for valid inferences from rounded income data

Questions on income in surveys are prone to two sources of errors that can cause bias if not addressed adequately at the analysis stage. On the one hand, income is considered sensitive information and response rates on income questions generally tend to be lower than response rates for other non-sensitive questions. On the other hand respondents usually don't remember their exact income and thus tend to provide a rounded estimate. The negative effects of item nonresponse are well studied and most statistical agencies have developed sophisticated imputation methods to correct for this potential source of bias. However, to our knowledge the effects of rounding are hardly ever considered in practice, despite the fact that several studies have found strong evidence that most of the respondents round their reported income values. In this paper we illustrate the substantial impact that rounding can have on important measures derived from the income variable such as the poverty rate. To obtain unbiased estimates, we propose a two stage imputation strategy that estimates the posterior probability for rounding given the observed income values at the first stage and re-imputes the observed income values given the rounding probabilities at the second stage. A simulation study shows that the proposed imputation model can help overcome the possible negative effects of rounding. We also present results based on the household income variable from the German panel study 'Labour Market and Social Security.'