Health insurers are increasingly using plan designs that incentivize consumers to shop for health care based on price. This dissertation studies the effects of one such plan design on demand and equilibrium prices. Tiered hospital networks group hospitals by price ranking and vary consumers' out-of-pocket prices to reflect the price variation faced by the insurer. Proponents argue that tiered networks reduce health care spending by steering consumers toward lower-priced hospitals, and by giving insurers an additional bargaining lever in price negotiations with hospitals. To evaluate these claims, I estimate a structural model of health care demand and insurer-hospital bargaining over prices in the Massachusetts private health insurance market. The model extends the standard Nash bargaining framework to explicitly account for the multiplicity of possible tier outcomes. I find that the effects of tiered networks on demand alone can lead to moderate or sizable reductions in hospital spending, ranging from 1% to 8% depending on the consumer population and the concentration of the hospital market. The effects on negotiated hospital prices add an additional 2% to 4% savings, for a total savings from tiered networks of up to 12% under favorable market conditions. I conclude that insurance plan designs with demand-side incentives can have large health care spending reduction effects.