The worth of cities in Germany

This paper extends the urban growth model of Duranton and Puga (2022) to explore the impact of cities on local firms and households and the aggregate economy of Germany. We adopt alternative micro-foundations for agglomeration economies and a non-linear specification of human capital accumulation. This allows us to characterize the social optimum and to bring the model in line with semi-endogenous growth. We also innovate by incorporating consumptive amenities and fiscal transfers into the model. On the empirical side we exploit the structural equations of the model and rich sets of micro-data for Germany's labor markets, housing rents, and household travel-to-work data, to estimate the population elasticities of urban benefits and costs. We are the first to establish elasticities for urban costs for Germany, an estimated elasticity of commuting costs with respect to distance travelled of 0.071, and an estimate for the population elasticity of travel congestion of 0.068. Our estimates for static and dynamic agglomeration elasticities are 0.017 and 0.020, respectively. We innovate on the calibration strategy to capture the important role of consumptive amenities and fiscal transfers in Germany. The model innovations and calibration are shown to be strongly supported by several pieces of evidence. Our key policy counterfactual is a proportionate increase of the population in Germany's Top Seven metropolises by 10% which implies a significant overall welfare benefit of 1.12% per person. This involves mild losses for city incumbents but strong gains for city newcomers. We also address the effects of a counter-factual shift to the social optimum and a counterfactual removal of fiscal transfers. Our final exercise evaluates the implications of cities and agglomeration economies for aggregate growth in Germany. We find that these account for 0.011 additional percentage points of growth in income per capita per year.