The three essays of my dissertation examine how behavioral responses to health policy can shape, and sometimes undermine, the intended impact of policies. The first essay, "Chasing the Missing Patients: Exploring the Unintended Consequences of Free Health Screenings," examines two possible unintended consequences of removing cost sharing for health screening for people at high risk for chronic conditions, as is done in the Affordable Care Act. First, free screenings could attract patients with lower uptake of medical treatment, reducing the impact of the policy on treatment and changing the composition of diagnosed patients. Second, expanding screening could increase adverse selection and reduce the stability of health insurance markets. Using data from three biomarker studies reflecting different populations affected by the Affordable Care Act, we find evidence for the former prediction but not the latter. This essay is joint work with Lisandro Colantonio, Monika Safford, and David Meltzer. The second essay, "Does Identification of Previously Undiagnosed Conditions Change Patient Care Seeking Behavior?", shows that screening leads to doctor visits for previously undiagnosed conditions for many but not all patients, with marginally lower effects among patients lacking a usual healthcare provider. To identify the effects of screening, we exploit the REasons for Geographic And Racial Differences in Stroke (REGARDS) epidemiological study as a natural experiment. This essay is joint work with Lisandro Colantonio, Monika Safford, and Elbert Huang. The third essay, "Policy Analysis with Endogenous Migration Decisions: The Case of Left-Behind Migrant Children in China," models parental decisions as responses to local policy to show that migration effects could undermine the benefits of place-specific government services for children. Addressing a puzzle in the empirical literature on children who are left-behind by migrant parents, I use a theoretical model to sign the effect of being left-behind on child well-being for a policy-relevant subset of children: children who become left-behind as a result of a policy change. For these children, becoming left-behind reduces their well-being. To show that these theoretically derived effects could be empirically important, I use panel data on Chinese families before and after a health policy change.