Government subsidized insurance is ubiquitous, yet estimation of demand in such markets remains challenging. Premium charged for a given deductible is determined by actuarial construction, thus observed choice-pairs are endogenous leading to biased estimation under standard econometric approaches. A theoretical model and simulation study are developed, and a new identification strategy proposed. An empirical application using Federal Crop Insurance Program--a $100 billion/year program--data reveals that demand is quite elastic after accounting for this endogeneity. Mistreatment of such endogeneity is likely partly responsible for pervasive faulty findings of inelastic insurance demand in related applications. Policy implications are discussed.