Like elsewhere in the developing world, wireless markets now play a crucial role in Latin American economic growth. Mobile telephone networks increasingly provide the communications infrastructure that has largely been lacking throughout the region. Yet, governments have generally made only modest allocations of bandwidth available to Latin American wireless operators, either absolutely (in terms of spectrum each country could allocate) or relative to other countries in Asia or the European Union. Using an empirical model estimated on mobile phone data for 40 international markets, we show that very large social gains are available to countries that succeed in permitting more liberal use of radio spectrum. Two of the most striking examples of this approach are Guatemala and El Salvador, each of which utilizes about 50% more bandwidth for mobile telephony than the Latin American mean. We conduct simulations, using our calibrated model, to project country-by-country gains from expanding access to radio spectrum. Substantial efficiency increases are possible, which dominate gains associated with extracting public funds via auctions, the area of focus in the economic literature.