This paper examines the determinants of the decision of low-income renters to move out of their current dwelling. Maximum score estimation is shown to be superior to ordinary discrete choice estimation techniques (probit, logit) for this problem, and for similar discrete choices that require revering a previously optimal decision. The estimation reveals psychological costs from moving for typical low income renters of at least 8% of their income ; these costs are even higher for older, longer tenure, or minority households. Policies that displace low income renters will have large social costs. In addition, the estimation results are used to calculate implicit household willingness to pay (WTP) for neighborhood amenities. This WTP based on mobility behavior is much greater than WTP estimates derived using hedonic methods, and is argued to be more accurate.