What Can Be Learned from Spatial Economics?†

Journal of Economic Literature 2019, 57(3), 575–643 https://doi.org/10.1257/jel.20181414

Stef Proost and Jacques-François Thisse*

Spatial economics aims to explain why there are peaks and troughs in the spatial distribution of wealth and people, from the international and regional to the urban and local. The main task is to identify the microeconomic underpinnings of centripetal forces, which lead to the concentration of economic activities, and centrifugal forces, which bring about the dispersion of economic activities at the regional and urban levels. Transportation matters at both scales, but in a different way. The emphasis is on the interregional flows of goods and passenger trips at the regional level and on individual commuting at the urban level. ( JEL F12, L13, R12, R23, R30, R40)

1. Introduction mid-nineteenth century, compounded by the near-disappearance of communication patial economics deals with bringing costs, imply that distance and location have Slocation, transport, and land into eco- disappeared from economic life? Why do nomics. These three concepts are closely lasting and sizable regional disparities exist intertwined and gathered under the cat- in many countries? Why do firms locate in egory R of the JEL Classification System. areas where labor and land are expensive? We show how spatial economics addresses Does building interregional transport infra- many issues, including the following: Why structures help to reduce inequality across are economic activities unevenly distributed space? Why do cities exist and why do they across space at different spatial scales? Does differ in size? Why are workers better paid the steady drop in transport costs since the and housing more expensive in large than in small cities? Are workers sorted by skills across cities? Is road pricing the ideal instrument to tackle traffic congestion? We discuss * Proost: Department of Economics, KULeuven. Thisse: CORE-UCLouvain, HSE University and CEPR. various approaches, ranging from classical We are very grateful to Steven Durlauf and three referees location theory to quantitative spatial models. for many comments and suggestions. We also thank Jan Spatial economics is both at the core and Brueckner, Miren Lafourcade, Sun Kyoung Lee, Robin Lindsey, Mario Polèse, Stephen Redding, and Kenneth periphery of economics. It is at the core in Small for insightful remarks. The second author acknowl- that economic growth has always been, and edges the financial support of the Russian Science Founda- still is, geographically localized and uneven, tion under grant 18-18-00253. † Go to https://doi.org/10.1257/jel.20181414 to visit the while economic historians have convincingly article page and view author disclosure statement(s). argued that cities have played a fundamental

575 576 Journal of Economic Literature, Vol. LVII (September 2019) role in the process of economic and social disappeared from economic life. New forces, development (Bairoch 1988, Hohenberg and hitherto outweighed by natural factors, are Lee 1985). Therefore, space and its parent shaping an economic landscape that, with its concepts—such as location, transport, and many barriers and large inequalities, is any- land—should be an important component thing but flat. of economists’ toolbox. However, spatial Spatial economics deals with other import- economics is fraught with many of the dif- ant issues. Housing and transport, which are ficulties encountered in economic the- quintessentially space-related commodities, ory (externalities, increasing returns, and rank first and second in household expendi- imperfect competition). Therefore, it hardly ture. In the United States, the average share comes as a shock that spatial economics and of household expenditures on housing is its constituent subfields—such as regional, 24 percent, while it is 33 percent in France. urban and transportation economics—were, Spending on transport amounts to 17 per- and are still, at the periphery as they are cent in the United States and 13.5 percent poorly represented in textbooks and gradu- in France. Per year, the opportunity cost of ate programs. Yet, the empirical evidence is the time spent in commuting comes to three compelling. to six weeks of work for a typical New Yorker By using nighttime images, Florida and, on average, to four weeks of work for (2017) finds that the largest 681 metropol- a resident of Greater Paris. These numbers itan areas distributed over the globe house do not account for the fact that commut- about 24 percent of the world’s population ing seems to be one of the most unpleasant and produce 60 percent of the global out- activities in individuals’ daily life (Kahneman put. In the United States, 20 metropolitan et al. 2004). areas produce about 50 percent of the GDP Space is the substratum of human affairs, but are home to approximately 30 percent of but it is also a consumption and production the population. By contrast, the 28 capital good in the form of land. The worldwide regions of the European Union accounted for supply of land is perfectly inelastic but vastly 23 percent of its GDP. Greater Paris, which exceeds the demand for it. Therefore, put- represents 2 percent of the area of continen- ting aside the agricultural land rent, the tal France and 19 percent of its population, price of land should be zero. Yet, housing produces more than 30 percent of its GDP. costs may be very high and vary enormously Equally surprising, distance still matters in with the size and composition of cities for international trade. One of the most robust reasons that do not depend on the qual- empirical facts in economics is the gravity ity of the housing structure. According to law linking bilateral trade flows to the GDP Albouy, Ehrlich, and Shin (2018), in 2006 of countries and the distance between them. (i.e., before the subprime mortgage crisis), Head and Mayer (2014) summarize the state the total value of urban land in the United of the art as follows: “Holding constant the States exceeded twice the American GDP. product of two countries’ sizes, their bilateral Therefore, the price of land in cities must trade will, on average, be inversely propor- reflect the scarcity of “something” that dif- tional to the distance between them.” These fers from land per se. facts and many others run against the com- Locations are linked through various types mon belief that we live in a world where the of flows: of goods, people (commuters and playground has been leveled. Despite spec- passengers), factors of production (capi- tacular drops in communication and trans- tal and labor), and information. Therefore, port costs, distance and location have not one could expect trade theory to be the Proost and Thisse: What Can Be Learned from Spatial Economics? 577 economic field that paid the most atten- land, and thus may be viewed as spatial tion to the spatial dimension. Yet, for a long economics without land. Urban economics time, trade theory focused on an extremely studies the formation of cities, their spatial strange geography with countries that are structure, and their social composition. As close enough for the cost of shipping goods cities differ in size and specialization, they internationally to be zero, but distant enough form what is called the urban system. Urban for no workers or capital owners to find their economics is spatial economics with land way from one country to the other (Leamer because land use is critical in the working of 2007). This research strategy is especially cities. Urban economics abides to technolog- surprising since Ohlin challenged the com- ical externalities through market size effects mon wisdom long ago: “International trade and knowledge spillovers. theory cannot be understood except in Transportation economics spans both relation to and as part of the general loca- regional and urban economics, but each in a tion theory, to which the lack of mobility of different way. In the regional context, trans- goods and factors has equal relevance” (1968 portation economics studies the interregional [1933], p. 97). Eventually, the gravity law led and international freight trips of inputs and trade economists to recognize, if belatedly, outputs, as well as passenger trips (whether that free trade does not mean costless trade. for business or leisure). In the urban context, Economists and regional scientists have the emphasis is mainly on commuting by var- developed different theories and models ious means of transportation. Most of trans- to account for the existence of a variety of portation economics takes the location of spatial clusters. However, the differences firms and households as given. This is where among theories and models are less pro- the link is missing with regional and urban nounced than they might seem. One of the economics, where locations are endogenous. main thrusts of this survey is to show that a Thus, there is a need for more integration few basic principles may be used to under- between, on the one hand, regional or urban stand the reasons for a great number of and, on the other, transportation economics. spatial clusters. In what follows, we discuss The literature in spatial economics has paid regional, urban, and transportation econom- too little attention to what has been accom- ics. What distinguishes regional from urban plished in transportation economics (and economics is not a simple issue. We contend vice versa). that the main difference lies in the spatial The paper is organized as follows. unit of reference. Section 2 discusses the trade-off between Regional economics focuses on the mobil- increasing returns and transport costs, ity of goods and production factors within a which shapes the space-economy at differ- large, economically integrated space (e.g., ent scales. In addition, we explore a question a nation or trade bloc). Because it focuses that has generated endless discussions: how on issues arising on a global scale where best to describe the process of competition spillovers are likely to be absent, regional across space. To answer this question, we economics relies on the combination of borrow tools from general equilibrium the- increasing returns and imperfect competi- ory and industrial organization. Section 3 tion, while trading goods across regions is focuses on the so-called “regional ques- costly. Since market prices do not accurately tion,” that is, the existence of sizable and reflect the social value of individual deci- lasting disparities in GDP per capita within sions, pecuniary externalities matter. Until nations such as the Italian regional divide, or recently, regional economics has neglected regional trade blocks characterized by strong 578 Journal of Economic Literature, Vol. LVII (September 2019) spatial inequality like the European Union. agglomeration of firms and households in Speculation about regional disparities has a relatively small number of cities. In this never been in short supply. However, no context, cities are not just the containers of one before Krugman (1991) had proposed economic activities, but rather key players in a full-fledged general equilibrium model the social fabric. Agglomeration economies showing how these disparities can arise at a explain why cities exist and why city size mat- stable equilibrium in a setting involving mar- ters. Congestion is the main friction in cities, ket forces alone. Once set in motion, these and transportation economics offers some forces generate “snowball effects” that are promising insights for easing this friction. self-reinforcing. In section 5, we discuss different families We follow in Krugman’s footsteps and adopt of models that could be used to develop a the “new economic geography” approach synthesis of regional and urban economics, to regional economics. What distinguishes including urban systems and quantitative this field from trade theory is the mobility spatial modeling. Section 6 concludes with of firms and households. Admittedly, atten- suggestions for future research. tion to new economic geography has waned Even though ongoing research focuses during the last decade. However, it seems to mainly on the empirics of agglomeration, have regained interest thanks to the appli- our emphasis is primarily on theory. The fifth cation of new analytical tools, while its main volume of the Handbook of Regional and ideas have been taken on board in quanti- Urban Economics features several insight- tative spatial models. In addition, since the ful chapters discussing the recent empiri- key parameter of new economic geography is cal literature (Duranton, Henderson, and the level of transport costs, this approach is a Strange 2015). By contrast, many ideas and natural candidate for studying the effects of results obtained in spatial economic theory trade and transport policies on the location have been forgotten or are being rediscov- of economic activity. ered under different guises. Furthermore, In section 4, we move on to studying cit- they remain fairly disparate and in need of a ies, which are the most extreme form of synthesis. In this survey, we aim to show that spatial inequality. Urban economics, in the the state of the art is sufficiently advanced wake of its founding fathers (Alonso 1964, to sketch a unified field that should attract Mills 1967, Muth 1969), focused for a long more attention in the economics profession. time on the monocentric city model in which Yet, doing so does not mean that we may jobs are supposed to be concentrated in the leave empirical works aside. Reflecting our city’s central business district. One of the idiosyncrasies, we have chosen those that are great merits of this model is its emphasis directly related to the bodies of theory we on the importance of non-tradables pro- discuss. duced within the city for residents, whereas regional economics remains in the tradition 2. What Are the Specificities of Spatial of trade theory by focusing on tradables. Economics? Ever since the early 1970s, interest in urban economics has advanced rapidly and shows In this section, we first expand on the no sign of abating. The reason for this suc- spatial concentration of activities by going cess is probably that the monocentric city beyond purely geographical factors. Next, model is based on the perfectly competi- we introduce spatial economics’ fundamen- tive paradigm. More recently, the interest tal trade-off between increasing returns has shifted to the reasons explaining the to scale and transport costs. Somewhat Proost and Thisse: What Can Be Learned from Spatial Economics? 579

unfortunately, this trade-off does not fit into forces—some working toward concentration, the competitive general equilibrium model. and others toward dispersion—in spaces that This is why less standard assumptions, such are otherwise undifferentiated by natural or as spatial inhomogeneities, spatial external- political factors. Given this methodological ities, and imperfect competition, have been choice, we are left with some fundamental important for the development of the field. questions: What are the macro-spatial con- We conclude with a discussion of the strate- sequences of a myriad of micro-decisions gic locational choices made by firms, a topic made by economic agents? What are the that underpins spatial equilibrium analysis. main economic forces that push toward the agglomeration or the dispersion of firms and 2.1 Does Geography Matter? households? How do spatial frictions, such According to Diamond (1997), spatial dif- as transport and commuting costs, affect the ferences between edible plants (with abun- economic landscape? dant nutrients) and wild animals (capable of This choice does not reflect any preju- being domesticated to help man in his agri- dice on our part. We do believe that natu- cultural and transport activities) explain why ral factors matter for the organization of the only a few regions have become independent space-economy. In a recent and fascinating centers of food production. Though relevant paper, Henderson et al. (2018) show that for explaining the emergence of civilization in 35 percent of within-country variation in a few areas, we must go further to understand night light, used as a proxy for the level of why, in the wake of the Industrial Revolution, economic activity, is associated with phys- trade and cities have grown so rapidly. ical geography. The remaining 65 percent It is true that a number of natural features are the raison d’être of spatial economics. differentiate locations and they may have Moreover, we also believe that natural fac- long-run implications for the organization tors do not explain why huge metropolitan of the space-economy (Gallup, Sachs, and areas such as Tokyo, New York, or Shanghai Mellinger 1999; Bosker and Buringh 2017). exist. Geography is more useful in under- The fact that the two biggest American cities, standing where cities are rather than why New York and Los Angeles, are also the two cities exist, even though both probably inter- biggest ports of the United States is proba- act in some way. Thus, when the aim is to bly not an accident. However, Moscow and explain the actual location of economic activ- Paris, which rank first and third among the ity, natural factors must be taken into con- top European cities, have no serious compar- sideration. According to Allen and Arkolakis ative advantages in terms of access to the sea (2014), 20 percent of the spatial variation in nor any other great natural amenities. In this income across the United States in 2000 can case, one must consider historical and politi- be explained by geography alone. cal factors, rather than geographical ones, to Geography also matters in a more subtle explain the importance of these two cities. way: the choice of the spatial scale. Quite In this survey we have chosen to follow the often, economists use different, yet equally founding fathers of spatial economics, such unclear, words such as locations, regions, or as Lösch (1940) and Hoover (1948), in their places interchangeably without being aware methodological choice. For these authors that they often correspond to different spa- (and for us), the issue that should rank first tial units. In so doing, they run the risk of on the research agenda is to explain the exis- drawing implications that are valid at a cer- tence of different types of economic agglom- tain spatial scale but not at another, because erations through the interplay of economic the agglomeration or dispersion forces at 580 Journal of Economic Literature, Vol. LVII (September 2019) work at the local level are not necessarily the to the local environment in which firms oper- same as those acting at the global level. ate. Their concrete manifestation can vary considerably from one case to another, but 2.2 The Fundamental Trade-off of Spatial the basic idea is the same: each firm benefits Economics from the presence of other firms. The presence of increasing returns has a Our aim in this section is to explain the major implication for the spatial organiza- fundamental trade-off between increasing tion of the economy: not everything can be returns and transport costs, a trade-off that produced everywhere. It is in this sense that is valid at all spatial scales (Fujita and Thisse location matters. Though a large number of 2013). The intuition behind this trade-off is activities became “footloose,” many large easy to grasp. In the absence of increasing areas in many countries account for no or lit- returns, firms would be able to spread their tle economic activity. Indeed, one should not production over an arbitrarily large number infer from the low value of (monetary and of locations without any efficiency loss, while nonmonetary) transport costs that location bringing transport costs down to zero. In this matters less. It is quite the opposite. In the case, the economy boils down to backyard presence of increasing returns, low transport capitalism, that is, a world in which Friday costs make firms more sensitive to minor is no help to Robinson Crusoe. If transport differences between locations. All of this is costs were nil, with increasing returns, firms seemingly a paradox: the inexpensive shipping would concentrate their production in a few of goods makes competition tougher, and thus giant plants to benefit from the highest pos- firms care more about small advantages than sible level of efficiency. Such counterfactuals they do in a world where they are protected confirm the relevance and importance of the by the barriers of high transport costs. fundamental trade-off of spatial economics. 2.2.2 Moving Goods, People, and It has been rediscovered several times and Information Remains Costly goes back at least to Lösch (1940). We now briefly discuss the two main ideas that stand A high number of personal services are not behind this trade-off and serve as the ground tradable, i.e., they must be consumed where rules for this survey. they are produced. In addition, what has been built, e.g., roads, subways, and housing, 2.2.1 Scale Economies Matter for the cannot be moved. In those cases, transport Location of Economic Activity costs may be considered as infinite. The most natural way to think of increas- Goods.—The great many estimations ing returns is when a plant needs a mini- of the gravity equation show that distance mum capacity to operate. This gives rise to remains a strong impediment to the spa- overhead and fixed costs, which are typically tial exchange of goods (Anderson 2011, associated with mass production. In this Head and Mayer 2014). Anderson and van case, scale economies are internal to firms. Wincoop (2004) estimate that the average Similarly, local public goods are often pro- cost of delivering a good from the point of vided in the form of a facility designed to manufacture to the destination represents supply collective services to consumers (e.g., 170 percent of the producer price, which is fire stations or public hospitals), or as a road quite high. However, this number is some- or subway network. Increasing returns may what inflated as it includes retail costs. This is also materialize under a very different form, not an isolated finding. Even within-country where they are external to firms but specific trade tends to be very much localized. Using Proost and Thisse: What Can Be Learned from Spatial Economics? 581 data on shipments by individual US manu- workers implies that the local labor supply is facturing plants, Hillberry and Hummels infinitely elastic. By contrast, when workers (2008) find that the number of commodities are imperfectly mobile, the local labor supply shipped and the number of plant–destina- has a finite elasticity. The empirical and the- tion pairs fall dramatically with distance. The oretical implications of assuming perfectly value of shipments within a 4 -mile radius of mobile individuals must be interpreted with the plant is 3 times higher than those beyond care because mobility costs affect the spa- this radius. tial arbitraging between amenities, housing, People.—To the best of our knowledge, and wages. Describing migration choices by there is no integrative work on migration means of discrete choice models is a possible comparable to that in the trade literature way out. on the gravity equation, though several Information.—It is perhaps more sur- papers suggest that frictions exist that would prising that informational frictions remain make migration gravitational in nature (e.g., substantial in certain activities. Whereas Kennan and Walker 2011). As the mobility of the media steadily stress the globalization of people is governed by a broad range of eco- finance, the empirical evidence highlights nomic, intangible, time-persistent, and idio- the importance of distance between lend- syncratic factors, it is more difficult to study ers and borrowers in explaining the design than trade flows. In a classical paper devoted of loan contracts (Hollander and Verriest to the evolution of the US states over the 2016). Likewise, there must be compelling 1950–90 period, Blanchard and Katz (1992) reasons for businesspeople to meet in per- find that “the dominant adjustment mech- son despite the high opportunity cost asso- anism is labor mobility, rather than job cre- ciated with traveling. Here, Giroud (2013) ation or job migration. Labor mobility, in turn, documents that the opening of new airline appears to be primarily a response to changes links, reducing the travel time between in unemployment, rather than in consump- headquarters and plants, has generated an tion wages.” On the other hand, using the increase of 7 percent in plants’ productiv- British Household Panel Survey from 1991 to ity in multiunit US firms. Campante and 2009, Bosquet and Overman (2019) observe Yanagizawa-Drott (2018) show that bet- that 43.7 percent of workers worked only in ter passenger connections through lon- the area in which they were born. ger-range flights (larger than six thousand That many people continue living in miles) generate more business links and deprived areas should be evidence that capital flows with the major hubs in Europe migration costs are of first-order impor- and improve local economic activity in the tance. Due to family bonds, social networks, vicinity of these hubs. tacit information, and language and cultural The existence of transfer costs has a major differences, people are heterogeneous in implication for the spatial organization of their attitudes toward migration. When indi- the economy: these costs imply that what is viduals are identical and perfectly mobile, near to us matters more than what is far. In the spatial equilibrium condition implies the presence of indivisibilities, transfer costs the equalization of utility across space (see are unavoidable because there is a need Alonso 1964, Henderson 1974, Roback 1982 for proximity to sites that are spatially sep- for the pioneering contributions). We recog- arated. Consequently, firms and consumers nize that this assumption vastly simplifies the operate within a system of push-and-pull analysis. However, it is far from being innoc- forces whose balance is their most preferred uous. For example, the perfect mobility of locations. 582 Journal of Economic Literature, Vol. LVII (September 2019)

The above discussion leads us to formulate illustrated by the following example, the what we see as the fundamental trade-off in intuitive argument is beautifully simple spatial economics: (Koopmans and Beckmann 1957). Consider an economy with one worker The spatial distribution of activities is the outcome of a trade-off between different types of and one producer who are price takers scale economies and costs that are generated by and with two locations, A and B, each of the transfer of people, goods, and information. which is endowed with one unit of land. In equilibrium, the producer is located at A; he This trade-off—the unifying idea of this produces one unit of the consumption good survey—is key in the balance between by using one unit of land and one unit of agglomeration and dispersion forces and is labor. The worker is located at B; she con- valid on all spatial scales (cities, regions, coun- sumes one unit of the consumption good tries, and continents). Pomeranz (2000) con- and one unit of land and supplies one unit of firms the historical relevance of thistrade-off labor. Assume first that the equilibrium land when he observes that the geographical dis- rent at A is higher than or equal to that in ∗ ∗ ∗ ∗ tribution of resources played a key role in the B (R A R B ). Let p A (p B ) be the price of ≥ ∗ ∗ success of England and the failure of China in the consumption good at A (B) and w B (w A ) the Industrial Revolution. Distances between the wage paid to the worker at B (A). Let coal deposits in Northwest China and the t 0 be the unit cost of shipping the con- > Yangtze Delta, which hosted a large num- sumption good between A and B and 0 τ > ber of skilled workers, were very large. Thus, the worker’s commuting cost between A transportation costs were much too high to and B. The no-arbitrage condition implies ship coal to the artisans who could have been that the price (wage) gap is just equal to able to combine it with new technologies. By the cost of moving the good (the worker) contrast, distances were considerably shorter between A and B; therefore, it must be that in England. Coal, skills, and demand were p ∗ p ∗ t (w ∗ w ∗ ). If the pro- B = A + A = B + τ close to each other at a time where shipping ducer were located at B, he would earn a coal was still very expensive and the transmis- higher profit because he bears a lower pro- sion of knowledge mainly oral. This allowed duction cost (w ∗ R ∗ w ∗ R ∗) and B + B < A + A the corresponding English sites to benefit earns a higher revenue (p ∗ p ∗) by sav- B > A from scale economies in the production of ing transport costs without paying a higher steel and metallic items. rent. Therefore, there is no competitive equilibrium such that R ∗ R ∗. Assume 2.3 Space and General Equilibrium A ≥ B now that the competitive equilibrium is such that R ∗ R ∗. In this case, the worker 2.3.1 The Spatial Impossibility Theorem A < B would be better off at A because she earns The history of the relationship between a higher labor income while paying a lower spatial economics and general equilibrium rent. Since the level of equilibrium prices theory is both complex and obscure. It is is unspecified, there is no competitive equi- complex as it is fraught with difficulties— librium such that neither the producer nor such as increasing returns and imperfect the worker wants to change place. Thus, competition—that have been put aside for for a competitive equilibrium to exist, the simplicity. It is obscure because the several worker and the producer should be located attempts, made over the last fifty years, to together, which is impossible because there clarify this relationship have just muddled is not enough land in A and B. Starrett the debate with confusing answers. Yet, as (1978) gives a general proof. Proost and Thisse: What Can Be Learned from Spatial Economics? 583

THE SPATIAL IMPOSSIBILITY THE- constant returns at a total factor productiv- OREM: Consider an economy with a finite ity drawn randomly, which reflects regions’ number of locations. If consumers’ prefer- technological comparative advantage (Eaton ences are the same across locations, firms’ and Kortum 2002). Admittedly, appealing production functions are the same across to spatial inhomogeneities may be a fruitful locations, and transport is costly, then there modeling strategy. For example, assuming exists no competitive equilibrium involving the existence of a central business district trade across locations. where jobs are concentrated enables one to study the structure of the monocentric city Thus, if a competitive equilibrium exists, while using general competitive analysis (see the spatial impossibility theorem implies section 4.2). Yet, the question of why this that each location operates as an autarky. center exists is omitted. Assuming that some If there is no efficiency reason for firms to locations are endowed with attributes that distinguish between locations and if activ- make firms more productive than elsewhere ities are divisible, each one can operate at is tantamount to assuming the answer to a an arbitrarily small level and transport costs question we want to explain: Why are there are reduced to zero. By contrast, when there differences in productivity across space? are indivisibilities in production, some goods Even though there might be a few suitable must be traded across locations. In this case, places to host particular production activities, what makes a location desirable depends on relying solely on comparative advantage to the locations chosen by the other agents. By explain the existence of large urban agglom- implication, the price system must perform erations and sizable trade flows amounts to two different jobs simultaneously: (i) support playing Hamlet without the prince. trade between locations (while clearing mar- To fix ideas, consider the above example kets in each location), and (ii) prevent firms where it is now assumed that location A is and consumers from relocating. The spatial endowed with a strong productivity advan- impossibility theorem says that it is impos- tage and location B with a strong amenity sible to hit two birds with one stone. The advantage. In this case, a competitive equi- equilibrium prices supporting trade carry librium involving trade exists because the the wrong signals from the viewpoint of loca- firm and the worker have strongly diverging tional stability. As a consequence, the price preferences for location attributes. This type system does not convey all the information of assumption and result conflicts with our needed by an agent. Note the importance aim to identify conditions under which firms of the following indivisibility for the above and workers choose to locate together. By argument: the land that the worker (the pro- contrast, we acknowledge that accounting for ducer) lives on is concentrated in a single locational and natural advantages is needed location. In other words, each agent has an in empirical research (Diamond 2016, Lee “address” in space. and Lin 2018). However, care is needed in order to avoid using a deus ex machina. 2.3.2 Spatial Inhomogeneities The other two solutions that allow one There are different strategies to obviate to escape the spatial impossibility problem the consequences of the spatial impossibil- became the basis for much of modern devel- ity theorem. The first consists of introducing opments in spatial economics. In regional exogenous spatial inhomogeneities, such as economics, which regained interest in the in Ricardian models of trade where firms 1990s under the heading of “new economic produce under perfect competition and geography” (Krugman 1991), one calls upon 584 Journal of Economic Literature, Vol. LVII (September 2019) monopolistic competition and internal econ- monopoly because it is too expensive for con- omies of scale. In urban economics, spatial sumers located near the midpoint between externalities regained interest with the work firms i 1 and i to make any purchase. On − of Glaeser et al. (1992) and of Henderson, the contrary, when t is sufficiently low, each Kuncoro, and Turner (1995). However, firm competes with its two neighbors for before proceeding, we want to underscore the consumers located between them. The the idea, developed in the spatial and indus- market power of a firm is then restrained by trial organization literature, that space would the actions of its neighboring firms. In other give rise to a special type of oligopolistic words, its spatial isolation gives a firm only competition. The detour is important by local monopoly power, for this firm’s demand itself, but it also helps in understanding the depends on the prices set by the neighboring modeling choices made in the subsequent firms. sections. Since a reduction in firmi ’s price significantly affects the demands of its two neigh- 2.4 Spatial Competition boring firms, they react by reducing their In his review of Chamberlin’s (1933) book, own prices. The reactions of firms i 1 and − Kaldor (1935) argued that consumers’ dis- i 1 affect in turn the demands of firms + persion molds competition across space in a i 2 and i 2 through a ripple effect. This − + very specific way: whatever the total number market structure is, by nature, oligopolistic in of firms in the industry is, each one competes that each firm is concerned directly with only more vigorously with its immediate neigh- a small number of competitors, in this case, bors than with more distant firms. Such mar- two. Vickrey (1964) and Beckmann (1972) ket description, which came to be known as have shown that the market outcome is given spatial competition, departs radically from by a unique Nash equilibrium in which all the perfectly competitive setting. The argu- firms charge the same price, p ∗ c t , = + Δ ment goes as follows. Since consumers are where c is the common marginal production spatially dispersed, they differ in their access cost. Therefore, spatial separation endows to the same firm. Consequently, a consumer firms with market power. More specifically, buys from the firm with the lowest full price, as travel rate t, interfirm distance , or both Δ that is, the posted price plus the travel cost to decrease, firms charge a lower price because the corresponding firm. This in turn implies competition becomes more intense. In the that every firm has some monopoly power limit, when travel costs vanish, firms price at over the consumers situated in their vicin- marginal cost, as in Bertrand. Vickrey’s and ity, which enables firms to choose their own Beckmann’s contributions went unnoticed. prices in a strategic environment. It was not until Salop (1979) that scholars in The earliest analyses of this problem are industrial organization started paying atten- by Vickrey (1964) and Beckmann (1972), tion to spatial competition models. who studied how homogeneous firms equi- Yet, how do firms choose where to produce distantly distributed over a one-dimensional under spatial competition? Hotelling (1929) space compete to attract consumers who proposed a solution in a path-breaking paper are evenly distributed over the same space. in which two sellers choose, first, where to Each consumer buys one unit of the good, set up their stores along Main Street, which while traveling costs are proportional in dis- is described by a compact segment, and, tance. Firm i has only two neighbors located then, the price at which they supply their at distance on each side. When the travel customers. Whereas the individual purchase Δ rate t takes on a high value, firmi is a local decision is discontinuous—a consumer Proost and Thisse: What Can Be Learned from Spatial Economics? 585 buys from only one firm—firms’ aggre- competition. Therefore, since competition gated demands are continuous with respect is relaxed through product differentiation, to prices, except in the case when one firm firms may locate where the market potential undercuts the other. Assuming that each is the highest. Furthermore, under a sym- consumer is negligible solves the apparent metric and bell-shaped population density, contradiction between discontinuity at the Anderson, Goeree, and Ramer (1997) show individual level and continuity at the aggre- that firms move toward the city center gated level. Hotelling considers a rich setting where the population density is the highest. involving both “dwarfs” (consumers) whose When the population density becomes more behavior is competitive and “giants” (firms) concentrated around the center, equilib- whose behavior is strategic. rium locations are closer and prices lower. Hotelling’s conclusion was that the pro- Therefore, firms face more competition in cess of spatial competition leads the two return for a better access to a larger num- firms to locateback-to-back at the mar- ber of customers. We will see in section 3 ket center. If true, this provides us with a that the home market effect is built on rationale for the agglomeration of firms the same trade-off between proximity and that sell to spatially dispersed customers. competition. Unfortunately, Hotelling’s analysis con- The two-stage game approach struggles to tained a mistake—when firms are suffi- handle a setting with several firms. In addi- ciently close, the corresponding subgame tion, when consumers like variety, market does not have a Nash equilibrium in pure areas overlap. This implies that firms no lon- strategies—that invalidates his main con- ger have a natural hinterland, but are able to clusion. This led d’Aspremont, Gabszewicz, retain customers from very different market and Thisse (1979) to modify the Hotelling segments. De Palma et al. (1985) propose setting by assuming that consumers’ shop- to model consumers’ shopping behavior by ping costs are quadratic in distance. This means of the multinomial logit. In this case, assumption captures the idea that the consumers need not buy from the cheapest marginal cost of time increases with the shop nor from the closest one. Instead, their length of the trip. In this modified version, individual demands are smoothly distributed d’Aspremont and coauthors show that any across firms according to agravity-like rule. price subgame has a unique Nash equi- Let 0 be the degree of dispersion of α > librium in pure strategies. Plugging these consumers’ preferences expressed by the prices into the profit functions, they show standard deviation of the random term (up to that firms now choose to set up at the two a numerical constant), while Main Street has extremities of Main Street. In other words, a unit length by normalization. If consumers’ firms selling a homogeneous good choose to individual choices are independent, then de be separated because geographical separa- Palma et al. have shown the following result. tion relaxes price competition. In the 1980s and 1990s, a great many THE GEOGRAPHICAL CLUSTERING papers in industrial organization revisited OF FIRMS. If 2t, then at the Nash α ≥ this setup. The main message is simple: the equilibrium of the simultaneous game with market center is the most attractive place if n 2, firms colocate at y ∗ 1 2 and price ≥ = / the duopolists sell goods that are sufficiently at p ∗ c n (n 1). = + α / − differentiated in vertical or horizontal attributes. When travel costs are low, geographi- In other words, when the preference cal isolation is no longer a protection against for variety is sufficiently strong ( is high α 586 Journal of Economic Literature, Vol. LVII (September 2019) enough) and or travel costs are sufficiently 2.5 Which Modeling Strategy to Choose? / low (t is small enough), firms locate at the market center and price above marginal cost. If the aim is to avoid the consequences of But what happens when travel costs the spatial impossibility theorem and the pit- are not low enough for 2t to hold? falls of spatial competition models, one has α ≥ Osawa, Akamatsu, and Takayama (2017) to appeal to monopolistic competition or to have recently revisited Hotelling’s model perfect competition with spatial externali- by assuming a finite number of equidistant ties. Although there is nothing that prevents locations along a circle and a continuum of our using either modeling approach accord- firms selling differentiated varieties. When ing to the issue at hand, we find it reason- firms sell their varieties at the same price, able to assert that the choice of a particular firms are evenly distributed across locations modeling strategy depends on the spatial when t is large. As t steadily decreases, firms scale under consideration. Since their extent get agglomerated in a decreasing number is often geographically limited, business and of commercial districts whose size rises. consumption externalities are mainly relevant Eventually, when t becomes sufficiently when studying issues arising on a local scale, small, all firms are agglomerated. We will like in a city. This is why urban economics see in the next section that several mod- assumes perfect competition and abides by els in regional economics lead to a similar technological externalities (section 4). The prediction. advantage of using externalities is that they Spatial competition models deliver an are consistent with perfect competition and important message: close competitors mat- constant returns, which implies zero equilib- ter more to a firm than distant competitors. rium profits. When the focus is on issues aris- These models are also appealing because ing on a global scale, spillovers are likely to they are well suited for studying several be absent. In this context, regional economics facets of competition in space. Since firms relies on the combination of internal increas- are indivisible and strive to expand their ing returns and monopolistic competition to market share by getting closer to consum- capture the pecuniary externalities generated ers, thereby reducing shopping costs, they by the mobility of production factors (see encapsulate the fundamental trade-off of section 3). Under internal increasing returns, spatial economics. Unfortunately, spatial the zero-profit condition of monopolistic competition models rely on fairly specific competition implies that all firms’ revenues assumptions and are developed in partial are paid to production factors. equilibrium settings. When they are gen- eralized or cast in a general equilibrium 3. The Regional Question framework, they very quickly become difficult to deal with. In particular, showing the The welfare of people is equally affected existence of a Nash equilibrium turns out to by the mobility of commodities and produc- be very problematic. Despite these limits, tion factors. A shock in transport or trade spatial models have proven to be a powerful costs affects firms’ and consumers’ locational tool in empirical works devoted to the retail choices. It is, therefore, crucial to have a good sector (see Aguirregabiria and Suzuki 2016 understanding of how these agents react— for a survey).1 moving to other places or staying put—to

1 Spatial competition models are also the backbone political science, pioneered by Downs (1957) who built on of the political science theory of party competition in Hotelling (1929). Proost and Thisse: What Can Be Learned from Spatial Economics? 587 assess the full impact of trade and transport competition rules out strategic interactions policies. In this section, we first discuss how by considering a large number (i.e., a con- the interregional distribution of activities tinuum) of firms producing a differentiated varies with transport costs and with a few manufactured good or tradable service. Each other forces that have not received much variety is produced by a single firm and each attention. We build on the home market firm produces a single variety using a fixed effect and the core–periphery model. Next, and constant marginal requirement of labor. we analyze how the benefits and costs of new The mass of firms is determined by free interregional transport infrastructures can entry and each firm has a unique address. If be assessed once it is recognized that firms a variety is moved from A to B and if one and workers are geographically mobile. unit of this variety must arrive at the destination, 1 units must be sent from A to B. τ > 3.1 What Drives Regional Disparities? The case in which 1 amounts to admit- τ = ting that transport costs are zero. The level Standard theories predict a market out- of transport cost is defined by the missing come in which production factors receive share 1 having melted on the way multi- τ − the same reward regardless of where they plied by the price of the variety prevailing in operate. When each region is endowed with A. Hence, a higher value of implies higher τ the same well-behaved production function, transport costs. This ingenious modeling capital (for example) responds to market dis- trick, proposed by Samuelson (1954) and equilibrium by moving from regions where called the iceberg transport cost, allows the capital is abundant and receives a lower integration of positive shipping costs without return toward regions where it is scarce and having to deal explicitly with a transport sec- receives a higher return. If the price of con- tor. Nevertheless, we will see in section 3.5 sumption goods were the same everywhere that using the iceberg cost is not an innocu- (perhaps because obstacles to trade have ous assumption. been abolished), the marginal productivity 3.1.1 The Home Market Effect of both labor and capital, hence the equilibrium wages and capital returns, would also Consider an economy formed by two be the same everywhere due to the equaliza- regions, A and B, K units of capital, and L tion of capital–labor ratios. units of labor. Each individual owns one unit However, we are far from seeing such a of labor and K L units of capital. Labor is / platonic world. To solve this contradiction, spatially immobile; region A’s population Krugman (1980, 1991) takes a radical depar- share is equal to 1 2. Capital is mobile θ > / ture from the standard setting by assuming between regions, and capital owners seek the that the main reason for the uneven devel- highest rate of return; the share of capital λ opment of regions is that firms operate invested in A is endogenous. Labor markets under imperfect competition and increasing are local and perfect. returns. This has been accomplished by com- In this setup, the interregional distribu- bining the Dixit and Stiglitz (1977) constant tion of firms is governed by two forces pull- elasticity of substitution (CES) model of ing in opposite directions: the agglomeration monopolistic competition and iceberg trans- force is generated by firms’ desire for market port technology. Consumers are identical and access, which allows them to better exploit have a preference for variety expressed by a scale economies and to save on transport CES utility function. Unlike spatial compe- costs, while the dispersion force is generated tition models discussed above, monopolistic by firms’ desire to avoid competition in the 588 Journal of Economic Literature, Vol. LVII (September 2019) product and labor markets (Krugman 1980; the smaller region (Nocke 2006). The spatial Fujita, Krugman, and Venables 1999; and selection of firms thus leads to a productiv- Baldwin et al. 2003). This adds competition to ity gap between regions. Furthermore, the the fundamental trade-off of spatial econom- HME still holds, which means that some ics (discussed in section 2), and this becomes high-cost firms choose to locate in the larger the proximity–competition trade-off. The region with the more productive firms solution to this trade-off is not straightfor- (Okubo, Picard, and Thisse 2010). Using ward. Indeed, by changing their investment US data on the concrete industry, Syverson locations, capital owners affect the intensity (2004) observes that inefficient firms barely of competition within each region. This ren- survive in large competitive markets, but the ders the penetration of imported varieties magnitude of this effect remains controver- easier or more difficult, which in turn affects sial (Combes et al. 2012). the operating profits made in each market. Since the aim of the above contributions is Since operating profits are redistributed to to isolate the impact of market size on firms’ capital owners, their investment decisions, locations, it is assumed that wages are equal hence their income, also affect the spatial across regions, although relative wages vary distribution of demand, which influences the with the level of transport costs. As firms location of firms. congregate in the larger region, competition This push-and-pull system reaches equi- in the local labor market intensifies, which librium when the capital return is the same should lead to a wage hike in A. Since con- in both regions. The upshot is that the larger sumers in region A enjoy higher incomes, region hosts a more-than-proportionate local demand for the good rises and this share of firms because that region can pro- should make this region more attractive to duce at a lower average cost and supply a firms located in B. However, this wage hike bigger pool of consumers. However, the generates a new dispersion force, which intensity of competition in the larger region lies at the heart of many debates regarding keeps some firms in the smaller region. Due the deindustrialization of developed coun- to its size advantage, the larger region not tries, i.e., their high labor costs. Takahashi, surprisingly attracts more firms than the Takatsuka, and Zeng (2013) have shown in a smaller one. What is less expected is that the full-fledged general equilibrium model that initial size advantage is magnified, that is, the the equilibrium wage in region A is greater equilibrium share of firms exceeds . Since than the equilibrium wage in region B. λ θ ( ) K 0, capital flows from the region Furthermore, the HME still holds. In other λ − θ > where it is scarce to the region where it is words, though the wage paid in the larger abundant. This result has been coined the region is higher, market access remains crit- home market effect (HME). ical when determining the location of firms. It is well documented that firms differ in How does lowering interregional trans- productivity (see Bernard et al. 2007 for a port costs affect the HME? At first glance, survey). Importantly, the HME may be gen- the proximity of large markets should matter eralized to heterogeneous firms, which are less to firms when transport costs are lower. sorted across spatially separated markets by In fact, the opposite holds true: more firms decreasing productivity. While the low-cost choose to set up in the larger region when it firm can afford more competition in the becomes cheaper to ship goods between the larger region, high-cost firms seek protec- two regions. This somewhat paradoxical result tion against the devastating effects of com- can be understood as follows. Lower transport petition from efficient firms by locating in costs make exporting to the smaller market Proost and Thisse: What Can Be Learned from Spatial Economics? 589 easier, but lower transport costs also reduce positive correlation between the economic the advantages associated with geographical performance of territories and their market isolation in the smaller region where there potential, defined as the sum of local GDPs is less competition. These two effects push or employment discounted by distance. toward more agglomeration, implying that Redding and Sturm (2008) use the separa- the smaller region becomes deindustrialized tion of East and West Germany between to the benefit of the larger one. The HME is 1949 and 1990 as a natural experiment to thus prone to having unexpected implications study how the loss of market access for cities for transport policy: by making the haulage in West Germany located close to the bor- of goods cheaper in both directions, the con- der affected these cities’ growth. They find struction of new transport infrastructure may that, in the period 1949–90, the population lead firms to pull out of the smaller region. growth of West German cities situated close This result may come as a surprise to those to the border with East Germany was much who forget that highways run both ways. lower than in cities further from this border. Unfortunately, the HME cannot be read- This is clear evidence of a market size effect. ily extended to multiregional setups because After a careful review, Redding (2013) con- there is no obvious benchmark against cludes that “there is not only an association which to measure the “more than propor- but also a causal relationship between mar- tionate” share of firms (Behrens et al. 2009; ket access and the spatial distribution of Matsuyama 2017). The new fundamental economic activity.” However, care is needed ingredient that a multiregional setting brings because the market potential used in most is that the accessibility to spatially dispersed empirical studies is a crude approximation markets varies across regions. When there of a region’s attractiveness (Head and Mayer are only two regions, the overall impact can 2004). be captured through the sole variation in the The HME explains why large markets cost of trading goods between them. By con- attract firms. However, this effect does not trast, when there are more than two regions, explain why some markets are bigger than any global or local change in the transport others. The problem may be tackled from network is likely to trigger complex effects two different perspectives. First, workers that vary in nontrivial ways with the structure migrate from one region to the other, thus and shape of the transportation network, as leading to some regions being larger than we will see in section 3.5. others. Second, the internal fabric of each Given this caveat, it is no surprise that region determines the circumstances in the empirical evidence regarding the HME which a region accommodates the larger is mixed (Davis and Weinstein 1999, 2003; number of firms. In what follows, we con- Head and Mayer 2004; Hanson 2005; sider the former approach; the latter is dis- Costinot et al. 2019). Intuitively, however, cussed in section 5. it is reasonable to expect the forces high- 3.1.2 Can a Core–Periphery Structure Be a lighted by the HME to be at work in many Stable Equilibrium Outcome? real-world situations. Yet, how can this be checked? Although it is hard to test the One of the most natural ways to think of HME because prices are unobservable, a agglomeration is to start with a symmetric wealth of evidence suggests that market and stable world and to consider the emer- access is correlated to the level of activities. gence of agglomeration as the outcome of a Starting with Redding and Venables (2004), symmetry-breaking mechanism. The result- various empirical studies have confirmed the ing asymmetric distribution involves spikes 590 Journal of Economic Literature, Vol. LVII (September 2019) that can then be interpreted as spatial clus- spatially immobile and evenly distributed ters. It was not until Krugman (1991) that a between the two regions. As a consequence, full-fledged general equilibrium mechanism their demand for the manufactured good is was proposed. More specifically, Krugman rooted in the region where they live. When identified a set of conditions for a symmet- the agricultural good can be traded at no cost, ric distribution of firms and households the equalization of earnings between regions between two regions to become an unsta- allows farmers to have the same demand ble equilibrium in a world that otherwise functions for the manufactured good. The remains symmetric. resulting dispersion of demand prompts The workhorse of the core–periphery (CP) manufacturers to choose different locations model is again the Dixit–Stiglitz iceberg because they enjoy a proximity advantage in model. What distinguishes the CP model from supplying the local farmers. the HME is that workers are now spatially At first sight, when workers are mobile, mobile. The difference in the consequences the following two effects should lead to the of capital and labor mobility is the starting agglomeration of the manufacturing sector point for Krugman’s paper that dwells on in one region. First, when a region is bigger, pecuniary externalities. When workers move the HME implies that this region hosts a to a new region, they bring with them both more than proportionate share of manufac- their production and consumption capabili- turing firms, which pushes nominal wages ties. More specifically, workers produce in the up. Second, the presence of more firms region where they settle, just as capital does, means a wider range of local varieties and, but they also spend their income there, which for that reason, a lower local price index—a is not generally the case with capital owners. cost-of-living effect. Accordingly, the real Hence, the migration of workers, because it wage increases and the bigger region sparks a shift in both production and con- attracts additional workers. The combina- sumption capacities, modifies the relative tion of these two effects gives rise to a pro- size of the labor and product markets in the cess of cumulative causality, which fosters origin and destination regions. These effects the agglomeration of firms and workers in have the nature of pecuniary externalities one region—the core—while the other one because they are mediated by the market, but becomes the periphery. migrants do not take them into account when Even though this process seems to gener- making their decisions because the impact of ate a “snowball” effect, it is not clear that it each migrant is negligible. Such effects are always develops according to the foregoing of particular importance in imperfectly com- prediction. The above argument ignores sev- petitive markets, since prices fail to reflect eral key impacts of migration on the labor the true social value of individual decisions. market. The increased supply of labor in the Hence, studying the full impact of migration region of destination tends to push nominal requires a general equilibrium framework, wages down. In addition, the increase in local which captures not only the interactions demand for tradable goods leads to a higher between the product and the labor markets, demand for labor, but the increased compe- but also the double role played by individuals tition in the product market tends to reduce as both workers and consumers. firms’ profits, hence wages. The final impact Krugman (1991) adds a genuine disper- on nominal wages is thus hard to predict. sion force to the baseline model by consider- Furthermore, when firms are concentrated ing a second sector, called agriculture, which in the core, sales in the periphery decrease. employs a second type of labor. Farmers are A priori, the combination of all these effects Proost and Thisse: What Can Be Learned from Spatial Economics? 591 may spark a “snowball meltdown,” which some places to build a comparative advan- may result in the spatial dispersion of firms tage by making them bigger than others. and workers. When agents are mobile, supply and The timing of events is as follows. First, demand schedules are shifted up and down workers choose their locations. Second, in complex ways by workers’ relocation. given the interregional population distribu- It is no surprise, therefore, that coming tion, production takes place. Turning to the up with a full analytical solution of the CP specific conditions for agglomeration or dis- model should be impossible. This is what persion to arise, the level of transport costs led Krugman to resort to numerical anal- turns out to be the key parameter. On the ysis. Subsequent developments have con- one hand, if transport costs are sufficiently firmed Krugman’s results, but it has taken high, the interregional shipment of goods is quite some time to prove them all. The discouraged, which strengthens the disper- formal stability analysis was developed in sion force. The economy then displays a dis- Fujita, Krugman, and Venables (1999), but persed pattern of production in which firms it was not until Robert-Nicoud (2005) that a focus mainly on local markets. On the other detailed study of the correspondence of spa- hand, if transport costs are sufficiently low, tial equilibria was provided. then firms concentrate in the core. In this Krugman’s paper triggered a huge flow of way, firms can exploit increasing returns by research, but the quality of this research is selling more in the growing region without unequal. In what follows, we briefly discuss a losing much business in the smaller region. few shortcomings of the CP model. The mobility of labor may exacerbate the HME, since the size of local markets changes (i) The CP model explains why agglom- with labor migration. The CP model, there- eration arises, but does not predict fore, allows for the possibility of conver- where this happens. Indeed, when gence or divergence between regions. In transport costs are sufficiently low, particular, regions that were once very sim- the manufacturing sector may con- ilar may become very dissimilar. Krugman’s centrate in region A or in region B. A work appealed because regional disparities natural way to cope with this problem emerge as a stable equilibrium, which is is to endow one region with a com- the unintentional consequence of decisions parative advantage. When the num- made by a large number of economic agents ber of A-farmers, say, exceeds that of pursuing their own interests. B-farmers, Sidorov and Zhelobodko To sum up, we have the following result. (2013) show that the interval of -values sustaining agglomeration in τ THE CORE–PERIPHERY STRUCTURE: region A is always wider than that Assume that workers are mobile. When associated with region B. When the transport costs are sufficiently low, the man- number of A-farmers is sufficiently ufacturing, or tradable service, sector is high, regardless of the transport cost agglomerated in a single region. Otherwise, level, there exists a unique equilib- this sector is evenly dispersed between the rium, which is such that all firms two regions. set up in region A. This shows how a comparative advantage biases the The main message of Krugman’s contri- market in favor of one region, with- bution is clear: in the presence of increas- out necessarily excluding the other ing returns, lowering transport costs allows region as a nest of the manufacturing 592 Journal of Economic Literature, Vol. LVII (September 2019)

sector. In a remarkable paper, Davis In addition, workers’ attachment to and Weinstein (2002) document the their region of origin acts as a strong resilience of urban agglomerations in dispersion force. When markets are Japan. After the massive bombing of sufficiently integrated for the real Japanese cities in World War II, a city income gap to fall below the utility typically recovered the population loss generated by homesickness, the and share of manufacturing that it agglomeration process is reversed. In had before the war. Even Hiroshima this case, market integration fosters and Nagasaki returned to their pre- first divergence and then conver- war growth trends after twenty-five gence; in other words, the economy years. develops according to the so-called Nevertheless, however small a bell-shaped curve of spatial develop- region’s size advantage is, the CP ment (Tabuchi and Thisse 2002). This model suggests that this region shows that assuming heterogeneous becomes the core when the snowball or homogeneous workers may lead to effect is at work. Instead of compar- much contrasted results. ative advantage, history would act as a selection device among different (iii) The welfare analysis of the CP model, equilibria. For example, transport despite its simplicity, delivers an technologies used in the nineteenth ambiguous message. Since competi- century led particular sites in the tion is imperfect, the equilibrium is United States to form “portage cities,” suboptimal. However, the inefficiency i.e., sites where a boat or its cargo was of the market outcome does not tell us carried over land between navigable anything about the excessive or insuf- waterways. Bleakley and Lin (2012a) ficient concentration of firms and find that these cities have mostly people in big regions. Neither config- retained their economic importance uration (agglomeration or dispersion) despite the disappearance of their Pareto dominates the other: under original advantage. In sum, geogra- the CP structure, workers living on phy and history interact in complex the periphery always prefer disper- ways to determine the location of sion since they have to import all vari- activities. eties, whereas those living in the core always prefer agglomeration since (ii) The sudden, discontinuous shift from all varieties are locally produced. In dispersion to agglomeration is the other words, market integration gen- result of assuming that workers are erates both welfare gains and welfare homogeneous and all react in the losses through the geographical redis- same way to marginal variations in tribution of activities. real wages, very much as consumers react to a marginal price under- Workers and farmers in the region that cutting in the Bertrand duopoly. attracts the core have a higher welfare than Once one recognizes that individu- the farmers in the region that becomes als have different attitudes toward the periphery. Therefore, one may use the non-monetary attributes associ- compensation mechanisms to evaluate the ated with migration, the agglomera- social desirability of a move, using market tion process is gradual and sluggish. prices and equilibrium wages to compute Proost and Thisse: What Can Be Learned from Spatial Economics? 593 the compensation to be paid either by those (1995). Their idea is beautifully simple and who gain from the move or by those who suggestive: the agglomeration of the final are hurt by it (Charlot et al. 2006). When sector in a particular region occurs because transport costs become sufficiently low, the of the concentration of the intermediate winners can compensate the losers so that industry in the same region, and vice versa. they sustain the utility level they enjoyed Assume that many firms belonging to the final under dispersion. This is because firms’ sector are concentrated in one region. The efficiency gains are high enough to offset high demand for intermediate goods in this the losses incurred by peripheral workers. region attracts producers of these interme- In this case, regional disparities are the geo- diate goods. In turn, the intermediate goods graphical counterpart of greater efficiency. are supplied at a lower cost in the core region, However, when transport costs take on which prompts even more final-goods firms intermediate values, no clear recommenda- to move to the core. Such a cumulative caution emerges. This lack of clear-cut results, sality process feeds on itself, so the resulting even in a simple setting such as Krugman’s, agglomeration can be explained solely by may explain why so many contrasting views the demand for intermediate goods, without exist in a domain where there is good rea- resorting to labor mobility as in Krugman’s son to believe that the underlying tenets are setting. correct. Giving intermediate goods a prominent role is a clear departure from the CP model 3.2 The Evolution of Regional Disparities: and allows one to focus on other forces at Alternative Approaches work in modern economies. To this end, note What do the implications of the CP model that once workers are immobile, a higher con- become when they are studied within alter- centration of firms within a region translates native settings? into a hike in wages for this region. This gives rise to two opposite forces. On the one hand, 3.2.1 Input–Output Linkages final demand in the core region increases Moving beyond the Krugman model to because consumers enjoy higher incomes. As search for alternative explanations appears in Krugman, final demand is an agglomeration warranted in order to understand the emer- force; however, it is no longer sparked by an gence of large industrial regions in econo- increase in population size, but by an increase mies, which are characterized by a low labor in income. On the other hand, an increase spatial mobility. In this respect, a major in the wage level generates a new dispersion shortcoming of the CP model is that it over- force, which lies at the heart of many debates looks the importance of intermediate goods. regarding the deindustrialization of developed Yet, the demand for consumer goods does countries, i.e., their high labor costs. In such not account for a high percentage of firms’ a context, firms are led to relocate their activi- sales, often overshadowed by the demand ties to the periphery where lower wages more for intermediate goods. Therefore, when than offset lower demand. Hence, as trans- making location choices, it makes sense port costs fall, there is first agglomeration and for intermediate-goods producers to care then dispersion of production. In sum, eco- about the places where final goods are pro- nomic integration should yield a bell-shaped duced. Similarly, final-goods producers are curve of spatial development, which describes likely to pay close attention to the location a rise in regional disparities in the early stages of intermediate-goods suppliers. This is the of the development process and a fall in the starting point of Krugman and Venables later stages. 594 Journal of Economic Literature, Vol. LVII (September 2019)

3.2.2 The Acquisition of Skills also experienced spectacular productivity gains. This situation has led Tabuchi, Thisse, In the CP model, farmers cannot acquire and Zhu (2018) to reformulate the CP model the skills that would allow them to find jobs by focusing on technological progress in the in the manufacturing sector. However, a manufacturing sector. In addition, these mechanism similar to that in the CP model authors recognize that workers are imper- is at work when immobile individuals may fectly mobile. Migration costs act here as invest in education. To show how this mech- the main dispersion force. In the CP model, anism works, consider a setting in which the since prices and nominal wages converge as manufacturing sector uses both capital and transport costs fall, the real wage gap, hence skilled labor; capital is mobile while labor the incentive to move, shrinks. What drives is immobile. If a few firms move away from Krugman’s result is the change in the sign their region, the unskilled workers resid- of the real wage differential when transport ing in the destination region have a higher costs fall below a given threshold. By con- incentive to be trained. The pool of skilled trast, in the paper by Tabuchi and coauthors workers thus grows, which attracts more when one region is slightly bigger than the firms. The higher income that accrues to the other, technological progress in manufac- newly skilled shifts the demand for the final turing reduces the labor marginal (respec- product upward. Consequently, the region tively, fixed) requirement in the two regions, becomes more attractive for the manufac- making the larger region more attractive by turing firms, which in turn results in even increasing wages and decreasing the prices more workers acquiring the skills needed of existing varieties (respectively, by increas- to be hired by the newly established firms. ing wages and the number of varieties) Once more, although all workers stay put, therein. Workers move to the larger region the process of cumulative causality sustains when productivity gains are strong enough a snowball effect that involves a growing to make the utility differential greater than concentration of firms and skills where spa- their mobility costs. Therefore, technological tial mobility is replaced by sectoral mobility progress tends to exacerbate the difference through training. As in the CP model, the between the two regions and thus raises the manufacturing sector is dispersed when incentive to move from the smaller to the transportation costs are high and agglom- larger region. In short, technological prog- erated when these costs are sufficiently low ress in manufacturing favors agglomeration. (Toulemonde 2006). This result points to Since innovations often require skilled one of the main reasons for the existence of workers who are more mobile than unskilled spatial inequality: the uneven distribution of workers, Tabuchi and coauthors show that human capital, an issue that we will encoun- the core is likely to host the most skilled ter again in section 4. workers. This sheds light on the following important question: is a higher interregional 3.2.3 Technological Progress in labor mobility the right way in which to Manufacturing lessen regional disparities? Not necessarily. The standard pro-migration argument The foregoing models focus exclusively on heavily relies on the assumption that work- falling transport costs. There is no doubt that ers are homogeneous. However, people are the transport sector has benefited from huge not homogeneous: migrants are often the productivity gains over the last two centu- top-talent and most entrepreneurial indi- ries. However, numerous other sectors have viduals of their region. When the lagging Proost and Thisse: What Can Be Learned from Spatial Economics? 595 region loses its best workers, those who are However, full agglomeration (full dispersion) left behind will be worse off. In this case, arises only for very low (very high) values of interregional income and welfare gaps are transport costs. In between these two polar increasingly caused by differences in the cases, the space-economy displays richer geographical distribution of skills and human patterns in which the manufacturing sector capital. For example, the spatial distribution is concentrated in a relatively small or rela- of human capital explains about 50 percent tively large number of regions. of regional disparities in France (Combes, Equally important, during the agglomera- Duranton, and Gobillon 2008). We will tion process, some regions decline from the return to this issue in sections 4.1 and 5.1. beginning of the market integration process. By contrast, some other regions first attract 3.3 Beyond the Two-Region Setting firms and workers over a wide range of values of transport costs before declining. In 3.3.1 The Racetrack Economy other words, a region may first benefit from The dimensionality problem mentioned in decreasing transport costs and then lose firms the study of the HME also occurs in the CP and population later on. To put it bluntly, the model. Full agglomeration in a two-region winners and losers of market integration vary setting does not necessarily mean that the with the degree of integration within the manufacturing sector is concentrated in a economy. single region when the economy is multi- 3.3.2 The Continuum of Locations regional. Akamatsu, Takayama, and Ikeda (2012) and Ikeda, Akamatsu, and Kono Another solution to the dimensionality (2012) have studied the case of a racetrack problem is the use of an infinite number economy where workers and firms are ini- of locations in a seamless world, which is tially located in 2 n regions equidistantly the representation used by von Thünen, distributed around a circle ; farmers are Hotelling, or Beckmann. The real line is the  uniformly spread along . Transport costs simplest possible homogeneous space on  between any two regions thus vary with these which spatial patterns that display more or regions’ relative positions on . Starting from less specialized and agglomerated regions  a transport cost value that is large enough for may emerge. In a two-region, two-sector the even distribution of the manufacturing setting, regional specialization and spatial sector among the 2 n regions to be a stable concentration do move together. However, equilibrium, a gradual decrease in transport working with an infinite space comes at the costs leads to a pattern in which workers and cost of models that are technically difficult n 1 firms are partially agglomerated in 2 − alter- to solve. nate regions. As these costs steadily decrease, To the best of our knowledge, the CP model displays a sequence of bifurca- Rossi-Hansberg (2005) is the first attempt tions in which the number of manufacturing made to reconcile a large number of regions is reduced by half and the spacing locations, positive transport costs, and between each pair of neighboring manufac- agglomeration and dispersion forces within turing regions doubles after each bifurcation an integrated setup. Locations are ordered until the manufacturing sector is agglom- along the interval X [0, 1] and a region = erated into a single region. Therefore, the is a connected subset of X . There are two process of agglomeration described in the sectors, the final and the intermediate, each CP model remains valid in the case of sev- of which produces a homogeneous good; eral regions distributed over a circular space. and two primary inputs, land and labor. 596 Journal of Economic Literature, Vol. LVII (September 2019)

Rossi-Hansberg assumes that intermediate Loosely speaking, lower transport costs and final producers operate under perfect increase the specialization of regions and competition, constant returns, and intrain- the geographical dispersion of industries. dustry externalities that decay exponentially These results are to be contrasted with with distance. Final-good firms need the those obtained by Krugman and Venables intermediate good and intermediate-good (1995), where declining transport costs first firms receive final goods in return to pay for foster agglomeration and specialization and labor and land. Labor is perfectly mobile then lead to dispersion. The main reason for across space and between sectors. Whereas this difference in results lies in competition firms consume land, consumers do not. The for land between firms, which is a strong dispersion force thus stems from competi- dispersion force (see section 4). tion for land between final and intermediate 3.4 Where Do We Stand? good producers. Working with a continuum of locations ren- Technological progress in manufactur- ders market-clearing conditions nontrivial. ing and or transport tends to foster the / For example, the law of motion of a good may agglomeration of economic activities. All be described as follows: when there is trade approaches appeal to cumulative causality, between two locations, an intermediate loca- which thus seems to be the main driver of tion x X may be viewed as importing the regional disparities. On the other hand, by ∈ shipment arriving from [0, x), adding exports ignoring the fact that the agglomeration of or subtracting imports at x , and shipping the activities usually materializes in the form resulting volume away from x toward (x, 1]. of cities, regional economics overlooks In equilibrium, the excess supply of this the various costs typically generated by good at x 0 and x 1 must be equal to the geographical concentration of activi- = = zero. In such an environment, the price of a ties. However, accounting for these costs good at x depends on how much of the good may have a significant impact on the con- is traded and lost over the whole pattern of clusions drawn from the CP model. More trade, which is determined through the loca- specifically, Helpman (1998) has argued tions of all firms, which in turn depend on that decreasing freight costs could trigger the interplay between transport costs and the dispersion, rather than the agglomer- spillover effects. ation, of economic activities when the dis- If transport costs are very high, persion force stems from a given stock of Rossi-Hansberg (2005) shows that there is housing rather than from immobile farm- no trade. Thus, each location is an autarky ers. In this case, housing competition puts hosting both types of firms. However, when a brake on the agglomeration process, and transport costs decrease, more regions are thus Krugman’s prediction is reversed. The involved in trade relations and regional difference in results is easy to understand. specialization increases. In particular, if Housing prices rise when workers move to shipping the intermediate good gets the larger region, which strengthens the cheaper, it is less profitable to produce dispersion force. Simultaneously, cheaper this good close to final producers, while transport facilitates trade. Combining these a growing specialization allows firms to two forces shows how dispersion arises benefit from stronger spatial externalities. when transport costs steadily decrease. Furthermore, the final and or intermedi- Anticipating what we will see in section 4, / ate sector is spatially concentrated in a sin- lowering the transport costs of goods acts gle region when transport costs go to zero. against the gathering of consumers within Proost and Thisse: What Can Be Learned from Spatial Economics? 597 the same city region because the lower connect some of them, we study a / transport costs ease the various conges- firm’s plant that sources inputs and tion costs for the consumer that are asso- ships outputs to some nodes on ciated with the workings of a city (see the network. When quantities and Rossi-Hansberg 2005 for a different, but prices are treated parametrically, the related, mechanism). Hence, what is going profit-maximizing location problem on within and between regions is key to simplifies to minimizing total trans- understanding the regional question. So far, port costs. Transport rates weakly the most robust conclusion is that lowering decrease with distance because transport costs fosters agglomeration as in of the fixed costs of loading and Krugman, then leads to redispersion as in unloading that are minimized at the Helpman (Tabuchi 1998, Puga 1999, Fujita nodes. In this case, the optimal site and Thisse 2013). is a node in the network (Hurter and Martinich 1989). In other words, 3.5 Does Transportation Matter for the the set of all possible locations along Interregional Economy? roads reduces to the subset of nodes, The supply of transport infrastructure is i.e., a market town, a resource town, often presented as the panacea to reduce a crossroad. By assigning different regional disparities. In this section, we take a degrees of centrality to particular step-wise approach to this difficult question. nodes of a transportation network, After an illustration of the role of transport net- the new link may favor some nodes works in the location of economic activity, we at the expense of others, which define transport costs more carefully, as trans- may induce the relocation of some portation economics brings a few surprises firms. for regional economists. The next step is to identify the main methodological challenges (ii) Consider a simple spatial competition in estimating the effects of transportation setting with two firms located respec- infrastructure on economic activities. We will tively at x 0 and x 1 that com- = = discuss two types of approaches: a structural pete in delivered prices instead of equation approach derived from spatial gen- mill prices, as in section 2.4. Firms 1 eral equilibrium models and a reduced-form and 2 produce the same good at con- approach. Both help to determine the relative stant marginal costs such that c t 2 − importance of the many economic mecha- c c t. A simple, Bertrand-like < 1 < 2 + nisms at work. In the final step, we turn our argument shows that, in equilib- attention to the political economy question: is rium, each firm supplies the market there evidence that the money spent on trans- segment in which it has the lower port infrastructure is invested wisely? delivery cost. Therefore, the bound- ary between the two market areas 3.5.1 Transport Networks: What Is Their is located at x (c c t) 2t. m = 2 − 1 + / Impact? When a highway connecting x 0 = and b x is built, the transport 1 > m We consider three different, but equally rate decreases to t t over [0, b ], ̅ < 1 strong, arguments. but remains equal to t over ( b1 , 1]. In this case, the more efficient firm (i) Given a transport network defined by supplies a wider range of customers a set of nodes and a set of links that because the highway allows this firm 598 Journal of Economic Literature, Vol. LVII (September 2019)

to be more aggressive on [ xm , b2 ]. What are the main transport issues that Hence, the highway triggers a shift of interest spatial economists? There are at customers from the inefficient to the least two. First, regional economic models efficient firm. Assume now that the have the merit of showing that the perfor- highway connects b x and x 1. mance of the transport sector affects the 2 < m = Firm 2 now invades firm1 ’s market economy in many ways. Hence, what hap- area, which implies a shift of cus- pens in this sector should have an impact tomers from the efficient toward the on the space-economy. Having said that, it inefficient firm. In sum, the effect is remarkable that spatial and transportation of a regional highway varies with economics have developed in a rather the way it connects firms, while the unconnected way. Second, there seems to spatial distribution of firms’ out- be a chicken-and-egg problem that gen- puts depends on the industry’s cost erates endless debates in the media and conditions. in academic journals: does the construction of new transport infrastructure foster (iii) Transport infrastructure was built in regional growth, or is this infrastructure East and West Africa to allow for- built because the corresponding regions are mer colonies to export their mineral developing fast? The first question is signifi- resources to developed countries cantly related to what is meant by transport overseas. Bonfatti and Poelhekke costs and how they are modeled and mea- (2017) show that coastal countries sured. Since storage and transport are, to endowed with mines import relatively a certain extent, substitutes, what matters more from overseas and relatively less for firms is the level oflogistics costs, which from neighbors than do landlocked account for both types of costs. Freight countries with mines because the lat- costs have received the most attention up to ter needed to be connected to their now, but we should keep in mind that trade neighbors to export overseas. This in services accounts for one-third of world suggests that the transport networks exports and even more for intranational designed during the colonial period trade. Trade in services calls upon very dif- still shape the intensity and nature of ferent transport and communication chan- trade flows in Africa (see also Jedwab nels: it can be based on electronic delivery, and Moradi 2016). In short, transport but it also consists of services supplied networks built long ago may have a between branches of a large firm. As for the lasting effect on the current location second question, it strikes us as mainly an of activities. empirical issue that has major policy implications, since the construction of a new With all this in mind, it is hard to believe transport infrastructure is often presented that transport networks do not matter for as the remedy to local backwardness. the organization of the space-economy. 3.5.2 Defining Interregional Transport As transport geographers have long Costs argued (see, e.g., Thomas 2002), the spatial distribution of activities depends on The trade and spatial economics literature the structure of the transport network recognizes the existence of various types of through the relative values of freight spatial frictions, but often assumes that an costs along the shortest routes connecting iceberg transport cost is sufficient to reflect locations. the impact of these frictions. When the Proost and Thisse: What Can Be Learned from Spatial Economics? 599 iceberg cost is added to the CES isoelastic For example, Behrens et al. (2007) revis- demand functions, it is only the level of the ited the CP model in which each country is demand functions that matters, not its elas- formed by two regions. These authors show ticity. The question we investigate here is the that the welfare impact of trade liberaliza- relevance of the iceberg cost assumption in tion depends on the internal geography of modeling the impact of the transport sector the two countries. Accounting for density on the space-economy. economies renders the two internal geog- To the best of our knowledge, the ice- raphies interdependent. Indeed, the orga- berg cost has never been used in transpor- nization of activities within each country tation economics. The simplest setup in the affects the volume of trade, which in turn literature assumes that freight costs for a changes the level of transport costs, and given value of the load are described by the hence the distribution of activities within lower envelope of several affine cost func- each country. In particular, the transport tions where each function represents the policy of a national government may have freight cost associated with a transport mode. a marked impact on the internal geography The intercept of these lines takes on its low- of its trading partners. This makes a case for est value for trucking and its highest value international cooperation when designing for air transportation, while their slopes may transport policies. vary with the size of the vehicles and the fre- Second, when combined with CES pref- quency of service. This implies endogenous erences, the iceberg cost assumption implies shipping costs. More generally, transporta- that halving the producer price of a good tion economists stress the following effects entails its delivered price being also cut by that are not taken into consideration by the 50 percent. In other words, the pass-through iceberg cost. First, transport modes: one is 100 percent. This conflicts with the theory needs to distinguish among transport modes of spatial pricing where freight absorption since they are differentiated by their market allows for the penetration of remote mar- structure and technology. Second, density kets, as well as with the empirical evidence economies: transport rates decrease with the that suggests an incomplete pass-through size of shipments. Third, distance economies: (e.g., De Loecker et al. 2016). Thus, iceberg freight rates also decrease with the haulage costs cannot capture the richness of the pric- distance. ing patterns adopted by firms. However, the Yet, does not taking these effects into main results discussed in sections 3.1 and account matter to spatial economists? First 3.2. hold true in a setting with linear demand of all, countries trade with themselves more functions and additive transport costs, which than with the rest of the world, while most implies freight absorption (Ottaviano and of the trade and economic geography liter- Thisse 2004). Third, treating freight rates ature assumes that internal transport costs as exogenous amounts to assuming that the are nil. Shipping goods between two loca- transport sector is a perfectly competitive tions within the same country or between black box; recognizing that freight rates are two countries involves different costs. endogenous affects the location of economic Since labor and capital are more mobile activity. Conversely, trade volumes change within than between countries, the same with firms’ locations, which affects the decrease in transport costs is associated freight rates set by oligopolistic carriers. In with different responses in firms’ and work- other words, the location of economic activ- ers’ locations. Somewhat surprisingly, the ity depends on carriers’ behavior, which itself literature devoted to this topic is meager. depends on the way firms and workers are 600 Journal of Economic Literature, Vol. LVII (September 2019) distributed across space (Behrens, Gaigné, while economic geography stresses the and Thisse 2009). Combes and Lafourcade importance of increasing returns in manu- (2005) for France and Winston (2013) for facturing, it sets aside the fact that transpor- the United States showed that deregulation tation features even stronger economies of has been key in the freight rate decrease. scale (Mori 2012). Accounting for the pres- Last, the iceberg cost function can- ence of different types of scale economies in not account for density economies since the transport sector should rank high on the the value of the iceberg transport cost agenda of spatial economists. τij between regions i and j is a constant given a priori. On the other hand, when the num- 3.5.3 Does Transport Infrastructure ber of regions is finite, the iceberg cost Stimulate Regional Economic function can take distance economies into Activity? account, since the values of are cho- τij sen arbitrarily. However, the use of this Redding and Turner (2015) identify two function in continuous location models, as major methodological challenges. The first in Fujita, Krugman, and Venables (1999) is the chicken-and-egg problem, as regions and others is more problematic. When with high transport needs are likely to one unit of a variety is moved from i to j, receive infrastructure. In this case, the con- only a fraction exp ( tD) arrives at desti- struction of a new transport infrastructure − nation, where t 0 measures the inten- is endogenous, rather than exogenous. The > sity of the distance–decay effect and D the second one is the identification of the cre- distance between i and j. Therefore, we ation of new activities in the region where have exp (tD). The unit transport cost the infrastructure is built against the dis- τ ≡ is equal to the price of the good at i times placement of activities from other regions. the quantity lost en route, which is equal to Solving the second problem requires spe- 1 exp (tD) 1. Hence, the continu- cial attention for the relocation mechanisms τ − = − ous iceberg cost function is increasing and that may be at work. Take an infrastructure convex in D. This has an odd implication measure that targets the trade link between that went unnoticed previously: since the A and B. The increase in economic activity marginal transport cost increases with dis- in A can result from a genuine net increase tance, breaking up a trip into several shorter in A, but may also result from a relocation and connected segments over the distance from B to A and or from a relocation from / D is less costly. In other words, using such another region, C, to A. The solution will be a function amounts to assuming that there to estimate simultaneously the effects of the are distance diseconomies. Furthermore, change in the costs of one transport link on as transport costs tend to increase quickly, all the regions. remote markets do not matter that much. It Different approaches are used and their is, therefore, not very surprising that the sim- pros and cons are well known (Holmes ulation of a shock affecting a region is found 2010). There is the general equilibrium to be very localized, e.g. in Hanson (2005). approach, whose advantage is that it can To sum up, gathering all spatial frictions take into account all the direct and indirect generated by trade into a single iceberg effects associated with a new transport infra- trade cost is not an innocuous assumption; structure. For example, a location that is the main reason is that the level of unit trans- not directly affected by new transport infra- port costs is endogenous to the spatial struc- structure can be indirectly affected through ture of the economy. Somewhat ironically, the redistribution of labor associated with Proost and Thisse: What Can Be Learned from Spatial Economics? 601 the decrease in transport costs along some the United States (1870–90), respectively. least-cost routes. This approach has been Railroads in India decreased transport costs developed in the framework of quantitative and increased agricultural output in the con- spatial economics, which we discuss in sec- nected districts by 17 percent. Since rail- tion 5.2, as it spans both regional and urban roads allowed the different regions to exploit economics. the gains from trade, there was also an overall The structural equation approach is also increase in income for India. In a related embedded in general equilibrium, but only way, Donaldson and Hornbeck (2016) aim to a few equations derived from a general quantify the aggregate impact of the US rail- equilibrium setting are estimated. The way on the agricultural sector in 1890. The advantage of this approach, compared with development of the railway system from 1870 the quantitative spatial approach, is that it is to 1890 has increased, directly or indirectly, estimated, rather than calibrated. The behav- the accessibility to a growing number of ioral parameters are specific to the problem American counties, and has affected accord- at hand, including their confidence intervals, ingly the value of agricultural land rent. rather than being borrowed from the litera- More specifically, Donaldson and Hornbeck ture. The disadvantage is that the structural build on Eaton and Kortum (2002) to deter- equation approach is less exhaustive than the mine a market-access reduced-form mea- general equilibrium one. The third approach sure and develop an empirical strategy to is the reduced-form approach, which estimate how a better access to counties requires less data and resources. However, has fostered higher agricultural land rents the causality link is sometimes difficult to therein. They find that removing all rail- assess, so that the main challenge is proba- roads in 1890 decreases the total value of bly constructing the appropriate counter- US agricultural land by 60.2 percent, that factual for the absence of planned transport is, 3.2 percent of US GDP in 1890, which infrastructure. Moreover, the reduced-form suggests again a high return for this invest- approach rules out the possibility of measur- ment. Unlike manufacturing, agriculture is ing welfare effects. a dispersed activity that uses a large amount In what follows, we discuss the results of of land. It is, therefore, not terribly surpris- the structural equation and reduced-form ing that crops located along, or close to, approaches. Papers are diverse and difficult tracks benefited from the construction of to compare, as they test the impact of dif- railroads. ferent transport modes (railways, highways, Berger and Enflo (2017) analyze the effects air transport, and high-speed railway) in dif- of 150 years of railways on urban growth in ferent periods (nineteenth versus twentieth Sweden. They find that the connection to century) for different sectors (agriculture or the railway gave cities a strong increase in manufacturing), as well as in countries having population in the first twenty years. Later reached different levels of economic devel- on, the development of railways was much opment. Since this is an expanding field, we less effective in spurring population growth review only a few of the main papers (see in the connected cities. Urban growth was Redding and Turner 2015 for a more com- then largely due to a relocation effect from prehensive survey). the nonconnected towns to the connected In two rich, meticulous papers, Donaldson towns. As the relative urban growth effect of (2018) and Donaldson and Hornbeck (2016) the initial railroad development shock in the study the effect of the development of rail- nineteenth century was maintained in the roads in colonial India (1870–1930) and twentieth century, there was again evidence 602 Journal of Economic Literature, Vol. LVII (September 2019) for path dependence regarding the impact of decreased that of the in-between regions. transport networks on spatial development. The unconnected regions were less affected. Chandra and Thompson (2000) conduct In other words, trade integration reinforces an analysis of the impact of interstate high- core cities at the expense of intermediate ways on US rural counties between 1969 and regions, which is consistent with the preva- 1993. Because the interstate highways were lence of distance economies in the transport not planned to connect the rural counties, sector and of increasing returns in manufac- the interstate highway can be seen as an turing sectors. exogenous variable. They find that a new Reductions in travel costs also affect the interstate highway increases total earnings in spatial equilibrium through the organiza- the rural counties the highway goes through. tion of firms. Indeed, firms are packets of However, it tends to cause a decline in total functions, such as management, research earnings in adjacent counties. This is mainly and development (R&D), finance, and pro- evidence for new infrastructures causing a duction, which need not be located under relocation effect of economic activity, rather the same roof. Before the emergence of new than a net growth effect. Duranton, Morrow, information and communication devices and and Turner (2014) study the impact of inter- the development of airlines and high-speed city trade effects of highways in the United railways, firms that delivered services to States. They find that highways have a large other regions relied on local representatives, influence on where production takes place. while headquarters of multiplant firms had However, there is no large effect on the local managers to whom they delegated deci- value of production. Thus, highways could sions. Lin (2017) finds that Chinese intercity divert economic activity to depressed areas high-speed railway has led to a significant but would not generate net growth effect. hike in the number of cognitive jobs in con- Storeygard (2016) analyzes the growth nected cities, and Charnoz, Lelarge, and effect of the variation of road transport costs Trevien (2018) use the development of the between the main port cities and 289 hin- high-speed railway network in France to terland cities in sub-Saharan Africa. The oil show how the decrease in passenger travel price increase from $25 in 2002 to $97 in time between headquarters and affiliates 2008 serves as an external shock to transport has allowed management functions to be costs. Storeygard finds an elasticity of−0.28 concentrated in headquarters. Blonigen and between the level of road transport costs and Cristea (2015) use the deregulation of the urban economic activities whose variations aviation sector in the United States to iden- are determined via nighttime light satellite tify the effect of provision of air services on data. However, this elasticity measures only regional growth. They find that the increase the short-run effects of trade flows. in air services has a significant effect on Studies on China are interesting, as there regional growth, with service and retail expe- is both a strong growth in economic activity riencing the strongest growth effects. and an increasing supply of transport infra- As noted previously, we find the conclu- structure. However, results for China may sions that can be drawn from these papers differ from other countries because there difficult to compare. The papers differ not are still restrictions on labor mobility. Faber only by their estimation procedures, but (2014) and Baum-Snow et al. (forthcoming) they also focus on different periods, different show that the construction of new highways transport modes operating under different in China increased the industrial output technologies, and different sectors. We need of the connected metropolitan areas and more work accounting explicitly for these Proost and Thisse: What Can Be Learned from Spatial Economics? 603 differences before providing a clear-cut areas. In the last twenty years, urban invest- answer about the net impact of transport ment projects have to demonstrate that all infrastructure. Even though it is reasonable communities suffering the nuisance of the to believe that the railway was useful for the investment are somewhat compensated development of US and Indian agriculture in by large abatement efforts before they can the nineteenth century, this does not mean go through. Glaeser and Ponzetto give the that building new highways reduces today’s example of the Anderson Memorial Bridge regional disparities within postindustrial that connects Cambridge with Boston countries. Admittedly, a transport infrastruc- that took a year to build in 1915, but over ture, or a few of them, may have a strong eight years to rebuild a century later mainly impact on the location and growth of activ- because it had to deal with inhabitants living ities in the corresponding regions. However, in a well-educated and dense environment. many transport infrastructures are likely The inefficiency of investment expenditures to have no impact, as the quasi-ubiquity of is the result of political inefficiencies that these infrastructures will no longer affect go beyond the transport committee bias of firms’ locations. In brief, though the provi- Knight (2004). sion of more efficient transport infrastruc- A first inefficiency is that the cost of fed- ture may help to promote regional growth, eral financing for public goods that generate we do believe that it does not constitute the mainly benefits in a city are not very visible, universal panacea promoted by many policy so there is a tendency to overinvest because makers. every city only perceives 1 n of the cost, / where n is the number of cities. The second 3.5.4 The Political Economy of Transport inefficiency is due to the opposition power Infrastructure of local groups that suffer the direct nui- Transport costs are also the result of politi- sance from the investment project. As their cal decisions regarding the nature of the trans- damage is direct and the benefits are dissi- port system. In the United States, the federal pated, these opposition groups push invest- government finances a large share of interstate ment projects to become too costly, as they highways using revenues from the gasoline are forced to include excessive abatement. A tax. Knight (2004) finds that the workings of third inefficiency is the federal funding rule the transport committees in Congress allowed that is not sufficiently geared to the needs building majorities for a regional allocation of of densely populated cities and cities whose funds, which was very inefficient: about half transport infrastructure is used intensively of the investment money was wasted. In addi- by nonresidents. tion, the econometric evidence provided by In the European Union, federal funds Baum-Snow (2007) and Duranton and Turner for transport investments are one of the (2012) suggests that highways tend to be allo- main instruments used by the European cated to cities that grow more slowly than a Commission for its regional policy. In the randomly selected city. late 1990s, the European Union launched a Glaeser and Ponzetto (2018) study the large transport infrastructure program with cycle of transport investments in the United thirty priority projects. An ex ante assess- States. The United States invested heavily, ment of this package yields three main find- until the late 1950s, in big urban projects. ings (Proost et al. 2014). First, only twelve This was followed by a period of low invest- out of the twenty-two projects pass a sim- ment because of social opposition of the “not ple cost–benefit analysis test. Second, most in my back yard” style in the major urban projects benefit only the region where the 604 Journal of Economic Literature, Vol. LVII (September 2019)

investment is to take place, so that the posi- misallocation of federal funds can be avoided tive spillover argument does not seem to war- by relying on local user pricing. Whenever rant the investment. Finally, the projects do the local user pricing cannot discriminate not systematically favor the poorest regions. between local voters and nonvoters while the To conduct the cost–benefit analysis, Proost revenues of user pricing have to be invested et al. rely on the spatial general equilib- in local infrastructure, local user pricing rium model of Bröcker, Korzhenevych, and techniques can be more efficient than fed- Schürmann (2010). In this model, the EU eral funding (De Borger and Proost 2016). has 236 continental regions and each region In sum, using federal or European Union produces a differentiated and tradable good. funds to finance local transport infrastruc- Labor is spatially immobile, an assumption ture is, at best, a mixed bag. that contrasts with that of perfect mobility made in many papers. A node of a trans- 4. Why Do Cities Exist? port network represents a region and all regions are connected. The network con- The above section addresses the issue tains data for all major links in the European of regional imbalance by using ideas and road, rail, ferry and air transport networks, concepts borrowed from the trade and including their specific characteristics such geography literature. In this section, we as speed limits and likelihood of congestion. recognize that cities are often the engine of Transport cost calculations are based on regional development and turn our attention shortest route through the geographic infor- to the subfield of urban economics where mation system transport network database. land and spatial externalities are key. New or upgraded links affect trade flows and Despite the numerous costs and dis- local production, as well as goods and fac- advantages associated with city size, the tor prices. In addition, the model accounts growing number of urbanites, which char- for the funding of investments when assess- acterizes many countries, is evidence that ing households’ welfare. We consider this people vote with their feet. Even though model—which has a rich description of the urbanization and economic growth do transport sector and includes several general not necessarily go hand in hand, cities are equilibrium effects—as one of the forerun- often better places to live than the alter- ners of the quantitative spatial modeling native outlying and rural areas. The main approach discussed in section 5.2. distinctive feature of a city is the very De Rus and Nombela (2007) use a cost– high density of population within a com- benefit analysis to determine the level of pact area that also accommodates a large demand needed to make a high-speed rail- amount of buildings and a great variety of way (HSR) socially beneficial. They find infrastructures. that a link needs some 10 million passengers According to Glaeser (2011), the main per year. Many new HSRs in the European reason for the existence of cities is to con- Union do not meet this target. When an nect people. Without the need to be close HSR has to cover all its costs, there will be an to one another, how can we explain why in insufficient number of passengers for most many countries, competition for land gets projects to be economically viable. tougher, as shown by the rising share of The above findings illustrate the role housing costs in consumers’ expenditures. of political economy factors in the selec- Households and firms seek spatial proximity tion of projects. As many large projects because they need to interact for a variety of have dispersed local benefits, some of the economic and social reasons. In particular, Proost and Thisse: What Can Be Learned from Spatial Economics? 605 as new ideas are often a new combination 4.1 Agglomeration Economies of old ideas, connecting people is crucial for the Schumpeterian process of innovation to Why do consumers choose to live in big unfold. This need has a gravitational nature cities where they pay high rents, bear long in that its intensity increases with the num- commutes, live in a polluted environment, ber of agents set up nearby and decreases and face high crime rates? It is due to the with the distance between them. However, much better pay in large cities than in small even though people prefer shorter trips to towns. Yet, why do firms pay their employees longer trips, they also prefer having more higher wages? If firms do not bear lower space than less space. Since activities cannot costs and or earn higher revenues in large / be concentrated on the head of a pin, firms cities, they should rather locate in small and households compete for land within towns where both land and labor are much an area that has a small physical extension, cheaper. The reason for the urban wage compared with the large regions that are the premium is that the productivity of labor is focus of regional economics. higher in larger cities than in smaller ones, As shown by Beckmann (1976), individu- and labor productivity is higher since a great als’ desire to interact with others in a stable number of advantages are associated with a and enduring environment may be sufficient high density of activities.2 These advantages to motivate them to cluster within compact are encompassed under the name “agglom- areas where they consume relatively small eration economies.” They involve both pecu- land plots. Beckmann’s contribution already niary and non-pecuniary external effects tells us how the fundamental trade-off of while they can be intraindustry or inter- spatial economics highlights the reason for industry.3 For a long time, agglomeration cities: the population distribution is the out- economies were used as black boxes hiding come of a tension between the propensity rich microeconomic mechanisms that lead to interact with others through a variety of to increasing returns at the aggregate level. mechanisms that have the nature of bene- These boxes have been opened and we now fits external to firms and consumers—the have a much better understanding of these agglomeration forces—and various spatial various mechanisms, though their relative frictions and crowding effects associated importance remains an unsolved empirical with population size—the dispersion forces. question. The size of a city is determined as the bal- In what follows, we distinguish between ance between these forces. agglomeration economies that accrue first to While regional economics focuses on firms, and then to consumers. internal increasing returns and the shipment of commodities, urban economics emphasizes the trade-off between increasing returns external to firms and workers’ com- 2 See Glaeser and Maré (2001), Moretti (2012), and mutes. In the next subsection, we analyze Diamond (2016) for the United States; Combes, Duranton, more in depth what we mean by agglomer- and Gobillon (2008) for France; Mion and Naticchioni ation economies. Next, we discuss the main (2009) for Italy; and Gibbons, Overman, and Pelkonen (2014) for the United Kingdom. urban centrifugal forces, that is, commuting 3 The idea of agglomeration economies dates back to and housing costs. We conclude this section Marshall (1890). Intraindustry economies are also called with an analysis of transport congestion and localization economies or Marshall–Arrow–Romer (MAR) externalities; interindustry economies are called urbaniza- the potential of different urban transport tion economies or Jacobs externalities. This cornucopia is policies. sometimes a source of confusion. 606 Journal of Economic Literature, Vol. LVII (September 2019)

4.1.1 The Nature of Business Agglomeration in larger cities, since firms have less Economies monopsony power (Manning 2010). A larger labor market also raises the job Agglomeration economies appear in very seeker’s chances of finding employ- different guises. It is, therefore, convenient ment and makes workers less prone to organize the various mechanisms associ- to changing occupations (Di Addario ated with population density in the follow- 2011, Bleakley and Lin 2012b). Last, ing three categories: sharing, matching, and a better match allows workers to focus learning (Duranton and Puga 2004). Their more on their core tasks in large, common feature is that they all lead to an rather than in small, cities (Kok 2014). aggregate production function displaying increasing returns. (iii) Learning in cities may come as a surprise to those who believe that (i) Sharing primarily refers to local pub- the new information and communi- lic goods that contribute to enhancing cation technologies have eliminated firm productivity, such as facilities the need to meet in person. When required by the use of new informa- different agents possess different bits tion and communication technologies of information, gathering them gen- and various transportation infra- erates knowledge spillovers, which structures. Sharing also refers to the is a shorthand expression for the access to a large pool of specialized external benefits that accrue to peo- workers and to the wide range of ple from the proximity of research business-to-business services avail- centers, knowledge-based firms, and able in large cities. Even though firms high-skilled workers. As ideas are, by outsource a growing number of activi- nature, intangible goods, one would ties to countries where labor is cheap, expect the internet to play a major they also use specialized services role here. Observation shows, how- available only where these services ever, that research and innovation are produced. are among the most geographically concentrated activities in the world (ii) Matching means that the number of (Feldman and Kogler 2010). This opportunities to better match workers is only seemingly a paradox. To be and job requirements, or the suppliers sure, once research has produced and customers of business-to-business new findings, they can be distributed services, is greater in a thick market worldwide at no cost. However, the with many different types of workers effect of proximity resurfaces when it and jobs than in a thin one. This idea comes to the creation and acquisition was formalized almost thirty years of knowledge (Glaeser 1999, Leamer ago by Helsley and Strange (1990). and Storper 2001). Since they face a large number of potential employers, workers living R&D often demands long periods of in large cities do not have to change exchange and discussion, during which places to switch to another employer. knowledge is gradually structured through This makes workers more prone to repeated trial and error. Thus, extensive, changing jobs. Therefore, workers repeated informal contacts between agents with the same skills earn higher wages located close to one another facilitate the Proost and Thisse: What Can Be Learned from Spatial Economics? 607 diffusion of new ideas and raise the level of Strange (2008) who find that adding50,000 coordination and trust. Although the web is college-educated workers within 5 miles probably the best available library, the profu- would increase a college-educated indi- sion of information it offers makes it hard to vidual’s wage by roughly 6 to 12 percent. pick up the few bits of information that are Bacolod, Blum, and Strange (2009) and relevant. Learning from other people is often Combes, Démurger, and Li (2015) observe the easiest way to know what is going on and that the urban wage premium associated where to search. Hence, innovation would be with large cities stems from cognitive skills geographically concentrated because greater rather than motor skills. Thus, like in endog- creativity is possible when researchers enous growth theory, everything seems to gather. For example, Greenstone, Hornbeck, work as if the marginal productivity of a and Moretti (2010) find that locating a large skilled worker would increase with the num- new plant in a region increases the produc- ber of skilled workers around him (Moretti tivity of other plants in that region. Different 2004, Glaeser and Resseger 2010). However, works point in the same direction, i.e., the there would be a rapid geographical attenu- spatial extent of knowledge spillovers is ation of the positive effects generated by the often limited (Arzaghi and Henderson 2008, concentration of human capital. Belenzon and Schankerman 2013, Buzard In a world that is becoming more and more et al. 2017).4 Furthermore, spillovers are as information intensive, the value of knowledge local in the 1990s as they were in the 1980s and information is higher than ever for cer- (Lychagin et al. 2016). Thus, contrary to tain economic activities. As a consequence, Cairncross (2001), who argued that “new cities should still be the best locations for ideas will spread faster” so that “poor coun- information-consuming activities, especially tries will have immediate access to informa- when firms operate in an environment of tion that was once restricted to the industrial rapid technological change and fierce com- world,” the empirical evidence concurs with petition. Thus, cities specialized in high-tech Glaeser (2011) for whom, even in the era industries attract high-skilled workers, who in of the internet, “ideas cross corridors and turn help make these places more successful. streets more easily than continents and seas.” Therefore, confirming what we saw in sec- There is nothing new under the sun here. tion 3, spatial inequality increasingly reflects Economic historians such as Hohenberg and the differences in the distribution of skills and Lee (1985) have long highlighted the fact human capital across cities. The flip side of that information is one of the main reasons the spatial sorting of workers is the existence why cities exist. Those results also substan- of stagnating or declining cities trapped in tiate the idea that moving people is more industries with a limited human-capital base, costly than moving goods. which are associated with low wages and few Even though the empirical evidence is local consumer businesses. Thus, even if the still thin, knowledge spillovers tend to ben- spatial concentration of human capital boosts efit skilled workers more. In larger and economic and technological development, it more educated cities, workers exchange might also come with a strong regional divide more than in cities populated by less-skilled (Moretti 2012). This is likely to have politi- workers. This is confirmed by Rosenthal and cal and social consequences that should not be overlooked: the places left behind might revolt against the ongoing situation through a 4 International spillovers also decline with distance (Keller 2002). They spread through very different channels, rise in populist voting (Colantone and Stanig such as international trade and foreign direct investments. 2018). 608 Journal of Economic Literature, Vol. LVII (September 2019)

Large cities may be productive for at caution since some econometric problems least three reasons: besides the presence of have not been properly addressed. agglomeration economies such as those dis- First, using a simple reduced form such cussed above, large cities could host a dispro- as (1) omits the explanatory variables whose portionate share of highly productive workers effects could be captured by employment and/or of more efficient firms. We briefly density. For example, overlooking variables discuss the role of workers’ sorting below, that account for differences in, say, aver- as well as in section 5.1. As for the selection age skills or local public goods, is equiva- of efficient firms, Combes et al. (2012) find lent to assuming that skills or public goods that there are no significantdifferences in are randomly distributed across cities and selection between large and small French are taken into account in the random term. cities after controlling for agglomeration This is highly implausible. One solution is economies and workers’ sorting. to consider additional explanatory variables, mainly the distribution of skills, the compo- 4.1.2 How to Measure Business sition of the industrial mix, and the market Agglomeration Economies? potential of cities. In doing so, we face the Ever since the seminal work of familiar quest of adding an endless string of Sveikauskas (1975) and Ciccone and Hall control variables to the regressions. Using (1996), research on city size, employment city and industry fixed effects, and individ- density, and productivity has progressed ual fixed effects when individual panel data enormously. Our purpose is not to pro- are available, instead allows one to control vide an in-depth discussion of the method- for the omitted variables that do not vary ological issues raised by the measurement over time. However, time-varying variables of agglomeration economies (Rosenthal remain omitted. and Strange 2004; Combes, Duranton, Second, the correlation of the residuals and Gobillon 2011; Combes and Gobillon with explanatory variables, which biases OLS 2015). Rather, we have chosen to pin down estimates in the case of omitted variables, can some of the main difficulties that are more also result from endogenous location choices. directly related to their interpretation. Indeed, shocks are often localized and thus The basic equation links the average wage have an impact on the location of agents, who wc in city c to this city’s employment or pop- are attracted by cities benefiting from pos- 5 ulation density de nc: itive shocks and repelled by those suffering negative shocks. These relocations obviously (1) log w log den . have an impact on cities’ levels of economic c = α + β c + εc activity and, consequently, their employment An ordinary least squares (OLS) regression density. As a consequence, employment den- yields an elasticity that varies from 0.03 to sity is correlated with the dependent vari- β 0.09. Hence, doubling the employment den- able and, therefore, the residuals. To put sity is associated with a productivity increase it differently, there is reverse causality: an varying from 2.1 percent to 6.4 percent. unobserved shock initially affects wages and However, there are good reasons why these thus density through the mobility of work- results should be approached with extreme ers, not the other way around. This should not come as a surprise; once it is recognized that agents are mobile, there is a two-way 5 Henderson (2003) has pioneered a different approach by checking whether the total factor productivity at the relationship between employment density firm level is affected by the density of neighboring plants. and wages. The most widely used solution Proost and Thisse: What Can Be Learned from Spatial Economics? 609 to correct endogeneity biases, whether they tend to be stronger when firms are smaller. result from omitted variables or reverse cau- In other words, specialized and vertically sality, involves using instrumental variables. disintegrated firms should benefit more from This consists in finding variables that are spatial proximity than larger firms, probably correlated with the explanatory variables but because they have a smaller pool of their not with the residuals. own resources to draw from. Last, the sorting of high-skilled workers Despite the wealth of valuable results, it into large cities accounts for a large part of the is fair to say that the dust has not yet settled. urban wage premium (Combes, Duranton, If we want to design more effective policies and Gobillon 2008). Taking into account for city development or redevelopment, we additional explanations for worker productiv- need a deeper understanding of the drivers ity (such as nonobservable individual charac- behind the process of agglomeration in cit- teristics or the impact of previous individual ies that vastly differ in size, as well as in his- locational choices on current productivity) toric and geographic attributes. Measuring has led to a fairly broad consensus recog- the relative strength of the various types of nizing that, everything else being equal, the agglomeration economies in different urban elasticity of labor productivity with respect to environments is one of the main challenges current employment density is slightly below that spatial economics faces (Puga 2010, 0.03. This elasticity measures the static gains Moretti 2011). generated by a higher employment density The existence of agglomeration economies (Combes et al. 2012). Recently, De la Roca has important implications. Once the activi- and Puga (2017) also highlight the existence ties that generate external economies of scale of significant gains stemming from individ- are established, firms and workers tend to uals’ accumulation of experience when they become sticky. The cumulative nature of the work in large cities, which they bring with agglomeration process makes the resulting them when they move to smaller cities. In pattern of activities particularly robust to var- this case, static estimates also reflect some ious types of shocks. This effect is reinforced sort of average of dynamic effects. by the various investments in buildings and It is not disputable that agglomeration infrastructures made by private agents and economies do exist. However, several issues local governments (Henderson and Venables remain unclear. For example, it is hard 2009). So, if there is a priori a great deal of to test results that are explained by a spe- flexibility in the location of activities, agglom- cific agglomeration economy, such as those eration economies may foster the emergence discussed above, and not by another. In a of a putty-clay geography. recent comprehensive study, Faggio, Silva, Notwithstanding the immense interest of and Strange (2017) give a qualified answer the above contributions, it is worth stress- to these questions. They confirm the pres- ing that urban economists pay little (if any) ence of the various effects discussed above, attention to the market structure of the but stress the fact that agglomeration econo- industry they study, although there are big mies are the reflection of very heterogeneous differences across sectors. For example, the phenomena. For example, low-tech indus- business literature stresses the importance of tries benefit from spillovers, though less than “co-opetition” where firms share knowledge, high-tech industries. Both intraindustry and but compete fiercely on the product market. interindustry external effects are at work, but Such a market structure fosters a higher pro- they affect industries to a different degree. ductivity and pushes wages upward. Further, Firm size also matters: agglomeration effects when imperfections on the product market 610 Journal of Economic Literature, Vol. LVII (September 2019)

(e.g., monopolistic competition) are combined cities than in smaller cities, which is in line with a perfectly elastic labor supply, workers with economic geography models where the are underpaid because the marginal produc- larger region’s price index is lower than the tivity of labor is assessed at the firm’s marginal smaller region’s. Using barcode data allows revenue rather than the market price. Handbury and Weinstein (2015) to compare prices of identical food products avail- 4.1.3 Consumer Agglomeration Economies able in the same chain store. Their data set Cities are also great places of consump- includes the prices of hundreds of thousands tion, culture, and leisure (Glaeser, Kolko, of goods purchased by 33,000 consumers in and Saiz 2001). Very much like firms, con- 49 US cities. Controlling for product, retailer, sumers living in large cities benefit from and consumer characteristics, they find that sharing, matching, and learning through a prices are almost independent of population greater number of tradable and non-tradable size. Handbury and Weinstein also find that goods and services, better transport and the number of available products increases communication infrastructures, and a wider by 20 percent when the city size is doubled. array of contacts, cultural amenities, and When the price index accounts for this avail- opportunities for social relations. There is a ability effect, groceries are slightly cheaper in need to study how the supply of differenti- larger cities than in smaller ones. For exam- ated products affects the welfare of urbani- ple, when identical products are available in ties as a high urban density allows consumers New York City and Des Moines, Iowa, prices to have access to a wide variety of goods and in New York are 1.3 percent lower. As for to save travel costs. A typical example of a services, the story might well be different. non-tradable is provided by restaurants, Workers producing consumption services which account for more than 5 percent of must be paid a higher wage to compensate household expenditures. By using tools them for the higher housing and commuting developed in the study of product differenti- costs they bear in a bigger city. As a result, the ation, Couture (2016) shows that consumers price of services should be higher. However, are willing to bear substantial travel costs to the quality and variety of consumption ser- enjoy their most preferred restaurants, thus vices is also often higher in larger cities (see confirming the importance of a wide range of Gobillon and Milcent 2013 for a concrete varieties as a consumption amenity. A large example based on French hospitals). number of people also facilitate the provi- In short, aside from housing costs, the sion of local public goods that could hardly impact of city size on the cost of living be obtained in isolation. remains an open question. The issue is not The access to a large diversity of goods is purely academic. When housing costs are a major asset to consumers who have a pref- included, it is reasonable to expect the cost erence for variety and or display heteroge- of living to rise with city size. In this case, / neous tastes and incomes. Since a larger city the fact that federal or national income tax is hosts a bigger population of heterogeneous based on nominal incomes implies a misallo- consumers, oligopoly theory holds that mar- cation of workers across cities. Since mobil- kets are more competitive, and provide a ity is driven by differences in real incomes, broader range of varieties and higher-quality workers are induced to move from efficient, goods (Campbell and Hopenhayn 2005, high-wage cities to less efficient,low-wage Berry and Waldfogel 2010, Schiff 2015). As a cities. Albouy (2009) finds that the result- result, everything else being equal, the mar- ing misallocation of workers from the North ket prices of goods should be lower in larger to the South of the United States and away Proost and Thisse: What Can Be Learned from Spatial Economics? 611 from dense to less dense areas would gen- interdependence across location decisions erate a welfare loss estimated at $28 billion stressed in section 2.2. It is, therefore, com- in 2008. pliant with the competitive paradigm. Each However, consumption amenities may consumer uses land in a single location and generate perverse effects under the form commutes between her workplace and res- of inefficient cities, which arise mainly in idence. Therefore, the monocentric city developing countries. In other words, urban- model studies the urban version of the fun- ization need not mean industrialization and damental trade-off of spatial economics, i.e., trade. Using a sample of 116 developing the trade-off between housing size at one countries over 1960–2010, Gollin, Jedwab, location—approximated by the amount of and Vollrath (2016) find that countries heav- land used at one location—and the acces- ily dependent on natural resources are asso- sibility to the CBD—which is measured ciated with the emergence of “consumption inversely by commuting costs.6 cities,” which produce mainly non-tradable Consumers, since they dislike long com- services. On the other hand, “production mutes, compete for land with the aim of being cities,” which rely on the development of as close as possible to the CBD. However, manufacturing activities and the production since they also prefer more space, consumers of tradable goods, perform much better. In will not cram into the vicinity of the CBD. the former case, urbanization is a symptom Therefore, some of them commute over long of the Dutch disease. distances. By allocating to some consumers a plot of land near the CBD, the commut- 4.2 The Trade-off between Commuting and ing costs borne by other consumers are indi- Housing Costs rectly increased as they are forced to set up The positive effects associated with city farther away. Hence, determining where size come with various negative effects such consumers are located in the city is a general as expensive housing, long commutes, traf- equilibrium problem. A perfectly competi- fic congestion, pollution, and crime. These tive land market may sustain a distribution effects bring about the so-called urban costs. of identical consumers across locations so As a result, cities may be viewed as the out- as to equalize utility in equilibrium. The come of a trade-off between agglomeration argument is disarmingly simple: land users economies and urban costs. behave as if they were involved in a gigantic auction. Consumers, given their income and 4.2.1 The Monocentric City Model preferences, are characterized by a bid rent Von Thünen (1826), who studied the function that specifies the willingness to pay spatial distribution of crops around a mar- for one unit of land at any distance x from the ket town, proposed the first analysis of the CBD. A particular land plot is then assigned way land is allocated across different activi- to the highest bidder. Since the number of ties. The authoritative model of urban eco- consumers is large (formally, a continuum), nomics, which builds on von Thünen, is the winner pays the highest bid and, in con- the featureless monocentric city model in sequence, the land rent is the upper enve- which a single, exogenously given central lope of consumers’ bid rent functions. business district (CBD) accommodates all jobs. Locations within a city are thus heterogeneous. Since the only spatial characteris- 6 The best synthesis of what has been accomplished with the monocentric city model remains the landmark tic of a location in this model is its distance book by Fujita (1989). Duranton and Puga (2015) is the from the CBD, the model breaks down the most detailed and recent survey of urban land use models. 612 Journal of Economic Literature, Vol. LVII (September 2019)

Consider a one-dimensional space Furthermore, the lot size occupied by a ℝ+ with a dimensionless CBD located at x 0. consumer must increase with the distance = The opportunity cost of land R 0 is constant from the CBD. Although a longer com- and each location is endowed with one unit mute is associated with a lower net income of land. A mass N of consumers shares the Y T(x), the spatial equilibrium condition − same income Y and the same preferences yields a compensated demand for land that U(z, h), where z is the quantity of a compos- depends on the land rent and the endoge- ite good and h the amount of space used. nous utility level that is common to all con- The price of the composite good, set equal sumers. The utility level is treated as a given to one, is determined by market forces by every consumer who is too small to affect outside the city. Denoting the land rent it. Since housing is a normal good, a lower prevailing at x by R (x), and the commut- price for land therefore implies a higher land ing cost borne by a consumer residing at x consumption. In other words, as the distance by T(x), the budget constraint is given by to the CBD increases, the lot size increases, z(x) h(x) R(x) Y T(x). whereas the consumption of the composite + = − Let V(R(x), Y T(x)) be the indirect good decreases. This, in turn, implies that − utility. Since consumers are identical, they the population density decreases with the enjoy the same equilibrium utility level in distance from the CBD. Hence, lower com- all locations. As a consequence, the deriv- muting costs foster urban decentralization. ative of V(R(x), Y T(x)) with respect to x Despite its extreme simplicity, the − must be equal to zero. Using Roy’s identity, monocentric city model tells us something we obtain the Alonso–Muth equilibrium important: when more consumers become condition: agglomerated, land consumption acts as a dispersion force. To see how it works, consider the urban cost C(N; u) to be borne (2) h(x) _dR _dT 0. d x + d x = for the mass N of consumers to enjoy the utility level u. The cost C(N; u) is obtained Since a longer commute generates a by summing the commuting costs, the pro- higher cost (d T d x 0), the land rent must duction cost of the composite good, and the / > decrease with the distance to the CBD for opportunity cost of land occupied by urban- this condition to hold. As a consequence, (2) ites, which are needed for consumers to means that a marginal increase in commuting reach the utility level u: costs associated with a longer trip is exactly compensated for by the marginal drop in (3) C(N; u) housing expenditure. To put it bluntly, peo- B ple trade cheaper land for higher commuting T(x) Z(h(x); u) R n(x) dx, = 0 [ + + 0] costs. If commuting costs were independent ∫ of distance (d T d x 0), the land rent where Z (h(x); u) is the quantity of the com- / = would be constant and equal to the opportu- posite good for U [ Z(h(x); u), h(x)] u to = nity cost of land R 0. As a consequence, com- hold, while B is the endogenous city limit, muting costs are the cause and land rents the and n (x) 1 h(x) the population density. It = / consequence. In the featureless monocentric can be shown that C(N; u) is strictly increas- city model, the “something” that explains ing and strictly convex in N as well as strictly why the urban land rent exceeds the oppor- increasing in u (Fujita and Thisse 2013). tunity cost of land is the physical proximity Hence, for the utility level to remain the to the CBD. same, the average urban cost borne by the Proost and Thisse: What Can Be Learned from Spatial Economics? 613 incumbents increases with new residents. In regulations. Nevertheless, we may be confi- other words, land use and commuting costs dent that this cost will be anything but small generate agglomeration diseconomies with because land restrictions foster misallocation respect to population size. of labor across cities.7 The land rent level reflects not only the Thus, contrary to a belief shared by the proximity to the CBD, but also the “artificial media and the public, the rise in housing scarcity” of land that stems from restrictive costs in many cities is driven mainly by exces- land use regulation, the provision of open sive regulation of the housing and land mar- spaces, or public policies that maintain the kets. Public policies typically place strong prices of agricultural products far above the restrictions on the land available for hous- international level. For example, the imple- ing and offices. By instituting the artificial mentation of urban containment hurts new rationing of land, these policies reduce the residents by reducing their welfare level or price elasticity of housing supply; they also it motivates a fraction of the city popula- increase the land rents and inequality that go tion to migrate away (Glaeser, Gyourko, and hand in hand with the growth of population Saks 2006). In addition, by restricting the and employment. Since the marginal urban population size, such policies prevent the cost d C(N; u) dN grows, the beneficiaries of / most productive cities from fully exploit- these restrictions are the owners of existing ing their potential agglomeration effects. plots and buildings. Young people and new Admittedly, environmental and esthetic con- inhabitants are the victims of these price siderations require the existence of green increases and crowding-out effects that often space. However, the benefits associated make their living conditions difficult, or deter with providing such spaces must be mea- in-migration (Ganong and Shoag 2017). sured against the costs they impose on the The monocentric city model has produced population. Cheshire, Nathan, and Overman a wide variety of results that are consistent (2014) report that “in 2010, housing land in with several of the main features of cities. the South East of England was worth 430 Nevertheless, the basic model of urban eco- times its value as farmland.” We may wonder nomics does not perform so well when it what shadow price to assign to green spaces comes to predicting the social structure of to rationalize such a price discrepancy. cities. For example, when consumers are After a comprehensive econometric analy- heterogeneous in income, the model leads sis of the various social welfare effects gener- to a fairly extreme prediction: households ated by land regulation, Turner, Haughwout, are sorted by increasing income order as and van der Klaauw (2014) conclude that the distance to the CBD rises (Hartwick, marginal reductions in land use regulation Schweizer, and Varaiya 1976; Fujita 1989). are likely to have substantial welfare bene- Hence, the wider the income gap between fits, especially at the edges of existing devel- two households, the greater the distance oped areas. Even more surprising, Hsieh between their residential locations, and and Moretti (2019) find that lowering con- vice versa. This is not what we observe in straints on the housing supply in New York, many countries where metropolitan areas San Francisco, and San Jose to the level of display pronounced U-shaped or W-shaped the median American city from 1964 to 2009 would increase the US GDP by 8.9 percent, an astronomical number. It is clear that more 7 A high stock of outdated buildings may also act as a break on city growth. Hornbeck and Keniston (2017) show work is needed to accurately assess the social how the Great Boston Fire of 1872 provided a unique cost of the plethora of land and housing opportunity for new buildings. 614 Journal of Economic Literature, Vol. LVII (September 2019) spatial income distributions (Rosenthal and when the city has two employment centers Ross 2015). For example, when dwellings located at x 0 and x N, respectively. = = are differentiated by age, the affluent are Since C (N, z) C (N, z), the equilibrium 2 < 1 attracted by both suburban locations where utility level is higher in a duocentric city than they consume big land plots and by down- in a monocentric city. So, we are left with the town locations where central redevelopment following question: Why is there a CBD—or makes the housing stock young; this gener- a small number of business districts—in a ates a U-shaped spatial income distribution city? Scale economies and spillovers are the (Brueckner and Rosenthal 2009). In this case, usual suspects. using income-independent commuting costs seems restrictive for studying households’ 4.2.2 The Emergence of City Centers residential choices because there is ample evidence suggesting that the opportunity cost Ogawa and Fujita (1980) tackled this of time increases with income (Small 2012, question in a path-breaking paper that Koster and Koster 2015). There is a need for went unnoticed for a long time, probably more general approaches that account for because urban economics was still at the heterogeneous consumers and differentiated periphery of economics. These authors urban environments. What makes such analy- use a gravity-like reduced form for spill- ses difficult is that the market outcome is given overs and combine consumers and firms in by the solution to a multidimensional match- a full-fledged general equilibrium model ing problem in which housing consumption in which goods, labor, and land markets is income dependent, something that multi- are perfectly competitive. Spillovers act as dimensional matching is so far unable to deal an agglomeration force as their intensity is with. subject to distance-decay effects. However, More importantly, the monocentric model the clustering of firms increases the average remains silent on why jobs would be geo- commuting distance for workers, which in graphically concentrated. Indeed, firms may turn leads to workers paying a higher land alleviate the burden of urban costs in large rent. Therefore, firms must pay workers a metropolitan areas through the emergence of higher wage as compensation for the higher secondary employment centers (Henderson land rent they have to pay. In other words, and Mitra 1996). To illustrate this, con- the dispersion force stems from the inter- sider the example of a fixed lot size, that action between the land and labor mar- is, the consumption of housing is the same kets. The equilibrium distribution of firms across locations (h 1), while commut- and workers is the balance between these = ing costs are linear in distance (T (x) tx). opposing forces. Note the difference with = When the city is monocentric at x 0, the monocentric city model: interactions = for a given consumption z of the compos- among agents make the relative advantage ite good, the level of urban cost is obtained of a given location for an agent depen- by integrating R(x) tx tN over [0, N], dent on the locations chosen by the other + = that is, agents, while the agglomeration of firms renders land more expensive at the city C (N, z) tN 2 z, center. 1 = + Firms produce a homogeneous good using while the urban cost becomes a fixed amount of labor and one unit of land, and a mass N of workers who each consume C (N, z) _ t N 2 z one unit of land and the final good each. The 2 = 2 + Proost and Thisse: What Can Be Learned from Spatial Economics? 615 output level Y of a firm located at x [ b, b] Given the importance of the subject ∈ − depends only on the firm distribution: matter, it is surprising that only a handful of papers have explored more general or b (4) Y(x) Y | x y | m(y) dy, alternative settings. This paucity makes = − b τ − ∫− it hard to adopt a structural approach to where is the distance-decay parameter and studying knowledge spillovers. Fujita and τ m(y) is the density of firms at y [ b, b]. Ogawa (1982) consider a negative expo- ∈ − Ogawa and Fujita (1980) show that the nential decay function and show by using equilibrium urban configuration is unique simulations that polycentric configurations and monocentric, incompletely integrated exist. One of the main difficulties encoun- or dispersed, depending on the commuting tered by these authors lies in the multi- rate t and distance-decay parameter . plicity of equilibria. Independently, Lucas τ First, when commuting costs are high in and Rossi-Hansberg (2002) use a neo- relation to the distance-decay parameter, as classical production function where land in preindustrial cities when people moved and labor are the two inputs while firms on foot, the equilibrium involves a complete and workers choose their land consump- mix of business and residential activities with tion. Besides a general existence theorem, everyone living where they work. In this their simulations yield results consistent case, land is unspecialized. As commuting with those obtained by Fujita and Ogawa costs fall, two employment centers, which (1982). are themselves flanked by residential areas, Berliant, Peng, and Wang (2002) replace are formed around a district where firms and the local firm density by aLucas-like exter- workers are uniformly mixed. Eventually, nality subject to a distance-decay effect. when commuting costs are sufficiently low More precisely, a firm produces according (due to mass transport and the use of cars), to the following Cobb–Douglas production the city becomes monocentric. We summa- function: rize this as follows.

Y(x) A(x) K α L β , THE CITY STRUCTURE: Assume a lin- = ear distance-decay spillover and linear commuting costs. Then, there exists a posi- where the total factor productivity A(x) 1 tive constant K such that the city structure is [a(x)K ] −α−β is endogenized through the = ̅ (i) monocentric if t K 2, (ii) incompletely following channels: (i) the aggregate capital < τ / integrated if K 2 t K, and (iii) mixed stock K , and (ii) the spatial distribution τ / ≤ ≤ τ ̅ if K t. of firms through the local spillover effect τ < a(x) x 2 2 where is the = α − − βσ σ We may rewrite these inequalities in terms absolute deviation of the firm distribution. of the distance-decay parameter. Hence, the Berliant and coauthors show that the monocentric city emerges when exceeds equilibrium displays one of the three τ 2t K, that is, when the spillovers are very configurations identified by Ogawa and / localized. Under (4), O’Hara (1977) shows Fujita (1980). The sensitivity of results to how the presence of skyscrapers in CBDs the functional form used for the spillovers may be explained by adding a construction makes it hard to test their magnitude and sector to the model. In equilibrium, the is evidence that more work is needed building height decreases with the distance from both the theory and empirical from the center of the CBD. viewpoints. 616 Journal of Economic Literature, Vol. LVII (September 2019)

4.3 Congestion Costs 4.3.1 Reducing Congestion via Road Pricing

Complaining about transport conditions Ever since the pioneering work of Pigou in cities is as common as talking about the (1932), there has been general (but not uni- weather. The origin of the discomfort lies versal) agreement among economists that in the various negative external costs expe- road pricing is the ideal instrument to tackle rienced during most trips. The main exter- congestion. The argument is straightfor- nal travel costs within cities are due to road ward. Beyond a certain traffic density, travel congestion, followed by local air pollution, speed falls as the number of cars increases. accidents, and climate effects (Parry, Walls, Although the costs of travel delays are and Harrington 2007). Climate and air pol- borne by drivers collectively, each individ- lution are not specific to transport or urban ual driver neglects the external cost of the living conditions. These externalities can be delays they impose on others. The result is tackled efficiently by reducing the emissions excess travel and inefficiently low speeds. per unit of activity: cleaner fuels, catalytic Efficiency can be restored by impos- converters, safer cars, and better design of ing a toll equal to the marginal external houses. Ignoring crime, the most important cost. negative externality linked to cities is con- According to static peak-load pricing gestion. That neither the United States nor theory, this can be explained as follows. the European Union has managed to address Consider two locations, A and B, linked by a these negative externalities efficiently in road. In the absence of congestion, the cost their pricing policies and infrastructure deci- of a trip is constant and normalized to zero. sions is probably a major impediment to effi- A population of N homogeneous users resid- cient urban growth. Correcting the external ing in A wish to travel to B at the same time, effects generated by urban density and mak- but the capacity of the road is insufficient to ing the best use of agglomeration economies allow this. In the simplest formulation, the may be one of the main challenges of urban road has a bottleneck with a flow capacity of s and transportation economics. cars per unit time. In this case, the (average) People travel within cities for a wide range cost of a trip is given by ATC (N) N s, = α / of reasons, such as commuting to work, where is the shadow price of travel α business contacts, dropping children off at time. Since the total travel cost is TTC(N) schools, shopping downtown or in subur- N 2 s, the marginal social cost of a trip = α / ban malls, and attending various family and is MTC(N) 2 N s and the marginal = α / social events. Urban economics focuses pri- external cost is N s. Users internalize the α / marily on the trade-off between agglomera- external cost if they pay a toll equal to N s. α / tion economies and the accessibility to the Furthermore, if the inverse demand curve workplace. In accordance with this trade-off, for trips is D(N), the optimal number of trips the size and structure of cities are, to a sig- is given by the solution to D(N) 2 N s. = α / nificant extent, driven by the performance of By contrast, the equilibrium number of the urban transportation system. To assess trips in the absence of a toll is given by the the possible impact of various policies, it is equation D(N) N s. The conventional = α / important to distinguish between two funda- peak-load pricing model thus dictates that, mentally different instruments: a better use with marginal social cost pricing, the num- of existing transport infrastructure through ber of trips must be reduced. This creates a pricing and regulation, and the addition of potential conflict between reducing traffic transport capacity. congestion and increasing city productivity Proost and Thisse: What Can Be Learned from Spatial Economics? 617 by maintaining a strong spatial concentration same as with no toll, so that the equilibrium of jobs. number of trips is still given by the solution The solution proposed by Pigou is static. to D(N) N s. Consequently, with the = α / However, road congestion is inherently a time-varying toll, the total social variable dynamic phenomenon, as travelers do not costs of travel are halved without reducing the have to depart at the same time (Vickrey number of trips made at all. In other words, 1969). Consider the pioneering bottleneck the benefits associated with density are not model developed by Arnott, de Palma, and much affected (Arnott 2007). However, con- Lindsey (1993). Drivers share the same ideal gestion costs are not eliminated, since sched- time to reach their destination and incur a ule delay costs, which are hidden in Pigou's so-called schedule delay cost if they arrive static model, are unchanged. earlier or later. Let denote the unit cost of So far, we have assumed that car users β early arrival (with ) and the value time in the same way. However, the β < α γ > α unit cost of late arrival. If the rate at which empirical evidence suggests that individuals vehicles arrive at the head of the bottleneck are heterogeneous in their travel time values exceeds s, a queue develops. The total cost (Small, Winston, and Yan 2005). In this case, of a trip is the sum of the queuing delay cost, by substituting high-value trips (business the schedule delay cost, and the toll (if any). and highly skilled commuters) for low-value Let T denote the toll levied at time T, and trips, road pricing generates an additional τ( ) N(T) the number of vehicles in the queue at benefit. By reducing the number of drivers time T. A driver who departs at time T incurs during the peak period, road pricing favors a trip cost of C(T) NT s (time productivity by making business-to-business = α ( )/ + β early) (time late) T . trips cheaper. Furthermore, individuals are + γ + τ ( ) Since drivers are homogeneous, the equi- also heterogeneous in terms of schedule librium travel cost must be the same through- delay preferences (Koster and Koster 2015). out the period during which drivers depart. Combining heterogeneity both in values If there is no toll, the queuing time increases of time and in schedule delay preferences, from zero at the beginning of the travel period van den Berg and Verhoef (2011) show how to a maximum for the individual who arrives imposing a time-varying toll at a bottle- on time, and then decreases back to zero neck can exploit the heterogeneity of pref- at the end of the travel period. Arnott and erences to produce a Pareto improvement coauthors show that the equilibrium travel even before the toll revenues are redistrib- cost is equal to N s where ( ). uted. The issue is important because there δ / δ ≡ β γ/ β + γ The equilibrium is inefficient because the is growing evidence that individuals who queuing time is a deadweight loss. Queuing have a long commute are more prone to can be prevented by levying a time-varying being absent from work, arriving late at the toll that starts at zero, increases linearly at workplace, and or making less effort at work / rate to a maximum for the individual who (van Ommeren and Gutiérrez-i-Puigarnau β arrives on time, and then decreases linearly 2011). at rate back to zero. In this case, the queu- Despite these caveats, we may conclude γ ing cost is eliminated, while schedule delay that the smart pricing of a bottleneck can costs are unchanged since the bottleneck still transform queuing into toll revenue; bring operates at capacity and the interval during about time and productivity gains; be a which drivers arrive is unchanged. The social sensible alternative to the building of new, cost of travel falls from N s to N 2s, while expensive transportation infrastructures; and δ / δ / the private cost inclusive of the toll is the dampen the sprawling of activities. 618 Journal of Economic Literature, Vol. LVII (September 2019)

4.3.2 The Difficult Road to Congestion time benefits, may vastly underestimate the Pricing total benefits of substantial improvements in accessibility. Kanemoto (2013) revisits Congestion pricing has been studied the basic setting of CBA by building a link intensively in transportation econom- between spatial and transportation eco- ics. However, while we have a fairly good nomics. A transport project that reduces understanding of the main issues at stake commuting costs within a city attracts work- when agents have fixed locations, the lit- ers from other cities, so that the additional erature does not say much about the loca- agglomeration benefit comes at the expense tional effects of congestion pricing. Three of an agglomeration loss in other cities. In main lessons can be drawn. First, the design this case, the overall benefits are negative of the road pricing scheme is very import- if agglomeration economies in the other ant for the magnitude of the total net wel- cities are larger. By contrast, if the project fare effects (Anas and Lindsey 2011). For affects the transport costs of goods produced example, Stockholm has implemented a in imperfectly competitive markets, the more efficient scheme than has London: additional benefits are always positive and the Stockholm system has lower transaction proportional to firms’ markups. Thus, care is costs and uses more finely differentiated needed when we come to measuring wider charges depending on the time of the day. benefits. Indeed, as shown by the bottleneck model, In the United States, where road pricing time differentiation is crucial to capturing seems to be banned from the public debate, the full gains of congestion pricing. A sim- there is more focus on optional varieties of ple differentiation based on day–night, as road pricing such as pay lanes. As pay lanes in London, foregoes a large share of these send motorists to an unpriced alternative gains and has to rely mainly on reducing the (the other lanes), they can generate net total number of peak car trips to alleviate welfare benefits only when car users dif- congestion. Second, in the 10–20 percent fer in their value of time or when there is a reduction in car use necessary to eliminate fine-tuned pricing of the bottleneck (Small most queues, only a relatively small share and Yan 2001). Hall (2018) revisits the bot- (40 percent or less) of the suppressed car tleneck problem when congestion at the bot- trips are replaced by mass transit; the rest tleneck increases with the queues and shows disappeared due to car sharing, combining that a pay lane can lead to a Pareto improve- trips, or simply foregoing the trip (Eliasson ment even before the redistribution of reve- et al. 2009). nues. Indeed, if a sufficiently large number Third and last, standard cost–benefit anal- of high-income drivers use the pay lane, yses (CBA) are confined to effects within congestion is eased on the free lanes. In the the transport sector, while urban economics European Union, only a few cities (London, suggests that there are wider benefits due to Stockholm, Milan, and Göteborg) have better accessibility that are in line with those implemented congestion pricing schemes. associated with higher density. Anderstig Most national and local governments, alike, et al. (2016) estimate a reduced-form rela- favor other policies such as high gasoline tionship between accessibility and labor prices, large investments in infrastructures, income in Stockholm. They find that the and subsidies in mass transit. total income gains could well be as important One may wonder why, despite high poten- as the direct time benefits. Thus, a standard tial benefits, road pricing is so unpopular. CBA of congestion pricing, focusing only on De Borger and Proost (2012) propose a Proost and Thisse: What Can Be Learned from Spatial Economics? 619 political economy analysis. The population that includes congestion costs and agglomer- is a priori divided into three categories: ation economies using data from Columbus, nondrivers, drivers who can easily switch to Ohio. Congestion pricing may have negative transit (called marginal drivers), and those effects because the congestion tax, although who face high switching costs. When toll effective in reducing congestion, weakens revenues are evenly redistributed across agglomeration effects through more dis- people, nondrivers support congestion pric- persed employment. Although it seems pre- ing. Therefore, nondrivers and marginal mature to draw firm conclusions from a small drivers could form a majority for congestion number of papers, it appears that congestion pricing. However, if all drivers know only the pricing has various unexpected effects that average switching costs to public transport, need to be carefully investigated. These marginal drivers expect to bear a cost that papers also confirm one of the main tenets of might be much higher than what it actually the survey: a shock to parameters may lead to would be. As a result, a majority of the pop- very different results under fixed or variable ulation may be against congestion pricing. locations. However, if road pricing is implemented, the uncertainty is resolved. As a consequence, 4.3.3 Does Transport Infrastructure marginal car users know that their switching Extension Solve the Congestion costs are lower than what they expected and Problem? may therefore support congestion pricing ex post. Hence, a majority of drivers may Building new road infrastructure raises vote against road pricing ex ante and even the value of the road capacity s and reduces against an experiment, since they view their the average travel cost AC(N) for any given expected gains as being negative, whereas a N. However, this argument overlooks the fact majority may support it when implemented. that the volume of traffic does not remain As shown by the examples of London and the same when road capacity is expanded: Stockholm, there was an ex ante majority the new capacity attracts more car users against road pricing but an ex post majority (N increases). Eventually, expanding the in favor of it. The final decision hinges on the road capacity may create its own demand, a local government’s ability to organize such an phenomenon known as the Downs paradox experiment. (Arnott and Small 1994). This paradox is The conventional wisdom holds that, by nothing other than a demand for transporta- making commuting more expensive, con- tion that is elastic with respect to the level of gestion pricing should lead to denser cities. travel costs. Yet, is this paradox more than an A handful of recent papers shed a differ- intellectual curiosity? Duranton and Turner ent light on the merits of congestion pric- (2011) revisited the problem for American ing when it is recognized that agents can cities for the years 1983, 1993, and 2003, change locations in response to substantial while paying special attention to the simul- changes in travel costs. Using the bottle- taneity problem between road capacity and neck model discussed above, Takayama and traffic density. Their conclusions cast serious Kuwahara (2017) show that densification doubts on the merits of infrastructure-based may not happen when commuters are het- congestion policies. First, Duranton and erogeneous. On the contrary, the sorting of Turner confirm that new roads gener- individuals may lead to equilibria in which ate more traffic. More importantly, in the the city is less dense. Brinkman (2016) cal- absence of road pricing, they find that “new ibrates a spatial general equilibrium model road capacity is met with a proportional 620 Journal of Economic Literature, Vol. LVII (September 2019) increase in driving.” In other words, the elas- fostered a 20 percent population growth ticity of road use with respect to the num- in those suburban municipalities where ber of urban lane kilometers is close to one, off-ramps were located. Finally, each addi- thus making the Downs paradox a result. tional kilometer closer to the nearest high- Yet where do the additional travelers come way off-ramp increased municipal density from? Duranton and Turner (2011) find that growth by 8 percent. All this confirms the new cars and new trucks share the respon- impact of increasing highway capacity on sibility for the extra trips almost equally. In population distribution within metropolitan addition, road extension attracts mass tran- areas. sit passengers. This reduces the frequency These results have two major implications of public transportation, which in turn that go against many policy recommenda- increases waiting and schedule delay costs, a tions: when road pricing is not implemented, vicious circle that may lead to the disappear- building new roads may not be the appro- ance of the transit alternative (Arnott and priate policy to reduce traffic congestion. Small 1994). Eventually, roads will attract In addition, the new roads are likely to have even more users. This result is not rare in the unintended, and possibly undesirable, effects United States, where car use is cheap and on the urban morphology. Therefore, con- transit alternatives few. In the case of Japan, gestion pricing is back to center stage as the Hsu and Zhang (2014) find an even slightly main tool to curb urban congestion. Despite higher elasticity of road use with respect to the lack of enthusiasm of policy makers for road capacity. this instrument, the large number of results Very much like decreasing transport costs obtained by urban transportation economics affects the locations of firms, large projects should encourage governments to assess the that substantially lower commuting costs are merits of smart pricing schemes against the likely to affect household residential choices. merits of new transportation projects. For example, Baum-Snow (2007) finds that, Given the long-run implications of trans- between 1950 and 1990, a new highway pass- port infrastructure and the externalities they ing through a central city reduces its popu- may generate, cities need to be planned. lation by about 18 percent. His estimates Economists have developed CBA techniques imply that the aggregate central city pop- to assess the desirability of transport proj- ulation would have grown by about 8 per- ects. CBA techniques have progressed over cent had the interstate highway system not the last fifty years from the Dupuit consumer been built. While central cities were still surplus to methods that correct for external- the origin or destination of 66 percent of ities and market imperfections, wider eco- all commutes in 1960, this share dropped nomic benefits, and the opportunity cost of to 38 percent in 2000. This suggests that public funds. However, CBA methods face jobs have followed residents in their subur- great hurdles in assessing these effects cor- banization. However, care is needed since rectly (Redding and Turner 2015). Hence, several effects are at work here (Brueckner there is a need for broader operational mod- 2000). In the same vein, Garcia-López, Holl, els integrating land use and transport infra- and Viladecans-Marsal (2015) studied the structure (LUTI) with the range of general effects of highways on urbanization patterns equilibrium interactions between locations in Spain. They find that, between 1960 and emphasized in theoretical models of eco- 2011, a highway originating in a central city nomic geography. Unlike most CBA meth- caused an 8–9 percent decline in the cen- ods, LUTI models are general equilibrium tral city population. In addition, a highway settings where the urban space consists of a Proost and Thisse: What Can Be Learned from Spatial Economics? 621 finite set of locations. In each location, land peak period is lower than its social marginal can be used for production and/or housing, cost in the absence of congestion pricing while locations are linked to each other via (P SMC ), subsidizing mass tran- car < car transport infrastructure. The LUTI models sit is efficient insofar as the subsidy may also take into account agglomeration SMC P 0 can make car users PT − PT > economies. switch to public transportation. More spe- There are two types of models. In the cal- cifically, for a given subsidy, the fraction φ ibrated version, one gathers information on of new transit passengers who would be car the present equilibrium and complements users in the absence of the subsidy must this with various elasticities taken from the satisfy the following relationship at peak literature to make the model match the time: present observations. Anas and Liu (2007) provide a good illustration of this approach. (5) P SMC ( P SMC ). PT = PT + φ ⋅ car − car Their work may be viewed as a spatial quantitative model of the sort discussed in Parry and Small (2009) found that a subsection 5.2. A good example of the second sidy close to 90 percent of the average type of model is by Teulings, Ossokina, and operational costs for urban rail transport is de Groot (2018) who use detailed micro- socially desirable when 0.5. However, φ = data to estimate a spatial general equilib- empirical studies find values for that φ rium model for the 3000 ZIP codes in the are often smaller than 0.5. For example, if Netherlands. The model allows for changes 0.2, the optimal subsidy for the peak φ = in population density, job location, and time drops from 90 percent to 10 percent. modal choice in an economy with heteroge- Rail and metro systems display increas- neous workers and several transport modes. ing returns because of strong traffic den- In assessing the impact of a new tunnel in sity economies. Hence, first-best pricing Greater Amsterdam, Teulings and coauthors gives rise to a huge deficit. This requires a find that the welfare benefits consist mainly Ramsey–Boiteux pricing scheme that takes of time savings, but changes in land use into account the opportunity cost of pub- may account for up to 30 percent of all lic funds and adds an extra margin for the benefits. less-elastic users to further reduce the deficit characterizing almost all public trans- 4.3.4 What Can Mass Transit Achieve? port systems. Bus systems exhibit smaller Implementing low prices for urban transit scale economies, so that accurate peak load is often presented as a second-best pricing pricing can allow bus systems to break even tool that makes up for the missing road con- more easily. Moreover, buses also contrib- gestion pricing. In fact, cheap transit fares ute to road congestion, unless they have a have not solved the problem of road con- separate lane. Hence, there is a need for gestion; they have created a new one—mass more efficient bus pricing systems. They transit congestion. For cheap public trans- should account for the differences in cost portation prices to help solve the road con- between peak and off-peak trips and vary gestion problem, it must be a good substitute with the area and distance traveled, as well for car use (Parry and Small 2009). In (5), the as with the congestion level of roads. This optimal transit fare is equal to its social mar- would increase the overall efficiency of the ginal cost, corrected by the gap between the urban transport system and alleviate the price and the social marginal cost of car use. financial problems of urban public trans- Since the price of an additional car in the port agencies. 622 Journal of Economic Literature, Vol. LVII (September 2019)

The mix of road and mass transit is the system involving large and medium-sized result of a political choice made in a city cities, towns, and villages that produce and with heterogeneous users. Brueckner and trade different commodities and host dif- Selod (2006) show that a voting equilibrium ferent types of workers. Two generations of need not yield the best mix of capacities. models shed light on different aspects of this problem. The first one focuses on the size and specialization of cities, while the second 5. Toward a Synthesis of Regional and addresses their skill composition. Urban Economics 5.1.1 Cities Differ in Size and Specialization It should now be clear that we need a better integration of different types of spatial Despite valuable early contributions by frictions discussed in the two sections above Christaller (1933) and Lösch (1940), it is to understand how forces acting on differ- fair to say that Henderson (1974, 1988) was ent spatial scales shape the economy. Most the first to develop a compelling and origi- countries trade more with themselves than nal approach that allows the formation of an with the rest of the world, while large cities urban system to be described. His setting are major actors in the process of trade. It is, involves an endogenous number of special- therefore, fundamental that one understands ized cities that trade commodities. Hence, how the intensity of interregional and inter- the urban system resembles a wide array national trade is influenced by the size and of small open economies where firms oper- structure of cities and, conversely, how trade ate under perfect competition and external and market integration affect the structure of economies of scale. The market for cities is cities. This task must be accomplished within characterized by competition among land multi-region frameworks that capture as developers. The land developers understand many general equilibrium effects as possible. that they may benefit from organizing cities In what follows, we consider two different in a way that maximizes the local land rent, approaches. First, we discuss the forma- while internalizing the external effects gener- tion of urban systems, a natural framework ated by the agglomeration of firms belonging to consider as the performance of regional to a particular industrial sector. In equilib- economies is often determined by the econ- rium, the utility level is the same across cities omies of the cities they include. The second and each city has a positive, finite size. As cit- approach is the quantitative spatial modeling ies vary in their industrial specialization, they strategy. At first sight, the two approaches have different sizes, since industries differ in appear to have no elements in common; they the external economies they can create. are also analytically fairly different. However, To highlight the forces at work in each may be viewed as an attempt to take on Henderson’s urban system, consider an board different ingredients of regional and economy with n 1 sectors, each produc- > urban economics. By mixing the “old” and ing a homogeneous and tradable good by the “new” in various combinations, they offer using labor. There is a large number L of new and alternative lines of research. identical consumers, each endowed with one unit of labor and Cobb–Douglas preferences 5.1 The Urban System, or Why Not All U x α 1 x α n h, where h 1 stands = 1 ⋯ n = Cities Are Alike for the fixed lot size and0 0 and < αi < i 1. Trading goods between cities ∑ α = The most enduring problem in spatial eco- is costless, so each good is available at the nomics is probably the existence of an urban same price across cities. In each city, there Proost and Thisse: What Can Be Learned from Spatial Economics? 623 is again a tension between external econ- returns become stronger in the production of omies associated with the agglomeration commodity i, there are fewer type-i cities but of firms at the CBD and the diseconomies they become larger; and (ii) when commut- generated by the need to consume land and ing costs rise, all cities become smaller, but commute to the CBD. The production func- the number of cities of each type increases. tion of sector i 1, , n is given by F i (N) Increasing returns prevent the proliferation 1 = … N +γi where 0 1 is the degree of cities (m ∗ when 0), while = < γi < i → ∞ γi → of increasing returns in sector i 1, , n; commuting costs prevent cities from being = … good n is chosen as the numéraire. Goods indefinitely large (L ∗ when t 0). i → ∞ → are indexed for 0 to It follows from (7) that large (small) cit- γ1 > ⋯ > γn > hold. Commuting requires tx units of the ies are specialized in the production of numéraire to cover distance x. Wages, goods with high (low) degrees of increasing the land rent, and the number and size of returns: L ∗ L ∗ . In larger cities, 1 > ⋯ > n type-i cities adjust to equalize utility across workers are paid higher wages, but the wage cities. difference is offset by higher land rent and Fujita and Thisse (2013) show that the commuting costs. Surprisingly, there may ∗ equilibrium involves be fewer large cities than small because m i depends on i. Hence, we need to impose 2 α ∗ _(1 i ) _t restrictions on the consumption and pro- (6) m i i − γ L, = α γi 4k duction parameters to get a pyramidal urban system. i 1, , n 1, = … − Duranton and Puga (2005) go one step further by recognizing that firms are pack- type-i cities whose size is given by ages of different functions, such as headquarters and production plants. Due to (7) L ∗ _ γi _4k , i 1, , n, the development of new information and i = 1 t = … − γi communication devices, firms are now able to distribute these functions among geo- (1 ) where k 4 t γ1/ −γ1 1 decreases graphically separated units in order to ben- ≡ ( γ1/ ) ( − γ1) with t. Since urban costs are higher in larger efit from the attributes specific to different cities than in smaller, wages are higher in the locations. However, caution is needed. Since former than in the latter. This reflects the production requires both embodied and fact that larger cities have a higher degree of disembodied knowledge, the transmission increasing returns. of bits of information via e-devices remains Hence, the equilibrium number of type-i incomplete and imperfect (Leamer and cities decreases with stronger scale econo- Storper 2001). When communication costs mies, but increases with lower commuting between spatially separated headquarters costs. Equilibrium city sizes increase with the and plants are high, firms remain integrated intensity of increasing returns, but decrease and the urban system displays the pattern when commuting becomes more expensive. described above. By contrast, when commu- A higher expenditure share on good i leads nication costs are sufficiently low, Duranton to a larger number of type-i cities whose size and Puga (2005) show that headquarters get remains the same. Based on (6) and (7), the concentrated in a few large cities where they fundamental trade-off between increasing use a wide array of business-to-business ser- returns and commuting costs shapes the vices, while plants are located in specialized urban system as follows: (i) when increasing and smaller cities. In other words, cities shift 624 Journal of Economic Literature, Vol. LVII (September 2019) from sectoral specialization to functional common utility level. Eliminating differ- specialization. ences in efficiency, amenities, or frictions Fujita, Krugman, and Mori (1999) develop leads to a significant reallocation of people a very different approach that relies on eco- across cities, but only to small gains in wel- nomic geography. There are several tradable fare (at most 2 percent). The perfect mobil- goods produced under increasing returns ity of labor is likely to play an important role and monopolistic competition. Land is used in “re-optimizing” the city distribution and by farmers to produce the agricultural good, limiting losses in welfare. The same exer- but neither firms nor manufacturing workers cise is undertaken for 212 Chinese cities. use land. Under CES preferences, each good This also generates significant changes in is characterized by a specific elasticity of sub- city size, but the gains in welfare are now stitution. Intercity trade is costly, but the unit substantial, exceeding 40 percent in some transport cost is the same across goods. As cases. One possible explanation for this dif- the total population grows, Fujita, Krugman, ference in results might be the presence of and Mori (1999) show that a hierarchical substantial constraints on internal migration urban system emerges: higher-rank cities in China, which prevent the large Chinese provide a larger number of manufactured cities from reaching their efficient size (Au goods. Hence, cities are diversified. In addi- and Henderson 2006, Bosker et al. 2012). tion, there is two-way trade across cities This modeling approach helps one under- because cities produce differentiated goods. stand how some of the main driving forces Horizontal relations among cities are thus of spatial economics interact to determine superimposed on the pyramidal structure of the city distribution. However, the model is the urban system. There is also trade between too stylized to trace back the origin of differ- cities and the rural areas where farmers live ences in productivity and amenities. and work. However, this approach remains The Zipf law.—The actual number and in the tradition of the CP model as cities size of cities seem to obey a simple, but have no spatial extension. intriguing, empirical rule, which keeps draw- Last, Desmet and Rossi-Hansberg (2013) ing attention. In 1913, the German geogra- construct yet another model to understand pher Felix Auerbach found an unexpected the formation of a system of cities with- empirical regularity: the product of the pop- out appealing to specialization and trade. ulation size of a city and its rank in the distri- The population consists of identical and bution appears to be roughly constant for a perfectly mobile individuals. The city size given country. To put it differently, if there is distribution is the outcome of the inter- a single type-1 city, the two type-2 cities have play between three effects, i.e., produc- half the population P1 of the largest city, the tive efficiency, consumption amenities, and three type-3 cities host a third of that popu- spatial frictions. Amenities are exogenous lation, and so on. Denote by Pi the popula- shocks that affect preferences, while the tion of cities of rank i in the urban hierarchy. main friction stems from commuting in a Formally, the Zipf law rule holds that monocentric city. Commuting requires a public infrastructure financed by a tax on log i log P blog P labor. The model is calibrated to the US = 1 − i cities with more than 50,000 inhabitants. This model is then used to assess the effects with b 1. A high number of estimations of = of the aforementioned three components b suggest a value close to 1 . Even if a power on the size distribution of cities and the function provides a good approximation Proost and Thisse: What Can Be Learned from Spatial Economics? 625 of the population distribution, is b 1 cities first-order stochastically dominates = the best estimation? Using an algorithm to that in small cities. So, we need to determine determine, in a consistent way, city bound- what large and small cities look like when aries with high-resolution geographical data, workers are heterogeneous in skills. This is Rozenfeld et al. (2011) find that the Zipf law precisely what the new generation of mod- is a good approximation of the population els aims to explain by studying the sorting of distribution for Great Britain and the United heterogeneous workers between and within States. These authors also find that the same cities. Importantly, these models explicitly rule applies to the area distribution. The address the issue of human capital whose pooled estimate of the coefficientb obtained empirical relevance was stressed in sec- by Nitsch (2005) in a meta-analysis combin- tion 4.1. In equilibrium, individuals do not ing 515 estimates from 29 studies suggests want to change place and occupation, while a value close to 1.1 ! Can such a remarkable all markets clear. Unlike Henderson (1974, result be micro-founded by an urban eco- 1988), these models do not rely on the pres- nomics model? ence of “large agents” such as developers. In Using the above solution of Henderson’s other words, cities emerge through the inter- model sheds light on the Zipf law. Multiplying play between choices made by a large num- ∗ ∗ m i and N i yields the total population ber of small agents. P (1 ) L living in type-i cities. Agglomeration, sorting, and selection.— i = αi − γi Renumbering the sectors for P The economy consists of a continuum of 1 > ⋯ > Pn 1 Pn to hold, we obtain monocentric cities and a continuum of indi- − > viduals who differ in skill s . An individ- ∈ ℝ+ ln i ln ln (1 ) ln ln (1 ). ual’s productivity hinges on two factors: his = α1 + − γ1 − αi − − γi skill and his matching with a specific city. Since this expression involves demand- An individual knows his skill, but the qual- and supply-side parameters that are a priori ity c of the match with the city is a priori independent, there is a priori no reason to unobservable. When an individual locates expect the right-hand side to be equal to the in a city, he observes his own productivity, left-hand side. given by c s , where c is φ = × ∈ ℝ+ ∈ ℝ+ A considerable effort has been made the realization of a random variable. This to explain the Zipf law (see, e.g., Gabaix variable accounts for the environment that 1999; Eeckhout 2004; Hsu 2012; Behrens, determines the quality of the match between Duranton, and Robert-Nicoud 2014). The the individual and the city. Knowing his pro- plethora of existing setups relies on heavy, ductivity, the individual chooses to be an and sometimes ad hoc, models that provide, entrepreneur or a worker. Individuals are at best, approximations of the Zipf law. This risk neutral and consume a final good and a is the reason why we believe that this law is a fixed lot size. Hence, individuals maximize mystery and likely to remain so. their consumption of the final good. This good is produced by using a CES bundle of 5.1.2 Cities with Heterogeneous Workers differentiated inputs, where 1 is the σ > In Henderson-like models, cities are elasticity of substitution across inputs. An populated with identical and homogeneous entrepreneur sets up a firm that uses labor workers. Yet, it is well documented that cit- to produce a variety. Intermediate firms are ies host heterogeneous workers, and thus heterogeneous, compete under monopolis- differ in their respective social composition. tic competition, and their number is equal In particular, the wage distribution in large to the number of entrepreneurs. Under 626 Journal of Economic Literature, Vol. LVII (September 2019) commuting costs linear in distance to the 1, rather than . It follows from (8) that λ > φ CBD (tx ), per capita urban costs are equal to Y L increases by a factor equal to 2 1. / λ > tL 4 where L is the city size. However, the cutoff changes with the skill / The great merit of the model developed distribution, which is now F ( ). It can be λφ by Behrens and coauthors is that it allows shown that the new cutoff is equal to . λφmin one to (i) separate agglomeration economies Hence, the intermediate sector involves associated with city size, the sorting of work- more productive firms, which pay a higher ers, and the selection of efficient firms; and wage, so the entrepreneurs also earn more. (ii) study how these forces interact to shape In other words, a higher-skilled popula- the urban system. It is natural to begin with tion generates a human capital externality a city c whose population L and productivity in which the productivity of an individ- distribution F ( ) are given. ual increases with that of his coresidents. φ Since individuals are heterogeneous, Behrens and coauthors show how the inter- there is a cutoff such that an individual play between these externalities interact for φmin chooses to be an entrepreneur if , skill and population size to be complements, φ > φmin while those with a productivity smaller than that is, the earnings of workers and entre- become workers. Since the production preneurs increase with both their individ- φmin function is CES, the share of entrepreneurs ual skill and the city size. This is consistent is independent of the population size L. with De la Roca (2017), who observes that This provides a rationale for the absence of Spanish migrants who move to big cities selection found by Combes et al. (2012) in are positively selected by their educational French cities. Behrens and coauthors show level and individual productivity. that the production function of the final sec- Since highly skilled individuals benefit tor may be rewritten in terms of workers’ from living and working in large and expen- productivity: sive cities while the number of potential cities is large, there exists a unique equilibrium 1 ( 1) in which cities are homogeneous in skill. ∞ 1 / σ− (8) Y σ− dF( ) However, due to the variations in the quality [ min ] = ∫φ φ φ c of the match, cities host people who differ in productivity, hence workers and entrepre- φmin ( 1) [ dF( )] ⋅ L σ/ σ− . neurs are heterogeneous. The equilibrium × ∫0 φ φ urban system displays the following major characteristics. The size of a city increases The total output per capita is thus with the intensity of agglomeration econ- 1 ( 1) proportional to L / σ− , as in the case omies (1 ( 1)) and the skill level of its / σ − of homogeneous individuals (Fujita and residents (s), but decreases with urban costs Thisse 2013, chap. 4). Raising L leads to a (t). Hence, the fundamental trade-off of higher number of intermediate firms, which spatial economics is augmented by a skill makes the final sector more efficient and effect that magnifies the agglomeration leads firms to pay a higher wage. Hence, economies. Since two cities sharing the there are agglomeration economies asso- same skill have the same size, it is possible ciated with population size. The city has to retrieve their number from the skill dis- a finite size if urban costs rise faster than tribution. When the cumulative distribution per capita income, that is, 2. Assume of skills is concave, there are fewer bigger σ > now that the productivity of each individual cities. In this case, the urban system dis- of the same population is given by with plays a pyramidal structure with the most λφ Proost and Thisse: What Can Be Learned from Spatial Economics? 627 efficient cities at the top and the least efficient learning and producing. They may exchange at the bottom. ideas with and learn from anyone. However, There is no question that the work of an individual learns more from interacting Behrens and coauthors provides a rich with more-skilled individuals. Learning, one description of the urban system as cities dif- of the main agglomeration economies dis- fer in skills and accommodate individuals cussed in section 4.1, is here endogenous, who differ in productivity. What makes this costly, and city-specific. By increasing the paper unique is that the model identifies productivity of individuals involved in the conditions implying that skill and population exchange of ideas and knowledge, the exter- size are complements. That the aggregate nality generated by learning plays the role of productivity of bigger cities exceeds that of external increasing returns. smaller cities while the former pay a higher Key to Davis and Dingel (2019) is the idea nominal wage than the latter concurs with that individual skills and the quality of the Henderson (1974; 1988), which is reassur- learning environments are complements. ing. Both settings thus provide a rationale for More specifically, the concentration of skilled the existence of the urban wage premium. workers magnifies each worker’s own pro- However, unlike Henderson, cities produce ductivity advantage. This is the agglomera- the same final good since the production tion force. Obviously, urban costs are higher function is the same across cities. Therefore, in bigger cities. Therefore, services are also the urban system is formed by autarkies. more expensive because their producers must City size and learning.—To the best of our be compensated for these higher costs, which knowledge, Davis and Dingel (2019) are the makes urban costs even stronger as a disper- first who have shown how costly and freely sion force. Producers of tradables will choose chosen face-to-face contacts across hetero- to live in big cities where urban costs are high geneous individuals may drive urbanization and services expensive if their earnings are and the emergence of an urban system. sufficiently high. In equilibrium, individuals Again, the economy consists of a continuum choose an occupation, a city, and an alloca- of monocentric cities and a continuum of tion of time to maximize utility, and all mar- individuals who differ in skill. Individuals kets clear. Davis and Dingel show that, when consume three goods: non-tradable services, urban costs are not too high, there is spatial tradable goods, and housing. Individuals sorting along the skill dimension: large cities choose to produce non-tradable services are more skill-abundant and skill premiums or tradable goods. Urban costs are equal to are higher in bigger cities, in line with the tL 4 where L is the city size. The indirect empirical evidence provided by the authors. / utility of an individual with income y in city Otherwise, as in the CP model, stable equilib- c is V(s, c) y np tL 4, where p (n) is ria have equal-sized cities when the agglom- = − c − / c the price (consumption) of non-tradables. eration force is weak relative to urban costs. Non-tradables are produced under con- The complementarity between skills.— stant returns and the corresponding individ- Eeckhout, Pinheiro, and Schmidheiny ual income is city-specific and normalized to (2014) observe that the standard deviation pc. By contrast, the output of an individual of the skill distribution rises with city size. producing tradables depends on his skill and More specifically, these authors find that his learning opportunities, which are deter- the distribution of skills in US cities has mined by the composition of the local pop- thick tails in large cities, i.e., these cities ulation. Individuals producing tradables can host disproportionately both high-skilled freely divide their available time between workers and low-skilled service providers. 628 Journal of Economic Literature, Vol. LVII (September 2019)

Hence, the social structure of big cities is Unfortunately, apart from Fujita, Krugman, more heterogeneous than that of small cit- and Mori (1999), the new urban system mod- ies. Eeckhout and coauthors argue that the els still assume that intercity trade is costless complementarity between heterogeneous or cities produce the same good. In other workers drives the spatial sorting across words, all the settings fail to recognize that cities. Therefore, the key issue is to deter- cities are anchored in specific locations and mine which combination of skills mutually embedded within intricate networks of trade boosts their productivity: Do the high-skilled relations that are critical in explaining cities’ workers benefit from the presence of sizes, industrial mixes, and social structures. medium-skilled or low-skilled coworkers? Therefore, cities are like “floating islands.” Differences in cities’ total factor produc- A comprehensive theory of urban systems tivity lead to differences in demand for skills. should explicitly account for city location. Using CES-aggregators for the production For this, we must assume positive transport function with three types of labor ranked by costs. This proves to be a difficult task because increasing order of skill, Eeckhout and coau- commodities are sold at different prices in thors characterize the market outcome for different cities. Furthermore, local and global each of four technology patterns: extreme forces interact to determine the geography of skill and top skill, each with complements or production and employment, as the size of substitutes. They show that the skill distribu- cities depends on the interplay between the tion has thicker tails in the larger city under emergence of employment centers within the extreme-skill complementarity (1 and 3). cities and trade flows between cities. This is a Under the top-skill complementarity (2 and task that quantitative spatial modeling aims to 3), only the highly skilled are disproportion- accomplish. ately represented in the larger city. Top-skill 5.2 Quantitative Spatial Economics and extreme-skill substitutability yields the mirror-image results. All of this pleads in Most economic geography models, by favor of complementarity between high- and focusing on two symmetric regions, are low-skilled workers. highly stylized settings. Likewise, by assum- The above papers complement each other ing a featureless space with a given CBD, well. Behrens and coauthors show that a the monocentric city model abstracts from population size externality and a composition spatial characteristics that affect both con- externality make skill and population com- sumers’ locational choices and the layout of plements, which generate spatial sorting. cities. The difficulty in accounting for spatial Davis and Dingel (2019) show that a learn- inhomogeneities and the lack of an analytical ing externality magnifying individual pro- solution to the dimensionality problem has ductivity gives rise to spatial sorting through led to the development of a new strand of big cities displaying a disproportionate literature, called quantitative spatial models. and increasing share of skills. According to Eeckhout and coauthors, the spatial sorting 5.2.1 What Are Quantitative Spatial of skills is driven mainly by the complemen- Models? tarity between high-skilled and low-skilled workers, which entails big cities hosting dis- The aim of quantitative spatial models proportionately both high- and low-skilled (QSMs) is to overcome the above limits by workers. It is reasonable to expect the three developing general equilibrium settings that ideas to be part of the story. Combining them consider theory seriously (see Desmet and within the same setting is another issue. Rossi-Hansberg 2013, Allen and Arkolakis Proost and Thisse: What Can Be Learned from Spatial Economics? 629

2014, Ahlfeldt et al. 2015, and Redding Uniqueness may be obtained by introducing 2016 for the pioneering contributions). restrictions on the parameters for the dis- QSMs take us further than the regional persion forces to dominate the agglomera- general equilibrium model à la Bröcker, tion forces. Alternatively, adding a sufficient Korzhenevych, and Schürmann (2010) amount of heterogeneity to the model often discussed in section 3.5, and even further allows uniqueness to be proven (Herrendorf, than the land use models à la Anas and Valentinyi, and Waldmann 2000). As Liu (2007) discussed in section 4.3. More observed by Redding and Rossi-Hansberg specifically, QSMs take on board the main (2017), having a large amount of data may be agglomeration and dispersion forces uncov- sufficient to show that the mapping is unique ered in regional and urban economics, such (see, e.g., Ahlfeldt et al. 2015). as market access, the relationship between At this stage, QSMs are used to make pre- productivity and density, and urban costs. dictions about the impact of policies on the Inevitably, they must leave out other effects, equilibrium spatial distribution of activities, so that the specification of the theory model which amounts to undertaking numerically a is a key issue. QSMs also account for a large wide array of large comparative statics exer- number of locations that are differentiated cises that cannot be done analytically. Here, exogenously by given amenities and or pro- QSMs have several merits that are worth / ductivity differences. Therefore, these mod- stressing. First, the predictions take into els may be viewed as settings that provide rich account all the general equilibrium effects syntheses of regional and urban economics. captured by the model, something difficult The main purpose of quantitative spatial to achieve with the reduced-form approach. models is not (necessarily) to provide new Second, the model yields quantitative pre- theoretical results but to assess public pol- dictions. More specifically, a theory model icy interventions or the impact of shocks. can tell us that a specific shock has a positive To achieve their goal, these models must impact on some key variables, but the model admit a small number of exogenously given is often unable to say how strong or how weak parameters (e.g., the elasticity of substitution the effect is. By contrast, the quantitative under CES preferences), while the other model gives us information about the mag- parameters are calibrated on the observed nitude of the effect, while the reduced-form variables, i.e., the data. The model is then approach focuses on qualitative relationships “inverted” to retrieve from the data the val- between parameters and variables. ues of the other, unobservable variables. Third, undertaking large comparative This inversion is possible if a one-to-one statics with such models allows one to check relationship exists between the model’s the theoretical robustness of the results parameters and the data. When this is so, obtained with the “toy models” consid- the model is exactly identified and the equi- ered in sections 3 and 4. Fourth, quantita- librium spatial distribution of activities is tive spatial models permit new questions unambiguously determined. One feature of to be addressed. For example, we know quantitative models is worth stressing here: little about how commuting and trade fric- the equilibrium must be unique to ensure tions interact to shape the urban system, an that the model-based counterfactuals have issue that Behrens et al. (2017) explore. As unambiguous implications. Yet, settings expected, commuting and trade costs matter with increasing returns or externalities typ- for the size of cities. What is less expected ically display several equilibria. In this case, is that Behrens et al. also find that neither the inverse mapping need not be unique. type of friction significantly affects the US 630 Journal of Economic Literature, Vol. LVII (September 2019)

city-size distribution. This suggests that where wr (Pr) is the nominal wage (the CES changing spatial frictions affect the relative price index) in region r. In this case, work- size of cities, but not much their location and ers are sorted according to their productivity, rank in the urban hierarchy, as in Desmet whereas others will be gathered along their and Rossi-Hansberg (2013). In other words, preferences for specific amenities. the absolute level of spatial frictions would 5.2.2 What Do Quantitative Spatial Models be less important than their relative levels. Deliver? Last, different models are isomorphic to each other (e.g., internal economies When studying the impact of transport of scale and monopolistic competition projects, the big advantage of QSMs is that versus external economies of scale and they can take into account all the effects asso- perfect competition). In this case, the pre- ciated with the new infrastructure. Obviously, dictions are valid for a family of models, the connected locations are directly affected, not just for the model used. For example, but some of the unconnected locations are a setting under perfect competition and the affected indirectly because some least-cost Armington assumption is isomorphic to a routes may go through the new links. Helpman-like model with multiple regions, Consequently, the new infrastructure leads internal economies of scale, and monop- to a redistribution of labor across regions. olistic competition (Allen and Arkolakis A prominent example of the general equi- 2014). However, the latter and an Eaton librium approach can be found in Allen and and Kortum (2002) model, where goods are Arkolakis (2014), who develop a continuous produced under constant returns and per- location model for the United States and fect competition, do not generate the same use a rich, in-depth treatment of transport predictions (Redding 2016). costs, which are modeled by taking into Researchers working with QSMs seem to account all geographic details, including the have a taste for Helpman-like models (1998) modal choice. Production is assumed to be where the dispersion force lies in a fixed sup- perfectly competitive; preferences are CES ply of land at each location. This is probably and the Armington assumption explains why because this force captures the basic idea trade occurs. Allen and Arkolakis use their that a growing population generates higher setting to assess the effects of the interstate urban costs (see section 4). Other research- highway system by recomputing all bilateral ers stress more differences in amenities transport costs without the interstate high- and productivity. To illustrate, consider the way option. This would reduce total GDP following simple example. Let A (s) 0 by 1.1 percent to 1.4 percent, which means r > be the amenity stock available in region r, that the interstate highway system is a pro- which need not be evaluated in the same ductive investment as a whole, even though way across workers who have different skill the network is likely to be far from optimally levels, s. For example, individuals may be designed. heterogeneous in their attitudes toward Redding (2016) undertakes various large amenities (see Diamond 2016 and Redding comparative statics experiments by changing 2016 who describe migration by discrete the value of transport costs between some choice models). Under CES preferences, location pairs in a grid network. According the indirect utility of an s-worker residing in to Helpman (1998), falling transport costs region r is then as follows: foster the dispersion of activities. Using a Helpman-like approach, Redding finds that _wr Vr (s) Ar (s) , the populations of the largest centers tend = Pr Proost and Thisse: What Can Be Learned from Spatial Economics? 631 to decrease after a transport improvement production externalities (15 percent versus affecting vertical and horizontal routes of 7 percent). Last, the elasticity of produc- the network, which is reassuring. More tivity with respect to density within cities importantly, by using a multi-regional gen- is significantly higher than that reported in eral equilibrium model, his analysis allows across-city estimations (7 percent versus one to determine which regions are posi- 3 percent). Unfortunately, the various spatial tively or negatively affected by the transport externalities used in the paper remain black improvement, and by how much the equilib- boxes. In particular, the specifications used rium regional populations change. do not allow one to discriminate between The same quantitative methods may also the different agglomeration economies dis- be used to study how the internal structure cussed in section 4, while it is not clear what of a city, which consists of a discrete set amenities there really are. of blocks, is affected by various shocks (Redding and Rossi-Hansberg 2017). Along 5.2.3 How to Combine Geography and these lines, the best illustration of what has Growth? been achieved is probably the setting developed by Ahlfeldt et al. (2015), which is both Since the forces at work in growth and tractable and amenable to empirical analysis. geography models are similar, a solid foun- These authors consider a fabulous natural dation for cross-fertilization exists between experiment, i.e., the fall of the Berlin Wall. the two fields. However, requiring agents to From the end of World War II to 1989, the care about the overall distribution of activi- city of Berlin was divided into East Berlin ties over space and time vastly increases the and West Berlin, which could be considered complexity of the problem. Furthermore, as two local economies separated by prohib- working with aggregates is ill-suited itively high transport and communication because different sectors obey very differ- costs. The division of Berlin affected West ent spatio-temporal patterns. Hence, we Berlin through various channels, including have to consider a multi-sector economy, the loss of spillovers generated by the con- which adds an additional degree of diffi- centration of jobs in the prewar CBD and culty. So far, this is beyond reach. In a pio- the drop in the number of employment neering paper, Desmet and Rossi-Hansberg opportunities in East Berlin. The fall of the (2014) propose a solution that consists of Berlin Wall was an unanticipated and sud- adding enough structure to the model for den shock. Ahlfeldt et al. (2015) use this the agents to ignore the future paths with- event as a natural experiment to see how out affecting the payoffs of their current the resulting changes in distance between decisions. The argument involves two main location pairs have affected the location of steps. activities within West Berlin. More specifi- Land and innovation.—Desmet and cally, their aim is to explain both qualitatively Rossi-Hansberg (2012) make a welcome and quantitatively the observed changes contribution by showing that land is key in in city structure, including a relocation of firms’ decision to invest in new technolo- the CBD. gies. Consider a one-sector economy where For our purpose, the following results are a large number of firms produce a homo- worth emphasizing. First, both spatial pro- geneous good under constant returns using duction and consumption externalities are land and labor. Space is given by X [0, 1]. = substantial and highly localized. Second, Each firm uses a unit lot size and there is consumption externalities matter more than a single firm in each location. Thus, land at 632 Journal of Economic Literature, Vol. LVII (September 2019) x X has the nature of an essential and sectors, manufacturing and services, and two ∈ non-replicable input. Since the marginal inputs, land and labor. Firms choose how productivity of labor is decreasing, a firm’s much to produce and how much to invest in marginal cost increases. As a result, each technology at each period. Goods and ser- firm has awell-defined size. A firm’s pro- vices are traded by incurring iceberg trans- duction function is well-behaved and given port costs. When firms innovate, they can by Q AF(1, L) where L is the number secure the benefits of innovation during the = of workers and A is a Hicks-neutral shifter current period. Before the next period, the that describes the firm’s level of technology. new knowledge is diffused across locations Note that innovation cannot be appropriated according to an exponential distance-decay via patents and is specific to one location. function. This spillover is the agglomeration Finally, the cost of acquiring technology A is force of the model. As for the dispersion given by C (A) units of the output. force, it stems from the non-replicability of Since land is assigned to the highest bid- land, which leads to decreasing returns at the der, the equilibrium land rent at x under free firm level. Since each firm is negligible while entry, is given by the benefits of a current innovation last for only one period and diffuse across locations R(x) max p(x)A(x)F(1, L) w(x)L(x) p(x)C(A) , in the subsequent period, its current deci- = A, L { − − } sion to innovate has no impact on the stock where p(x) and w (x) are the output price of knowledge available in the next periods. In and wage at location x. Hence, in a per- other words, the firm’s decision to innovate fectly competitive environment with entry, is a static one. As a manufacturing or service firms choose to invest in better technologies firm’s production function increases with its because the land rent accounts explicitly for available stock of knowledge, there is more the costs they bear to acquire these technol- innovation in a more productive location. ogies. To put it differently, by innovating, This is the source of local growth. Geography firms can enhance their bid for land and matters because both transport costs and ensure the best locations. Thus, firms invest technology diffusion are affected by distance. in innovation until profits net of the cost of At this stage, Desmet and Rossi-Hansberg innovation are equal to zero. If land is not (2014) calibrate their model by borrowing a production factor, for any new technology parameter values from the literature and A, a firm chooses its labor input to equal- solving it numerically under CES prefer- ize price and marginal cost and, therefore, ences. The aim is to replicate the evolution incurs a loss equal to p (x) C(A). In this case, of the manufacturing and service sectors in firms choose to produce using the current the United States since 1950. Discussing all technology. their results would take us too far off course, Spatial development.—Desmet and so we will limit ourselves to those that are Rossi-Hansberg (2014) use the above idea directly related to our purpose. First, the to build the dynamics of a spatial economy model is able to show that the productivity on the basis that firms accumulate knowl- of the service industry has been catching up edge through two different channels, i.e., since 1995. This is explained by the spatial the firms’ decisions to innovate and the spill- concentration of service firms and the result- overs received from firms located nearby. ing innovation interactions. In every period, labor is freely reallocated Second, assume that manufacturing between sectors and across space; workers firms are spatially concentrated (e.g., in the do not consume land. There are two final Northeast and Midwest of the United States), Proost and Thisse: What Can Be Learned from Spatial Economics? 633 which makes them more productive because Despite its appeal, the setting proposed the diffusion of knowledge is localized. By by Desmet and Rossi-Hansberg (2014) contrast, the service firms are dispersed and, has awkward features. For example, the hence, less productive. As productivity grows equilibrium is independent of the relative steadily in manufacturing, more and more costs of shipping goods and services. This workers shift to services. When shipping the is a bit odd because shipping goods is much manufactured good is costly, the service firms cheaper than shipping services, which are choose to locate closer to the manufacturing often non-tradable. As in Rossi-Hansberg cluster so their workers have better access (2005), individuals do not consume land to goods. This increasing spatial concentra- and thus may move to and work in a cluster tion triggers the technological takeoff of the without affecting the corresponding land service firms. In other words, high transport values. Otherwise, the price of land would costs foster the collocation of service and man- be much higher in the cluster and in nearby ufacturing firms in adjacent clusters. As ser- locations, which makes the corresponding vice firms become increasingly concentrated, areas less attractive. In this case, it is not their productivity rises even further because clear that the collocation of the two sectors they keep innovating. As a result, the relative may emerge. price of goods declines as the manufacturing 5.2.4 Limits of Quantitative Spatial Models firms cluster in one area while the growth of the service cluster enhances competition for There is no question that the payoffs of land. This makes it more expensive for manu- QSMs are high. However, QSMs come at facturing firms to innovate, thus giving these a cost. First, specific functional forms must firms an incentive to move toward less dense be assumed. Consequently, the results are areas (e.g., the South of the United States). conditional on the corresponding functions. A two-region setting is too confined for these In our opinion, one of the main pitfalls of various patterns to unfold and is, therefore, QSMs is precisely the repeated use of the unable to capture such a dynamic evolution same functional form for preferences, so that in firms’ locational choices. we do not know how robust the predictions Last, we have seen that high transport found in the literature are. More specifically, costs entail static welfare losses through the CES is almost ubiquitous. Admittedly, fewer gains in specialization. The previous the CES is very convenient and has great argument shows that high transport costs merits that are too well known to be dis- generate welfare gains by fostering more cussed here. However, the CES is also very innovation through the progressive clus- peculiar. Indeed, the CES combined with the tering of the service sector. The numer- iceberg cost leads to a broad range of prop- ical analysis undertaken by Desmet and erties that are, unfortunately, difficult to gen- Rossi-Hansberg suggests that the dynamic eralize (Parenti, Ushchev, and Thisse 2017). gains associated with high transport costs But should we worry about this? It seems so offset the static welfare losses. In short, a because lowering transport costs intensifies dynamic, multi-regional setting may lead to competition and leads to lower prices and results that differ significantly from those a smaller number of firms. Furthermore, a obtained by using a static two-region model, constant elasticity of substitution is a bold such as those discussed in section 3.8 assumption that disregards the fact that the

8 Desmet and Rossi-Hansberg (2015) use a frame- climate change on the use of land for agriculture and work similar to the one above to study the effects of manufacturing. 634 Journal of Economic Literature, Vol. LVII (September 2019) entry of new varieties crowds the space of this approach highly desirable. A small num- product characteristics and makes varieties ber of papers that use quasi-natural exper- closer substitutes (Salop 1979). In this case, iments as an identification strategy suggest the elasticity of substitution increases with that the data do not reject the CES (Redding the number of varieties, which generates the and Sturm 2008, Donaldson 2018). However, pro-competitive effects generally associated when models are calibrated exactly, a poor with entry. The CES model of monopolistic choice of functional specifications eas- competition is unable to account for these ily passes unnoticed. Therefore, it is not first-order effects. unreasonable to question the validity of the Second, it is commonplace to use an structural approach when it systematically upper-tier Cobb–Douglas utility nesting uses the same specific model. At a time of CES lower-tier utilities. Under the com- rapid advances in computational power and bination of Cobb–Douglas–CES utilities, numerical methods, robustness checks about the welfare effect of a sectoral shock in the functional forms are called for. whole economy is confined to the direct welfare effect in the sector. Yet, one expects a positive shock to one sector to trigger a real- 6. Concluding Remarks location of budget and labor over all sectors. This puts some severe limitations on the gen- We have surveyed different strands of eral equilibrium effects. literature in an effort to show that a few Last, CES preferences display a very spe- general ideas can be used to answer the cial property: in a one-sector economy, the questions raised in the introduction, as well monopolistically competitive outcome is as many others. On the way we have, several socially optimal. However, in a multi-industry times, encountered the trade-off between economy, the optimality property ceases increasing returns and obstacles to the to hold because the allocation of resources mobility of goods, people, and information, across sectors is not optimal, as relative prices both of which appear under different guises. across markets are distorted while relative Nevertheless, despite this common thread, prices within markets are not. But does it spatial economics is still searching for a matter? The answer is probably yes. Behrens general framework that would encompass et al. (2016) is a telling example about the regional, urban, and transportation econom- possible welfare biases associated with this ics. Given the complexity of the issue, the combination. They consider a multi-sector search is likely to continue for a long time. model of monopolistic competition with This is why we advocate an agnostic attitude. CES and constant absolute risk aversion Simple and stylized settings that can be (CARA) preferences, respectively, and assess fully solved analytically are useful in under- the welfare loss within and between sectors standing how various effects interact. The generated by positive markups. Quantifying merit of such models is that they bring the CARA and CES models on French and to the fore new effects that stem from the British data, Behrens et al. (2016) find that blending of regional and urban economics. there is a substantial aggregate welfare loss In this respect, the work of Akamatsu et al. of 6 percent to 8 percent under CARA pref- (2017) looks promising. These authors link erences, while the welfare loss is much lower different models within a unifying setup that under CES preferences (less than 1 percent). relies on just two basic classes of dispersion In short, SQMs rely on settings that have forces. This allows them to make predic- clear theoretical assumptions, which makes tions about the impact of transport costs in Proost and Thisse: What Can Be Learned from Spatial Economics? 635 settings that are significantly more general. of identical agents lack robustness. For Quantitative spatial models are able to tackle example, firms’ heterogeneity is critical to the same issues from a broader perspec- understanding firms’ behavior in the inter- tive. Unfortunately, general results are hard national marketplace and the implications to prove while the main results obtained in of different policies. The heterogeneity of simple settings may not carry over to het- individuals is probably as important as that erogeneous geographical settings. Among of firms. Discrete choice models, which have other things, quantitative models can be started being used in quantitative spatial used to test the relative robustness of results economics, should be given more attention obtained with simple models. to capture the heterogeneity of individuals. We concur with Holmes (2010) that the There is also a need to investigate new ana- same agnostic attitude should prevail in lytical tools. For example, potential games empirical research. Although a structural have already proven very useful in study- approach is preferable because it considers ing congestion in travel flows (Beckmann, several general equilibrium effects, there McGuire, and Winsten 1956) and the CP is still room for reduced-form approaches model (Oyama 2009). More work along where key parameters are estimated. After these lines is called for.9 all, some of the structural parameters used in It is our contention that spatial econom- quantitative models are often borrowed from ics has reached a sufficiently mature level estimations undertaken in other papers. We to trigger cross-fertilization. The work of also need a more systematic confirmation of Moretti (2011) and Zenou (2009), which lies results. At some point, it will become nec- at the interfaces of labor and spatial econom- essary to explore more systematically the ics, provides an illuminating example of what robustness of the conclusions drawn from could be accomplished by combining fields. a long string of empirical papers devoted In particular, one may wonder why urban and to agglomeration (dis)economies and to the regional economics remain so far from trans- impact of transport projects. portation economics. For example, housing The mobility of agents is solved under and local labor markets are intimately inter- extreme assumptions. A large number of twined with the transport markets. What is regional and urban economic models assume more, the issue has a strong policy relevance. identical individuals and costless mobility, How to plant the seeds of urban economics while transport economics often assumes in urban planning, and how urban planning that agents are fixed. These are signs of a may affect what urban economics teaches us, poor understanding of the issue. A more is also critically in short supply. realistic modeling of residential mobility Transportation economists should pay costs would help one to better understand more attention to the wider benefits associ- the evolution of spatial patterns. Most con- ated with the construction of new transport tributions also assume that firms and workers infrastructure, while regional and urban move together. However, it is far from being economists should pay more attention to obvious that the mobility of firms and individuals obey the same rules. Hence, studying 9 Researchers appear to have missed the fact that many the steady states of models in which firms spatial models have the particular structure of a population and individuals do not react in unison would game, i.e., games with a large number of small and anon- be a welcome addition to the literature. ymous players (firms or workers), a finite number of pure strategies (the locations), and continuous payoffs. Such It is well known that results obtained in games always have a Nash equilibrium in pure strategies many economic fields under theassumption and display convenient properties (Sandholm 2010). 636 Journal of Economic Literature, Vol. LVII (September 2019) the role of transport networks. Spatial econ- Paper 17-E-125. omists should no longer treat the transport Akamatsu, Takashi, Yuki Takayama, and Kiyohiro Ikeda. 2012. “Spatial Discounting, Fourier, and sector as a black box, but rather as an indus- Racetrack Economy: A Recipe for the Analysis of trial sector per se that has its own specificities. Spatial Agglomeration Models.” Journal of Economic In addition, the almost ubiquitous iceberg Dynamics and Control 36 (11): 1729–59. Albouy, David. 2009. “The Unequal Geographic Bur- assumption misses important characteristics den of Federal Taxation.” Journal of Political Econ- of transport costs such as density economies omy 117 (4): 635–67. and distance economies. Transportation Albouy, David, Gabriel Ehrlich, and Minchul Shin. 2018. “Metropolitan Land Values.” Review of Eco- economists also expect regional and urban nomics and Statistics 100 (3): 454–66. economists to help them assess the locational Allen, Treb, and Costas Arkolakis. 2014. “Trade and and welfare impacts of real-world projects. the Topography of the Spatial Economy.” Quarterly Journal of Economics 129 (3): 1085–140. Examples are numerous and include the Alonso, William. 1964. Location and Land Use: Toward provision of new transport infrastructures a General Theory of Land Rent. Cambridge, MA: in the United States, the construction of a Harvard University Press. Anas, Alex, and Robin Lindsey. 2011. “Reducing Urban large mass transport infrastructure such as Road Transportation Externalities: Road Pricing in the Grand Paris Express, the construction Theory and in Practice.” Review of Environmental of highways in Western China, and the wide Economics and Policy 5 (1): 66–88. Anas, Alex, and Yu Liu. 2007. “A Regional Economy, array of transport projects discussed at the Land Use, and Transportation Model (RELU- European Commission. TRAN): Formulation, Algorithm Design, and Test- A final comment is in order. Economic ing.” Journal of Regional Science 47 (3): 415–55. Anderson, James E. 2011. “The Gravity Model.” development and underdevelopment is one Annual Review of Economics 3: 133–60. of the facets of the lumpy distribution of Anderson, James E., and Eric van Wincoop. 2004. activities. The material covered in this survey “Trade Costs.” Journal of Economic Literature 42 (3): 691–751. is relevant for economies where institutions, Anderson, Simon P., Jacob K. Goeree, and Roald such as land titles, patents, building regula- Ramer. 1997. “Location, Location, Location.” Jour- tion authorities, work well and governments nal of Economic Theory 77 (1): 102–27. Anderstig, Christer, Svante Berglund, Jonas Eliasson, supply essential infrastructure. 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