How do you uncouple the effect that the people moving into cities have on the city fertility rate from the effect the city has on the fertility rate of the people moving into it? Cities offer things that are valuable to people who don't want children (like, high utility activity for the time they aren't spending raising the children they don't have, compared to places that aren't cities) so they are especially attractive to people who don't want children, and you would expect any place that is attractive to people who don't have children to have a low fertility rate.
http://www.berliner-mieterverein.de/magazin/online/mm0914/09...
> n auf Kernstädte fest. Auch Familien orientieren sich mehr und mehr in Richtung der City-Bereiche. Bis zur Jahrtausendwende waren viele 25- bis 49-Jährige hinaus ins grüne Umland gezogen, um dort ihre Kinder großzuziehen. Das scheint sich umzukehren. Der in den 90er Jahren weit verbreitete Trend zur Suburbanisierung sei weitgehend zum Erliegen gekommen, so die Wissenschaftlerin in ihrer Studie.