Identification and Estimation with Partial Respondents and Anchoring Effects

Household surveys often suffer from nonresponse on variable such as income, savings or wealth. The work by Charles F. Manski in the 1990s shows how bounds on conditional quantiles on the variable of interest can be derived, allowing for any type of non-random item nonresponse. The width between these bounds can be reduced using follow up questions in the form of unfolding brackets for initial non-respondents. However, evidence from both the psychology and economic literature suggest that such design is vulnerable to anchoring effects. In this paper Manski's bounds are extended to incorporate information provided by bracket respondents allowing for three alternative nonparametric assumptions on anchoring. The new bounds are applied to earnings in the 1996 wave of the Health and Retirement study. The results show that introducing categorical questions in the form of unfolding designs can be useful to increase the precision of the bounds, even if anchoring is allowed for.