We present a model of household saving toward a mortgage loan under an exogenous down payment requirement and preference for owning over renting. Our model explains a set of empirical observations such as the dual effect in the form of some households, in response to higher down payments, becoming discouraged savers while those who do not abandon purchasing plans save more. We also employ instrumental variable‐based methods to investigate the down payment saving behavior of first‐time home buyers in the United States. The empirical results based on Panel Study of Income Dynamics (PSID) data support the inelastic down payment elasticity of saving implied by our model.