Bounds, health habits and anchoring income effects

Surveys are often design so that initial non-respondents to some continuous amount can disclose partial information with follow-up questions. These questions are often based on prompting responses with a sequence of bids that classify the undisclosed amount within a category. Secondary variables may reduce the problem of nonresponse but are unlikely to eliminate the problem altogether, thus, identification of the population parameters remains problematic. Furthermore, eliciting partial information by ‘anchoring' the answers to a set of bids may induce anchoring bias. This paper develops from Horowitz and Manski (1995, 1998) to derive bounding intervals with partial information that allow for anchoring effects according to the experimental finding in Jacowitz and Kahneman (1995). The bounds provide regions of identification allowing for any type of non-random nonresponse. The method is illustrated using the 1996 wave of the Health and Retirement Study to show that bounding intervals can be used to detect for differences in health habit between income sub-groups in the population.