Time-inconsistency may play a central role in explaining inter-temporal behavior, particularly among poor households. However, little is known about the distribution of time-inconsistent agents, and time-preference parameters are typically not identified in standard dynamic choice models. We formulate a dynamic discrete choice model in an unobservedly heterogeneous population of possibly time-inconsistent agents. We provide conditions under which all population type probabilities and preferences for both time-consistent and sophisticated agents are point-identified and sharp set-identification results for native and partially sophisticated agents. Estimating the model using data from a health intervention providing insecticide treated nets (ITNs) in rural Odisha, India, we find that about two-thirds of our sample comprises time-inconsistent agents and that both sophisticated and native agents are considerably present-biased. Counterfactuals show that the under-investment in ITNs attributable to present-bias leads to substantial costs that are about four times the price of an ITN.