New Economic Geography Explanations of Urban and Regional Agglomeration

Urban Dynamics and Growth, CEA, vol. 266 Roberta Capello and Peter Nijkamp (editors) q 2004 Published by Elsevier B.V.

CHAPTER 18

New Economic Geography Explanations of Urban and Regional Agglomeration Kieran P. Donaghy Department of Urban and Regional Planning, University of Illinois at Urbana-Champaign, 111 Temple Hoyne Buell Hall, 611 East Lorado Taft Drive, Champaign, IL 61820, USA

Abstract The purpose of this chapter is to examine the ‘new economic geography’ (NEG) in terms of how well it explains urban and regional agglomeration. The chapter reviews Krugman’s core – periphery model of regional agglomeration with an eye toward what motivates the analysis and how the model accomplishes its ends. It then proceeds to an examination of how several other types of agglomeration, both urban and regional, can be modeled by modifying key assumptions. The chapter concludes with an assessment of what the NEG has accomplished and where its challenges lie, particularly in regard to empirical application. Keyword: agglomeration economies JEL classifications: R11, R12, R30 18.1. Introduction

Patterns of urban and regional agglomeration have received much attention in urban economics over the last several decades. Casual Research assistance by Nazmiye Balta and suggestions and constructive criticisms by Lewis Hopkins, the editors, and two referees are gratefully acknowledged.

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observation would suggest that this is attributable in no small way to a number of dramatic contemporaneous developments that have called for study and explanation. These include (1) the emergence of new urban forms, such as edge cities; (2) the increasing spread of the urban footprint through suburbanization, sprawl, and leapfrogging development; (3) the formation and reinforcement of industrial belts and megalopolises; and (4) the change in economic relationships between cities that have come about through globalization and the attendant fragmentation of production systems. In view of the number of factors involved, explaining patterns of agglomeration convincingly is not easy; giving formal expression to intuitions of what is involved is less so; and determining which of possibly many factors identified by theorists have been causally effective in the cases of particular cities and regions is perhaps most difficult. The ‘new urban economics’, which Button (2000) identifies with contributions by Beckmann, Mills, and Muth in the 1960s and 1970s, and subsequent work, was intended to explain the emergence of simple urban forms: monocentric cities formed around central business districts, surrounded by residential suburbs. Important as these contributions were in getting analytical urban economics untracked, the evolution of simple urban forms into the complex conurbations noted above has limited the relevance of these contributions and placed greater explanatory demands upon urban economists. Considerable progress has been made in both formal modeling and empirical analysis. Anas et al. (1998) provide a comprehensive survey of many of the developments in the analysis of urban form, whereas Fujita (1996) and Berliant and Wang (2004) have reviewed contributions to formal modeling of the growth of urban economies as it relates to agglomeration. More recently Black and Henderson (1999) have contributed a general model of endogenous urban growth in a city system in which they explore not only how urbanization affects the efficiency of the growth process but also how growth affects patterns of urbanization. Turning to specific agglomeration phenomena, we note that extensions of the ‘new urban economics’ have produced formal models that explain how polycentric cities can emerge from

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monocentric ones (Fujita and Ogawa, 1982), why leapfrogging or discontinuous development might occur (Ohls and Pines, 1975; Fujita, 1982; Wheaton, 1982), and why in view of current transport pricing and governmental subsidies urban (suburban and ex-urban) sprawl is a reasonable outcome (Brueckner, 2000, 2001, 2003; Brueckner and Kim, 2003). Henderson and Mitra (1996) have modeled how edge cities form through the intermediation of developers and government policies. Stylized explanations of the formation of industrial belts and megalopolises, the entrenchment of primary cities, the formation of suburban concentrations of industry, and the formation of new cities in central place systems have also been advanced along other lines of inquiry by the so-called ‘new economic geographers’, whose work is informed largely by international trade theory. The new economic geography (NEG) is perhaps best described as an approach to modeling the spatial distribution of agglomerations of economic activities. This approach explicitly incorporates increasing-returnsto-scale production technologies, consumer preferences for greater variety of goods, monopolistic competition between firms, costly trading of goods between locations (hence a role for geography or distance), and processes of cumulative causation, which give rise to pecuniary externalities and the self-organizing formation of various patterns of agglomeration.1 Intuitive accounts of the roles played by the above-mentioned factors were expounded by Marshall (1936) and Isard (1956) and more recently by Jacobs (1969, 1984), but formal incorporation of these factors into models of agglomeration has been a relatively recent accomplishment (Abdel-Rahman and Fujita, 1990). The principal aim of the NEG thus far seems to be the development of ‘clarifying examples’ of agglomeration (Krugman, 1995; Ottaviano and Thisse, 2001), which calls for (if not entails) simplification wherever possible to increase the transparency of the work done by each assumption in a model. In fact, one 1

In their review of the NEG, Papageorgiou and Pines (1999) identify another basic assumption, or an implication of the previously mentioned assumptions, on which models in this tradition are based, even if not explicitly acknowledged in the literature: “each individual interacts not only with one firm as an employee or, perhaps, with several firms as a consumer, but with every manufacturing firm in the economy wherever it is located.” Fujita and Thisse (2002) identify the intellectual lineage of all assumptions at work in NEG models.

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of the principal exponents, Paul Krugman, openly acknowledges the highly unrealistic nature of the assumptions employed and the heavy reliance upon ‘modeling tricks’, an issue we will return to below.2 The purpose of this chapter is to examine a part of this growing body of literature in terms of how well it helps us to make sense of some agglomeration phenomena which other approaches have been less successful in explaining. The plan of the chapter is as follows. In Section 18.2 we will review the most basic of the NEG models, Krugman’s (1991a) core – periphery model, and its assumptions and implications, with an eye toward what motivates the analysis and how the model accomplishes its ends. While this model was intended to account for regional agglomeration, variations of it have been used to explain different types of urban agglomeration as well. So we proceed in Section 18.3 to examine how several different agglomeration phenomena can be modeled by modifying key assumptions. In Section 18.4 we take stock of what the NEG has accomplished and where its challenges lie. In particular, we consider issues of empirical application, other research programs with which it has affinities, and promising directions it might take. 18.2. Krugman’s core– periphery model

What is perhaps the most well-known model of the NEG is that of Krugman (1991a).3 The question motivating its development is “Why and when does manufacturing become concentrated in a few regions, leaving others relatively undeveloped” (Krugman, 1991a, p. 484)? To answer this question Krugman strips the problem down to its ultimate simples. In the economy modeled there are two 2

Krugman characterizes his modeling approach as a combination of: “Dixit-Stiglitz (consumer preferences), iceberg (transportation technologies), the computer and evolution (Krugman, 1998)”. 3 The model is recapitulated in appendices of Krugman (1991b, 1995) and in Chapters 4 and 5 of Fujita et al. (1999b), with varying notation. It is also discussed in Chapter 9 of Fujita and Thisse (2002). Many of the ideas exposited in Krugman (1991a) were previously introduced in Abdel-Rahman and Fujita (1990). In reviewing the model, I present a logically consistent hybrid of its various published forms and supply intermediate steps in its derivation for readers not already familiar with the moves of the monopolistic competition/IRS dance. See Gandolfo (1998) for a helpful discussion of the literature on monopolistic competition in international trade.

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industries, agriculture and manufacturing, and R regions. The agricultural good is produced with a constant-returns-to-scale (CRS) technology, whereas production in manufacturing enjoys increasingreturns-to scale (IRS). The agricultural good can be shipped costlessly, whereas manufactured goods cannot. 18.2.1. Consumer behavior

All individuals in this economy are assumed to have the same utility function m 12m CA U ¼ CM

where 1 $ m $ 0;

ð18:1Þ

in which CA denotes the consumption level of the agricultural good and CM the consumption level of an aggregate (or composite) of manufactured goods. From Equation (18.1) one may infer that manufacturers’ share of expenditures will always be m and farmers’ share will be 1 2 m: CM is a constant-elasticity-of-substitution (CES) aggregate of the consumption levels of N differentiated varieties or ‘brands’ of manufactured goods, ci ; i ¼ 1; …; N; " CM ¼

N X

ðs21Þ=s ci

#s=ðs21Þ ;

ð18:2Þ

i¼1

where s ¼ 1=ð1 2 rÞ . 1 is the elasticity of substitution between the varieties, and r; 1 $ r $ 0; is the substitution or preference intensity parameter.5 Given income, Y, the price of the agricultural good, PA ; and the price for each manufactured good, pi ; the consumer’s problem is to maximize utility subject to the budget 4

Fujita et al. (1999) remark that ‘agriculture’ may be viewed as the residual sector encompassing industries other than agriculture that are location bound. In Krugman (1991a) the number of regions considered is two. The following gloss of the model follows the more general multi-regional presentation of Krugman (1995) and Fujita et al. (1999b). 5 The closer is r to 0, the more are manufactured goods perfect substitutes for each other; the closer is r to 1 the greater is the consumer’s demand for variety. This characterization of consumer preferences was introduced by Spence (1976) and Dixit and Stiglitz (1977).

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constraint PA CA þ

N X

pi ci ¼ Y:

ð18:3Þ

i¼1

Because the homogeneous solved in two manufactures, ci ¼

functional forms of Equations (1) and (2) are of degree one, this optimization problem can be parts. For a chosen consumption level of aggregate CM , the compensated demand for the ith variety is

s p2 i CM ; N X 12s pi

ð18:4Þ

i¼1

and the minimum cost of purchasing a unit of the composite good, PM ; is " #ðr21Þ=r N X r=ðr21Þ pi : ð18:5Þ PM ¼ i¼1

The compensated demand for the ith variety can be written in terms of PM as   p i 2s ci ¼ CM : ð18:6Þ PM Rewriting the budget constraint as PA CA þ PM CM ¼ Y;

ð18:7Þ

and solving for the utility maximizing levels of CA and CM one obtains the uncompensated consumer demand functions CA ¼ ð1 2 mÞY=PA ;

CM ¼ mY=PM :

ð18:8Þ

From Equations (18.6) and (18.8) the amounts demanded of the manufactured good varieties are given by ci ¼ mY

s p2 i s21 : P2 M

ð18:9Þ

Substitution from Equation (18.8) into Equation (18.1) yields

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the indirect utility function m 2ð12mÞ ; U ¼ mm ð1 2 mÞm YP2 M PA

ð18:10Þ

which is useful for demonstrating consumer preference for variety. Assuming that the price of each variety of manufactured good is the same, p ; then from Equation (18.5), the price index of the aggregate of manufactured goods can be written as PM ¼ N ðr21Þ=r p :

ð18:11Þ

From Equation (18.11) it is clear that this price index is decreasing in the number of manufactured good varieties. Moreover, the substitution of Equation (18.11) into Equation (18.10) yields a restatement of the indirect utility function that, in view of the conditions placed upon m and r; is clearly increasing in the number of manufactured good varieties, N; mÞ : U ¼ mm ð1 2 mÞm YN mð12rÞ=r p 2m P2ð12 A

ð18:12Þ

18.2.2. Producer behavior

In this economy there are two factors of production: agricultural and manufacturing labor. Since agriculture is a CRS activity, agricultural labor used in producing any quantity of QAj ; the agricultural good in region j; LAj ; can be set equal to the production level by suitable choice of units, i.e. Laj ¼ QAj :

ð18:13Þ

Because of IRS in manufacturing, the amount of labor required to produce the ith manufactured good in region j, LMij ; includes a ‘fixed-cost’ amount, a and an amount that varies with the production level of the good, QMij ; LMij ¼ a þ bQMij :

ð18:14Þ

Assuming that the prevailing wage rate paid to workers in region j is wj ; the cost of producing a unit of manufactured good i is wj LMij ¼ wj ða þ bQMij Þ:

ð18:15Þ

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K.P. Donaghy

Hence, the marginal cost is wj b and the average cost is wj ða=QMij þ bÞ: The total amount of manufacturing labor available in region j at any given time, LMj ; is then N X LMj ¼ LMij ; j ¼ 1; 2: ð18:16Þ i¼1

Most generally, let LA and LM denote the economy-wide supplies of the two types of labor, which are allocated in fixed amounts across the regions. Regional shares of agricultural labor, fj ; are exogenously given (and in Krugman (1991a) are equal). Regional shares of manufacturing labor, lj ; evolve over time. At any given point of time, the regional full-employment conditions will be LAj ¼ fj LA ; N X

LMij ¼ lj LM :

ð18:17Þ

i¼1

Agricultural workers are assumed to be immobile, but manufacturing workers are assumed to migrate to locations where higher real wages are paid. Defining the average real wage, v ; to be

v ¼

R X

lj vj ;

j¼1

where vj denotes the wage paid to manufacturing workers in region j; Krugman (1995) assumes that migration occurs according to the following law of motion, dlj ¼ glj ðvj 2 v Þ; dt

ð18:18Þ

where g is the disequilibrium adjustment parameter. The interpretation of Equation (18.18) is that “workers move away from locations with below average real wages and toward sites with above average real wages (Krugman, 1995, p. 96).”6 6

While this disequilibrium – adjustment or error – correction formulation of dynamics is admitted to be ad hoc, even if commonly used in evolutionary game theory (Fujita et al., 1999, p. 77), it can be motivated as the solution to a multilevel optimization problem. (See, e.g., Salmon, 1982.)

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The firms in Krugman’s model are assumed to be non-strategic monopolistic competitors of the Chamberlinian type.7 Each produces a single good and considers itself unable to influence either the aggregate demand for manufactures, CM , or the price index, PM . Hence, in view of the compensated demand functions (18.6), the firm will perceive itself to be facing a downward sloping demand curve. This will be the case in a monopolistically competitive market in which economies of scale lead each firm to produce a differentiated good for which it has no competitors and the number of firms will be identical to the number of products, N. From Equation (18.6), the inverse demand function for manufactured good i can be written as 1=s

21=s

pi ¼ ðPM CM Þci

;

ð18:19Þ

and the marginal revenue as 1=s

ðs21Þ=s

d½ðPM CM Þci

=dci ¼ ½ðs 2 1Þ=spi :

ð18:20Þ

If the firm follows the policy of equating marginal costs with marginal revenues, i.e.

bwj ¼ ½ðs 2 1Þ=spi ;

ð18:21Þ

and wj is the wage rate of workers in region j; its profit-maximizing strategy will be to set its price as a fixed mark-up over marginal costs, i.e. pi ¼ ½s=ðs 2 1Þbwj :

ð18:22Þ

Noting that Equation (18.22) implies that all manufactured goods i produced in region j will be priced equivalently, we can write pi ¼ pj : If firms are free to enter or exit the market until profits are zero, the output of any manufactured variety i will be a QMi ¼ ðs 2 1Þ: ð18:23Þ b This remarkable condition implies that all manufactured goods will be produced at the same level and scale, and this output level, 7

See Anas and Li (2001) for a reworking of the model with strategic competition among firms.

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K.P. Donaghy p

QMi ¼ Q ; depends only on the parameters characterizing the production technology and the consumers’ sub-utility function. Moreover, the proportion of total manufactured goods (or varieties) produced in any region j; Nj =N; will be equivalent to that region’s share of the manufacturing labor force, lj ; or Nj =N ¼ lj :

ð18:24Þ

18.2.3. Transportation costs

While, by assumption, it is costless to transport agricultural goods between regions, a fixed proportion of a unit of a manufactured good, t, is used up per unit of distance the good is shipped.8 If the amount of good i; xijk ; is shipped over a distance of Djk ; from region j to region k; the amount that arrives, zijk ; is given by zijk ¼ e2tDjk xijk :

ð18:25Þ

This transport technology implies that if a manufactured good produced at location j is sold at the producer’s, mill, or f.o.b. (free on board) price, pj ; then the user’s, delivered, or c.i.f. (carriage, insurance, and freight) price at any location k; Pjk ; is Pjk ¼ pj etDjk :

ð18:26Þ

In view of Equation (18.26), the price index of the aggregate of manufactured goods (Equation (18.5)) may take on a different value in each region. Taking into account iceberg transport costs of goods shipments received from regions j ¼ 1; …; R; and the implication of Equation (18.22) that all varieties produced at any location j have the same price, the true price index of the manufactured goods aggregate faced by consumers at location k; Tk ; is given by 2 31=ð12sÞ R X j ¼ 1; …; R: ð18:27Þ Tk ¼ 4 Nj ðpj etDjk Þ12s 5 j¼1

From Equation (18.9), the amount of a manufactured good i 8

This is Samuelson’s (1952) ‘iceberg’ transport technology.

New Economic Geography Explanations

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produced in j demanded in k will be

mYk ðpj etDjk Þ2s Tkðs21Þ ;

ð18:28Þ

where Yk is aggregate income at location k: For this amount to arrive at k; etDjk times this amount must be shipped. The total sales of a variety of manufactured good produced at j to all locations, k ¼ 1; …; R; will then be9 QMj ¼ m

R X

Yk ðpj etDjk Þ2s T s21 etDjk :

ð18:29Þ

k¼1

And from Equation (18.23), we know QMj ¼ Qp : From the pricing rule (18.22) the nominal wage paid at j can also be expressed as wj ¼



s21 s

"

R m X Yk ðetDjk Þ12s T s21 p Q k¼1

#1=s :

ð18:30Þ

m Since the cost of living index in each region j will be Tjm P12 Aj ; the real wage of manufacturing workers in j; vj ; will be m vj ¼ wj Tjm P12 Aj :

ð18:31Þ

18.2.4. Normalizations and short-run equilibrium

To simplify notation and the analysis, Krugman normalizes several quantities. Since, by assumption, it is costless to transport agricultural goods, the wage rate of farmers will be the same in all regions. The size of the labor force – farmers and workers – in the economy can be normalized to 1. Then, letting manufactured goods’ expenditure share m also denote the number of workers, the number of farmers is 1 2 m. This normalization has the added effect of setting economy-wide income to 1. If all prices and wages are expressed in terms of the agricultural good, nominal income in 9

From Equation (18.29) we may infer that, no matter how far a good manufactured in region j is shipped, nor how proportional the resulting increase in its delivered price, the mill price elasticity of aggregate demand for the good will be each consumer’s constant price elasticity of demand, s:

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K.P. Donaghy

region j is given by Yj ¼ ð1 2 mÞfj þ mlj wj :

ð18:32Þ

Setting b ¼ ðs 2 1Þ=s; the f.o.b. price of manufactured goods in j will equal the wage rate ð18:33Þ pj ¼ wj : and the equilibrium output level, Qp ; will equal the size of the workforce, Lp ; of any manufacturing firm in the economy Qp ¼ Lp ¼ Lj :

ð18:34Þ

Setting a ¼ m=s; the number of firms related to the size of the manufacturing labor force becomes Nj ¼ LMj =m and the zero-profit output level Qp ¼ Lp ¼ m: These normalizations permit the true-price index and wage Equations (18.27) and (18.30) to be rewritten as " #1=ð12sÞ R 1 X L ðw etDjk Þ12s Tj ¼ m k¼1 j k " ¼

R X

#1=ð12sÞ

lk ðwk etDjk Þ12s

;

ð18:35Þ

k¼1

and wj ¼

"

R X

#1=s Yk ðetDjk Þ12s T s21

:

ð18:36Þ

k¼1

Finally, with the agricultural good as numeraire, and PA ¼ 1; the real wage equation reduces to

vj ¼ wj Tj2m :

ð18:37Þ

The nominal-income, true-price-index, nominal-wage, and realwage Equations (18.32) and (18.35) –(18.37) together, when solved for all R regions, characterize a short-run equilibrium in this economy. In a stable equilibrium the real wage paid in each region will be the same, hence there will be no incentive for workers to move. Except in special cases, these 4 R non-linear equations do not admit of an analytical solution. They are solved numerically

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in conducting simulations. Krugman (1995) and Fujita et al. (1999b) conduct comparative-static exercises with a two-region version of the model for which the true-price and wage equations have been linearized around a symmetric equilibrium – i.e. where L1 ¼ L2 ; T1 ¼ T2 ; and w1 ¼ w2 — and demonstrate several important properties of the short-run solution. Other things being equal, if a region has a larger share of manufacturing firms, it will have a lower true-price index because a smaller share of its region’s consumption of manufactured goods will bear transport costs (the price-index effect). A region with the larger home market will have a disproportionately larger manufacturing sector, hence will also export manufactured goods (the home-market effect). A region with a higher demand for manufactured goods (and more varieties of goods) will offer a higher real wage to manufacturing workers (because the price index is decreasing in the number of varieties). And a region with large concentrations of manufacturing will tend to have a large demand for manufactured goods, reflecting the demand for goods by its workers. All of these short-run effects reinforce any initial advantage a region might enjoy through a long-run process of cumulative causation. An important feature of the model is the presence of both centrifugal (or dispersive) and centripetal (or aggregative) forces. The former appear in the form of immobile farmers demanding manufactured goods, while the latter are manifested in linkages and scale economies. In numerical simulations conducted with the model for two regions and different parameter settings, reported in Krugman (1991a), there are only two possible long-run equilibrium outcomes: a symmetric distribution between the regions of manufacturing and aggregation of all manufacturing in one region. In simulations with the multiple-region version of the model reported in Krugman (1995) symmetric equi-spaced distributions of manufacturing centers result. Generally speaking, with lower transportation costs, there is greater concentration, and with higher transportation costs there is less. 18.3. Developments in the new economic geography

Since the appearance of Krugman (1991a) there has been a proliferation of studies in which assumptions of the original model

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have been modified. In this section we take up a subset of these studies which examine what difference modifications in assumptions about consumer utility, transportation costs, production technology, labor and firm mobility, and adjustment dynamics make for explanations of various urban and regional agglomeration phenomena.11 (It should be borne in mind that because the labor force and output levels of firms are constant in the economy of Krugman’s (1991a) model, there is no growth as such, only regional aggregations and reaggregations of economic activities.) Tabuchi (1998) examines possible causes for concentration and dispersion of firms and workers between regions by considering urban agglomeration economies due to product variety and agglomeration dis-economies due to intra-city congestion. Hence, he attempts a synthesis of Krugman (1991a) with Alonso (1964) and Henderson (1974) that involves several modifications. First, he incorporates the land-consumption (consumption-of-space) assumption of Alonso’s model, which introduces the impacts of the price mechanism of the land rent market, and second, the cost of commuting. These changes are introduced through the utility function and the budget constraint. What Tabuchi finds, contra Krugman (1991a), is that for certain parameter settings there is “a Ushaped relationship between the decrease in transportation costs and spatial agglomeration” (Tabuchi, 1998, p. 334).12 Lanaspa and Sanz (2001) consider a series of modifications to the assumption that transport costs vary proportionately with distance and independently of other elements of the model. In particular, they examine how congestion costs, which increase with the size of a region, and infrastructure, which requires a threshold population level to be put in place, affect the distribution of manufacturing activity among regions. They find that, for certain parameter value settings, stable asymmetric equilibria may be obtained, providing 10

Many have been incorporated into the chapters of Fujita et al. (1999b) and Fujita and Thisse (2002). More complete surveys of studies in this line of inquiry concerning other agglomeration effects are provided by Ottaviano and Puga (1998), Papageorgiou and Pines (2000) and Fujita and Thisse (2002). 11 While several of the studies considered below deal with regions and not cities, the analytical approaches they take are amenable to the study of cities and urban agglomeration phenomena. 12 This same result is obtained by Helpman (1998), inter alia, although for different reasons.

New Economic Geography Explanations

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justification for the existence of “economic landscapes in which large industrial belts coexist with smaller ones” (Lanaspa and Sanz, 2001, p. 437). Both of the two previously discussed studies have examined two-region scenarios in which the distance between the centroids of the regions (or CBDs of the urban centers of the regions) are given. Alternatively, Mori (1997) considers an economy distributed over a continuous interval of space. In this economy there are costs associated with the transport of agricultural goods as well as manufactured goods. Both firms and workers can move. Mori makes use of a ‘market potential’ function, defined as the ratio of economy-wide demand for a firm’s output to its equilibrium output level, to indicate when and where it is profitable for firms to locate and hence cities to form. He identifies conditions under which falling transportation prices in the presence of increasing returns to scale imply the formation of a megalopolis consisting of large core cities connected by an industrial belt, instead of a greater concentration of manufacturing activity at point locations. The result of both firms and workers seeking the arrangement that is most advantageous to them is that no land that is exclusively agricultural in use is left between any two cities as firms aggregate toward an interval. Mori suggests that to increase realism, the ‘agricultural’ area in his model might be replaced by a residential area of workers who commute to urban jobs. Also relaxing the assumption that shipment of agricultural goods is costless, Fujita and Krugman (1995) seek to derive conditions under which all manufacturing activity will concentrate in a central city and the conditions under which this pattern will be sustainable.13 The economy they consider is spread across a onedimensional continuous interval of space. In this model, the normalization of labor employed in Krugman (1991a) is relaxed and the population is allowed to grow gradually. The forces of aggregation and dispersion remain as in Krugman (1991a). Fujita and Krugman find for a range of values of the preference intensity parameter r that “when the population increases from a low level, the benefits of a larger manufacturing sector dominate, but as 13

Note that even concentration represents a balance of agglomerative and dispersive forces. A condition that parameters must satisfy to prevent agglomerative forces from pulling all manufacturing activity into a ‘black hole’ is that ðs 2 1Þ=s . m:

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K.P. Donaghy

the population continues to increase the disadvantages of an ever more distant agricultural frontier prevail” (Fujita et al., 1999b, p. 140).14 They determine that the population size that maximizes real wages is greater when the variety of manufactured goods is greater, when manufactured goods’ expenditure share is larger, and when the costs of transporting both agricultural and manufactured goods are lower. Using a market potential function, in which potential is defined as the ratio of the maximum real wage that zero-profit manufacturing firms could pay workers at a given distance from the city center to the real wage paid to farmers at the same distance, Fujita and Krugman identify the critical population level at which it is profitable for a manufacturing firm to exit the central city, hence the population level at which the monocentric structure of the spatial economy is destroyed. They also identify conditions that combinations of key parameters must satisfy if the monocentric equilibrium is to be sustained. In an extension of the previously discussed paper, involving multiple cities and multiple groups of industries, Fujita et al. (1999a) develop a general spatial equilibrium model whose equilibrium solution yields a hierarchical central place system of cities. Agglomeration forces continue to derive from consumer preference for variety in manufactured goods and scale economies in their production, while dispersion forces derive from the demand for consumer goods by the agricultural populations. The setup of the analysis assumes that the economy already has an established structure of multiple cities, in which new cities can nonetheless emerge. ‘Higher order’ cities have more industries than ‘lower order’ cities and achieve their status by being upgraded from lower order cities. Adjustment dynamics come from labor migration in response to real-wage differentials and in equilibrium the real wage is equalized across locations. A given system of cities is sustainable if the market potential (as defined in terms of the ratio of real wages in manufacturing and agriculture) at any location other than those already occupied is less than 1. To study the self-organization of the city system, the authors conduct dynamic simulations in which they introduce hierarchical groups of manufactured goods. As in 14

Fujita and Krugman (1995) reappears as Chapter 9 of Fujita et al. (1999b).

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the previously discussed study, an exogenously growing population drives the economy’s growth. As the economy’s population increases, existing cities bifurcate and urban populations disperse until, in the long run, there are, for a given order of city, equalsized cities with equal market areas.15 And as in Christaller’s central place system, higher order cities produce all the manufactured goods produced by lower order cities and more. In the next two studies considered intermediate goods play a prominent role. Fujita and Hamaguchi (2001) develop a monopolistic competition model of a spatial economy in which manufacturing firms require a large variety of intermediate goods (instead of consumers demanding a large variety of final manufactured goods).16 Agglomeration forces “arise from the vertical linkages between the manufacturing and intermediategood sector”, whereas “dispersion forces arise from the demand for the manufactured goods by the agricultural workers who are spatially dispersed due to the necessity of land input” (Fujita and Hamaguchi, 2001, p. 79 – 80). The authors argue for the relevance of this model to the explanation of resurgence of some declining cities in developed countries because of the recent increase in demand for producer services as firms seek to outsource and reduce overhead costs. Solutions of the model yield two types of monocentric configurations. In the first, an ‘integrated city equilibrium’, transaction costs of intermediate goods are high and both manufacturing and intermediate sectors agglomerate in a single city. In the second, an ‘I-specialized city equilibrium’, the city specializes in the provision of intermediate goods. Fujita and Hamaguchi find that the former case represents a ‘primacy trap’ in which population growth alone will never lead to the formation of new cities. Walz (1996) considers a two-region economy in which growth emanates from product innovation in the intermediate-goods sector, 15

A significant part of the analysis in the NEG not discussed in this chapter has to do with bifurcations of solutions that occur at critical parameter values. While actual cities do not bifurcate, the bifurcating solutions of models indicate the possibility of multiple equilibria and the historical contingency of actual city-system formations. Fujita and Thisse (2002) take such model solutions to imply a ‘putty-clay’ geography. 16 The model is in a sense dual to Fujita and Krugman (1995), in which the agglomeration forces arise from consumers’ love for variety.

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whose increase in varieties leads to higher productivity in the finalgoods sector. While final goods are freely traded, intermediate differentiated goods, which are supplied by monopolists, are costly to trade. The production of intermediate goods requires specific R&D investments and the interregional trade in R&D products is associated with control and information costs. Unlike most other models in the NEG, explicit intertemporal optimizations by firms and consumers yield micro-foundations for dynamic adjustments in the model. Solution of the model determines the locations of goods production, R&D activities, and mobile workers. Under various conditions, the solution of the model results in a core– periphery pattern, equal-sized regions, or diverse production patterns and growth rates. Interestingly, and not unlike historical experience with various regional policies, policies designed to bring regions into convergence may actually result in unintended consequences and increase the gap between their production and growth structures. To the extent that intermediate good producers are located in cities, lessons from this model may be extended to city systems as well. 18.4. Accomplishments and challenges

Several broad assessments of what the NEG has accomplished have already been published.17 Our concern lies more narrowly with the ability of this body of work to help us to understand certain aspects of urban and regional agglomeration. The authors of the papers we have considered have succeeded in developing models whose solutions are consistent with different patterns of agglomeration, giving formal expression to powerful intuitions and endogenizing factors previously taken to be exogenous. In so doing they have provided materials for possible explanations of these phenomena. These achievements represent a significant contribution to ‘positive’ urban economics. But several of the most central contributors to this work, Fujita et al. (1999b), have also called for empirical investigation of the models they have developed and 17

See inter alia, Ottaviano and Puga (1998), Papageorgiou and Pines (1999), Martin (1999), and the critical forum in the Journal of Economic Geography, 2001, 1:131– 152.

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normative applications thereof. So we consider a set of issues concerning how well these models might fit into a larger, empirically oriented, research program of explaining agglomeration phenomena. Certainly all modeling and theorizing entails making some simplifying (and occasionally over-simplifying) assumptions, which, we might agree with Krugman (1995), are essential for conducting instructive thought experiments. Problems with simplification arise when we move from thought experiments with models to causal explanations of real-world phenomena. We need to be concerned about the extent to which the worlds of NEG models do not correspond to the world we are trying to explain. For, pace Friedman (1953), to test and confirm causal explanations empirically, the models we use to articulate those explanations must pick out actual causal mechanisms, even if highly stylized (Miller, 1987; Runde, 1998). Hence, in applied work we need at least roughly accurate characterizations of the behavior we hope to explain and, no less importantly, measurable variables. To meet these requirements, operationalized NEG models may need to incorporate more of the actual ‘furniture of the world’ and take on board considerably more complexity than they now carry.18 We consider several aspects of NEG models for which lack of realism presents problems for applied work. That the Dixit-Stiglitz setup may not correspond to any actual state of affairs, as Krugman (1995) readily acknowledges, is a worry, in view of the work it is called upon to do in most NEG models. And as Strange (2001) points out, while the Dixit-Stiglitz specification is a convenient way to get aggregation economies into a model, it does matter to the analysis whether aggregation economies derive from consumer preferences for variety, from demand for variety of intermediate goods by firms producing final goods (Ethier, 1982), or from labor – market pooling, input sharing, or educational 18

Note that demand for parsimony of Occam’s razor only applies to models and explanations that are equally successful in accounting for the phenomena in question – i.e. in identifying effective causes at sufficient causal depth. A separate concern lies with the extent to which the results of NEG models are robust to choice of functional forms and transport technologies. See, e.g., Fujita and Hamaguchi (2001) on this acknowledged weakness.

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improvement and skill acquisition (Quigley, 1998). We should also be mindful that, wherever they derive from, agglomeration economies will affect patterns of agglomeration differently at different distances (Anas et al., 1998). The role given to farmers’ demand for final goods in attenuating centripetal forces in these models is, in the view of Pines (2001), certainly unrealistic in developed economies, even if we read ‘agriculture’ as a residual sector, as Fujita et al. (1999b) suggest. Not only is the characterization of the role of agricultural production and land use problematic, but also are the characterizations of consumers and firms. There are at least two issues here. Contrary to the implication of the basic assumptions of NEG models (see footnote 1), consumers do not interact even remotely with every firm producing final goods; alternatively, neither does every such firm interact with every firm producing intermediate goods. Moreover, in the ‘information’ or ‘e-commerce’ economy consumers and firms do not purchase goods and services in patterns that would suggest the operation of a central place system. (See, e.g. Pred, (1977) for a somewhat dated but still realistically relevant depiction of the interactions of firms in city systems of advanced economies.) The characterization of firm mobility also needs refinement. Jones and Kierzkowski (1990, 2001), whose work is also based on models of monopolistic competition in international trade, have focused on one of the most fundamental empirical regularities of worldwide production and distribution: the vertical and horizontal fragmentation of firms and industries. The reality that they depict is not one of firms moving ‘lock, stock, and barrel’ from one region or point of aggregation to another. In this world, where production processes are being broken out more and more finely into blocs, the production of intermediate goods and producer services is dispersing increasingly across many regions (of many countries). And the largest share of goods in transit consists of semi-finished goods shuttling between firms’ own far-flung establishments. It is this dynamics of globalization, induced by information and communication technology innovations, underpriced transport, and the availability of low-wage labor, that is radically altering the economic geographies of North America, Europe, and Asia and needs to be formally endogenized in models purporting to explain

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the ongoing evolution in the spatial distribution of economic activities.19 Other important actors on the urban scene who are conspicuous by their absence in the NEG stories about agglomeration phenomena are developers and government. Certainly these actors strongly influence decisions of firms and workers through the provision of infrastructure, the entrepreneurial undertaking of risky investments, and the jump-starting of aggregation. Indeed, it is arguable that some growth phenomena, such as edge cities, cannot be adequately explained without making reference to the behavior of these actors. As discussed above, one of the important contributions of the NEG, and Fujita et al. (1999a) in particular, has been to demonstrate how a central place system can emerge from the basic assumptions of NEG models. One concern, however, is that (to the best of my knowledge) these models have not been able to replicate the evolution of uneven development patterns as have other models of self-organizing complex systems in the tradition of, say, Allen (1998). Admittedly, models in the latter tradition lack economic micro-foundations or a role for price mechanisms and so are not fully in the ‘urban economics tent’. But as Anas et al. (1998) have noted, attempts to supply micro-foundations for Allen-type models along the lines of Chen (1993, 1996) may hold promise. Finally, we turn to empirical investigations of the NEG. Most economists who have tried to test propositions implied by the NEG have carried out studies with data collected at the regional level (see, e.g., Hanson (1997) and Fingleton (2001), and papers discussed by Ottaviano and Puga (1998)). It is encouraging for the NEG project that evidence of IRS economies of production have been found at this level.20 A limited number of studies have also been carried out at urban and sub-regional scales. Analyzing data at the urban scale, Glaeser et al. (1992) have found evidence of agglomeration economies arising from a demand for variety of goods and Fingleton 19

Fujita et al. (1999a) acknowledge the need to incorporate multi-locational firms in NEG models. Krugman and Venables (1995) have shown how NEG models can illuminate other aspects of globalization that contribute to regional and international inequality. 20 In addition to the papers cited, Donaghy and Dall’Erba (2003), using a growth model based on a generalized CES production technology, have obtained direct estimates of returns-to-scale parameters in the regional economies of Spain that indicate IRS in all regions.

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(2003) has found evidence of increasing returns to the density of economic activities. LaFountain (2003) has found that pecuniary externalities are a source of agglomeration for some industries, but not others, at the county level. We discuss the latter two studies in greater detail. Fingleton (2003) has found that as the density of workers in local areas of Great Britain increases there is a more than proportionate increase in wage levels. He infers from this that there is also a more than proportionate increase in the level of output of final goods and services. In the greater London area, in particular, he has found that enhanced worker efficiency is relative to in-commuting, which in turn is contingent upon transportation infrastructure. Working with 2-digit SIC code industry data at the county level, LaFountain (2003) has examined empirical support for three alternative models of firms’ location decisions and agglomeration. These include ‘market access’ models of the NEG, in which pecuniary externalities are the source of agglomeration, production ‘externality’ models, in which firms’ production possibilities depend on the action of firms at the same location, and ‘natural advantage’ models, in which the endowments of different locations render them more or less attractive to different types of producers.21 LaFountain has found that for six of the 18 industries she has analyzed – food, printing and publishing, stone, clay and glass, fabricated metals, industrial machinery and equipment, and miscellaneous manufacturing industries – the data are consistent with predictions of the market access model.22 Issues raised by the NEG might also be investigated empirically at sub-urban scales and with more explicit spatial content, in view of the fact that we now possess methodologies in applied spatial 21

In a predecessor to LaFountain (2003), Kim (1995) distinguished between the three location-decision models for the US manufacturing sector as a whole but did not consider the role that urbanization externalities may play or identify which model best explains the location decisions of firms in individual industries. 22 LaFountain (2003) has also found that data on seven industries – paper, chemicals, petroleum, and coal products, primary metals, electronic and other electric equipment, transportation, equipment, instruments, and furniture and fixture industries – are consistent with predictions of the ‘natural advantage’ model, and that data on the textiles and apparel industries are consistent with the predictions of the ‘externality’ model. Data on the lumber and Wood product and the rubber and plastics industries are not consistent with predictions of any of the three classes of models.

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econometrics to investigate spatial dynamic models in one or two dimensions of space (Donaghy, 2001; Donaghy and Plotnikova, 2004). While questions about the availability of spatial time-series with sufficient observations to test such models may exist, it would appear that the NEG is at a stage of development where applied empirical work may help to push it along and supply important feedback to the theorizing that has been conducted to date through abstract modeling and numerical simulations. As it assumes greater realism, the NEG may in turn be able to contribute insights that will inform concrete normative assessments and suggest appropriate policy interventions.

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