We provide a new method to empirically analyze discrete choice models with state dependence and individual-by-product fixed effects, and use it to analyze consumer choices in a policy-relevant environment (a subsidized health insurance exchange). The method infers state dependence from consumers' switching choices in response to changes in product attributes. Moment inequalities are constructed that do not depend on the fixed effects and do not rely on assumptions about initial conditions. The method infers much smaller switching costs on the health insurance exchange than would be inferred from standard logit and/or random effects methods. A counterfactual policy evaluation illustrates that the policy implications of this difference are substantive.