Time-varying Agglomeration Economies and Aggregate Wage Growth

Over the last fifty years, there has been a steady growth of cities over the world although cities do not grow at the same rate (Duranton and Puga, 2014). Most countries have seen the rise of urban giants concentrating population and employment, which can generate agglomeration economies. Returns to agglomeration economies may also have evolved with the rise of services industries and the improvement of transports. The aggregate productivity and labour earnings thus vary over time both from the change in city size at given returns to agglomeration and from change in returns to agglomeration at given distribution of city sizes.
In this paper, we study the contribution of city agglomeration economies to labour earnings in France over the 1976-2015 period using wage panel data. Our contribution is fourfold. We first delineate cities every year to properly consider the evolution of city sizes, in terms of both overall population but also land area. We then estimate how returns to agglomeration economies on wages evolve over time. We assess to what extent the evolution of aggregate labour earnings is affected by changes in returns to city agglomeration variables and changes in their values. Finally, we model a system of cities with agglomeration economies to study the equilibrium effects of changes in agglomeration economies on labour earnings. We derive and evaluate formulas for both the direct effect stemming from changes in returns to agglomeration variables, and the indirect effect coming from the influence of these changes on values of city characteristics.

For our study, we need time-varying delineations of cities to accomodate variations in their footprint due to changes in agglomeration economies, and local productivity and amenity shocks. We delineate cities every year from 1976 onwards using the dartboard approach proposed by de Bellefon et al. (2021). We consider a grid of metropolitan France in 200m*200m pixels for which we compute the building volume density by year from information on building footprint, height and construction year from CEREMA and BDTOPO. Our approach allows us to consider expansions, absorptions and fusions of cities over time. Interestingly, we show that large cities may have different fate. 

Equipped with our yearly delineations of cities, we conduct estimations of time-varying agglomeration economies using administrative panel data (Déclarations Anuelles des Données Sociales-DADS) over the 1976-2015 period. In a first step, we regress individual daily wages on city-year fixed effects while controlling for individual observed and unobserved heterogenity, and industry. In a second step, we regress estimated city-year fixed effects on city variables (i.e. density, area and market potential). Importantly, we consider that coefficients of these variables may vary over time. We find that the elasticity of wages with respect to city density (resp. area) increases over time, from 0.011 to 0.042 (resp. 0.007 to 0.022), while the elasticity of wages with respect to proximity to other cities remains broadly stable. These estimates are barely affected when instrumenting agglomeration variables with city historical characteristics and geological features. Using a log-wage growth decomposition, we also show that changes in returns have a large effect on wage growth, whereas changes of values for agglomeration variables do little. Indeed, even if cities evolved, changes are slow compared to cross-section disparities across cities.

Finally, we propose a theoretical model to evaluate the direct and indirect effects of changes in returns to city density and area at equilibrium. Indeed, changes in these returns affect agglomeration economies and thus the respective attractiveness of cities depending on their characteristics. As a result, they trigger migrations across cities that impact local levels of density and area, and thus agglomeration economies. More precisely, the modelling consists in incorporating the effects of agglomeration economies on wages in a system of monocentric cities. Agglomeration economies are specified as a Cobb-Douglas function in city density and area, in line with our empirical specification. The model cannot be solved analytically, but we are able to conduct comparative statics for wages with respect to returns to agglomeration variables and to quantify not only the direct effect of changes in these returns, but also the indirect effect stemming from the influence of these changes on the values of agglomeration variables. Within a calibration exercise, we show that the indirect effect is rather small, which is consistent with the negligible role of changes in values of agglomeration variables found in our empirical investigation.