An Analysis of Nonignorable Nonresponse to Income in a Survey with a Rotating Panel Design

In a rotating panel survey, individuals are interviewed in some waves of the survey but are not interviewed in others. We consider the treatment of missing income data in the labor force survey of the Municipality of Florence in Italy, a survey with a rotating panel design where recipiency and amount of income are missing for waves where individuals are not interviewed, and amount of income is missing for waves where individuals are interviewed but refuse to answer the income amount question. It is thus a question of a multivariate missing data problem with two missing-data mechanisms, one by design and one by refusal, and varying sets of covariates for imputation depending on the wave of the survey. Existing methods for multivariate imputation such as sequential regression multiple imputation (SRMI) can be applied, but assume that the missing income values are missing at random (MAR). This assumption is reasonable when missing data arise from the rotating panel design, but less reasonable when the missing data arise from refusal to answer the income question, since in this case missingness of income is generally thought to be related to the value of income itself, after conditioning on available covariates. In this article we describe a sensitivity analysis to assess the impact of departures from MAR for refusals, based on SRMI for a pattern-mixture model. The sensitivity analysis avoids the well-known problems of underidentification of parameters of missing not at random models, is easy to carry out using existing sequential multiple imputation software, and takes into account the different mechanisms that lead to missing data.