The role of bureaucratic authority structures in facilitating economic growth has been a sociological concern since Max Weber's classic contributions almost 100 years ago. Using a recent and original data set, we examine the characteristics of core state economic agencies and the growth records of a sample of 35 developing countries for the 1970-1990 period. Our "Weberianness Scale" offers a simple measure of the degree to which these agencies employ meritocratic recruitment and offer predictable, rewarding long-term careers. We find that these "Weberian" characteristics significantly enhance prospects for economic growth, even when we control for initial levels of GDP per capita and human capital. Our results imply that "Weberianness" should be included as a factor in general models of economic growth. They also suggest the need for more attention by policymakers to building better bureaucracies and more research by social scientists on variations in how state bureaucracies are organized.