We estimate the effect of broadband infrastructure, which enables high-speed internet, on economic growth in the panel of OECD countries in 1996-2007. Our instrumental variable model derives its non-linear first stage from a logistic diffusion model where pre-existing voice telephony and cable TV networks predict maximum broadband penetration. We find that a 10 percentage point increase in broadband penetration raised annual per capita growth by 0.9-1.5 percentage points. Results are robust to country and year fixed effects and controlling for linear second-stage effects of our instruments. We verify that our instruments predict broadband penetration but not diffusion of contemporaneous technologies like mobile telephony and computers.