Productivity and the density of human capital

We estimate a model of urban productivity in which the agglomeration effect of density is enhanced by a metropolitan area's stock of human capital. Estimation accounts for potential biases due to the endogeneity of density and industrial composition effects. Using new information on output per worker for U.S. metropolitan areas along with a measure of density that accounts for the spatial distribution of population, we find that a doubling of density increases productivity by 2 to 4 percent. Consistent with theories of learning and knowledge spillovers in cities, we demonstrate that the elasticity of average labor productivity with respect to density increases with human capital. Metropolitan areas with a human capital stock one standard deviation below the mean realize no productivity gain, while doubling density in metropolitan areas with a human capital stock one standard deviation above the mean yields productivity benefits that are about twice the average.