In 1996, free choice of health insurers was introduced to the German social health insurance system. One objective was to increase efficiency through competition. A crucial precondition for effective competition among health insurers is that consumers search for lower‐priced health insurers. We test this hypothesis by estimating the price elasticities of insurers' market shares. We use unique panel data and specify a dynamic panel model to explain changes in market shares. Estimation results suggest that short‐run price elasticities are smaller than previously found by other studies. In the long‐run, however, estimation results suggest substantial price effects.