- Email: [email protected]
The periurban city: why to live between the suburbs and the countryside
Regional Science and Urban Economics 34 (2004) 681 – 703 www.elsevier.com/locate/econbase
The periurban city: why to live between the suburbs and the countryside Jean Cavailhe`s a, Dominique Peeters b,*, Evangelos Se´keris c, Jacques-Francßois Thisse d,e a
b
UMR INRA-ENESAD CESAER, Dijon, France De´partement de Ge´ographie and CORE, Universite´ catholique de Louvain, Voie du Roman Pays 34, Louvain-la-Neuve B-1348, Belgium c IRES, Universite´ catholique de Louvain, Belgium d CORE, Universite´ catholique de Louvain, Belgium e CERAS, Ecole nationale des ponts et chausse´es, France Accepted 20 August 2003 Available online 1 July 2004
Abstract The last 30 years have witnessed the emergence of a new pattern of urban development in France, called the periurban belt. It is defined as a belt outside the city occupied both by households and farmers. We develop a residential model in which households commuting to an employment center may choose to live with farmers in this mixed belt because they value the rural amenities created by farming activities. Both types of agents compete on the land market and the equilibrium conditions allow us to obtain an analytical solution and to provide some insights about the robustness of the periurban form against decreases in commuting costs. Finally, the model is calibrated on French data. D 2004 Elsevier B.V. All rights reserved. JEL classification: R14; R21 Keywords: City; Farming; Land rent; Mixed space
1. Introduction The last 30 years have witnessed the emergence of a new pattern of urban development in France, called the periurban belt.1 It is defined as a belt outside the city occupied both * Corresponding author. Tel.: +32-10-47-43-43; fax: +32-10-47-43-01. E-mail address: [email protected] (D. Peeters). 1 This phenomenon is not specific to France. It has been observed in other European countries (Caruso, 2002) as well as in the US (Nelson and Sanchez, 1997). 0166-0462/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.regsciurbeco.2003.08.003
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
682
by farmers and commuting households (Le Jeannic, 1997; Cavailhe`s and Schmitt, 2002). Hence, the periurban area may be viewed either as a rural area in the sense that the vast majority of its land is used for farming, or as an urban area with most of its working population commuting to the city where jobs are concentrated.2 The periurban household has been described as ‘‘living in natural surroundings, far from the city’s turmoil in roomy houses with gardens while keeping a city job with the associated income’’ (Le Jeannic, 1997). This is reminiscent of urban economics models with amenities. However, such models typically assume a specialized residential pattern with contiguous housing. Clearly, this does not fit the periurban area. In addition, those amenities are often exogenous whereas amenities arising in periurban areas depend on the level of agricultural activities. Yet, with its clear separation between residential and working places, the periurban space forms a ring around a city that displays the monocentric pattern common to most residential location models. Therefore, it seems to us that we may appeal to urban economic theory to study periurban areas. In this paper, we borrow ideas from land use theory and urban economics to develop a residential location model in which households may choose to live close to farmers because they value rural amenities created by the farmers.3 Rural amenities produced by farmers contribute to the well-being of consumers working in the city center, whereas farmers have a Thu¨nian behavior in that they benefit from the city proximity through reduced transport costs for their crops. Households and farmers compete on the same land market. The equality between the bid land rents of these two types of agents gives rise to a periurban equilibrium. This is achieved through the supply of rural amenities by farmers, the level of which is determined by the interactions between farmers and households whose densities are endogenous. In standard urban economics, the trade-off between the lot size and commuting costs yields a land rent profile that is decreasing with distance from the CBD. However, several applied findings contradict this result and have led to the development of models exhibiting negative rent gradients. The existence of amenities in the periphery of cities is one of the tools used to model these inverted gradients (Richardson, 1975; Brueckner et al., 1999; Goffette-Nagot, 2000; Irwin, this issue). Our analysis runs along the same lines as these models but has a very different purpose. Specifically, we build a new setting in which market equilibrium conditions give rise to several equilibrium land use patterns. One of these patterns is of particular interest to us, that is, a mixed farming-residential space. Stated differently, for some parameter configurations our model yields a mixed space, which is rarely found in the existing literature although it is pretty common in the real world.4 2
More details are given in Section 2. In doing so, we do not ignore the fact that cities are the source of a large array of amenities and that farming generates nuisances. The former are introduced into the model in a cursory fashion, because they are not central to our analysis. We also assume a positive net balance of agricultural nuisances (pollution, bad smells, noise) and amenities, such as natural landscapes, open spaces, the maintenance of a peaceful and unpolluted environment. 4 Early exceptions include Kanemoto (1980, ch. 6) as well as Ogawa and Fujita (1980). By using discrete choice theory to describe consumers’ behavior, Miyao and Shapiro (1981) show that consumers of different types may be located at the same place, whereas Anas and Xu (1999) consider a broader approach in which mixing involves both firms and workers. Finally, Bockstael and Irwin (this issue) generate a periurban belt based on households’ dislike of proximate residential land use. 3
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
683
Fig. 1. Net migrations according to the spatial typology.
The remainder of the paper is organized as follows. In Section 2, we provide a short description of the evolution of periurban areas in France and of their main distinctive features. Section 3 presents the model, whereas Section 4 deals with the periurban land market equilibrium. Section 5 focuses on the effects of the periurban spread on the environment and other variables affecting the quality of life. We also address the following question: is the periurban belt a permanent pattern of urban growth or just a transitory stage of evolution? Section 6 presents an attempt at calibrating our model on medium-sized French urban areas with parameters obtained from surveys or advice of experts. Findings predicted by the calibration and observed from the real word are similar. Section 7 concludes.
2. Periurban areas in France: a brief description As shown in Fig. 1, since the 1970s, French cities and their suburbs have lost inhabitants, whereas periurban belts have gained many.5 Periurban areas have expanded according to two different schemes. In the first one, which can be found around Paris and a few other densely urbanized areas, the pattern is polycentric with cities connected to a metropolis and periurban zones in the interstices, which are made of small towns and villages scattered among fields and forests. In the second one, which corresponds to the majority of cases, the pattern is monocentric, with a city surrounded by a periurban belt, which is also a mix of small towns, villages, farms, and forests. In what follows, we focus on the simpler case of a monocentric pattern. However, it should be clear that the same principles can be applied to a polycentric space. 5 Fig. 1 is based on the following statistical taxonomy. An urban area is made up of an urban core and its periurban belt. The urban core is the central city together with its suburbs, defined by the continuity of the builtup area and offering at least 5000 jobs. The periurban belt surrounds the urban core and is defined by its number of commuters: the threshold is 40 of its active population commuting to the urban core. The French statistical definition of an urban area is similar to that of an MSA in the US.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
684
Table 1 Evolutions of population and spatial extension Urban cores
Population (thousands) Number of jurisdiction % French area
Periurban
Rural area
Total
1990
1999
1990
1999
1990
1999
1990
1999
34,372 2793 7.4
35,708 3100 8.1
8862 10,431 22.1
12,257 14,930 33.1
13,381 23,341 70.5
10,553 18,535 58.9
56,615 36,745 100
58,519 36,565 100
INSEE, 1990 and 1999 census.
The periurban belts are characterized by the following main features. 1. The importance of commuting flows: in 1999, 79% of the labor force living in the periurban areas are commuters. Average commuting distances vary from 9 to 14 km in small and medium-sized urban areas; they are equal to 26 km in large urban areas, except Paris where the average commuting distance is 46 km (Talbot, 2001). 2. A lack of jobs: employment concentration in urban cores has increased during the second half of the 20th century from 62% in 1962 to 71.5% in 1990. From 1962 to 1990, the population of periurban belts has grown by 75% but its number of jobs by 7% only.6 3. A rural settlement: the population density is approximately 70 inhabitants/km2. In 1990, the average population in periurban jurisdictions was 935 inhabitants. 4. A rural land use: farming and forestry occupied about 75% of the periurban land. Therefore, it is fair to say that periurban areas depend on cities for their jobs while having strong rural characteristics in terms of land use, landscapes and dwellings. The central assumption of this paper is that the rural features of periurban areas represent a living environment valued by the residing households.7 The need for rural amenities may explain the observed growth of periurban belts. In 1990, according to the spatial taxonomy used at that time (see Footnote 5), periurban areas accommodated 8.9 million of inhabitants and covered 22% of the French territory. In 1999, using the spatial limits valid for this year, the periurban population had grown to 12.3 million (21% of the French population) and occupied 33 of the territory (see Table 1).
3. The model 3.1. Assumptions and notation Space is represented by the real line X=(l,l) with a CBD lying at the origin. It is assumed that all non-agricultural employment is concentrated in the CBD. There are two 6
This is to be contrasted with what has been observed in the US. However, it is worth mentioning that the last 1990s have seen a reversal of the urban concentration of employment in France. 7 The same holds in suburban or exurban areas in the United States where tastes for rural amenities are prominently displayed.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
685
types of agents competing on the land market: (i) a continuum of identical households working at the CBD, with density nh(x)z0 at xaX and (ii) a continuum of identical farmers, with density na(x)z0 at xaX. The total amount of space occupied by households and farmers at x cannot exceed the available quantity of land (which is normalized to 1): nh ðxÞSh ðxÞ þ na ðxÞSa ðxÞ ¼ 1
ð1Þ
where Sh is the size of residential plot and Sa the size of the farm. There is no clear evidence about the place of origin of periurban residents and farmers. Thus, the economy is assumed to be open in that households and farmers are free to migrate in and out, according to households’ utility and farmers’ profits obtained in the rest of the world. We call city (C) a specialized residential area (nh(x)>0 and na(x)=0). A periurban area (P) is a mixed space accommodating both households and farmers (nh(x)>0 and na(x)>0). Farms are located either in the periurban area or in the rural (R) space, where only farmers live (nh(x)=0 and na(x)>0). It is worth noting that we make no assumptions regarding the existence and the relative positions of the areas C, P and R with respect to the CBD, which depend on the parameters of the model influencing the bid rent curves. There are three consumption goods: a composite good available everywhere at the same price, housing which takes the form of a residential plot whose size is variable, and amenities. Amenities are consumed at their place of residence and have the nature of a local public good. The city provides urban amenities Ac. Because our aim is to provide an analysis of periurban areas, we keep the analysis simple by assuming that the quantity of urban amenities is given and evenly distributed within the city. Rural amenities Ap are supplied, as a by-product of farming, in the periurban area exclusively (na(x)>0), which accommodates nonfarmer households (nh(x)>0). Hence, amenities may be considered as a spatial attribute of housing, which directly enter the household’s utility function but not explicitly its budget constraint.8 3.2. The farmer in a Thu¨nian space Agriculture involves production under constant returns to scale and the only input is land (or, equivalently, a fixed combination between labor and land). Without loss of generality, it is assumed that one unit of land yields one unit of output. Two cases may arise. Firstly, the agricultural land rent is flat and equal to a positive constant RA. Secondly, and more importantly, farmers face an agricultural land rent decreasing from the CDB. The positive effects of city proximity on the price of farmland are, indeed, well documented (Chicoine, 1981; Shi et al., 1997; Colwell and Dilmore, 1999). This may be explained by the following two reasons: (i) direct sales of farm products or recreational services, which may be more profitable than sales to the food processing industry, but entail transport costs depending on distance from the city; (ii) expected gains from the sale of land for 8 For simplicity, we assume throughout this paper a completely mixed periurban belt, despite the fact that real patterns involve small towns and villages. Accounting for such small settlements would require the introduction of local interactions across people.
686
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
residential uses that are also distance-sensitive. In what follows, ‘‘direct sales’’ are assumed to act as a reduced form for these two factors. This assumption is made to capture in a very simple way the effect of distance on farmers’ bid rents described above (and because a dynamic model with expectations or option values is much more complex). Each farmer maximizes her profits with respect to the farm size, given the land rent and the prices of the crops sold either to the food processing industry or directly to the urban consumers. In this case, the transport rate to the city is given by s>0. Because returns to scale are constant, the profit per unit of land is constant across locations, thus allowing one for a straightforward determination of the farmer bid rent function U. In the case of food industry sales, we have U(x)=RA; in the case of direct sales, we have U(x)=Csx, where C is a constant depending on the price of the goods sold to the urban consumers. Hence, the farmer bid rent function is such that: UðxÞ ¼ maxfC sx; RA g Ignoring for the moment the presence of households, we thus obtain a space a` la Thu¨nen formed by a circle, the radius of which is equal to xd uðC RA Þ=s
ð2Þ
where farmers sell their crops directly in the city and outside this circle by an area where farmers sell to the food processing industry. Finally, farmers located at x produce rural amenities for a total amount of Ap(x), which depends on the area used for farming: Ap ðxÞ ¼ dna ðxÞSa ðxÞ
ð3Þ
where d is a positive constant and Sa(x) the amount of land used by a farmer at location x.9 3.3. The household in an urban or periurban environment Households’ well-being is determined by the usual trade-off between accessibility to the CBD and land consumption, but also by the amount of (urban or rural) amenities. As said above, a household residing at xaX consumes three goods: (i) land Sh(x) for which it pays the rent R(x), (ii) a composite good Z available everywhere at a given price pz and (iii) urban amenities Ac or periurban amenities Ap(x). Finally, the utility function is of the same Cobb-Douglas type regardless of the household’s location. A household working in the CBD gets an (exogenously determined) wage w and commutes at a unit cost of t. The residential land rent depends on the distance to the CBD and the quantity of amenities: R(x)=R[x,Ac,Ap(x)]. Thus, the budget constraint is as follows: RðxÞSh ðxÞ þ pz ZðxÞ ¼ w tx: 9 Because of the assumption of constant returns, it is not possible to determine the size Sa(x) of the farm, but only the total amount of land na(x)Sa(x) devoted to farming at location x.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
687
Ignoring for the moment the presence of farmers, the utility of a household in a purely residential city (subscript c) is given by: Uc ¼
1 aa bb
ZðxÞa Sh ðxÞb Acc
ð4Þ
In equilibrium, the household’s utility does not depend on x and is equal to U , that is, the utility it may obtain in the rest of the world. Without loss of generality, to ease the burden of notation, we make the following normalizations: (i) the composite good is taken as the nume´raire, i.e. pz=1, (ii) we choose the amenity unit such that Ac=1, and finally (iii) we assume that a+b=1 and set U =1. Hence, the demand functions Z(x) and Sh(x) for the composite good and for housing are derived from the first order conditions: Z*ðxÞ ¼ aðw txÞ
Sh*ðxÞ ¼
bðw txÞ RðxÞ
ð5Þ
so that the indirect utility function of the household living in the city is given by Vc ðxÞ ¼ RðxÞb ðw txÞ The household’s bid rent is then obtained from the indirect utility function Vc(x) as follows: Wc ðxÞ ¼ ðw txÞ1=b
ð6Þ
implying that the city expands up to the point xv defined by xv u
w RbA : t
ð7Þ
In the periurban environment with farmers (subscript p), the utility is Up ¼
1 aa bb
ZðxÞa Sh ðxÞb Ap ðxÞc
ð8Þ
The demands functions are still given by Eq. (5) and the indirect utility becomes Vp ðxÞ ¼ RðxÞb ðw txÞ½Ap ðxÞ c Hence, in the periurban area, the household’s bid rent is as follows: Wp ðxÞ ¼ ðw txÞ1=b Ap ðxÞc=b :
ð9Þ
Clearly, for a periurban area to arise, it must be that Ap(x) exceeds Ac=1. Given Eqs. (1) and (3), this in turn requires d>1. In other words, farming must produce a sufficient amount of rural amenities for a periurban area to exist.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
688
4. The city – periurban – rural equilibrium As mentioned in the introduction, several configurations may be sustained as spatial equilibria. The one that interests us is as follows: the CBD is surrounded by a specialized residential area, which is itself followed by a periurban ring and, finally, by a rural area. It is denoted C – P – R. 4.1. Equilibrium conditions As land is rented to the highest bidder, the periurban household – farmer mix exists if and only if the households’ land bid and the farmers’ land bid are the same. Let be A*(x) the p amount of rural amenities for which these two bids are equal. Two cases may arise. In the first one, farmers’ bid rent is Csx and the equilibrium condition for a periurban belt is given by: ðw txÞ1=b Ap*ðxÞcb ¼ C sx
ð10Þ
In the second one, farmers’ bid rent is RA so that the above condition becomes: ðw txÞ1=b Ap*ðxÞcb ¼ RA In what follows, we consider only the first case, which both yields richer patterns and seems to be more realistic than the second one. It follows immediately from Eqs. (6) and (10) that, in equilibrium, for x to belong to a periurban area, the level of amenities available at x, Ap*(x) must be equal to the ratio of the household periurban bid rent (which is equal to the farmer bid rent) to the household city bid rent, to the power b/c. The lower the elasticity of utility with respect to amenities (c) or the higher the elasticity of utility with respect to housing (b), the more periurban rural amenities there will be compared with urban amenities. By rearranging the terms of Eq. (10), we obtain the equilibrium level of rural amenities as follows: " #1=c UðxÞ b=c ðC sxÞb Ap*ðxÞ ¼ ¼ : ð11Þ Wc ðxÞ w tx The corresponding bid rents and market land rent are depicted in Fig. 2, where xc is the boundary between the city and the periurban belt and xp the outer boundary of the periurban belt.10 For simplicity, the household bid rent beyond xp is not represented. In other words, xc is the solution (if any) to the equation UðxÞ ¼ Wc ðxÞ whereas xp is the solution (if any) to ¼d A*ðxÞ p which is obtained from Eq. (3) when all land is used for farming. 10
For simplicity, the household bid rent beyond xp is not represented.
ð12Þ
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
689
Fig. 2. Land bids and land rent in the C-P-R configuration.
Finally, since the landowner rents her land to the highest bidder, the land rent prevailing at xaX is given by: R*ðxÞ ¼ maxfUðxÞ; Wc ðxÞ; Wp ðxÞg: 4.2. Existence of a C – P – R equilibrium Each of the following conditions is necessary and together they are sufficient for a periurban belt to exist. First, the wage earned at the CBD must be large enough relative to the agricultural rent for the farmers to be pushed away from the center. Second, the two bid rent curves Wc(x) and U(x) intersect if and only if xvWc(xd). Using Eqs. (2) and (7), xv1, the necessary and sufficient conditions for the C – P –R configuration to be an equilibrium are as follows: w > Cb
t w RbA z C > RA s C RA
ð13Þ
690
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
Observe that the second condition means that the parameters of the economy are such that the curve U is above the curve Wc over a nonempty interval. It is worth noting that the periurban area is (locally) stable when Eq. (13) holds. Indeed, if there were too many (resp., not enough) farmers for the appropriate configuration of parameters, the amenity level would be higher (resp., lower) than the equilibrium value A*(x), thus attracting (resp., repelling) households. Consequently, npSp would rise (resp., p fall), whereas naSa would vary in the opposite direction, entailing a decrease (resp., increase) in the quantity of amenities. Hence, Ap(x) will move toward its equilibrium value A*(x). p 4.3. Properties of the C – P –R equilibrium From the demand function (5) and the bid rent functions (6) and (9), we can determine the urban and periurban lot sizes, denoted respectively Sc*(x) and Sp*(x): Sc*ðxÞ ¼
bðw txÞ ¼ ½bðw txÞ a=b if na ðxÞ ¼ 0 Wc ðxÞ
ð14Þ
Sp*ðxÞ ¼
bðw txÞ bðw txÞ bðw txÞ ¼ if na ðxÞ > 0: ¼ Wp ðxÞ UðxÞ C sx
ð15Þ
If x belongs to a periurban area, then Sp*(x) is smaller than Sc*(x) because Wc(x)
ð16Þ
As rural amenities have the nature of a local public good, their Lindhal-Samuelson price PA*(x) at x is defined by the marginal rate of substitution between amenities and the composite good Z, obtained from Eqs. (5) and (8), times the number of households residing in x: PA*ðxÞ ¼
BUp =BAp w tx c 1 1 np*ðxÞ ¼ c np*ðxÞ ¼ Wp ðxÞ Ap*ðxÞ b Ap*ðxÞ d BUp =BZ
ð17Þ
As expected, in the periurban belt, the equilibrium price of the rural amenities depends positively on the land rent in the periurban area—hence on the income—and negatively on the amount of amenities. Finally, because the bracketed term is positive in equilibrium, the lower c/b, the lower the amenity price. In particular, PA*(x)=0 when consumers do not value rural amenities (c=0). Note that, if the parameters of Eq. (17) can be estimated, PA*(x) may be used to evaluate the consumer willingness to pay, or the producer willingness to receive, for rural amenities. Interestingly, such an expression would allow us to compute the implicit price
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
691
of the amenity by means of a method that differs from the standard hedonic price or contingent valuation methods. 4.4. The urban economics city For the sake of comparison, we also consider the traditional monocentric city of urban economics. This configuration, denoted C – R, is an equilibrium if and only if the following four conditions are satisfied (see Appendix A(2)):
w > Cb
t w RbA < s C RA
C > RA
wz
s b=a t
t þ C s
The first and the third conditions are as in the foregoing case. The second one says that xv(=xc)>xd (see Fig. 3), whereas the fourth condition allows one to rule out the special and not very realistic case in which the curves U(x) and Wc(x) intersect twice. It is tempting to think of the periurban area as a semi-anarchical scattering of housing that destroys landscapes and wastes land, which would corresponds to an extreme form of urban sprawl. Urban sprawl has been criticized for environmental reasons both in Europe (Camagni et al., 2002) and in the United States (Brueckner, 2000). It consumes excessive amounts of energy (cars, individual houses), thereby contributing to the greenhouse effect. Furthermore, urban sprawl implies inefficient use of public goods and infrastructure as a consequence of low population densities (Brueckner, 2000). However, there are positive aspects to the periurban belt: it helps relieve congestion in the city centers and gives a new lease of life to areas abandoned by traditional agricultural activities. Beyond these arguments, the question arises as to whether to take account of households’ preference for low densities (Richardson, 1975; Gordon and Richardson, 1997). Our model sheds
Fig. 3. Land bids and land rent in the C-R configuration.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
692
light upon this debate from two different perspectives: (i) the existence of urban sprawl and the trade-off between land consumption and amenities, and (ii) the impact of commuting costs on residential choices. 4.5. The periurban belt, urban sprawl and land consumption Firstly, as shown in Appendix A(1), the outer boundary xp of an urban area endowed with a periurban belt is farther from the CBD than the limit xv of a traditional urban economics city. This result is not terribly surprising because the periurban belt contains both households and farmers: the periurban pattern extends the area occupied by households farther from the CBD than a specialized city would do. In this sense, the periurban city leads to a larger consumption of natural land. Secondly, what characterizes a periurban area is the substitution between housing and amenities. Indeed, from Eqs. (14) and (15), we obtain: UðxÞ S*ðxÞ c ¼ Wc ðxÞ S*ðxÞ p which, given Eq. (11), becomes:
S*ðxÞ c Sp*ðxÞ
b
c ¼ ½A*ðxÞ >1 p
At location x, the residential plot in the periurban area is smaller than what it would be, if x were to belong to a purely urban area. The rural amenities make up for the difference, the substitution rate between housing size and amenities being b/c. For larger values of c, which suggests a marked taste for rural amenities, we can even end up having plots that decrease in size as we move away from the city. The alternative to a mixed periurban belt is, therefore, a specialized urban space with larger lot sizes. In this sense, the periurban area may be viewed as being residential land-saving. Hence, we may conclude that periurban development saves land in the intensive margin by making lots smaller than they would be if the city were purely urban, but it pushes the extensive margin of residential development farther out causing more sprawl. 4.6. The impact of decreasing commuting costs In open city models, a decrease in commuting costs leads to an increase in the city size and in the bid rents, thus implying a reduction in the lot size and a corresponding increase in density (Weathon, 1974; Fujita, 1989). In the periurban area, these results are changed as follows. Other things being equal, the decrease in commuting costs implies a decrease in the quantity of rural amenities,11 which entails: (i) a decrease in the proportion of farming in
11
This is shown by differentiating Eq. (11).
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
693
the periurban area (see Eq. (3))—the more accessible the periurban belt, the less rural it becomes; (ii) an increase in the size of residential plots12; and (iii) an increase in population density.13 As expected, a decrease in commuting costs has a well-determined impact on the city that expands and becomes denser (see Appendix A(3)). As for the periurban area, however, the effects are not that clear-cut and different evolutions may arise for intermediate values of the commuting costs. However, when t falls below a certain threshold, the periurban belt disappears and a specialized urban area with larger residential plots emerges. Indeed, a decrease in t leads to an upward shift of the households’ bid rent curve Wc (which keeps the same intercept) while that of the farmers remains unchanged (see Appendix A(2) for a formal argument). As a consequence, when commuting costs decrease (or, equivalently, w increases), the sequence of spatial configurations would be as follows: 1. When commuting costs are high relative to wages, the periurban belt is very small. 2. Within the city, keeping the level of urban amenities constant, the decrease in commuting costs generates a decrease in lot size and an increase in land rent. In the periurban area, the decrease in t, which does not affect the farmer rent, leads to a decrease in the equilibrium supply of rural amenities as well as to an increase in the size of housing plots. 3. Finally, when commuting costs fall below a certain threshold, land is specialized.
5. The calibration of the periurban city 5.1. The procedure The equilibrium outcome described in the foregoing sections has been obtained at the cost of many simplifying assumptions. Hence, one may wonder about the meaning of the conclusions obtained, especially when considering them for possible policy recommendations. Therefore, to assess the relevance of the model, we calibrate it on real data. To the best of our knowledge, not that many attempts have been made to validate models of urban economics on real data (see Anas, 1987, for a survey). Since then, Anas and Kim (1992) compare observed population density gradients to predictions derived from a standard urban economics model. Anas (1995) performs a calibration for the New York metropolitan area, whereas Anas and Arnott (1993) do something similar for Chicago. Very much as in Anas and Kim (1992), we propose a calibration of our model based on the minimization of a relative error term E. This term is equal to the sum of the
12 13
This shown by differentiating Eq. (15). Eq. (16) shows that n*(x)S *(x) varies with t as does A*(x), but in the opposite direction. h h p
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
694
squared deviation between actual and predicted values, divided by the square of the actual value in order to get dimensionless numbers because we add areas, distances and individuals:
min E ¼
X i
hi
ðX¯ ip X¯ ia Þ2 ðX¯ ia Þ2
ð18Þ
*(x),x where Xi=(Sc*(x),Sp*(x),n*(x),n c p c,xp,n*S a *). a In Eq. (18), superscripts p and a refer respectively to the predicted and actual values, while X¯ is the average of each variable.14 The variables have been weighted by hi according to the reliability of the actual values,15 which are econometrically estimated (b,s,U(0),Wc(0)), observed (w), obtained from advice of experts (t,RA), or computed by screening (d,c) in order to minimize Eq. (18). As our objective focuses on the French periurban areas, only the C – P –R configuration will retain our attention. 5.2. The practical relevance of the model The main problem encountered in using our theoretical model for a calibration on real world data is land zoning, with some tracts given over to development and others reserved for agricultural uses. So, can we calibrate a model based on market-determined forces, as assumed in our model, when the real land use seems to be planner-determined? The answer depends on the existence and nature of zoning. In France, land conversion is regulated by two procedures. The first one occurs in 61% of the 1967 periurban jurisdictions of the medium-sized urban areas selected for the calibration. In these jurisdictions, no zoning exists and the decision to develop a tract is made by the mayor. The second procedure is based on a ‘‘Plan d’occupation des sols’’ (in short, POS), which determines the zones for future development as well as those reserved for farming purposes. Nevertheless, the POS is frequently revised and, thus, a non-developable plot may later be considered for development. Whatever the procedure, the land conversion policy is more flexible in small periurban jurisdictions (recall that the corresponding average population is 935) than in large cities where land use is more controlled. Therefore, we may conclude that most decisions regarding land use are market-determined in periurban jurisdictions of medium-sized cities, which we have selected for our calibration. Hence, it is reasonable to assume that both farmland and residential land markets are submitted to the same distance-related forces. Therefore, although the agricultural and residential rents are not equal at a given distance from the city, as assumed in our model where U(x)=Wp(x) at x belonging to the periurban belt, both rents are linked and moved
14
For the size of the residential parcels, we use the median value. We assume hi=1, except for (i) the share of agriculture whose actual value is roughly known (we set hi=0.5) and (ii) the limits of the city and of the periurban area whose statistical and administrative definitions are not those used in our model (we set hi=0.75). 15
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
695
together. For the calibration, we assume that a multiplicative factor allows us to go from one curve to the other (see Appendix B). Three minor modifications are also needed: (i) space is considered as a disk generated by 2p-rotating the straight half line around its origin; (ii) the periurban rent curve is described by a negative exponential function, instead of being linear, because this allows one for a better fit of the periurban gradient; and (iii) the CBD is considered as a disk. Still, our setting remains very stylized. First, it is made up of rings around an urban center where the movements are approximated by straight-line distances. Second, the periurban area is totally mixed with housing spread across the agricultural land, although it is mostly made up of rural villages surrounded by agricultural land. Third, we consider only detached houses. Last, it is fair to say that the calibration procedure is dependent on several ad hoc assumptions as well as on the values of the parameters that are presented below. 5.3. The parameters Most data come from the Housing Survey conducted in 1996 by the INSEE on a sample of 29,043 households (subsequently referred to as HS96). We have selected 4658 households belonging to some of the 28 urban areas whose core jurisdictions range from 100,000 to 200,000 inhabitants,16 which represent one-sixth of the French population. The following values of the parameters have been selected17:
the household income: w=32,000 euros/year (source: HS96), which is the gross income of households who have moved recently; the share of income spent on housing18: b=0.158 (recall that a+b=1); the rate of discount used to annualize the value of a house: r=0.0512; the urban land rent at the city center: W(0)=115,000 euros/ha/year12; the agricultural rent at the city center: U(0)=1200 euros/ha/year and the coefficient of the agricultural rent: s˜ =0.045 euros/km19; the generalized transportation rate: t=310 euros/km/year20; the agricultural rent RA is set to 150 euros/ha/year21; 16
A calibration on the entire survey was impossible because too many factors are to be controlled. The medium-sized city sample is convenient because most of these urban areas are roughly monocentric and zoning is not too constraining. 17 Details may be obtained from the authors upon request. 18 Value estimated by regression from the HS96 data (see Appendix B). 19 Values estimated from the farmland market in the Dijon area. 20 This rate is equal to the sum of the direct monetary costs, evaluated from the rate applied by the French Internal Revenue Service (0.30 euro/km) and the opportunity cost of time, evaluated by experts at 0.18 euro/min. By allowing for 1.5 workers per household, 230 journeys-to-work/year and an estimation of the journey velocity based on HS96, we get 310 euros/km/year. 21 Value obtained from the French Agricultural Department.
696
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
Table 2 Comparison of predicted and observed values
City population Periurban population City boundary (km) Periurban boundary (km) City residential plots (m2) Periurban residential plots (m2) % of agriculture in periurban
Calibrated model
Real world
Difference (%)
94,073 81,433 7.6 21.3 521 676 92%
100,000 78,000 9.0 21.1 430 850 70%
5.9 4.4 14.8 1.0 21.2 20.5 31.7
the radius of the CBD is 0.8 km accommodating a population of 150,000 inhabitants (HS96).
6. Results The simulations were performed as follows. We started from the foregoing initial values for the parameters w, b, W(0), U(0), s, t, RA, choosing c and d in order to get a plausible magnitude for the results. Next, we allowed each parameter to slightly vary in turn around its initial value. The values minimizing E were kept. Finally, we screened the values of d and c and selected d=1.1 and c=0.20. The results turn out to be sensitive to the values of the land market parameters, but robust with regard to variations around the initial values of the other parameters. The error E is reduced when g rises from 0.07 to 0.11 and flattens for pairs between (d=1.275, c=0.12) and (d=1.225, c=0.23). Given that the urban amenities have been normalized to unity, the level of rural amenities is thus slightly above the one of urban amenities for what look like reasonable values of c. Table 2 shows the values of Xi found when minimizing the error E. It seems reasonable to believe that households’ taste for rural amenities, which is expressed through the value of c in the utility function, is of the order of magnitude of the exponent b (which corresponds to the share of housing in households’ expenditures), and that the amount of rural amenities is between 20 and 25 larger than the amount of urban amenities available at the city outskirts. As shown in Table 2, the predicted results are not very different from the actual values.22 The biggest difference is observed for the part of farming in land use, which is a variable difficult to observe in the dataset. The residential plots are slightly too large in the city and too small in the periurban area, and so probably because the Cobb-Douglas utility assumes fixed shares. For the other variables, discrepancies are small. The actual gradients (which are regression curves obtained from HS96) and those predicted by calibration, both for the density of population defined as nh/(nhSh+naSa) (Fig. 4) and the size of residential plots (Fig. 5), are fairly similar, except that the actual city 22 Note also that the differences between our calibrated model and the real world can partially be explained by the fact that our model assumes identical households, whereas in fact they differ in terms of income.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
697
Fig. 4. Results of the calibration: Population density.
density is higher than the predicted value. This does not appear as a major drawback since we focus on the periurban belt. Two results are worth noting.
The parameter c, which stands for amenity taste in households’ utility, is significantly different from zero. This agrees with the basic assumption of our model: amenities generated within the periurban mixed space do affect households’ utility.
Fig. 5. Results of the calibration: Residential plot area.
698
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
The value of c (g0.20) is close to that of b (g0.16). From these values, the calculation of the implicit price of the rural amenities should be possible from Eq. (17) if the values of the urban and periurban rents were reliable. Unfortunately, the multiplicative factor introduced into the calibration is an ad hoc operator, which does not allow for such an evaluation. Both a more sophisticated model and a new calibration are necessary to estimate the amenity shadow price.
7. Conclusions We have proposed a new model of land use that seems well adapted to French metropolitan areas, which are a combination of cities, as usually defined in urban economics, and of a mixed area of housing and farming activities, called the periurban belt. This model is very simple. On the one hand, we have Thu¨nian farming activities that incur transport costs due to the direct sales of their crops. On the other hand, we have identical households with a Cobb-Douglas utility whose variables are housing, rural amenities and a composite good; households work in a pre-determined CBD. Finally, equilibrium is reached through a competitive land market. Each of these assumptions is the simplest one that can be made in an urban economics framework. However, taken together, they allow for the determination of an analytical solution. This solution makes it possible to distinguish between different urban patterns and to analyze the mechanisms that generate them. Furthermore, the periurban belt found between the two specialized areas (urban and rural) is spread out since both housing and farms are to be found in it. On the one hand, the boundary of a metropolitan area with a periurban belt is farther from the CBD than that of a specialized city. Hence, it is an expensive configuration in terms of transport costs. On the other hand, the substitution between amenities and lot size and the ensuing limited size of residential plots make the periurban configuration more efficient than the specialized city in residential land use. Thus, from an environmental perspective the impact of the periurban remains ambiguous. It is also worth noting that the results of our model suggest what could well be a historical description of the various spatial patterns observed as commuting costs fall relative to wages. 1. The traditional city, with high unit commuting costs relative to wages. Households spend a large share of their resources on commuting; so that the urban expansion is low and, consequently, the city is very dense (sparing use of space and of residential plots). In our model, a periurban belt of limited extent exists, but in practice it could easily disappear for reasons not taken into account by the model (e.g., risk of living in urban outskirts, dumping of urban waste in those areas, and the like). 2. The French city, which arises for intermediate values of the commuting cost/wage ratio, is constituted by an urban area surrounded by a periurban belt. The periurban area is considerably expanded (high consumption of space) and takes the form of a mixed space involving both households and farmers. The amenities produced by farmers limit
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
699
residential plot sizes because of the substitution effect between lot size and amenity level (sparing use of housing land). 3. The American city (e.g., Atlanta) is characterized by a sprawling specialized city with no periurban belt and large residential lots. This configuration corresponds to lower unit commuting costs (or, equivalently, higher wages) than the French periurban city. Needless to say, by using a setting like ours we cannot expect to reproduce all the stylized facts of urban history. Even though the calibration of the model conducted on French data yields reasonably good results, much work remains to be done. It is our contention, however, that the approach taken here will be useful for future research. In particular, the relationship between the urban land rent and the shadow value of rural amenities should be given more attention because it might provide us with a new way to evaluate the social value of such amenities.
Acknowledgements We are grateful to R. Arnott, three referees as well as M. Blanc, S. Charlot, F. GoffetteNagot and B. Schmitt for helpful comments and discussions. This research was supported by the Ministe`re de l’Education, de la Recherche et de la Formation (Communaute´ fran ßcaise de Belgique), Convention 00/05-262 and by the Ministe`re de l’Agriculture et de la Peˆche (France), Convention 01.G5.02.03.A. We are also grateful to the Institut National de la Statistique et des Etudes Economiques (INSEE) for providing the HS96 survey to INRA.
Appendix A 1. Given Eqs. (11)– (13), we get: h ib=c s b=c Ap*ðxv Þ ¼ C ðw RbA Þ RA < d ¼ Ap*ðxp Þ t which implies xv
s 1=a t
s C þ w: t
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
700
Hence, the two curves do not intersect if and only if: wz
s ð1aÞ=a t
t þ C: s
Furthermore, it is readily verified that /(x) increases when t decreases because the derivative of Wc(x) with respect to t is negative. 3. We show that the radius xc of the urban area rises when commuting costs t fall. Totally differentiating the expression w txc ¼ ðC sxc Þb yields dxc xc ðC sxc Þ ¼ bsðw txc Þ tðC sxc Þ dt By definition of xc, we have
dWc ðxÞ
> dUðxÞ
dx
dx
x¼xc x¼xc When xp 0 so that
.
dxc <0 dt
Appendix B B.1 . Share of residential consumption in households’ budget and discount rate We start from a reduced form expressing the housing cost of a household (either an owner or a tenant): PþR¼
b0 þ b1 S þ Abi Ki ðw txÞ *I p þ ½ðb0 þ b1 S þ Abi ki Þðw txÞ *I l r
where P is the sale price of a detached house, R is the annual rent of a detached house (R=0 if P>0 and conversely), S is the lot size, w is the annual revenue of the household, t is the annual unit commuting cost, r is the discount rate, Ki are attributes of the dwelling, I is a dummy variable such that Ip=1 for owners and Ip=0 for tenants, and Il=1 for tenants and Il=0 for owners.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
701
We estimate the parameters by a non-linear regression from HS96 P (N=646 households in detached houses) and compute both r and b ¼ b0 þ b1 S¯ j þ i>1 bi K¯ ij (where the upper-bar describes the mean value of the variables). We get b=0.158 and r=0.0513 (R2=0.74). By comparison, the share of housing in households’ budget as estimated by the INSEE is 16% and the real rate of interest at 10 years according to Eurostat is 5% in 1996. B.2 . Land rents First, a regression based on HS96 gives an estimation of the land rent for the households who have recently purchased a detached house in 1996 in mediumsized cities. This leads to the following residential land rent function R1(x)= 125,000exp(0.063x). We have selected the following values for the calibration: Wc(0.8)=115,000 euros/year/ha. Second, an estimation of the agricultural land rent was obtained from an econometric estimation for the periurban belt of Dijon, which is a typical medium-sized French city (Cavailhe`s and Wavresky, 2003). We obtain R2(x)=1.95exp(0.042x)exp(1.078p), where p is a dummy that equals 1 in the periurban belt and 0 in the city. This function differs from U(x), the agricultural rent when the farmer directly sales her crops to the city because of land zoning (see Section 5.2). For the area of Dijon, an auxiliary land rent estimation was performed for unserviced land (i.e., without water, gas and electricity), which was bought for housing by households from developers. This estimation uses data collected by the Department of Equipment from 110 housing development projects. We obtain R3(x)=107.4exp(0.071x)exp(1,56p). This equation could have been used as a direct estimation for Wp(x)=U(x). Unfortunately, the dataset used in this regression is small (N=110 observations) and land prices are obtained directly from developers. Instead, the dataset we have used for estimating the agricultural rent includes a much larger number of observations (N=2023) and prices are true market prices. Therefore, we have retained the auxiliary regression to compute the multiplicative operator. Comparing R2 and R3, the mean value of the multiplicative operator is 85.23 This value times the estimated agricultural rent R2 is then used to compute the direct sale ˜ agricultural rent at the CBD: U(0.8)=1200 euros/year/ha and the gradient s=0.045/ 24 km. The estimation of the residential rent at the CBD may be considered as robust, the selected value being close to the observed value in the center of the medium-sized cities. By contrast, the value of the agricultural rent is more ‘‘speculative’’ due to both the need of a multiplicative operator and the absence of agricultural land in the CBD. 23
This value is not unrealistic. For example, the multiplier between land values for agricultural and urban uses found by Mori (1998) varies between 50 and 200 times in the areas surrounding expanding cities in Japan and Britain. Likewise, according to Evans (1991), the agricultural price around Reading is about 2000 and, with a building permit, it goes up to £500,000 or £1,000,000 (250 – 500 times more). 24 Some minor changes in the value of the parameters are made to improve the calibration, as explained in Section 4.4.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
702
B.3 . The size of the residential lots We observe the following values (HS96): Size of residential lots
Average area Median area Selected values
Urban areas (m2)
Periurban areas (m2)
632 400 430
1307 744 850
We have estimated an equation giving the size of the lots as a function of the distance from the center, which allows for a graphical comparison of these results with those obtained from the calibration (N=2510, R2=0.11): logS h ðxÞ ¼ 6:0 þ 0:07x 0:015x2 0:051city*x ð1:31Þ
ð8:6Þ
ð10:1Þ
where city*x is an interaction variable between the distance x and a dummy variable expressing that the site does or does not belong to the city (in brackets: Student’s t). B.4 . Population in the city and in the periurban area The city population and the periurban population are obtained from (i) the predicted size of the residential lots, (ii) the predicted share of the area occupied by agriculture in the periurban belt, and (iii) the observed share of the urban area not allocated to housing (streets, parks, non residential buildings and the like), which amounts to 57% of French urban cities.
References Anas, A., 1987. Modeling in Urban and Regional Economics Harwood Academic, Chur. Anas, A., 1995. Capitalization of urban travel improvements into residential and commercial real estate: simulations with a unified model of housing, travel mode and shopping choices. Journal of Regional Science 35, 351 – 375. Anas, A., Arnott, R., 1993. Development and testing of the Chicago prototype housing market model. Journal of Housing Research 3, 73 – 130. Anas, A., Kim, I., 1992. Income distribution and the residential density gradient. Journal of Urban Economics 31, 164 – 180. Anas, A., Xu, R., 1999. Congestion, land use, and job dispersion: a general equilibrium model. Journal of Urban Economics 45, 451 – 473. Brueckner, J.K., 2000. Urban sprawl: diagnosis and remedies. International Regional Science Review 23, 160 – 171. Brueckner, J.K., Thisse, J.F., Zenou, Y., 1999. Why is Central Paris rich and Downtown Detroit poor? An amenity-based theory. European Economic Review 43, 91 – 107. Camagni, R., Gibelli, M.C., Rigamonti, P., 2002. Forme urbaine et mobilite´: les couˆts collectifs des diffe´rents types d’extension urbaine dans l’agglome´ration milanaise. Revue d’Economie Re´gionale et Urbaine, 105 – 139.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
703
Caruso, G., 2002. La diversite´ des formes de la pe´riurbanisation en Europe. In: Perrier-Cornet, P.H. (Ed.), Repenser les Campagnes, pp. 67 – 99 L’Aube-Datar, Paris. Cavailhe`s, J., Schmitt, B., 2002. Les mobilite´s re´sidentielles entre villes et campagnes. In: Perrier-Cornet, P.h. (Ed.), Repenser les Campagnes, pp. 35 – 65 L’Aube-Datar, Paris. Cavailhe`s, J., and Wavresky, P. 2003. Urban influences on farmland periurban prices, INRA-CESAER, mimeo. Chicoine, D.L., 1981. Farmland values at the urban fringe: an analysis of sale prices. Land Economics 57, 353 – 362. Colwell, P.F., Dilmore, G.G., 1999. Who was first? An examination of the early hedonic study. Land Economics 75, 620 – 626. Evans, E., 1991. Rabbit hutches on postage stamps: planning development and political economy. Urban Studies 28, 853 – 870. Fujita, M., 1989. Urban economic theoryLand Use and City Size Cambridge Univ. Press, New York. Goffette-Nagot, F., 2000. Urban spread beyond the city edge. In: Huriot, J.-M., Thisse, J.-F. (Eds.), Economics of Cities, pp. 318 – 340 Cambridge Univ. Press, New York. Gordon, P., Richardson, H.V., 1997. Are compact cities a desirable planning goal? Journal of the American Planning Association 63, 95 – 106. Kanemoto, Y., 1980. Theory of Urban Externalities North-Holland, Amsterdam. Le Jeannic, T., 1997. Trente ans de pe´riurbanisation: extension et dilution des villes. Economie et Statistique 307, 21 – 41. Miyao, T., Shapiro, P., 1981. Discrete choice and variable returns to scale. International Economic Review 22, 257 – 273. Mori, H., 1998. Land conversion at the urban fringe: a comparative study of Japan, Britain and the Netherlands. Urban Studies 35, 1541 – 1558. Nelson, A.C., Sanchez, T.W., 1997. Exurban and suburban households: a departure from traditional location theory. Journal of Housing Research 8, 249 – 276. Ogawa, H., Fujita, M., 1980. Equilibrium land use patterns in a non-monocentric city. Journal of Regional Science 20, 455 – 475. Richardson, H.W., 1975. On the possibility of positive rent gradients. Journal of Urban Economics 4, 60 – 68. Shi, Y.J., Phipps, T.T., Colyer, D., 1997. Agricultural land values under urbanizing influences. Land Economics 73, 90 – 100. Talbot, J. 2001. Les de´placements domicile-travail. INSEE Premie`re Nj767 Weathon, W.C., 1974. A comparative static analysis of urban spatial structure. Journal of Economic Theory 9, 223 – 237.
The periurban city: why to live between the suburbs and the countryside Jean Cavailhe`s a, Dominique Peeters b,*, Evangelos Se´keris c, Jacques-Francßois Thisse d,e a
b
UMR INRA-ENESAD CESAER, Dijon, France De´partement de Ge´ographie and CORE, Universite´ catholique de Louvain, Voie du Roman Pays 34, Louvain-la-Neuve B-1348, Belgium c IRES, Universite´ catholique de Louvain, Belgium d CORE, Universite´ catholique de Louvain, Belgium e CERAS, Ecole nationale des ponts et chausse´es, France Accepted 20 August 2003 Available online 1 July 2004
Abstract The last 30 years have witnessed the emergence of a new pattern of urban development in France, called the periurban belt. It is defined as a belt outside the city occupied both by households and farmers. We develop a residential model in which households commuting to an employment center may choose to live with farmers in this mixed belt because they value the rural amenities created by farming activities. Both types of agents compete on the land market and the equilibrium conditions allow us to obtain an analytical solution and to provide some insights about the robustness of the periurban form against decreases in commuting costs. Finally, the model is calibrated on French data. D 2004 Elsevier B.V. All rights reserved. JEL classification: R14; R21 Keywords: City; Farming; Land rent; Mixed space
1. Introduction The last 30 years have witnessed the emergence of a new pattern of urban development in France, called the periurban belt.1 It is defined as a belt outside the city occupied both * Corresponding author. Tel.: +32-10-47-43-43; fax: +32-10-47-43-01. E-mail address: [email protected] (D. Peeters). 1 This phenomenon is not specific to France. It has been observed in other European countries (Caruso, 2002) as well as in the US (Nelson and Sanchez, 1997). 0166-0462/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.regsciurbeco.2003.08.003
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
682
by farmers and commuting households (Le Jeannic, 1997; Cavailhe`s and Schmitt, 2002). Hence, the periurban area may be viewed either as a rural area in the sense that the vast majority of its land is used for farming, or as an urban area with most of its working population commuting to the city where jobs are concentrated.2 The periurban household has been described as ‘‘living in natural surroundings, far from the city’s turmoil in roomy houses with gardens while keeping a city job with the associated income’’ (Le Jeannic, 1997). This is reminiscent of urban economics models with amenities. However, such models typically assume a specialized residential pattern with contiguous housing. Clearly, this does not fit the periurban area. In addition, those amenities are often exogenous whereas amenities arising in periurban areas depend on the level of agricultural activities. Yet, with its clear separation between residential and working places, the periurban space forms a ring around a city that displays the monocentric pattern common to most residential location models. Therefore, it seems to us that we may appeal to urban economic theory to study periurban areas. In this paper, we borrow ideas from land use theory and urban economics to develop a residential location model in which households may choose to live close to farmers because they value rural amenities created by the farmers.3 Rural amenities produced by farmers contribute to the well-being of consumers working in the city center, whereas farmers have a Thu¨nian behavior in that they benefit from the city proximity through reduced transport costs for their crops. Households and farmers compete on the same land market. The equality between the bid land rents of these two types of agents gives rise to a periurban equilibrium. This is achieved through the supply of rural amenities by farmers, the level of which is determined by the interactions between farmers and households whose densities are endogenous. In standard urban economics, the trade-off between the lot size and commuting costs yields a land rent profile that is decreasing with distance from the CBD. However, several applied findings contradict this result and have led to the development of models exhibiting negative rent gradients. The existence of amenities in the periphery of cities is one of the tools used to model these inverted gradients (Richardson, 1975; Brueckner et al., 1999; Goffette-Nagot, 2000; Irwin, this issue). Our analysis runs along the same lines as these models but has a very different purpose. Specifically, we build a new setting in which market equilibrium conditions give rise to several equilibrium land use patterns. One of these patterns is of particular interest to us, that is, a mixed farming-residential space. Stated differently, for some parameter configurations our model yields a mixed space, which is rarely found in the existing literature although it is pretty common in the real world.4 2
More details are given in Section 2. In doing so, we do not ignore the fact that cities are the source of a large array of amenities and that farming generates nuisances. The former are introduced into the model in a cursory fashion, because they are not central to our analysis. We also assume a positive net balance of agricultural nuisances (pollution, bad smells, noise) and amenities, such as natural landscapes, open spaces, the maintenance of a peaceful and unpolluted environment. 4 Early exceptions include Kanemoto (1980, ch. 6) as well as Ogawa and Fujita (1980). By using discrete choice theory to describe consumers’ behavior, Miyao and Shapiro (1981) show that consumers of different types may be located at the same place, whereas Anas and Xu (1999) consider a broader approach in which mixing involves both firms and workers. Finally, Bockstael and Irwin (this issue) generate a periurban belt based on households’ dislike of proximate residential land use. 3
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
683
Fig. 1. Net migrations according to the spatial typology.
The remainder of the paper is organized as follows. In Section 2, we provide a short description of the evolution of periurban areas in France and of their main distinctive features. Section 3 presents the model, whereas Section 4 deals with the periurban land market equilibrium. Section 5 focuses on the effects of the periurban spread on the environment and other variables affecting the quality of life. We also address the following question: is the periurban belt a permanent pattern of urban growth or just a transitory stage of evolution? Section 6 presents an attempt at calibrating our model on medium-sized French urban areas with parameters obtained from surveys or advice of experts. Findings predicted by the calibration and observed from the real word are similar. Section 7 concludes.
2. Periurban areas in France: a brief description As shown in Fig. 1, since the 1970s, French cities and their suburbs have lost inhabitants, whereas periurban belts have gained many.5 Periurban areas have expanded according to two different schemes. In the first one, which can be found around Paris and a few other densely urbanized areas, the pattern is polycentric with cities connected to a metropolis and periurban zones in the interstices, which are made of small towns and villages scattered among fields and forests. In the second one, which corresponds to the majority of cases, the pattern is monocentric, with a city surrounded by a periurban belt, which is also a mix of small towns, villages, farms, and forests. In what follows, we focus on the simpler case of a monocentric pattern. However, it should be clear that the same principles can be applied to a polycentric space. 5 Fig. 1 is based on the following statistical taxonomy. An urban area is made up of an urban core and its periurban belt. The urban core is the central city together with its suburbs, defined by the continuity of the builtup area and offering at least 5000 jobs. The periurban belt surrounds the urban core and is defined by its number of commuters: the threshold is 40 of its active population commuting to the urban core. The French statistical definition of an urban area is similar to that of an MSA in the US.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
684
Table 1 Evolutions of population and spatial extension Urban cores
Population (thousands) Number of jurisdiction % French area
Periurban
Rural area
Total
1990
1999
1990
1999
1990
1999
1990
1999
34,372 2793 7.4
35,708 3100 8.1
8862 10,431 22.1
12,257 14,930 33.1
13,381 23,341 70.5
10,553 18,535 58.9
56,615 36,745 100
58,519 36,565 100
INSEE, 1990 and 1999 census.
The periurban belts are characterized by the following main features. 1. The importance of commuting flows: in 1999, 79% of the labor force living in the periurban areas are commuters. Average commuting distances vary from 9 to 14 km in small and medium-sized urban areas; they are equal to 26 km in large urban areas, except Paris where the average commuting distance is 46 km (Talbot, 2001). 2. A lack of jobs: employment concentration in urban cores has increased during the second half of the 20th century from 62% in 1962 to 71.5% in 1990. From 1962 to 1990, the population of periurban belts has grown by 75% but its number of jobs by 7% only.6 3. A rural settlement: the population density is approximately 70 inhabitants/km2. In 1990, the average population in periurban jurisdictions was 935 inhabitants. 4. A rural land use: farming and forestry occupied about 75% of the periurban land. Therefore, it is fair to say that periurban areas depend on cities for their jobs while having strong rural characteristics in terms of land use, landscapes and dwellings. The central assumption of this paper is that the rural features of periurban areas represent a living environment valued by the residing households.7 The need for rural amenities may explain the observed growth of periurban belts. In 1990, according to the spatial taxonomy used at that time (see Footnote 5), periurban areas accommodated 8.9 million of inhabitants and covered 22% of the French territory. In 1999, using the spatial limits valid for this year, the periurban population had grown to 12.3 million (21% of the French population) and occupied 33 of the territory (see Table 1).
3. The model 3.1. Assumptions and notation Space is represented by the real line X=(l,l) with a CBD lying at the origin. It is assumed that all non-agricultural employment is concentrated in the CBD. There are two 6
This is to be contrasted with what has been observed in the US. However, it is worth mentioning that the last 1990s have seen a reversal of the urban concentration of employment in France. 7 The same holds in suburban or exurban areas in the United States where tastes for rural amenities are prominently displayed.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
685
types of agents competing on the land market: (i) a continuum of identical households working at the CBD, with density nh(x)z0 at xaX and (ii) a continuum of identical farmers, with density na(x)z0 at xaX. The total amount of space occupied by households and farmers at x cannot exceed the available quantity of land (which is normalized to 1): nh ðxÞSh ðxÞ þ na ðxÞSa ðxÞ ¼ 1
ð1Þ
where Sh is the size of residential plot and Sa the size of the farm. There is no clear evidence about the place of origin of periurban residents and farmers. Thus, the economy is assumed to be open in that households and farmers are free to migrate in and out, according to households’ utility and farmers’ profits obtained in the rest of the world. We call city (C) a specialized residential area (nh(x)>0 and na(x)=0). A periurban area (P) is a mixed space accommodating both households and farmers (nh(x)>0 and na(x)>0). Farms are located either in the periurban area or in the rural (R) space, where only farmers live (nh(x)=0 and na(x)>0). It is worth noting that we make no assumptions regarding the existence and the relative positions of the areas C, P and R with respect to the CBD, which depend on the parameters of the model influencing the bid rent curves. There are three consumption goods: a composite good available everywhere at the same price, housing which takes the form of a residential plot whose size is variable, and amenities. Amenities are consumed at their place of residence and have the nature of a local public good. The city provides urban amenities Ac. Because our aim is to provide an analysis of periurban areas, we keep the analysis simple by assuming that the quantity of urban amenities is given and evenly distributed within the city. Rural amenities Ap are supplied, as a by-product of farming, in the periurban area exclusively (na(x)>0), which accommodates nonfarmer households (nh(x)>0). Hence, amenities may be considered as a spatial attribute of housing, which directly enter the household’s utility function but not explicitly its budget constraint.8 3.2. The farmer in a Thu¨nian space Agriculture involves production under constant returns to scale and the only input is land (or, equivalently, a fixed combination between labor and land). Without loss of generality, it is assumed that one unit of land yields one unit of output. Two cases may arise. Firstly, the agricultural land rent is flat and equal to a positive constant RA. Secondly, and more importantly, farmers face an agricultural land rent decreasing from the CDB. The positive effects of city proximity on the price of farmland are, indeed, well documented (Chicoine, 1981; Shi et al., 1997; Colwell and Dilmore, 1999). This may be explained by the following two reasons: (i) direct sales of farm products or recreational services, which may be more profitable than sales to the food processing industry, but entail transport costs depending on distance from the city; (ii) expected gains from the sale of land for 8 For simplicity, we assume throughout this paper a completely mixed periurban belt, despite the fact that real patterns involve small towns and villages. Accounting for such small settlements would require the introduction of local interactions across people.
686
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
residential uses that are also distance-sensitive. In what follows, ‘‘direct sales’’ are assumed to act as a reduced form for these two factors. This assumption is made to capture in a very simple way the effect of distance on farmers’ bid rents described above (and because a dynamic model with expectations or option values is much more complex). Each farmer maximizes her profits with respect to the farm size, given the land rent and the prices of the crops sold either to the food processing industry or directly to the urban consumers. In this case, the transport rate to the city is given by s>0. Because returns to scale are constant, the profit per unit of land is constant across locations, thus allowing one for a straightforward determination of the farmer bid rent function U. In the case of food industry sales, we have U(x)=RA; in the case of direct sales, we have U(x)=Csx, where C is a constant depending on the price of the goods sold to the urban consumers. Hence, the farmer bid rent function is such that: UðxÞ ¼ maxfC sx; RA g Ignoring for the moment the presence of households, we thus obtain a space a` la Thu¨nen formed by a circle, the radius of which is equal to xd uðC RA Þ=s
ð2Þ
where farmers sell their crops directly in the city and outside this circle by an area where farmers sell to the food processing industry. Finally, farmers located at x produce rural amenities for a total amount of Ap(x), which depends on the area used for farming: Ap ðxÞ ¼ dna ðxÞSa ðxÞ
ð3Þ
where d is a positive constant and Sa(x) the amount of land used by a farmer at location x.9 3.3. The household in an urban or periurban environment Households’ well-being is determined by the usual trade-off between accessibility to the CBD and land consumption, but also by the amount of (urban or rural) amenities. As said above, a household residing at xaX consumes three goods: (i) land Sh(x) for which it pays the rent R(x), (ii) a composite good Z available everywhere at a given price pz and (iii) urban amenities Ac or periurban amenities Ap(x). Finally, the utility function is of the same Cobb-Douglas type regardless of the household’s location. A household working in the CBD gets an (exogenously determined) wage w and commutes at a unit cost of t. The residential land rent depends on the distance to the CBD and the quantity of amenities: R(x)=R[x,Ac,Ap(x)]. Thus, the budget constraint is as follows: RðxÞSh ðxÞ þ pz ZðxÞ ¼ w tx: 9 Because of the assumption of constant returns, it is not possible to determine the size Sa(x) of the farm, but only the total amount of land na(x)Sa(x) devoted to farming at location x.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
687
Ignoring for the moment the presence of farmers, the utility of a household in a purely residential city (subscript c) is given by: Uc ¼
1 aa bb
ZðxÞa Sh ðxÞb Acc
ð4Þ
In equilibrium, the household’s utility does not depend on x and is equal to U , that is, the utility it may obtain in the rest of the world. Without loss of generality, to ease the burden of notation, we make the following normalizations: (i) the composite good is taken as the nume´raire, i.e. pz=1, (ii) we choose the amenity unit such that Ac=1, and finally (iii) we assume that a+b=1 and set U =1. Hence, the demand functions Z(x) and Sh(x) for the composite good and for housing are derived from the first order conditions: Z*ðxÞ ¼ aðw txÞ
Sh*ðxÞ ¼
bðw txÞ RðxÞ
ð5Þ
so that the indirect utility function of the household living in the city is given by Vc ðxÞ ¼ RðxÞb ðw txÞ The household’s bid rent is then obtained from the indirect utility function Vc(x) as follows: Wc ðxÞ ¼ ðw txÞ1=b
ð6Þ
implying that the city expands up to the point xv defined by xv u
w RbA : t
ð7Þ
In the periurban environment with farmers (subscript p), the utility is Up ¼
1 aa bb
ZðxÞa Sh ðxÞb Ap ðxÞc
ð8Þ
The demands functions are still given by Eq. (5) and the indirect utility becomes Vp ðxÞ ¼ RðxÞb ðw txÞ½Ap ðxÞ c Hence, in the periurban area, the household’s bid rent is as follows: Wp ðxÞ ¼ ðw txÞ1=b Ap ðxÞc=b :
ð9Þ
Clearly, for a periurban area to arise, it must be that Ap(x) exceeds Ac=1. Given Eqs. (1) and (3), this in turn requires d>1. In other words, farming must produce a sufficient amount of rural amenities for a periurban area to exist.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
688
4. The city – periurban – rural equilibrium As mentioned in the introduction, several configurations may be sustained as spatial equilibria. The one that interests us is as follows: the CBD is surrounded by a specialized residential area, which is itself followed by a periurban ring and, finally, by a rural area. It is denoted C – P – R. 4.1. Equilibrium conditions As land is rented to the highest bidder, the periurban household – farmer mix exists if and only if the households’ land bid and the farmers’ land bid are the same. Let be A*(x) the p amount of rural amenities for which these two bids are equal. Two cases may arise. In the first one, farmers’ bid rent is Csx and the equilibrium condition for a periurban belt is given by: ðw txÞ1=b Ap*ðxÞcb ¼ C sx
ð10Þ
In the second one, farmers’ bid rent is RA so that the above condition becomes: ðw txÞ1=b Ap*ðxÞcb ¼ RA In what follows, we consider only the first case, which both yields richer patterns and seems to be more realistic than the second one. It follows immediately from Eqs. (6) and (10) that, in equilibrium, for x to belong to a periurban area, the level of amenities available at x, Ap*(x) must be equal to the ratio of the household periurban bid rent (which is equal to the farmer bid rent) to the household city bid rent, to the power b/c. The lower the elasticity of utility with respect to amenities (c) or the higher the elasticity of utility with respect to housing (b), the more periurban rural amenities there will be compared with urban amenities. By rearranging the terms of Eq. (10), we obtain the equilibrium level of rural amenities as follows: " #1=c UðxÞ b=c ðC sxÞb Ap*ðxÞ ¼ ¼ : ð11Þ Wc ðxÞ w tx The corresponding bid rents and market land rent are depicted in Fig. 2, where xc is the boundary between the city and the periurban belt and xp the outer boundary of the periurban belt.10 For simplicity, the household bid rent beyond xp is not represented. In other words, xc is the solution (if any) to the equation UðxÞ ¼ Wc ðxÞ whereas xp is the solution (if any) to ¼d A*ðxÞ p which is obtained from Eq. (3) when all land is used for farming. 10
For simplicity, the household bid rent beyond xp is not represented.
ð12Þ
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
689
Fig. 2. Land bids and land rent in the C-P-R configuration.
Finally, since the landowner rents her land to the highest bidder, the land rent prevailing at xaX is given by: R*ðxÞ ¼ maxfUðxÞ; Wc ðxÞ; Wp ðxÞg: 4.2. Existence of a C – P – R equilibrium Each of the following conditions is necessary and together they are sufficient for a periurban belt to exist. First, the wage earned at the CBD must be large enough relative to the agricultural rent for the farmers to be pushed away from the center. Second, the two bid rent curves Wc(x) and U(x) intersect if and only if xv
t w RbA z C > RA s C RA
ð13Þ
690
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
Observe that the second condition means that the parameters of the economy are such that the curve U is above the curve Wc over a nonempty interval. It is worth noting that the periurban area is (locally) stable when Eq. (13) holds. Indeed, if there were too many (resp., not enough) farmers for the appropriate configuration of parameters, the amenity level would be higher (resp., lower) than the equilibrium value A*(x), thus attracting (resp., repelling) households. Consequently, npSp would rise (resp., p fall), whereas naSa would vary in the opposite direction, entailing a decrease (resp., increase) in the quantity of amenities. Hence, Ap(x) will move toward its equilibrium value A*(x). p 4.3. Properties of the C – P –R equilibrium From the demand function (5) and the bid rent functions (6) and (9), we can determine the urban and periurban lot sizes, denoted respectively Sc*(x) and Sp*(x): Sc*ðxÞ ¼
bðw txÞ ¼ ½bðw txÞ a=b if na ðxÞ ¼ 0 Wc ðxÞ
ð14Þ
Sp*ðxÞ ¼
bðw txÞ bðw txÞ bðw txÞ ¼ if na ðxÞ > 0: ¼ Wp ðxÞ UðxÞ C sx
ð15Þ
If x belongs to a periurban area, then Sp*(x) is smaller than Sc*(x) because Wc(x)
ð16Þ
As rural amenities have the nature of a local public good, their Lindhal-Samuelson price PA*(x) at x is defined by the marginal rate of substitution between amenities and the composite good Z, obtained from Eqs. (5) and (8), times the number of households residing in x: PA*ðxÞ ¼
BUp =BAp w tx c 1 1 np*ðxÞ ¼ c np*ðxÞ ¼ Wp ðxÞ Ap*ðxÞ b Ap*ðxÞ d BUp =BZ
ð17Þ
As expected, in the periurban belt, the equilibrium price of the rural amenities depends positively on the land rent in the periurban area—hence on the income—and negatively on the amount of amenities. Finally, because the bracketed term is positive in equilibrium, the lower c/b, the lower the amenity price. In particular, PA*(x)=0 when consumers do not value rural amenities (c=0). Note that, if the parameters of Eq. (17) can be estimated, PA*(x) may be used to evaluate the consumer willingness to pay, or the producer willingness to receive, for rural amenities. Interestingly, such an expression would allow us to compute the implicit price
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
691
of the amenity by means of a method that differs from the standard hedonic price or contingent valuation methods. 4.4. The urban economics city For the sake of comparison, we also consider the traditional monocentric city of urban economics. This configuration, denoted C – R, is an equilibrium if and only if the following four conditions are satisfied (see Appendix A(2)):
w > Cb
t w RbA < s C RA
C > RA
wz
s b=a t
t þ C s
The first and the third conditions are as in the foregoing case. The second one says that xv(=xc)>xd (see Fig. 3), whereas the fourth condition allows one to rule out the special and not very realistic case in which the curves U(x) and Wc(x) intersect twice. It is tempting to think of the periurban area as a semi-anarchical scattering of housing that destroys landscapes and wastes land, which would corresponds to an extreme form of urban sprawl. Urban sprawl has been criticized for environmental reasons both in Europe (Camagni et al., 2002) and in the United States (Brueckner, 2000). It consumes excessive amounts of energy (cars, individual houses), thereby contributing to the greenhouse effect. Furthermore, urban sprawl implies inefficient use of public goods and infrastructure as a consequence of low population densities (Brueckner, 2000). However, there are positive aspects to the periurban belt: it helps relieve congestion in the city centers and gives a new lease of life to areas abandoned by traditional agricultural activities. Beyond these arguments, the question arises as to whether to take account of households’ preference for low densities (Richardson, 1975; Gordon and Richardson, 1997). Our model sheds
Fig. 3. Land bids and land rent in the C-R configuration.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
692
light upon this debate from two different perspectives: (i) the existence of urban sprawl and the trade-off between land consumption and amenities, and (ii) the impact of commuting costs on residential choices. 4.5. The periurban belt, urban sprawl and land consumption Firstly, as shown in Appendix A(1), the outer boundary xp of an urban area endowed with a periurban belt is farther from the CBD than the limit xv of a traditional urban economics city. This result is not terribly surprising because the periurban belt contains both households and farmers: the periurban pattern extends the area occupied by households farther from the CBD than a specialized city would do. In this sense, the periurban city leads to a larger consumption of natural land. Secondly, what characterizes a periurban area is the substitution between housing and amenities. Indeed, from Eqs. (14) and (15), we obtain: UðxÞ S*ðxÞ c ¼ Wc ðxÞ S*ðxÞ p which, given Eq. (11), becomes:
S*ðxÞ c Sp*ðxÞ
b
c ¼ ½A*ðxÞ >1 p
At location x, the residential plot in the periurban area is smaller than what it would be, if x were to belong to a purely urban area. The rural amenities make up for the difference, the substitution rate between housing size and amenities being b/c. For larger values of c, which suggests a marked taste for rural amenities, we can even end up having plots that decrease in size as we move away from the city. The alternative to a mixed periurban belt is, therefore, a specialized urban space with larger lot sizes. In this sense, the periurban area may be viewed as being residential land-saving. Hence, we may conclude that periurban development saves land in the intensive margin by making lots smaller than they would be if the city were purely urban, but it pushes the extensive margin of residential development farther out causing more sprawl. 4.6. The impact of decreasing commuting costs In open city models, a decrease in commuting costs leads to an increase in the city size and in the bid rents, thus implying a reduction in the lot size and a corresponding increase in density (Weathon, 1974; Fujita, 1989). In the periurban area, these results are changed as follows. Other things being equal, the decrease in commuting costs implies a decrease in the quantity of rural amenities,11 which entails: (i) a decrease in the proportion of farming in
11
This is shown by differentiating Eq. (11).
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
693
the periurban area (see Eq. (3))—the more accessible the periurban belt, the less rural it becomes; (ii) an increase in the size of residential plots12; and (iii) an increase in population density.13 As expected, a decrease in commuting costs has a well-determined impact on the city that expands and becomes denser (see Appendix A(3)). As for the periurban area, however, the effects are not that clear-cut and different evolutions may arise for intermediate values of the commuting costs. However, when t falls below a certain threshold, the periurban belt disappears and a specialized urban area with larger residential plots emerges. Indeed, a decrease in t leads to an upward shift of the households’ bid rent curve Wc (which keeps the same intercept) while that of the farmers remains unchanged (see Appendix A(2) for a formal argument). As a consequence, when commuting costs decrease (or, equivalently, w increases), the sequence of spatial configurations would be as follows: 1. When commuting costs are high relative to wages, the periurban belt is very small. 2. Within the city, keeping the level of urban amenities constant, the decrease in commuting costs generates a decrease in lot size and an increase in land rent. In the periurban area, the decrease in t, which does not affect the farmer rent, leads to a decrease in the equilibrium supply of rural amenities as well as to an increase in the size of housing plots. 3. Finally, when commuting costs fall below a certain threshold, land is specialized.
5. The calibration of the periurban city 5.1. The procedure The equilibrium outcome described in the foregoing sections has been obtained at the cost of many simplifying assumptions. Hence, one may wonder about the meaning of the conclusions obtained, especially when considering them for possible policy recommendations. Therefore, to assess the relevance of the model, we calibrate it on real data. To the best of our knowledge, not that many attempts have been made to validate models of urban economics on real data (see Anas, 1987, for a survey). Since then, Anas and Kim (1992) compare observed population density gradients to predictions derived from a standard urban economics model. Anas (1995) performs a calibration for the New York metropolitan area, whereas Anas and Arnott (1993) do something similar for Chicago. Very much as in Anas and Kim (1992), we propose a calibration of our model based on the minimization of a relative error term E. This term is equal to the sum of the
12 13
This shown by differentiating Eq. (15). Eq. (16) shows that n*(x)S *(x) varies with t as does A*(x), but in the opposite direction. h h p
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
694
squared deviation between actual and predicted values, divided by the square of the actual value in order to get dimensionless numbers because we add areas, distances and individuals:
min E ¼
X i
hi
ðX¯ ip X¯ ia Þ2 ðX¯ ia Þ2
ð18Þ
*(x),x where Xi=(Sc*(x),Sp*(x),n*(x),n c p c,xp,n*S a *). a In Eq. (18), superscripts p and a refer respectively to the predicted and actual values, while X¯ is the average of each variable.14 The variables have been weighted by hi according to the reliability of the actual values,15 which are econometrically estimated (b,s,U(0),Wc(0)), observed (w), obtained from advice of experts (t,RA), or computed by screening (d,c) in order to minimize Eq. (18). As our objective focuses on the French periurban areas, only the C – P –R configuration will retain our attention. 5.2. The practical relevance of the model The main problem encountered in using our theoretical model for a calibration on real world data is land zoning, with some tracts given over to development and others reserved for agricultural uses. So, can we calibrate a model based on market-determined forces, as assumed in our model, when the real land use seems to be planner-determined? The answer depends on the existence and nature of zoning. In France, land conversion is regulated by two procedures. The first one occurs in 61% of the 1967 periurban jurisdictions of the medium-sized urban areas selected for the calibration. In these jurisdictions, no zoning exists and the decision to develop a tract is made by the mayor. The second procedure is based on a ‘‘Plan d’occupation des sols’’ (in short, POS), which determines the zones for future development as well as those reserved for farming purposes. Nevertheless, the POS is frequently revised and, thus, a non-developable plot may later be considered for development. Whatever the procedure, the land conversion policy is more flexible in small periurban jurisdictions (recall that the corresponding average population is 935) than in large cities where land use is more controlled. Therefore, we may conclude that most decisions regarding land use are market-determined in periurban jurisdictions of medium-sized cities, which we have selected for our calibration. Hence, it is reasonable to assume that both farmland and residential land markets are submitted to the same distance-related forces. Therefore, although the agricultural and residential rents are not equal at a given distance from the city, as assumed in our model where U(x)=Wp(x) at x belonging to the periurban belt, both rents are linked and moved
14
For the size of the residential parcels, we use the median value. We assume hi=1, except for (i) the share of agriculture whose actual value is roughly known (we set hi=0.5) and (ii) the limits of the city and of the periurban area whose statistical and administrative definitions are not those used in our model (we set hi=0.75). 15
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
695
together. For the calibration, we assume that a multiplicative factor allows us to go from one curve to the other (see Appendix B). Three minor modifications are also needed: (i) space is considered as a disk generated by 2p-rotating the straight half line around its origin; (ii) the periurban rent curve is described by a negative exponential function, instead of being linear, because this allows one for a better fit of the periurban gradient; and (iii) the CBD is considered as a disk. Still, our setting remains very stylized. First, it is made up of rings around an urban center where the movements are approximated by straight-line distances. Second, the periurban area is totally mixed with housing spread across the agricultural land, although it is mostly made up of rural villages surrounded by agricultural land. Third, we consider only detached houses. Last, it is fair to say that the calibration procedure is dependent on several ad hoc assumptions as well as on the values of the parameters that are presented below. 5.3. The parameters Most data come from the Housing Survey conducted in 1996 by the INSEE on a sample of 29,043 households (subsequently referred to as HS96). We have selected 4658 households belonging to some of the 28 urban areas whose core jurisdictions range from 100,000 to 200,000 inhabitants,16 which represent one-sixth of the French population. The following values of the parameters have been selected17:
the household income: w=32,000 euros/year (source: HS96), which is the gross income of households who have moved recently; the share of income spent on housing18: b=0.158 (recall that a+b=1); the rate of discount used to annualize the value of a house: r=0.0512; the urban land rent at the city center: W(0)=115,000 euros/ha/year12; the agricultural rent at the city center: U(0)=1200 euros/ha/year and the coefficient of the agricultural rent: s˜ =0.045 euros/km19; the generalized transportation rate: t=310 euros/km/year20; the agricultural rent RA is set to 150 euros/ha/year21; 16
A calibration on the entire survey was impossible because too many factors are to be controlled. The medium-sized city sample is convenient because most of these urban areas are roughly monocentric and zoning is not too constraining. 17 Details may be obtained from the authors upon request. 18 Value estimated by regression from the HS96 data (see Appendix B). 19 Values estimated from the farmland market in the Dijon area. 20 This rate is equal to the sum of the direct monetary costs, evaluated from the rate applied by the French Internal Revenue Service (0.30 euro/km) and the opportunity cost of time, evaluated by experts at 0.18 euro/min. By allowing for 1.5 workers per household, 230 journeys-to-work/year and an estimation of the journey velocity based on HS96, we get 310 euros/km/year. 21 Value obtained from the French Agricultural Department.
696
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
Table 2 Comparison of predicted and observed values
City population Periurban population City boundary (km) Periurban boundary (km) City residential plots (m2) Periurban residential plots (m2) % of agriculture in periurban
Calibrated model
Real world
Difference (%)
94,073 81,433 7.6 21.3 521 676 92%
100,000 78,000 9.0 21.1 430 850 70%
5.9 4.4 14.8 1.0 21.2 20.5 31.7
the radius of the CBD is 0.8 km accommodating a population of 150,000 inhabitants (HS96).
6. Results The simulations were performed as follows. We started from the foregoing initial values for the parameters w, b, W(0), U(0), s, t, RA, choosing c and d in order to get a plausible magnitude for the results. Next, we allowed each parameter to slightly vary in turn around its initial value. The values minimizing E were kept. Finally, we screened the values of d and c and selected d=1.1 and c=0.20. The results turn out to be sensitive to the values of the land market parameters, but robust with regard to variations around the initial values of the other parameters. The error E is reduced when g rises from 0.07 to 0.11 and flattens for pairs between (d=1.275, c=0.12) and (d=1.225, c=0.23). Given that the urban amenities have been normalized to unity, the level of rural amenities is thus slightly above the one of urban amenities for what look like reasonable values of c. Table 2 shows the values of Xi found when minimizing the error E. It seems reasonable to believe that households’ taste for rural amenities, which is expressed through the value of c in the utility function, is of the order of magnitude of the exponent b (which corresponds to the share of housing in households’ expenditures), and that the amount of rural amenities is between 20 and 25 larger than the amount of urban amenities available at the city outskirts. As shown in Table 2, the predicted results are not very different from the actual values.22 The biggest difference is observed for the part of farming in land use, which is a variable difficult to observe in the dataset. The residential plots are slightly too large in the city and too small in the periurban area, and so probably because the Cobb-Douglas utility assumes fixed shares. For the other variables, discrepancies are small. The actual gradients (which are regression curves obtained from HS96) and those predicted by calibration, both for the density of population defined as nh/(nhSh+naSa) (Fig. 4) and the size of residential plots (Fig. 5), are fairly similar, except that the actual city 22 Note also that the differences between our calibrated model and the real world can partially be explained by the fact that our model assumes identical households, whereas in fact they differ in terms of income.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
697
Fig. 4. Results of the calibration: Population density.
density is higher than the predicted value. This does not appear as a major drawback since we focus on the periurban belt. Two results are worth noting.
The parameter c, which stands for amenity taste in households’ utility, is significantly different from zero. This agrees with the basic assumption of our model: amenities generated within the periurban mixed space do affect households’ utility.
Fig. 5. Results of the calibration: Residential plot area.
698
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
The value of c (g0.20) is close to that of b (g0.16). From these values, the calculation of the implicit price of the rural amenities should be possible from Eq. (17) if the values of the urban and periurban rents were reliable. Unfortunately, the multiplicative factor introduced into the calibration is an ad hoc operator, which does not allow for such an evaluation. Both a more sophisticated model and a new calibration are necessary to estimate the amenity shadow price.
7. Conclusions We have proposed a new model of land use that seems well adapted to French metropolitan areas, which are a combination of cities, as usually defined in urban economics, and of a mixed area of housing and farming activities, called the periurban belt. This model is very simple. On the one hand, we have Thu¨nian farming activities that incur transport costs due to the direct sales of their crops. On the other hand, we have identical households with a Cobb-Douglas utility whose variables are housing, rural amenities and a composite good; households work in a pre-determined CBD. Finally, equilibrium is reached through a competitive land market. Each of these assumptions is the simplest one that can be made in an urban economics framework. However, taken together, they allow for the determination of an analytical solution. This solution makes it possible to distinguish between different urban patterns and to analyze the mechanisms that generate them. Furthermore, the periurban belt found between the two specialized areas (urban and rural) is spread out since both housing and farms are to be found in it. On the one hand, the boundary of a metropolitan area with a periurban belt is farther from the CBD than that of a specialized city. Hence, it is an expensive configuration in terms of transport costs. On the other hand, the substitution between amenities and lot size and the ensuing limited size of residential plots make the periurban configuration more efficient than the specialized city in residential land use. Thus, from an environmental perspective the impact of the periurban remains ambiguous. It is also worth noting that the results of our model suggest what could well be a historical description of the various spatial patterns observed as commuting costs fall relative to wages. 1. The traditional city, with high unit commuting costs relative to wages. Households spend a large share of their resources on commuting; so that the urban expansion is low and, consequently, the city is very dense (sparing use of space and of residential plots). In our model, a periurban belt of limited extent exists, but in practice it could easily disappear for reasons not taken into account by the model (e.g., risk of living in urban outskirts, dumping of urban waste in those areas, and the like). 2. The French city, which arises for intermediate values of the commuting cost/wage ratio, is constituted by an urban area surrounded by a periurban belt. The periurban area is considerably expanded (high consumption of space) and takes the form of a mixed space involving both households and farmers. The amenities produced by farmers limit
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
699
residential plot sizes because of the substitution effect between lot size and amenity level (sparing use of housing land). 3. The American city (e.g., Atlanta) is characterized by a sprawling specialized city with no periurban belt and large residential lots. This configuration corresponds to lower unit commuting costs (or, equivalently, higher wages) than the French periurban city. Needless to say, by using a setting like ours we cannot expect to reproduce all the stylized facts of urban history. Even though the calibration of the model conducted on French data yields reasonably good results, much work remains to be done. It is our contention, however, that the approach taken here will be useful for future research. In particular, the relationship between the urban land rent and the shadow value of rural amenities should be given more attention because it might provide us with a new way to evaluate the social value of such amenities.
Acknowledgements We are grateful to R. Arnott, three referees as well as M. Blanc, S. Charlot, F. GoffetteNagot and B. Schmitt for helpful comments and discussions. This research was supported by the Ministe`re de l’Education, de la Recherche et de la Formation (Communaute´ fran ßcaise de Belgique), Convention 00/05-262 and by the Ministe`re de l’Agriculture et de la Peˆche (France), Convention 01.G5.02.03.A. We are also grateful to the Institut National de la Statistique et des Etudes Economiques (INSEE) for providing the HS96 survey to INRA.
Appendix A 1. Given Eqs. (11)– (13), we get: h ib=c s b=c Ap*ðxv Þ ¼ C ðw RbA Þ RA < d ¼ Ap*ðxp Þ t which implies xv
s 1=a t
s C þ w: t
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
700
Hence, the two curves do not intersect if and only if: wz
s ð1aÞ=a t
t þ C: s
Furthermore, it is readily verified that /(x) increases when t decreases because the derivative of Wc(x) with respect to t is negative. 3. We show that the radius xc of the urban area rises when commuting costs t fall. Totally differentiating the expression w txc ¼ ðC sxc Þb yields dxc xc ðC sxc Þ ¼ bsðw txc Þ tðC sxc Þ dt By definition of xc, we have
dWc ðxÞ
> dUðxÞ
dx
dx
x¼xc x¼xc When xp
.
dxc <0 dt
Appendix B B.1 . Share of residential consumption in households’ budget and discount rate We start from a reduced form expressing the housing cost of a household (either an owner or a tenant): PþR¼
b0 þ b1 S þ Abi Ki ðw txÞ *I p þ ½ðb0 þ b1 S þ Abi ki Þðw txÞ *I l r
where P is the sale price of a detached house, R is the annual rent of a detached house (R=0 if P>0 and conversely), S is the lot size, w is the annual revenue of the household, t is the annual unit commuting cost, r is the discount rate, Ki are attributes of the dwelling, I is a dummy variable such that Ip=1 for owners and Ip=0 for tenants, and Il=1 for tenants and Il=0 for owners.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
701
We estimate the parameters by a non-linear regression from HS96 P (N=646 households in detached houses) and compute both r and b ¼ b0 þ b1 S¯ j þ i>1 bi K¯ ij (where the upper-bar describes the mean value of the variables). We get b=0.158 and r=0.0513 (R2=0.74). By comparison, the share of housing in households’ budget as estimated by the INSEE is 16% and the real rate of interest at 10 years according to Eurostat is 5% in 1996. B.2 . Land rents First, a regression based on HS96 gives an estimation of the land rent for the households who have recently purchased a detached house in 1996 in mediumsized cities. This leads to the following residential land rent function R1(x)= 125,000exp(0.063x). We have selected the following values for the calibration: Wc(0.8)=115,000 euros/year/ha. Second, an estimation of the agricultural land rent was obtained from an econometric estimation for the periurban belt of Dijon, which is a typical medium-sized French city (Cavailhe`s and Wavresky, 2003). We obtain R2(x)=1.95exp(0.042x)exp(1.078p), where p is a dummy that equals 1 in the periurban belt and 0 in the city. This function differs from U(x), the agricultural rent when the farmer directly sales her crops to the city because of land zoning (see Section 5.2). For the area of Dijon, an auxiliary land rent estimation was performed for unserviced land (i.e., without water, gas and electricity), which was bought for housing by households from developers. This estimation uses data collected by the Department of Equipment from 110 housing development projects. We obtain R3(x)=107.4exp(0.071x)exp(1,56p). This equation could have been used as a direct estimation for Wp(x)=U(x). Unfortunately, the dataset used in this regression is small (N=110 observations) and land prices are obtained directly from developers. Instead, the dataset we have used for estimating the agricultural rent includes a much larger number of observations (N=2023) and prices are true market prices. Therefore, we have retained the auxiliary regression to compute the multiplicative operator. Comparing R2 and R3, the mean value of the multiplicative operator is 85.23 This value times the estimated agricultural rent R2 is then used to compute the direct sale ˜ agricultural rent at the CBD: U(0.8)=1200 euros/year/ha and the gradient s=0.045/ 24 km. The estimation of the residential rent at the CBD may be considered as robust, the selected value being close to the observed value in the center of the medium-sized cities. By contrast, the value of the agricultural rent is more ‘‘speculative’’ due to both the need of a multiplicative operator and the absence of agricultural land in the CBD. 23
This value is not unrealistic. For example, the multiplier between land values for agricultural and urban uses found by Mori (1998) varies between 50 and 200 times in the areas surrounding expanding cities in Japan and Britain. Likewise, according to Evans (1991), the agricultural price around Reading is about 2000 and, with a building permit, it goes up to £500,000 or £1,000,000 (250 – 500 times more). 24 Some minor changes in the value of the parameters are made to improve the calibration, as explained in Section 4.4.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
702
B.3 . The size of the residential lots We observe the following values (HS96): Size of residential lots
Average area Median area Selected values
Urban areas (m2)
Periurban areas (m2)
632 400 430
1307 744 850
We have estimated an equation giving the size of the lots as a function of the distance from the center, which allows for a graphical comparison of these results with those obtained from the calibration (N=2510, R2=0.11): logS h ðxÞ ¼ 6:0 þ 0:07x 0:015x2 0:051city*x ð1:31Þ
ð8:6Þ
ð10:1Þ
where city*x is an interaction variable between the distance x and a dummy variable expressing that the site does or does not belong to the city (in brackets: Student’s t). B.4 . Population in the city and in the periurban area The city population and the periurban population are obtained from (i) the predicted size of the residential lots, (ii) the predicted share of the area occupied by agriculture in the periurban belt, and (iii) the observed share of the urban area not allocated to housing (streets, parks, non residential buildings and the like), which amounts to 57% of French urban cities.
References Anas, A., 1987. Modeling in Urban and Regional Economics Harwood Academic, Chur. Anas, A., 1995. Capitalization of urban travel improvements into residential and commercial real estate: simulations with a unified model of housing, travel mode and shopping choices. Journal of Regional Science 35, 351 – 375. Anas, A., Arnott, R., 1993. Development and testing of the Chicago prototype housing market model. Journal of Housing Research 3, 73 – 130. Anas, A., Kim, I., 1992. Income distribution and the residential density gradient. Journal of Urban Economics 31, 164 – 180. Anas, A., Xu, R., 1999. Congestion, land use, and job dispersion: a general equilibrium model. Journal of Urban Economics 45, 451 – 473. Brueckner, J.K., 2000. Urban sprawl: diagnosis and remedies. International Regional Science Review 23, 160 – 171. Brueckner, J.K., Thisse, J.F., Zenou, Y., 1999. Why is Central Paris rich and Downtown Detroit poor? An amenity-based theory. European Economic Review 43, 91 – 107. Camagni, R., Gibelli, M.C., Rigamonti, P., 2002. Forme urbaine et mobilite´: les couˆts collectifs des diffe´rents types d’extension urbaine dans l’agglome´ration milanaise. Revue d’Economie Re´gionale et Urbaine, 105 – 139.
J. Cavailhe`s et al. / Regional Science and Urban Economics 34 (2004) 681–703
703
Caruso, G., 2002. La diversite´ des formes de la pe´riurbanisation en Europe. In: Perrier-Cornet, P.H. (Ed.), Repenser les Campagnes, pp. 67 – 99 L’Aube-Datar, Paris. Cavailhe`s, J., Schmitt, B., 2002. Les mobilite´s re´sidentielles entre villes et campagnes. In: Perrier-Cornet, P.h. (Ed.), Repenser les Campagnes, pp. 35 – 65 L’Aube-Datar, Paris. Cavailhe`s, J., and Wavresky, P. 2003. Urban influences on farmland periurban prices, INRA-CESAER, mimeo. Chicoine, D.L., 1981. Farmland values at the urban fringe: an analysis of sale prices. Land Economics 57, 353 – 362. Colwell, P.F., Dilmore, G.G., 1999. Who was first? An examination of the early hedonic study. Land Economics 75, 620 – 626. Evans, E., 1991. Rabbit hutches on postage stamps: planning development and political economy. Urban Studies 28, 853 – 870. Fujita, M., 1989. Urban economic theoryLand Use and City Size Cambridge Univ. Press, New York. Goffette-Nagot, F., 2000. Urban spread beyond the city edge. In: Huriot, J.-M., Thisse, J.-F. (Eds.), Economics of Cities, pp. 318 – 340 Cambridge Univ. Press, New York. Gordon, P., Richardson, H.V., 1997. Are compact cities a desirable planning goal? Journal of the American Planning Association 63, 95 – 106. Kanemoto, Y., 1980. Theory of Urban Externalities North-Holland, Amsterdam. Le Jeannic, T., 1997. Trente ans de pe´riurbanisation: extension et dilution des villes. Economie et Statistique 307, 21 – 41. Miyao, T., Shapiro, P., 1981. Discrete choice and variable returns to scale. International Economic Review 22, 257 – 273. Mori, H., 1998. Land conversion at the urban fringe: a comparative study of Japan, Britain and the Netherlands. Urban Studies 35, 1541 – 1558. Nelson, A.C., Sanchez, T.W., 1997. Exurban and suburban households: a departure from traditional location theory. Journal of Housing Research 8, 249 – 276. Ogawa, H., Fujita, M., 1980. Equilibrium land use patterns in a non-monocentric city. Journal of Regional Science 20, 455 – 475. Richardson, H.W., 1975. On the possibility of positive rent gradients. Journal of Urban Economics 4, 60 – 68. Shi, Y.J., Phipps, T.T., Colyer, D., 1997. Agricultural land values under urbanizing influences. Land Economics 73, 90 – 100. Talbot, J. 2001. Les de´placements domicile-travail. INSEE Premie`re Nj767 Weathon, W.C., 1974. A comparative static analysis of urban spatial structure. Journal of Economic Theory 9, 223 – 237.