policymakers demonstrate

370 Stef Proost and Jacques-François Thisse
those in large cities. Starting with the highly influential work of Glaeser et al.
(1992), Henderson et al. (1995), and Ciccone and Hall (1996), research on city
size, employment density, and productivity has progressed enormously during
the last two decades. An ordinary least squares (OLS) regression of the logarithm
of the average wage on the logarithm of the employment density across
cities yields an elasticity that varies from 0.03 to 0.10 (Rosenthal and Strange,
2004). However, this result could be explained by the fact that some econometric
problems have not been properly addressed.
First, using a simple reduced form omits explanatory variables whose effects
could be captured by employment density. For example, overlooking variables
that account for differences in, say, average skills or amenities is equivalent
to assuming that skills or amenities are randomly distributed across cities and
are taken into account in the random term. This is highly implausible. One
solution is to consider additional explanatory variables but, in so doing, we
face a familiar situation of adding an endless string of control variables to the
regressions. Instead, if we use city/region and industry fixed effects, we can
control for the omitted variables that do not vary over time. However, timevarying
variables remain omitted.
Second, the correlation of the residuals with explanatory variables – which
also biases OLS estimates in the case of omitted variables – can also result from
endogenous location choices. Indeed, shocks are often localized and thus have
an impact on the location of agents, who are attracted by cities that benefit from
positive shocks and repelled by those suffering negative shocks. These agents’
relocation has an impact on cities’ level of economic activity and, consequently,
on their density of employment. Employment density is correlated with the
dependent variable and, therefore, with the residuals. To put it differently, there
is reverse causality: an unobserved shock initially affects wages and thus density
through the mobility of workers, not the other way around. This should not
come as a surprise; once it is recognized that agents are mobile, there is a twoway
relationship between employment density and wages. The most widely
used solution to correct endogeneity biases, whether resulting from omitted
variables or reverse causality, involves using instrumental variables. This consists
of finding variables that are correlated with the endogenous explanatory
variables but not with the residuals.
Caution is therefore needed when measuring the impact of employment density
on labour productivity. Using advanced econometric methods and taking
into account additional explanations of workers’ productivity (such as nonobservable
individual characteristics or the impact of previous individual locational
choices on current productivity), urban economists have obtained more
accurate estimations of agglomeration gains. There is now a broad consensus
that, everything else being equal, the elasticity of labour productivity with
respect to current employment density is about 0.03 (Combes et al., 2012). This