Capping the prices health care providers can collect for out-of-network services is a commonly proposed strategy for reducing the in-network prices negotiated by providers and insurers. We present a model that implies that an out-of-network cap can greatly reduce in-network prices when providers must accept out-of-network patients (i.e., in emergency settings) but may be much less effective in other settings. In these other settings, the achievable price reductions can be bounded using estimates of how much volume a provider retains when it shifts out-of-network―and at what price. We use a large national claims database to examine episodes in which hospitals change network status and estimate that hospitals that shift out-of-network retain only 12% of their non-emergency in-network volume, albeit at prices more than twice as high. Using these estimates to calibrate the model-derived bound implies that an out-of-network cap can reduce in-network prices by at most 19% in non-emergency settings. This bound suggests that policymakers wishing to greatly reduce in-network prices in commercial insurance may need to consider other policy tools and that competition from traditional Medicare, not the presence of an out-of-network cap, may be the main reason that Medicare Advantage plans negotiate lower prices than commercial plans.