This paper examines the relationship between employment density and productivity using data on U.S. gross state output. Two models are presented: one based on local geographical externalities and the other on the variety of locally available intermediate services. Both models suggest a simple, estimable relationship between employment density and productivity. The study finds that agglomeration effects outweigh congestion effects in denser areas, and that the elasticity of productivity with respect to density is small but explains more than 50% of the observed state productivity differences. The first model considers externalities from the physical proximity of production, where higher density leads to increased productivity due to spillovers. The second model considers the variety of intermediate services available in dense areas, where higher density allows for greater specialization and productivity. Both models show a positive relationship between density and productivity. The paper uses data on state output and county employment to estimate the relationship between density and productivity. It finds that states with higher average density and greater inequality in density have higher levels of productivity. The results suggest that density is a more satisfactory concept than city size for understanding agglomeration effects. The paper also discusses the implications of these findings for growth theory. It suggests that externalities and locally tradable services weaken the link between differences in output per worker and differences in returns on capital. Additionally, rising density over time is an important factor in growth, as large U.S. cities are denser now than in earlier centuries, and a much larger fraction of the population is employed in cities or other dense areas. The paper plans to apply its estimates to historical data on the distribution of employment by county to measure the part of total growth that can be associated with rising density.This paper examines the relationship between employment density and productivity using data on U.S. gross state output. Two models are presented: one based on local geographical externalities and the other on the variety of locally available intermediate services. Both models suggest a simple, estimable relationship between employment density and productivity. The study finds that agglomeration effects outweigh congestion effects in denser areas, and that the elasticity of productivity with respect to density is small but explains more than 50% of the observed state productivity differences. The first model considers externalities from the physical proximity of production, where higher density leads to increased productivity due to spillovers. The second model considers the variety of intermediate services available in dense areas, where higher density allows for greater specialization and productivity. Both models show a positive relationship between density and productivity. The paper uses data on state output and county employment to estimate the relationship between density and productivity. It finds that states with higher average density and greater inequality in density have higher levels of productivity. The results suggest that density is a more satisfactory concept than city size for understanding agglomeration effects. The paper also discusses the implications of these findings for growth theory. It suggests that externalities and locally tradable services weaken the link between differences in output per worker and differences in returns on capital. Additionally, rising density over time is an important factor in growth, as large U.S. cities are denser now than in earlier centuries, and a much larger fraction of the population is employed in cities or other dense areas. The paper plans to apply its estimates to historical data on the distribution of employment by county to measure the part of total growth that can be associated with rising density.