With states facing tightening Medicaid budgets, the high cost of financing long-term care for the elderly through Medicaid has prompted proposals to make private long-term care insurance (LTCI) more affordable through tax incentives. The effectiveness of tax incentives for stimulating LTCI demand depends in part on the availability of Medicaid, since it is considered a substitute for LTCI. This paper examines the impact of tax subsidies and Medicaid financing on the demand for LTCI by developing and estimating a stochastic dynamic model of the decision to purchase private long-term care insurance. A key contribution of this paper is that the model also incorporates and accounts for endogenous decisions on Medicaid enrollment, nursing home use, and asset holdings, which reduces the estimate of the Medicaid crowd-out effect on LTCI demand. State-specific Medicaid enrollment criteria are explicitly accounted for in modeling the Medicaid enrollment decision. The parameters of the model are estimated using individual level data from the Health and Retirement Study for the years 1998 to 2002 by simulated maximum likelihood. Using the estimated parameters, counterfactual policy experiments are performed to investigate the effects of tax policy and Medicaid on LTCI demand. The main finding is that both effects are small. The estimated price elasticity of the LTCI demand is -0.08, implying that tax subsidies are expected to have only a limited effect in reducing the number of uninsured. Eliminating the Medicaid program increases LTCI holding by only 5.3%, implying that the demand for LTCI would remain small even without Medicaid.