Bounds on Quantiles in the Presence of Full and Partial Item Nonresponse

Microeconomic surveys are usually subject to the problem of item nonresponse, typically associated with variables like income and wealth, where confidentiality and/or lack of accurate information can affect the response behavior of the individual. Follow up categorical questions can reduce item nonresponse and provide additional partial information on the missing value, hence improving the quality of the data. In this paper we allow item nonresponse to be non-random and extend Manski’s approach of estimating bounds to identify an upper and lower limit for the parameter of interest (the distribution function or its quantiles). Our extension consists of deriving bounding intervals taking into account all three types of response behavior: full response, partial (categorical) response and full nonresponse. We illustrate the theory by estimating bounds for the quantiles of the distribution of amounts held in savings accounts. We consider worst case bounds which cannot be improved upon without additional assumptions, as well as bounds that follow from different assumptions of monotonicity.