Nonparametric Modeling of the Anchoring Effect in an Unfolding Bracket Design

Household surveys are often plagued by item non-response on economic variables of interest like income, savings or the amount of wealth. Manski (1989, 1994, 1995) shows how, in the presence of such non-response, bounds on conditional quantiles of the variable of interest can be derived, allowing for any type of non-random response behavior. Including follow-up categorical questions in the form of unfolding brackets for initial item non-respondents is an effective way to reduce complete item non-response. Recent evidence, however, suggests that such design is vulnerable to a psychometric bias known as the anchoring effect. In this paper, we extend the approach by Manski to take account of the information provided by the bracket respondents. We derive bounds which do and do not allow for the anchoring effect. These bounds are applied to earnings in the 1996 wave of the Health and Retirement Survey (HRS). The results show that the categorical questions can be useful to increase precision of the bounds, even if anchoring is allowed for