In 2005, the Indian Government launched a conditional cash-incentive program to encourage institutional delivery. This paper studies the effects of the program on neonatal mortality using district-level household survey data. We model mortality using survival analysis, paying special attention to the substantial heaping present in the data. The main objective of this paper is to provide a set of sufficient conditions for identification and consistent estimation of the baseline hazard accounting for heaping and unobserved heterogeneity. Our identification strategy requires neither administrative data nor multiple measurements, but a correctly reported duration and the presence of some flat segments in the baseline hazard which includes this correctly reported duration point. We establish the asymptotic properties of the maximum likelihood estimator and provide a simple procedure to test whether the policy had (uniformly) reduced mortality. While our empirical findings do not confirm the latter, they do indicate that accounting for heaping matters for the estimation of the baseline hazard.