Endogenous generation of amenities and the dynamics of city structure

https://doi.org/10.1016/j.regsciurbeco.2018.10.005Get rights and content

Highlights

  • The history of a city matters for understanding its current social structure.

  • The evolution of the city's structure is strongly related to the generation and the valuation of urban amenities.

  • Lock in effects appear: once an area has been occupied by a social group, it tends to stay occupied by the same group.

  • The combination of amenities and differentiated transport costs generates a multitude of stable spatial structures.

Introduction

The starting point of this paper is that history matters for explaining the social structure of a city as soon as there is an interaction between this social structure and the spatial distribution of amenities.

It is well known that the standard Alonso-Muth model leads to the conclusion that, if inhabitants only differ by their wealth, at equilibrium, central locations are occupied by poor households and the suburbs by middle class and rich households (Alonso, 1964, Muth, 1969). This structure is typical of most American cities (Glaeser et al., 2008) while, in most European cities, rich households live downtown and poor households live in the suburbs (Hohenberg and Lees, 1986).

More generally, as noted by Gaigne et al. (2017), the correlation between income and distance to the city centre is very low. They provide empirical evidence on Amsterdam and Rotterdam showing that income and amenity gradients are not necessarily monotonic with the distance to the centre. Many metropolitan areas display pronounced U-shaped or W-shaped spatial income distributions (Glaeser et al., 2008, Rosenthal and Ross, 2015).

Then, how to explain the existence of cities with a European structure or other more complex patterns? How to endogenously generate complex urban structures without making ad-hoc assumptions? An early explanation rests upon differences in transportation costs: when they are much higher for the rich than for the poor, and the income elasticity of commuting costs is higher than the income elasticity of demand for land, the rich live in the city centre and the poor in the suburbs (Wheaton, 1977). And, effectively, Glaeser and Kahn (2003) and Glaeser et al. (2008) find that rich households sort themselves in locations close to the central business district, depending on their preferences for house size and commuting costs.

However, following Brueckner, Thisse and Zenou in their seminal paper (Brueckner et al., 1999, BTZ from now on), the current debate mainly focusses on the role played by local amenities. If the rich are more sensitive to local amenities than the poor, they make higher bids for housing close to positive amenities (Fujita, 1989, Epple et al., 2010, Koster et al., 2016) and the social structure of the city is correlated to the geographical distribution of its amenities (Gaigne et al., 2017, Lee and Lin, 2018).

Moreover, as noted by BTZ, an important outcome of the long history of European cities is the existence of historical amenities generated by the built heritage (monuments, buildings, parks, fine architecture and other urban infrastructure), mainly located in the city centre. If rich households have a willingness to pay for these amenities that is high enough compared to that of the poor, the city centre attracts rich households and the resulting spatial structure follows the European pattern.1

In the BTZ and subsequent models, the dynamics of the development of the city are neglected. However, these dynamics matter, for two reasons. First, cities may change their structure as they develop. For example, in Paris, rich boroughs like Saint-Germain-des-Prés or Passy were peripheral when they started to be urbanised. Then, with the development of the Paris agglomeration, they became central. Then, we may observe different structures for young cities (typically a current American city) and old cities (like in Europe).

Second, even if the basic mechanisms structuring the city are the same, the type of development of the city may influence its structure. The stable structure of a city developing quickly may not be the same as the stable structure of a city developing slowly.

For analysing these dynamics, we start from the generalisation of the BTZ model proposed by Tivadar (2010). This BTZ-T model introduces an endogenous determination of local amenities: they are generated and valued by a social group, the rich. Moreover, it relaxes two simplifications made by BTZ, considering a continuum of locations and variable housing size.

We adapt the BTZ-T model to a dynamic framework. At each period, corresponding to a generation, the spatial distribution of historical amenities determines the equilibrium social structure of the city. This equilibrium structure determines the spatial distribution of modern amenities generated by the rich. The incorporation of these modern amenities in the stock of historical amenities determines the spatial distribution of the historical amenities for the next period. The interaction between the location choice of the rich, the generation of amenities, and strong preferences of the rich for these amenities, results in a spatial “lock-in” effect: the rich go on occupying the same areas previously occupied by their predecessors and where the amenity level is kept at a high level.

Our contribution is to show that this effect can explain the social structure of European cities and even more complex structures. In the first periods, the spatial differentiation generated by local amenities is weak, and then the rich choose peripheral locations, as predicted by the standard urban model. However, later on, the rich go on living in the same areas and surroundings, where the amenity level is higher than elsewhere. As the city growths, the rich area incorporates more central locations and the poor are obliged to locate in the periphery. The city passes through a period of “mixed” social structure: poor households located in the centre and the suburbs and rich in an intermediate area. The development of the city continues and finally the centre may be completely absorbed by the rich, the spatial structure corresponding to the European social pattern.

Moreover, combining differentiated transportation costs and amenities effects leads to more complex interactions, and a greater variety of long term spatial patterns can emerge. For example, introduction differences in transport costs, a large enough initial difference in transport may lead the rich to start living in the centre and, when this difference becomes small, the periphery starts being also occupied by the rich, the poor being located in a ring between the two rich areas. A V shaped pattern emerges, that cannot be explained by a static model.

In the next section we present the theoretical model, adapted from the BTZ-T model. In Section 3, we present numerical simulations that show the evolution of the interactions between local amenities and the social structure, focusing on three cases: a situation where the city develops according to a European pattern, an intermediate scenario and the opposite case, where the city's structure is “blocked” within an American structure. Then, we present two more complex scenarios including interactions between transportation and amenities effects and leading to new urban structures. The Section 4 presents some conclusions.

Section snippets

The BTZ-T model

In the original BTZ model (Brueckner et al., 1999), Brueckner, Thisse and Zenou proposed an amenity-based theory of location by income. Their model analyses the influence of the spatial pattern of amenities on the relative location of different income groups in a city. The model has two versions, respectively with exogenous and endogenous amenities. In the exogenous amenities model, the authors use a continuum of locations within a monocentric city, with two social groups: the rich and the

Numerical simulations

There are two core mechanisms in our model. The first one is the competition between households for occupying the urban space. At each period, this competition determines how the spatial distribution of amenities leads to an equilibrium social structure. The second mechanism comes from the generation of amenities, which determines the evolution of the spatial distribution of amenities and then the evolution of the spatial structure.

The structure of the model making analytical calculations quite

Conclusions

In this article, we developed the analysis of the impact of amenities on location in the urban space, initiated by Brueckner et al. (1999) and expanded by Tivadar (2010). Our main contribution is to explicitly take account of the dynamic processes governing the evolution of amenities and households' location decisions.

Our main result is that the historical development of a city, particularly the generation of local amenities, plays a determinant role in the social structure of the urban space

Acknowledgements

We benefitted from important remarks by two anonymous referees and the editor, that helped us making major improvements. The usual disclaimers apply.

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