Productivity quantifies how efficiently an economy uses the resources it has available, by relating the inputs to output. One key feature of productivity, and of economic activity in general, is that it is unevenly distributed across space and, in particular, across regions within a country. In this respect, a stylised fact of economic geography is that the productivity of firms increases with city size and urban density. However, evidence suggests that micro (firm-level) and macro (regional-level) elasticities of productivity with respect to population density are different.
In order to investigate these discrepancies, we construct two large datasets spanning the entire population of French and UK firms with at least an employee. Considering the last year of the data, i.e., 2017, the datasets we constructed span over 814,407 firms employing 17,441,714 workers for the UK and over 900,026 firms employing 12,406,277 workers for France.
In our study we first provide some highlights of the data and an overall picture of the evolution of aggregate UK and French productivity and markups. We subsequently analyse the spatial distribution of productivity in both countries at a fine level of detail — 228 Travel to Work Areas (TTWAs) for the UK and 297 Zones d`emploi (ZEs) for France — while focusing on the role of economic density.
Our analysis confirms that micro (firm-level unweighted regressions) and macro (firm-level regressions weighted by firm employment) estimations provides different results for both countries with the latter delivering a higher elasticity of productivity with respect to density. One reasons they could differ is a varying (across regions) correlation between firm size and firm productivity. For example, if denser regions are characterised by a higher correlation between firm size and firm productivity, unweighted differences in productivity across space will be magnified when weighting. Another reason for differences between coefficients is the heterogeneity (along the productivity dimension) of the elasticity of productivity with respect to density. For example, if more productive firms enjoy disproportionately from the density of economic activities, unweighted differences in productivity across space will again be magnified when weighting because (on average) more productive firms are larger.
We find evidence that the productivity return of density is increasing along the deciles of the productivity distribution while the correlation between firm size and productivity varies little across space. It is this the increasing productivity return of density that magnifies firm-level productivity differences for the UK and France when going from the micro to the macro.
In the UK the correlation between firm size and productivity within a region is low (compared to France) and sometimes negative. Also, the UK has a problem of productivity being quite unequal across space beyond density (big London gap while little Paris gap). The problem with France is instead the negative productivity return of density for the least productive firms, i.e., denser places in France nurture too many low productive firms.
