In the contingent valuation literature, anchoring bias poses problems when using an iterative bidding game to infer willingness to pay. This bias occurs when the willingness to pay estimate is sensitive to the initially presented starting value. More generally, whenever a survey format is used and not all of those contacted participate, selection bias raises concerns about the representativeness of the sample. In this paper, we estimate students' willingness to pay for student health care at Stanford University while accounting for both of these biases. As there is no cost sharing for students, we assess willingness to pay by having a random sample of students play an on line iterative bidding game. Our main results are that (1) demand for student health care is elastic by conventional standards; (2) ignoring anchoring bias would lead to a substantially biased measure of the demand elasticity; and (3) standard selection correction methods indicate no bias from selective non-response and newer bounding methods support this conclusion of elastic demand.