Bosquet & Overman (2016) find, using data from the British Household Panel Survey clustered by local labour markets, that the elasticity of wages with respect to birthplace size is 4.6%, which is around two thirds of the 6.8% elasticity of wages with respect to current city size. So the size of place of birth “explains” most of the well-known productivity enhancing size effects.
The authors claim that their results suggest that (1) the effect of birthplace on current location (clearly a high correlation between the two); and (2) inter-generational transmission (i.e. the correlation between incomes across generations); largely explain the effect of birthplace. In contrast, they find no role for (3) human capital formation (it’s not the case that people born in a high wage location gain better school results, conditional on parental income etc). Their results “highlight the importance of intergenerational sorting in helping explain the persistence of spatial disparities”, and show that “there is a geographic component to the inheritance of inequality”.
What does this tell us? Well (1) is just the usual agglomeration story: people can be, on average, identical across locations, but in bigger locations they are more productive through greater scope for specialisation etc. Given the high correlation between where people are born and where they end up, birthplace size will statistically “explain” the extra wages that actually come from pure size effects. And (3) tells us that educational quality does not vary systematically with size.
(2) however, is about talent. Talent is heritable, and partially explains the relatively high positive correlation between the earnings of parents and their children (though advantage and privilege also play a role in explaining this correlation). This paper is measuring a geographical concentration of talent. Highly paid talented workers are clustering in larger locations, and producing talented children who, on average, also stay in these locations and go on to earn high wages.
(1) is potentially a positive sum game: on the production side, productivity is higher if everyone clusters in a single large location, rather than spreading out evenly, because the scope for specialisation is higher; and on the consumption side, product variety is higher because it is much more worthwhile to supply niche products in a large market. It is easy to imagine that the consumption benefits of size may be scale invariant: city 2, twice the size of city 1, will be able to support x% more niche markets than city 1, independent of the absolute size of city 1. On the production side however, it seems that the positive externalities are more highly localised and hence less scale invariant. Ahlfeldt et al (2015) find that “externalities are highly localised within the city and after around 10 minutes of travel time, … externalities fall to close to zero”. This seems to imply that once a city is big enough to support some highly productive cluster, sector or industry, then doubling the size of the city cannot be expected to further increase productivity.
Conversely, (2) is a zero sum game: talent in one location is talent that is not located anywhere else.
Further, it is not clear that increased size ends up providing benefits to the inhabitants of a location since increased size also increases congestion, pollution and land costs. Paul Cheshire claims that the current literature suggests that “doubling a city’s size produces about a 5% increase in total factor productivity, holding everything else constant”, but points to French research that suggests that the benefits from this higher productivity are entirely swallowed by increased land costs if land supply is fixed, and 40% absorbed by increased land costs if land is elastically supplied.
To the extent that large cities are exploiting potentially positive sum gains from (1), it is possible that it is worthwhile, at the margin, to have public policy that encourages the movement of people from smaller places to the largest cities (so long as we ensure open-access and freedom to build so that the land costs are more like the 40% of agglomeration benefits, rather than the 100% of agglomeration benefits under inelastic supply of housing). But to the extent that the gains from size are actually due to the zero sum game of moving talent around, then it would be stupid for public policy to encourage talent to move to large congested, expensive cities and so not be present in places where land is cheaper.
And, of course, the UK seems to take the potentially less intelligent option. The Centre for Cities 2014 report, Cities Outlook 2014, had some fascinating statistics on migration flows within the UK. The following picture was particularly striking:
Update: The Paul Cheshire CityTalks episode from 23rd June is good. Don't agree with everything he says (in particular he only focuses on the benefits to the people who move, not the costs on the people who don't) but it is interesting throughout.
 The impact of higher productivity will show up in GVA statistics, but the gains from enhanced product variety do not show up in GVA statistics: rather £1 of expenditure on consumer goods buys more utility in a larger market because of this wider product variety.
 Although an individual’s utility likely increases by less when product variety rises by x% from an initial high level of product variety compared with an initial low level of product variety.