of each prefecture. To do this, we base ourselves on Tabuchi and Thisse (2007) and Behrens _et al._ (2014), and assume that each person _j_ ’s likelihood to choose to live in location _i_ (the urban or rural part of any of the 331 Chinese prefectures in our sample), is based on the utility he or she derives from living in that place. This utility depends linearly on real wages, _Wi_ , earned in location _i_ , location _i_ ’s amenities, _Ai_ , and an individual-specific idiosyncratic preference for living in location _i_ , _εij_ :<sup>13</sup> People choose to live in the location which provides them with the highest utility<sup>14</sup> , so that the probability that individual _j_ chooses to live in location _i_ is: Assuming that the _εij_ are drawn from a double exponential function with mean _π_<sup>_2_</sup> _μ_<sup>_2_</sup> _/6_ , this probability can be written in the following logit form (see McFadden, 1974): Here, _μ_ determines the importance of a person’s idiosyncratic preferences in determining his/her location choice. If _μ_ is very small, people basically choose their location only based on _Wi + Ai_ . That is, everybody chooses that location offering them the best combination of real wages and amenities. In this scenario, multiple cities can only exist if possible real wage differences between locations are perfectly offset by differences in amenities. By contrast if _μ_ is very large, people basically choose each location with equal probability _1/K_ , where _K_ denotes the number of possible locations. In this case people’s idiosyncratic preferences for each location are very heterogeneous and, as a result, real wages and amenities do not matter for each individual’s location choice.

Spatial equilibrium in the model is reached when the probability in (3) corresponds to the actual observed share of people living in location _i_ :

> 13 The idiosyncratic preferences could also reflect differences between people in the cost of migration cost, in the value they put on living close to their friends or relatives, or in the information they have about the potential benefits/cost of migration.

> 14 Many NEG-models (notably Krugman’s original 1991 contribution) assume that people only move in response to real wage differences. This would mean that in a spatial equilibrium real wages are equalized, both across the urban and rural sectors, as well as across all prefectures in China. Introducing other motives for migration (here amenities and other unobserved location-specific preferences) means that real wage differences between locations can persist in equilibrium. Moreover, the location-specific idiosyncratic preferences ensure that, in equilibrium, at least some people live in each and every location. Note that in Desmet and Rossi-Hansberg (2013) people are also perfectly mobile and decide where to live based on more than just real wages. However, they do not consider individual specific heterogenous preferences for living in each city. As a result, some cities disappear in their counterfactual scenarios (the same holds for Bosker _et al._ (2012), where in the equilibrium with labor mobility only a few cities remain in existence).

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