Urbanization and City Specialization: A Comparative Analysis of U.S. and Chinese Cities, Slides of Geography

Download Urbanization and City Specialization: A Comparative Analysis of U.S. and Chinese Cities and more Slides Geography in PDF only on Docsity! The Geography of Development within Countries Klaus Desmet SMU J. Vernon Henderson LSE August 29, 2014 Abstract This chapter describes how the spatial distribution of economic activity changes as economies develop and grow. We start with the relation between development and rural-urban migration. Moving beyond the coarse rural-urban distinction, we then focus on the continuum of locations in an economy and describe how the patterns of convergence and divergence change with devel- opment. As we discuss, these spatial dynamics often mask important differences across sectors. We then turn our attention to the right tail of the distribution, the urban sector. We ana- lyze how the urban hierarchy has changed over time in developed countries and more recently in developing countries. The chapter reviews both the empirical evidence and the theoretical models that can account for what we observe in the data. When discussing the stylized facts on geography and development, we draw on empirical evidence from both the historical evolu- tion of today’s developed economies and comparisons between today’s developed and developing economies. 1 Introduction As economies grow and develop, the spatial distribution of population, employment and production changes. Probably the most prominent feature of this spatial transformation is increased urbaniza- tion. Between 1950 and 2009 the world’s urban population more than quadrupled from 732 million to 3.4 billion, as the world moved from being under 30% urbanized to over 50%. Understanding the patterns of this rapid transformation is of paramount importance to policy makers. More than 80% of governments are concerned about the geographic distribution of people, and nearly 70% of them have implemented policies to reduce internal migration (United Nations, 2010). The goal of this chapter is to review what we know about the spatial distribution of economic activity and development. An important point we will make is that this spatial transformation can be viewed at different spatial scales and through different lenses. Which one is more useful will largely depend on the issue of interest. One traditional divide is to contrast rural and urban areas, but that fails to capture the full richness of a country’s spatial transformation. Rather than splitting up locations into two types (urban or rural), it is often useful to think of locations as a continuum, going from more rural (smaller and/or less dense) to more urban (larger and/or more dense). The distribution of population and economic activity along that continuum changes radically with development, and these changes mark how we view the overall geography of a country. What happens with aggregate employment and production often masks interesting differences across sectors. Manufacturing and services have exhibited very different spatial growth patterns over time. Once a country becomes more urbanized, these changes and the spatial distribution are often viewed through a more narrow lense that focuses on the urban sector. Within the urban sector there is enormous heterogeneity across the hierarchy of cities, and the transformation of activities differs across that hierarchy. Finally we note that, while much of what we see is driven by market forces, the role of government in economies has grown. As a result, in today’s developing countries economic policies can have a strong effect on both the location and the concentration of economic activities. This chapter reviews the models and evidence that characterize these processes. Section 2 starts by looking at the urban-rural divide and then focuses on the continuum. It analyzes population and income convergence versus divergence and the reshaping of the location patterns of people and economic activity, especially in today’s richer countries as they developed through the 19th into the 20th century. Another issue of interest that we discuss is the link between an economy’s overall spatial structure and its aggregate growth. Section 3 also focuses on the continuum, but takes a sectoral approach by looking at the structural transformation of economic activities as a country develops and matures. The distribution of economic activity differs across sectors, and these differences change over time as countries develop. Section 4 looks at the urban sector, with particular attention to the urban hierarchy. It explores aspects of the transformation of the urban sector over the last 100 years in more developed countries and the more recent, rapid changes in developing countries. Section 4 also discusses the key issue of how government policies in today’s developing countries affect the transformation and the concentration of economic activities. When discussing how the spatial distribution of economic activity changes with develop- ment, we draw on evidence both from comparing today’s developed and developing economies and from analyzing the long-run evolution of today’s developed countries. Although using historical evidence of today’s developed countries to explain the spatial patterns of present-day developing countries is useful, this should be done with care. For example, because of trade and comparative advantage, the role of the structural transformation from agriculture to manufacturing in explaining urbanization in today’s developing countries may be different from its role in 19th century Europe. 2 The Lucas (2004) model captures some of the stylized facts of rural-urban migration. First, as the economy develops, people move gradually from the rural to the urban sector. Over time, as the human capital frontier moves out, it becomes less costly to accumulate human capital, making cities more attractive. The human capital externality — the fact that cities are good places to accumulate human capital — is key for this result. Second, recent arrivals do not work, and instead spend their time improving their human capital. This is akin to the Harris and Todaro (1970) model where many of the recent arrivals are unemployed. The difference here is that unemployment is voluntary. Third, because the representative agent is a family, when migrants first arrive in the city, they are subsidized by the ones that stayed behind, and they later reimburse the rural part of the family through remittances. In contrast to Lucas (2004) where there is only one consumption good, in Henderson and Wang (2005) the urban and rural sectors produce different goods. There is accumulation of human capital fueling growth in both sectors, although human capital externalities in the urban sector are posited to be greater. Demand for food is completely income inelastic. As human capital accumu- lates, and people become richer, there is a shift of population and production out of the farm/rural sector into the urban/industrial sector and development. This leads to increased urbanization, as existing cities grow and new cities enter. The fact that urbanization and industrialization often tend to go hand in hand (in many countries and models) raises the question of which one drives which. There are good reasons to believe that causality runs both ways. In fact, Lucas (2004) and many other models of the structural transformation feature such circular causality. Empirically, while urbanization certainly helps industrialization, it is not necessarily the case that industrialization started in the large urban centers. In the historical case of the U.S. Northeast, for example, Williamson (1965) shows that the degree of urbanization exhibited convergence during the period of industrialization, suggesting that industrialization was particularly strong in the least urbanized places. The same was not true though for the U.S. as a whole, where there was divergence in urbanization during the 19th century. As in the U.S. Northeast, also in England many of the “hotspots” of the industrial revolution where initially relatively small towns that grew into large cities. Liverpool’s population, for example, got multiplied by more than 60 over the course of a century and a half, from 6,000 in 1700 to 376,000 in 1850 (Bairoch et al., 1988). For developing counties, the issue is in part related to the adaptation of technologies: their agricultural and industrial revolutions often involve the simultaneous importing of world technologies in both sectors. In many developing countries the rural sector has had fairly 5 high levels of non-farm activity and an important presence of traditional industries for decades. Rural-urban migration without industrialization. Although urbanization and industrial- ization often go together, this is not always the case. Gollin, Jedwab and Vollrath (2013) document that urbanization in Africa (and the Middle East) has proceeded at about the same pace as in Asia, in spite of having a much lower level of industrialization. Asia follows the standard development process: higher income, industrialization and urbanization all proceed simultaneously. This gives rise to what they refer to as “production cities”. In contrast, in Africa surplus income from the exports of natural resources leads to greater demand for nontradables which are produced in urban centers. This gives rise to what they refer to as “consumption cities”. This disconnect between industrialization and urbanization has also been noted by Fay and Opal (2000) and Henderson, Roberts and Storeygard (2013). We now describe the Gollin et al. model in some more detail. They propose a small open economy model with four sectors (food, tradable goods, nontradable goods, and natural resources). By assumption food production is a rural activity, whereas tradable and nontradable goods are produced in cities. Natural resources are sold internationally and have no domestic market. In this model a positive shock to natural resources (an increased stock or an increased price) will lead to urbanization without industrialization. Through a standard Rybczynski effect more labor will be employed in natural resources and less in food and tradable goods. In contrast, because of the positive income effect, the demand for nontradables will increase. As a result, the food and tradable good sector will shrink, and the nontradable good sector will expand. If the expansion of the nontradable sector outweighs the contraction of the tradable good sector, urbanization will increase in the absence of industrialization. In addition to focusing on the role of natural resources, the work by Gollin et al. also illustrates that comparative advantage and trade can change a country’s standard development path. Because of trade, not all countries may need to go through a structural transformation from agriculture to manufacturing as they develop. In that sense, international trade may make the rela- tion between development and the spatial concentration of economic activity more heterogeneous. A broader implication is that using the historical experience of developed countries to “predict” what will happen in developing countries, though useful, should be done with caution. Compara- tive advantage in early developers may very well be different from comparative advantage in late developers, thus changing the relation between development, industrialization and urbanization. 6 This connects back to the work of Matsuyama (1992) which we discussed earlier. That urbanization has proceeded without industrialization does not necessarily imply that urbanization has proceeded without growth. In fact, in Gollin et al. the growth of the urban non- tradable sector is a direct consequence of the positive income shock coming from natural resources. Not everyone agrees though. Fay and Opal (2000), for example, claim that Africa has urbanized in the absence of economic growth. However, given the severe measurement problems that plague income per capita in Africa, Henderson, Roberts and Storeygard (2013) are skeptical of that claim. In fact, when using human capital accumulation, as measured by average years in school, they find that the relation with urbanization is not different in Africa compared to the rest of the world. 2.2 Development: Continuum of Locations Although increased urbanization is a basic fact of development, limiting the focus to the urban- rural distinction may ignore some of the richer growth dynamics. After all, there are more dense and less dense rural areas, and there are bigger and smaller cities. In this subsection we take a comprehensive approach. Rather than focusing on cities of different sizes, we focus on all locations. This is important for at least four reasons. First, cities are not islands, and form part of the overall spatial distribution of population and economic activity. Second, when going back in time, or when focusing on developing countries, the percentage of population living in rural areas is not trivial. Third, some of the stylized facts that hold for cities may no longer hold when including all locations. Fourth, when we limit our focus to cities, we introduce a selection bias that we need to be aware of, since by definition cities are locations that have benefited from high growth at some point in the past. In what follows we start by analyzing some of the stylized facts related to growth across locations of different sizes and densities, and then briefly discuss some models that are able to capture the observed dynamics. We also review recent work that focuses on the link between the economy’s overall spatial structure and its aggregate growth. It emphasizes the need to develop models that reconcile the main macro growth facts with the observed spatial heterogeneity of economic activity. 2.2.1 Facts Population growth dynamics and Gibrat’s law. Several papers have looked at whether growth is orthogonal to size when considering the entire distribution of locations. Holmes and Lee 7 Rossi-Hansberg, 2009). A location is "young" if no more than 40 years have passed since the state or territory in which it is located first had two or more counties with positive population. A location is old if more than 60 years have passed since it experienced its final significant geographic change. -4% -2% 0% 2% 4% 6% 8% 10% 4 5 6 7 8 9 10 11 12 13 14 15 16 A nn ua l G ro w th R at e (n or m al iz ed ) Initial Log Population 1840-1860 (0.63; 407) 1860-1880 (0.75; 537) 1880-1900 (0.71; 826) 1900-1920 (0.32; 420) b. Young Locations: 1840-1920 -4% -2% 0% 2% 4% 6% 8% 10% 4 5 6 7 8 9 10 11 12 13 14 15 16 A nn ua l G ro w th R at e (n or m al iz ed ) Initial Log Population 1900-1920 (0.22; 582) 1920-1940 (0.19; 1329) 1940-1960 (0.19; 2086) a. Old Locations: 1900-1960 -4% -2% 0% 2% 4% 6% 8% 10% 4 5 6 7 8 9 10 11 12 13 14 15 16 A nn ua l G ro w th R at e (n or m al iz ed ) Initial Log Population c. Old vs Young Locations: 1900-1920 young locations old locations Figure 2.2: Population Growth 1800-2000 U.S. Counties Population distribution. Another important finding is that for the last 200 years the spatial distribution of population (and population density) has been close to lognormal. This is true, for example, when focusing on the distribution of population levels across U.S. counties as early as 1790, as can be seen in Figure 2.3 (Figure 10, Desmet and Rappaport, 2013). The distribution of population densities across MCDs in 1880 in Figure 2.4 (Figure I, Panel A, Michaels, Rauch and Redding, 2012) shows a similar picture. Although the population distribution has essentially remained lognormal (in both levels and densities), the dispersion has increased, mainly because the larger locations today are much larger than they were in the 19th century, whereas the smaller locations are not. Income growth dynamics. In addition to the focus on population dynamics, some papers have emphasized income per capita dynamics. While Michaels et al. (2012) show how the structural 10 0% 5% 10% 15% 20% 25% 30% 2 4 6 8 10 12 14 16 18 D en si ty Population Level (Log) 2000 1790 Figure 2.3: Log Population Distribution 1790-2000, U.S. Counties Figure 2.4: Log Population Densities 1880-2000, U.S. MCD 11 transformation can help us understand differential population growth across locations, Caselli and Coleman (2001) argue that the structural transformation can account for the observed income per capita convergence across U.S. regions over the last century. Between 1880 and 1980 the South/North relative wage increased from 0.4 to 0.9. In 1880 there was a strong negative corre- lation between income per worker and the share of employment in agriculture across U.S. states. Over the next century the states which had most agriculture initially were also the ones where agriculture declined the most and where income per capita growth was strongest. Taken together, Caselli and Coleman (2001) show that this can explain regional convergence in income per capita. This is broadly consistent with evidence provided by Kim and Margo (2004), who show that U.S. income per capita diverged across regions during the 19th and early 20th century, and then started converging dramatically. As in Caselli and Coleman (2001), they relate this to changes in industrial structure across regions. During the industrialization of the Northeast and the formation of the Manufacturing Belt, regional differences in specialization increased, and with it regional differences in income per capita. At the beginning of the 20th century, this trend got reversed, and regional specialization started to decline (Kim, 1998). This pattern of rising regional divergence followed by a process of regional convergence is common across countries. The relation between income per capita and regional dispersion in income per capita often exhibits an inverted-U shape pattern, a phenomenon Kim (2009) refers to as a “spatial Kuznets curve”. In agrarian economies regional differences are limited. Early industrialization leads to clusters of manufacturing activity emerging in particular locations, leading to an increase in regional income dispersion. As industrialization spreads and agriculture loses in importance across the economy, those income differences decline. This pattern has been documented in the 2009 World Development Report (World Bank, 2009) for both developing and developed countries. Relation between spatial agglomeration and growth. The discussion above has focused on the relation between development and the convergence (or divergence) in income per capita across space. Another, not less important, question is how the overall spatial structure of the economy affects aggregate, rather than local, growth. Since policy makers often try to affect the spatial distribution of economic activity — as mentioned in the Introduction, nearly 70% of governments implement policies that slow down urbanization — having a convincing answer to this question would seem to be of much interest. Unfortunately, empirical studies are scarce. One of the few 12 medium-density locations where the share of agriculture is on average decreasing with initial density. The structural transformation leads to greater population growth in those locations with a higher proportion of non-agriculture, thus implying a positive relation between initial population density and growth. An alternative explanation by Desmet and Rappaport (2013) focuses on transition dynam- ics and entry. In their one-sector model locations gradually enter over time. Upon entry, they draw a productivity from a distribution. Frictions on positive population growth slow the upward transition to each location’s steady state and so cause population growth from low levels to be characterized by convergence. The congestion arising from the fixed supply of land in each loca- tion gradually diminishes over time. This is consistent with either a decrease in land’s share of factor income (as in Michaels et al., 2012) or an increase in the effect of agglomeration on pro- ductivity (as in Desmet and Rossi-Hansberg, 2009). As this allows steady-state population levels to become more sensitive to underlying differences in exogenous productivity, it introduces a force towards divergence. Once entry is complete and the degree of net congestion stabilizes, the assumed orthogonality of productivity growth causes population growth to be orthogonal as well. Income growth dynamics. The models mentioned above remain silent on income per capita differences across space, essentially because there is only one type of labor and all workers are per- fectly mobile across locations. Caselli and Coleman (2001) introduce different skill types. Although workers are geographically mobile, regional differences in skill composition will lead to income per capita differences. To be more precise, they propose a North-South model of the structural transformation with three basic assumptions. First, TFP growth is higher in agriculture than in manufacturing. The production technologies in food and manufacturing in region i and time t use land (T ), labor (L) and capital (K) and are Cobb-Douglas of the form F it = Aift(T i ft) αT (Lift) αL(Ki ft) 1−αT−αL and M i t = Aimt(T i mt) βT (Limt) βL(Ki ft) 1−βT−βL , where the South has comparative advantage in agriculture and the North in manufacturing. As mentioned before, it is assumed that (exogenous) TFP growth in agriculture, gf , outpaces that in manufacturing, gm. 15 Second, there is a cost of acquiring non-farm skills and this cost drops over time. The demographic structure is the one of a dynasty, with a constant population and a probability of death each period. Each period each person is endowed with one unit of time. When born, a person decides whether to immediately start working on the farm, or to first spend ξtζ i units of time getting trained to work in manufacturing, where ξt captures the economy’s overall efficiency in providing training and ζi is distributed among the people of a generation according to a time- invariant density function µ(ζi). Assuming that ξt drops over time implies that training becomes cheaper over time. As a result, the cutoff ζi below which individuals invest in skill acquisition rises over time, implying more people becoming skilled. Third, the income elasticity of demand for agricultural goods is less than one. In particular, the period utility derived from consuming food, cf , and manufacturing, cm is u(cift, c i mt) = ( (cift − γ)τ (cimt) 1−τ )1−σ 1− σ , where γ > 0 is the subsistence constraint on food consumption, implying the less than unit income elasticity of demand for food. Because of the initially high cost of acquiring non-farm skills, the relative supply of man- ufacturing workers is low, implying a substantially higher manufacturing wage. Given that the South has comparative advantage in agriculture, this implies a wage gap in favor of the North, in spite of labor being mobile across regions. As the overall economy becomes richer because of general productivity growth, the demand for manufacturing goods increases, shifting labor from agriculture to manufacturing. This process is further reinforced by the faster TFP growth in agri- culture compared to manufacturing. With a declining weight of agriculture in the economy, average wage differences across regions drop. The falling cost of acquiring non-farm skills enhances this convergence across regions, and has the additional advantage of leading to a reduction in wage differences not just across regions, but also within regions between farm and non-farm workers. It is this latter feature which the model would not be able to capture if it did not assume a falling cost of acquiring manufacturing skills. Whereas this model predicts that the structural transformation leads to income convergence across regions, it is likely that in the early stages of industrialization the opposite happened. In the model part of the convergence between North and South happens because average wages converge as a result of the sectoral composition becoming more similar across regions. During the early stages of industrialization, when the North shifted increasingly into manufacturing, the opposite 16 should have happened. As mentioned before, this would be consistent with the evidence in Kim and Margo (2003) who describe a process of income divergence during the nineteenth century, followed by convergence, particularly strong during the second half of the twentieth century. An assumption in most of these models is that labor is freely mobile across regions. This does not necessarily contradict the evidence of nominal and real wages being substantially higher in the West than in the rest of the country during the 19th century (Easterlin, 1960; Rosenbloom, 1990; Mitchener and McLean, 1999). As in Caselli and Coleman (2001), this gap might be due to differences in skills. This does not seem to be the entire story though, since these differences also existed within occupations. Focusing on 23 occupations, Rosenbloom (1990) documents within- occupation average real wage differences of more than 50% between the West and the South in 1870; by the end of the 19th century this difference continued to exist, although it had been cut in half. This suggests that labor markets were not completely integrated, and that moving costs were driving a wedge between wages in the West and the rest of the country. Gibrat’s law and Zipf’s law. An interesting related question is how Gibrat’s law is connected to Zipf’s law. Theory says that proportionate (or random) growth should give rise to a lognormal distribution (Gibrat, 1931). That is, Gibrat’s law implies a lognormal distribution. Consistent with this, Eeckhout (2004), using data on census places, shows that growth between 1990 and 2000 satisfies Gibrat’s law and that the size distribution of places is lognormal. Since the lognormal distribution and the Pareto distribution are very different, Gibrat’s seems to be inconsistent with the observation that the city-size distribution conforms to Zipf’s.1 The puzzle is partly resolved when realizing that cities make up the upper tail of the size distribution of all locations, and at that upper tail the lognormal distribution is actually very similar to the Pareto distribution. So although Gibrat’s does not imply Pareto overall, in the upper tail they are similar (see Ioannides and Skouras, 2013, for a further discussion) . Note that there are restrictions on the stochastic process which can lead Gibrat’s law to imply Zipf’s law. For example, Gabaix (1999) shows that if cities cannot fall below a minimum size, then Gibrat’s law implies a city size distribution that converges to Zipf’s. The intuition is simple: we get the density function peaking at the minimum city size and at the same time the lower bound on size pushes more cities to become large, implying the fatter upper tail, characteristic of Zipf’s (see Duranton and Puga, 2014, for a review of this literature). 1Section 4.2.1 has a longer discussion on city-size distributions. 17 firm then decides on how many workers it wants to hire, how much it wants to bid for land, and how much to invest in innovation. Only the firm that offers the highest bid for land in a given location gets to rent the land. Investment in innovation, if it occurs, then leads to a new technology, Z+ (`, t). Production happens at the end of the period. We now turn to the firm’s problem. The objective function of a firm in a given location ` at time t0 is max {φ(`,t),Li(`,t)}∞t0 Et0 [ ∞∑ t=t0 βt−t0 ( p (`, t) ( φ(`,t) a−1 + 1 ) Z− (`, t)L (`, t)µ −w (`, t)L (`, t)−R (`, t)− ψ (φ (`, t)) )] , where β is the discount factor and R(`, t) is the firm’s bid rent which is chosen to maximize the probability of winning the auction to rent land. As discussed in Desmet and Rossi-Hansberg (2012), in this setup firms invest in innovation, in spite of operating in a perfectly competitive market, because it allows them to bid a higher price for land. Returning to the above maximization problem, recall that labor is freely mobile and that firms compete for land and labor every period with potential entrants that, because of diffusion, have access to the same technology. The decision of how many workers to hire and how much to bid for land are therefore static problems. The only problem that is in principle dynamic is the innovation decision, but here as well the dynamic problem simplifies to a static one. The continuity in the diffusion process and the spatial correlation in innovation realizations guarantee that a firm’s decisions do not affect the expected technology it wakes up with tomorrow. Hence, future allocation paths do not affect a firm’s decision today. This key result is what makes the dynamic spatial model solvable and computable. The importance of this framework is that it does not only have implications for the interac- tion between density and growth at the local level, but it also analyzes the interaction between the spatial distribution of economic activity and aggregate growth. When applying their framework to the evolution of the U.S. economy in the last fifty years, Desmet and Rossi-Hansberg (2014a) can account for the main spatial patterns, such as the evolution in the dispersion of land prices, as well as for the main macroeconomic stylized facts, such as the evolution of aggregate growth and wages. More broadly, the aim is to develop a unified framework to study the interaction between space and the macroeconomy. In other work, the same authors use a similar setup to quantitatively analyze the impact of global warming on both the spatial distribution of economic activity and global welfare (Desmet and Rossi-Hansberg, 2014b). 20 3 Development, Space and Industries Although we touched upon the structural transformation from agriculture to manufacturing, our main focus in the previous section was on aggregate population growth across different locations. In this section we delve deeper into the incentives of different industries to concentrate or disperse, and analyze the geography of sectoral employment growth. In particular, we are interested in the differences between manufacturing and services. This is related to the broader question of how the spatial distribution of economic activity changes with development, for at least two reasons. First, if spatial growth patterns differ across sectors, then a country’s overall spatial organization will change as it develops and the relative importance of different sectors changes. Second, for a given sector, spatial growth patterns may also change over time, as sectors transition from being young to being more mature. In what follows we discuss some of the recent empirical findings, as well as theories that can account for them. Manufacturing vs services. In recent decades U.S. manufacturing has become spatially more dispersed and services have become spatially more concentrated. Based on U.S. county employment data between 1970 and 2000, Table 1 shows that the difference in log employment between the 70th and the 30th percentile has decreased in manufacturing and increased in services. This implies manufacturing become more equally spread across U.S. counties, whereas the opposite is happening to services. When using the standard deviation of log employment as an alternative measure of the degree of concentration, the result is similar. Since services started off being less concentrated than manufacturing, this implies services becoming more like manufacturing in their degree of spatial concentration. 1970 2000 Log Employment Difference 70-30 Manufacturing 1.81 1.74 Services 1.29 1.52 Standard deviation Manufacturing 2.05 1.89 Services 1.40 1.52 Source: REIS, Bureau of Economic Analysis Table 1. Spatial Concentration of Employment 21 Does this mean that manufacturing is dispersing and services are concentrating across all locations? To get a more precise idea, Desmet and Fafchamps (2006) and Desmet and Rossi- Hansberg (2009) run nonlinear kernel regressions of the form Lit+s = φ(Lit) + eit, where Lit is log employment in year t and county i. Figure 3.1 (Figure 1, Desmet and Rossi- Hansberg, 2009) shows that the tendency towards greater geographic dispersion in manufacturing is happening across the entire distribution. Counties with less manufacturing have been experi- encing faster manufacturing employment growth than those with more manufacturing. In the case of services, the picture is more complex: the relation between size and growth is S-shaped. The tendency towards a greater geographic concentration of services employment has mainly affected mid-sized service employment clusters. European regions look similar to U.S. counties: deconcen- tration in manufacturing and greater concentration in services. -5% -3% -1% 1% 3% 5% 7% 9% 11% 0 2 4 6 8 10 12 14 A nn ua l G ro w th R at e Initial Employment (Log) Sectoral Employment Growth manufacturing 1900-1920 manufacturing 1970-2000 FIRE 1970-2000 Other Services 1970-2000 Source: Desmet and Rossi-Hansberg (2009) Figure 3.1: Sectoral Employment Growth in U.S. Counties Life cycle of industries and spatial distribution. One possible explanation for this trend is the greater land-intensity of services. As services compete for the same land as manufacturing in 22 1997, Figures 3.2a and 3.2b (Figure 9 and Figure 10; Desmet and Rossi-Hansberg, 2009) show employment growth in legal services and auto repair. As expected, legal services exhibit the S- shaped spatial growth pattern. In contrast, auto repair looks like a mature sector, with convergence across the entire distribution. -1% 0% 1% 2% 3% 0 2 4 6 8 10 A nn ua l G ro w th R at e Initial Employment (Log) Legal Services Employment Growth 1977-1997 95% confidence interval Figure 3.2a: Sectoral Employment Growth in U.S. Counties (Desmet and Rossi-Hansberg, 2009) -3% -1% 1% 3% 5% 7% 0 2 4 6 8 10 A nn ua l G ro w th R at e Initial Employment (Log) Auto Repair Employment Growth 1977-1997 95% confidence interval Figure 3.2b: Sectoral Employment Growth in U.S. Counties (Desmet and Rossi-Hansberg, 2009) In the same way that not all service activity is concentrating, not all manufacturing is dispersing. We would expect manufacturing activities that most strongly benefit from knowledge spillovers to have less of an incentive to disperse. This explains the findings of Fallah and Partridge (2012), who show that hi-tech manufacturing pays a relatively higher price for remoteness. In par- ticular, a 1 kilometer increase in distance from the nearest metropolitan area decreases employment growth by 0.2% in hi-tech manufacturing, compared to a 0.1% decrease in manufacturing overall. 25 We would therefore expect hi-tech manufacturing sectors to remain more clustered than the rest of the industry. The more general link between an industry’s life cycle and its spatial distribution has also been analyzed by Henderson (2010) who provides evidence of standardized manufacturing dispersing and high-tech manufacturing concentrating. In the specific case of the internet, Forman, Goldfarb and Greenstein (2005) show that its use diffused rapidly across the U.S. geography, but its more complex applications, such as e-commerce, predominantly located and developed in cities, where there was more easy access to complementary inventions and activities. The pattern of spatial concentration followed by spatial dispersion as industries mature has been noted in other countries. For example in Section 4, we will discuss data which indicate that Seoul transformed from being a manufacturing center to a service center from 1970 on. Similar to what happened in the U.S. and Europe, the loss of manufacturing employment in Seoul benefitted the rural areas and the small towns, which experienced an industrial transformation after 1980. Similarly, in the 1990s the correlation between the manufacturing-service ratio and the size of a city in China was -0.20, implying that larger cities were relatively more service-oriented (Au and Henderson, 2006a). Consistent with this, China’s 2008 economic census indicates that telecom- munications, software, information and broadcasting services are highly concentrated at the upper end of the size distribution of counties. It is of course important to note that the timing of these transformations may differ across countries. For example, whereas in the U.S. manufacturing had become a mature industry by, say, the 1960s, in Korea this same stage was only reached in, say, the 1980s. This underscores a point we made before: to understand the relation between development and space, it is important not just to know the relative sizes of different sectors, but also their ages. The appearance of clusters during the early stages of an industry’s life cycle is not a recent phenomenon. Trew (2014), for example, documents the emergence of industrial hotspots during 19th century England. In 1750 two counties in England, Lancashire and the West Riding, had be- tween 65% and 70% of all employment in the country’s secondary sector. These were not necessarily the most dense areas initially, but they experienced tremendous population growth as the industrial revolution took off. In the 19th century, Sheffield, for example, grew from a town of 60,000 to a large city of 450,000. London, the country’s biggest city, was also a major manufacturing center, as were some of the other large cities, such as Manchester and Birmingham (Shaw-Taylor and Wrigley, 2008). 26 Ruralization vs suburbanization. Although manufacturing clusters are spreading out, they often do not move far away. If so, manufacturing growth should be lower in the clusters itself but higher in areas close to clusters. Using data on U.S. counties for the last three decades of the 20th century, this is exactly what Desmet and Fafchamps (2005) find. In particular, having 1% more manufacturing employment locally lowered manufacturing employment growth by around 2% annually, whereas having 1% more manufacturing employment 40 to 50 kilometers away increased manufacturing employment growth by 0.1-0.2% annually. These figures refer to manufacturing clusters, rather than to aggregate clusters. When looking at total employment, the tendency of manufacturing is to suburbanize rather than to ruralize. If so, manufacturing growth should be relatively low in locations with high ag- gregate employment and relatively high in locations close to aggregate clusters. Again, this is what Desmet and Fafchamps (2005) find. Having 1% more total employment locally lowered man- ufacturing employment growth by around 0.2% annually, whereas having 1% more manufacturing employment 40 to 50 kilometers away increased manufacturing employment growth by a little less than 0.01% annually. Though small, the effects are statistically significant, and amount to some- thing much larger once we take into account that we are looking at average annual growth over a period of three decades. The cost of remoteness. The general tendency towards greater dispersion is mitigated in several ways. First, as already mentioned, hi-tech manufacturing tends to remain clustered in high-density areas to take advantage of knowledge spillovers. Second, the cost of remoteness does not only differ across sectors (hi-tech versus low-tech), but also across functions within sectors. With the fragmentation of the value chain, we are witnessing firms locating headquarters and business services in larger cities and production facilities in smaller cities. The evidence on this is reviewed in the next section when models of functional (as opposed to product) specialization by cities are discussed. In general, since 1950, larger cities have moved toward management as opposed to production activities while smaller cities have moved in the opposite direction (Duranton and Puga, 2005). Although the fragmentation of the value chain and the spatial division of labor respond to standard forces of comparative advantage, there are limits to their scope. For example, Tecu (2013) finds that an average U.S. chemical firm is 1.8% more productive in R&D (in terms of patents) if it increases production workers by 10% in the same metropolitan statistical area. In the average MSA, having an average size production facility increases the productivity of R&D by 2.5 times in the chemical 27 For developing countries, there are a few recent papers looking at specialization that offer a somewhat different perspective. One more innovative paper focuses on a different dimension: the division of labor between and within cities, as it varies across a less developed hierarchy. In Section 4.2, we also look at some recent patterns concerning urban specialization in China. Apparel Manufacturing Textile Product Mills Leather and Allied Product Manufacturing Textile Mills Furniture and Related Product Manufacturing Wood Product Manufacturing Food Manufacturing Plastics and Rubber Products Manufacturing Fabricated Metal Product Manufacturing Nonmetallic Mineral Product Manufacturing Primary Metal Manufacturing Paper Manufacturing Printing and Related Support Activities Electrical Equipment, Appliance, and Component Manufacturing Machinery Manufacturing Miscellaneous Manufacturing Beverage and Tobacco Product Manufacturing Transportation Equipment Manufacturing Petroleum and Coal Products Manufacturing Computer and Electronic Product Manufacturing Chemical Manufacturing .8 1 1. 2 1. 4 1. 6 Po pu la tio n el as tic ity o f e m pl oy m en t 11 12 13 14 Skill intensity (employees' average years of schooling) Figure 4.1: Relative Industry Composition Position in the Urban Hierarchy and Relationship to Industry Skill Intensity What big cities do and their skill composition. Figure 4.1 from Davis and Dingel (2013, figure 14) shows different manufacturing industries and their elasticities of local employment with respect to metropolitan area population. The figure tells us two things. First, traditional indus- tries producing standardized products like wood products, furniture and paper products have low elasticities, consistent with findings in the earlier work noted above. Higher tech industries like computers and electronics have higher elasticities consistent with the idea that high-tech produc- tion benefits from the diverse environments of large cities. Second, in general the skill intensity of industries is correlated with these elasticities, suggesting skill intensity also rises with city size (as the authors show separately). Skill intensity is measured by the average years of schooling of people working in an industry nationally. The only strong outlier is low skill apparel which has a high elasticity. This may reflect the recent surge in the immigrant proportion of the work force in 30 apparel where migrants’ first landing points are disproportionately cities like New York and Los Angeles. Figure 4.1 covers only manufacturing. Farming, Fishing & Forestry Bldg/Grnds Cleaning & Mntnce Food Preparation & Serving Construction & Extraction Production Transportation & Material Moving Installation, Maintenance & Repair Healthcare Support Personal Care & Service Office & Administrative Support Protective Service Sales & Related Management Arts, Design, Entertainment, Sports & Media Business & Financial Operations Architecture & Engineering Computer & Mathematical Healthcare Practitioners & Technical Community & Social Services Education, Training & Library Life, Physical & Social Science Legal .8 1 1. 2 1. 4 Po pu la tio n el as tic ity o f e m pl oy m en t 10 12 14 16 18 Skill intensity (employees' average years of schooling) Figure 4.2: Relative Industry Occupational Position in the Urban Hierarchy and Relationship to Industry Skill Intensity Figure 4.2 looks at the role of big cities for the universe of workers, focusing on occupational mix. Traditional occupations like farming, food preparation, and health care support have again lower city size elasticities and low education, while computer and mathematical, architecture and engineering occupations have higher elasticities and high skill levels. Taken together, today the U.S. has lower skill workers in standardized manufacturing and services in smaller cities, with higher skill workers in often more innovative and creative industries and occupations in larger cities. Specialization in the urban hierarchy. The next feature concerns the degree to which cities are specialized. For individual cities the standard measure of the degree to which a city is specialized is the ‘Gini’ specialization index taken from Krugman (1992), Kj = 1 2 n∑ i |sij − si|, where sij is the share of sub-industry i in city j’s total industry employment, si is industry i’s share in national total industry employment. The higher the index, the more specialized (less diverse) the 31 locality is. The range is from 0 where the city’s shares of different sub-industries perfectly mimic the nation’s share of different industries, to values approaching 1 for a city that is completely specialized in a minor product nationally. An alternative index takes the squares of the deviations, thus giving more weight to bigger deviations. However that index is mechanically affected by the count of industries in the SIC-classification which changes over time (the index falls mechanically as the number of industries rises). The Krugman Gini is free of that mechanical effect. The first two columns of Table 4.1 from Duranton and Puga (2005) show the Gini for different size classes of cities for 1977 and 1997 based on County Business Patterns data. Two things are apparent for the U.S. First, going down the urban hierarchy by city size class, specializa- tion increases sharply. Second, the specialization index has declined for size categories over time, consistent with the manufacturing diffusion analysis of Section 3. Population Sectoral specialization Functional specialization (millions) (Gini coefficient) (Management vs production) 1977 1997 1950 1990 > 5 .377 .374 +10.2% +39.0% 1.5-5 .366 .362 +0.3% +25.7% 0.5 -1.5 .397 .382 -10.9% -2.1% 0.25-0.5 .409 .376 -9.2% -14.2% 0.075-0.25 .467 .410 -2.1% -20.7% < 0.075 .693 .641 -4.0% -49.5% Source: Duranton and Puga (2005) Table 4.1: Specialization in Manufacturing and Function Specialization across Size Classes of Cities The next columns of Table 4.1 deal with a different aspect of activity composition across the urban hierarchy: how firms organize their internal functions by size class, leading to functional specialization by firms across the urban hierarchy. The authors calculate the average number of executives and managers relative to production workers in manufacturing in all cities for 1950 and for 1990. Then they calculate that number within each size class and show the percent deviation of the size class in that year from the national average. Bigger cities have relatively more managers and executives in both years, but the degree of differentiation of managers and executive shares between small and large cities has increased enormously over time. Underlying this is a large increase over time in functional specialization by firms nationally (Kim, 1999), with production 32 produced with diversified intermediate non-traded inputs). Each final good requires fixed inputs where the requirement is lower for one good than the other. However, if the two industries co- locate, these fixed costs can be reduced for firms in each sector. In their equilibrium there is a city specialized in the lower fixed costs good and the other, potentially larger city is diversified. Tabuchi and Thisse (2011) have a similar model and outcome but now the two goods differ in the unit costs of inter-city trade. In this case the specialized city is the one with the lower unit trade costs. While these models do give specialized versus diversified cities, the environment is not rich. The number of cities is exogenously set at two and the distinction between goods has limited intuition. In the recent literature, much more sophisticated modelling of production and labor force structure across the urban hierarchy has emerged. We turn to these in the next section, but as a reference point we review key aspects of the basic model reviewed in detail in both Duranton and Puga (2004) and Abdel-Rahman and Anas (2004). A benchmark model. For our benchmark, we use as micro-foundations for scale externalities the diversity of intermediate inputs framework. It is straightforward to reformulate the model to allow the scale benefits to be other micro-foundations, such as greater scale promoting greater specialization of workers in their tasks (Duranton and Puga, 2004; Becker and Henderson, 2000). A city has production functions for final and intermediate producers respectively of y = (∫ m 0 x(h)1/(1+ε)dh )1+ε and X(h) = βl(h)− α, where l(h) is labor input for firm h, x(h) and X(h) are respectively inputs of type h for a final good firm and output of the intermediate good producer of type h. For other notation, m is the endogenous number of intermediate good producers, L is the effective city labor force, Y is total final good output, the price of the final good is the numéraire, and the price of intermediate inputs is q. Using key results from standard cost minimization of final producers and from profit maximization and competition among intermediate producers,3 reduced form expressions for final good output per worker in the city and wages are respectively Y/L = CLε 3For cost minimization, we have that the direct elasticity of derived demand is approximated by −(1 + ε)/ε and that final price 1 = ( ∫m 0 q(h)−1/εdh)−ε = qm−ε, where the last term emerges in the symmetric equilibrium. Profit maximization conditions by intermediate producers and free entry allow us to solve for the wage level w = β/(1+ε)q, firm output X = α/ε, and the number of such producers in the city m = βε/((1 + ε)α)L. 35 and w = (β/(1 + ε))mε = (ε/α)ε (β/(1 + ε))1+ε Lε. Both output per worker and wages are increasing in city scale, as ultimately measured by total effective employment. Note the reduced form specification looks like black-box externalities. Given these positive benefits of increasing scale, what economic forces serve to limit city sizes and serve as a counter-balance to scale benefits from agglomeration? That requires introducing sources of urban diseconomies. Such diseconomies are typically modelled as coming from increases in urban commuting costs. The standard approach assumes a monocentric city with fixed lot sizes where all production occurs at a point in the city center. Following the specifics in Duranton and Puga (2004) for a linear city, each worker is endowed with one unit of time and working time is 1− 4τu, where u is distance from the city center and 4τ are unit commuting costs. It is then easy to derive expressions for effective labor force L, for total rents in the city, and for the net wage after rents and commuting costs, all as functions of city population N .4 For use below we have L = N(1− τN); net wage income = w(1− 2τN); total rents = wτN2. The final step is to introduce the mechanism to determine city sizes. The standard one following the first regime in Henderson (1974) assumes the existence of ‘large agents’ operating in national land markets who serve to coordinate agglomeration. These could be developers who own city land and set city sizes and any subsidies to workers or firms to maximize their profits, or alternatively (and equivalently) city governments who can tax away land rent income from landowners and set city sizes to maximize real income per worker. As an example, developers seek to maximize Profits=total rents - worker subsidies = wτN2 − sN = ( ε α )ε( β 1 + ε )1+ε τN2+ε(1− τN)ε − sN subject to ȳ = ( ε α )ε( β 1 + ε )1+ε N ε(1− τN)ε(1− 2τN) + s, where s is any subsidy developers pay workers to join their city and ȳ is the going real income available for workers in national labor markets, as perceived by any city. These subsidies could also go to firms but in this simple example this is irrelevant.5 Assuming that developers maximize 4Population comes from integrating over the two halves of the city, each of length N/2. The rent gradient is derived by equating rent plus commuting costs for a person at u with that of a person at the city edge where rents are 0. Total rents come from integrating over the rent gradient. 5There is no misallocation of resources here, despite fixed costs of production and monopolistic competition, because diversified inputs are the only factor of production and enter symmetrically. 36 profits with respect to s and N and that, with competition, cities earn zero profits, solving the problem gives the equilibrium (and efficient) city size6 N∗ = ε τ(1 + 2ε) ; ∂N∗/∂τ < 0, ∂N/∂ε > 0. As constructed, this is also the size that maximizes net income per worker, y, including the subsidy set equal to average land rents.7 This implies that y is an inverted U-shape function of N with equilibrium and optimum city size at this maximum. That equilibrium and optimal size coincide in this context depends on the use of subsidies to residents to effectively internalize scale externalities, as financed by land rents. If for example land rents go to absentee owners, as reviewed in Abdel- Rahman and Anas (2004), cities will be too small. There are some loose ends before proceeding to recent developments. What happens under the self-organization regime? The requirement for a Nash equilibrium in worker location choices is that no worker wants to change cities in equilibrium. Given that income, y, is an inverted U-shaped function of city size, this has two implications. The first is that the equilibrium size is at the peak or to the right of the peak where dy/dN < 0 . That is, if a worker moves to another city (by increasing its size) she would earn less than what she earned in the city she left (where real income would rise as she left). Thus it is also the case that cities to the left of the peak where dy/dN > 0 cannot be Nash equilibria. The second implication is that all cities be of the same size so as to equalize real incomes. There is then a continuum of equilibria in city sizes between the peak and a size to the right of the peak, Nmax where y(Nmax) = y(N ;N = 1). Beyond Nmax workers would deviate to form a city of size 1, which would then induce migration flows and self-re-organization until there was a new equilibrium where all cities again had a common size between N∗ and Nmax. Thus in general, city sizes under self-organization are over-sized, potentially enormously so. However, there are models where under self-organization there are unique and more reasonable city size solutions. In the absence of optimizing city land developers, Henderson and Venables (2009) show that in a world with durable housing capital as a commitment device equilibrium city sizes are unique and that, while cities are over-sized, they are only modestly so. Behrens, Duranton and Robert-Nicoud (2014) have another, reasonable self-organization equilibrium for the special 6There is also the Henry George theorem where all rents in the city are paid out to workers in subsidies to cover the marginal externalities they generate (more workers bring more varieties and greater efficiency of final good producers). In particular, dY/dN = (1 + ε)[(ε/α)ε(β/(1 + ε))1+εNε(1− τN)ε(1−2τN)], where the term in the square brackets is the private benefit of adding a worker (his net wage) and ε times the expression in square brackets is the externality which also equals s in equilibrium. 7That is, N∗ maximizes [(ε/α)ε(β/(1 + ε))1+εNε(1 − τN)ε(1 − τN)] such that dy/dN = 0 and d2y/dN2 < 0. 37 service inputs and labor. Both services and physical intermediate inputs are produced with labor and are non-tradable across cities. As in the nursery city model, there are workers belonging to spe- cific occupations (aptitudes) and thus firms in different sectors. Production units use sector-specific intermediate inputs. In contrast, headquarters of different firms in any city use a common set of business service inputs. So all types of headquarters use lawyers and accountants, but only apparel firms use textile inputs. Firms may spatially integrate so headquarters and production occur in the same city or they may be multi-location, with headquarter and production units in different cities. Most critically to get their results, multi-location production raises the cost of a production unit to acquire its headquarter services by a factor ρ > 1, relative to it being in the same location. However, having headquarters be in separate specialized business service cities allows a greater diversity of intermediate business services of benefit to all types of firms and their headquarters. Given these implicit trade-offs, the equilibrium has a multi-location pattern for firms and there are two sets of cities. One set are cities specialized in headquarter and business service production. The other set are cities specialized in the production of one type of final good and their corresponding intermediate inputs. The authors call this functional specialization by cities, where now the diversified city is one where headquarters of different production sectors enjoy a diversity of common business service inputs that are non-traded across cities. We note this functional specialization equilibrium will not exist if the cost of having production units acquire headquarter services from other cities is high enough.8 The third generation models. In the last few years several papers have introduced more sophis- ticated considerations into modelling urban hierarchies. Prior work, even in the second generation models, takes a simple approach to looking at urban specialization and diversity. Very recent work has introduced several innovations. First and foremost is allowing for labor heterogeneity, not just different labor types (horizontal differentiation), but also different labor talents or skills (vertical differentiation). This introduces the possibility of labor sorting by talent across the urban hierarchy. Second, in bigger cities competition among firms may be “tougher” and different qualities of firms may survive. Third, there may exist more complex sorting by industries across the urban hierarchy, based on more complex specifications of inter-industry interactions and scale externalities. Such sorting is critical to evaluation of urban productivity. In developing and even developed 8If ρ exceeds a critical value, then the equilibrium has only integrated production. Then each city type specializes in production of one type of final output and hosts just headquarters of the firms in that city and their corresponding intermediate physical and business service suppliers. 40 countries, some policy makers evaluate that bigger cities are inherently more productive. That has in certain instances become a basis for advocating that these cities should be effectively subsidized at the expense of smaller cities, an issue we will return to in Section 4.3.2. However, small cities persist in developed market economies, suggesting they are competitive and thus productive. The issue is that in the data we typically do observe higher measured output per worker in bigger cities, which could be a basis for the evaluation of policy makers. But this does not mean that bigger cities are more productive. The puzzle can be explained by the types of sorting just noted. First, we know from Figures 4.1 and 4.2 that more educated and higher skilled workers sort into bigger cities. So if we observe higher output per worker in a bigger city, the question is to what extent is that because of pure productivity effects versus because of higher quality labor. Models that tackle sorting across cities help us to better understand that issue. Second, if competition in bigger cities is tougher so that only higher productivity firms survive there, that also lowers the component of higher output per worker in bigger cities due to pure productivity effects. Third, there is industry sorting across cities, where only certain types of industries are found in bigger cities. In the early part of this section, we discussed the idea that industries with greater localization economies of scale should be found in larger types of cities, with also higher costs of living, while those with lower localization economies may be found in smaller types of cities. Equilibrium in national labor markets with equalized real wages will also require higher output per worker and wages in bigger cities to offset higher costs of living in those cities. The key is that different sizes of cities house different industries; or smaller cities are competitive in what they produce. However, recent work suggests the issue is more complicated when there are cross-industry externalities. Maybe an industry with high localization economies in a bigger city would really benefit from having an industry with lower localization economies co-locate there, but that may not be realized in a market equilibrium and makes local policy enactment and evaluation of productivity more complicated. There are several papers that tackle theoretical models of sorting of workers across cities, apart from empirical modeling which we do not cover here (e.g., Baum-Snow and Pavin, 2012). The first paper we look examines sorting across cities, with the distinction that the model links such sorting across cities to residential sorting within cities (David and Dingel, 2013). To achieve this neat link, sorting in that paper always goes in the direction of having more skilled workers sort into bigger cities. Another paper that only focuses on sorting across cities questions the presumption that there is monotonic sorting (Eeckhout, Pinheiro and Schmidheiny 2014). The third paper we 41 discuss combines sorting of workers across cities with the idea that competition may be tougher in bigger cities (Behrens, Duranton, and Robert-Nicoud 2014). This paper has a number of nice innovations, one being the endogenous formation of firms within cities. Finally we analyze the paper by Helsley and Strange (2014) on sorting of industries across cities in the face of cross-industry scale externalities. Sorting within and across cities. Davis and Dingel (2013) develop a model of sorting across and within cities, albeit in a context where the number of cities is set exogenously. Cities have internal space, required if workers are going to sort where to live within the city. Similar to the bench- mark model, final output is produced just with intermediate inputs, but now from a fixed set of intermediate input sectors. In Davis and Dingel, intermediate inputs are sold competitively, traded costlessly within and across cities, and produced by workers of different skills, where there is perfect substitutability among skills in production in any sector σ. The higher σ, the more “advanced” the sector is, as defined below. A worker living in city c at location δ in the city with skill ω chooses which sector σ to work in so as to maximize wages net of rents, or max σ p(σ)A (c)D(δ)H(ω, σ)− r(δ, c). The worker takes the price p(σ) of output in the sector as given. Locations in a city are ordered by values of δ with the most desirable at δ = 0, and D′ < 0. While the interpretation can be quite general, to fix ideas and to meet a regularity condition that better locations be ‘relatively scarcer’ in a smaller city, we adopt the Davis and Dingel example where all cities are circular with fixed lot sizes, δ is distance from the city center and D(δ) is linear. Note furthermore that r(δ, c) is rent at location δ in city c, and A (c) is an urbanization productivity level in the city where, for Lf(ω, c) being the quantity of ω skill people in city c, A (c) = J ( L ∫ ω∈Ω j(ω)f(ω, c)dω ) , J ′, j′ > 0. Heterogeneous individuals have density function f(ω) on support Ω ∈ [ω, ω̄]. An equilibrium will have relatively more high skill people in bigger cities and thus A is higher in bigger cities both because of scale and skill composition. Finally worker technology, H(ω, σ), is increasing in ω and super-modular (Costinot, 2009), so that H has a larger value for the same skill ω in a more advanced sector. To solve for the within and across city sorting, the authors utilize the perfect substitutability of skill in production of intermediate inputs. Then, in equilibrium the marginal returns to ω in sector σ are independent of the assignment of ω’s to the sector. With perfect substitutability, the workers choice of σ simplifies to M(ω) = maxσ p(σ)H(ω, σ) and defines G(ω) ≡ H(ω,M(ω))p(M(ω)), G′ > 42 self-organization. In their special case cities are talent-homogeneous, rather than the usual case of each city having a segment of the talent distribution. Each city has only one talent t and city sizes are increasing in talent. Cities under self-organization are too large but not catastrophically so. Intuitively, if cities get too big, people of the intended talent will want to move to less talented cities. The uniqueness and existence of such equilibria are not guaranteed. In summary, Behrens et al. (2014), similar to Davis and Dingel (2013), have talent or skill sorting across cities, with bigger cities being in part more productive simply because they have more talented workers. But the authors also deal with selection and the choice of people to become entrepreneurs, where the relative proportion of workers to firms is the same across cities of different sizes. In evaluating the sources of higher productivity in bigger cities, the modeling suggests that sorting by talent is a key source of higher output per worker, while selection is not. This finding parallels the empirical results in Baum-Snow and Pavin (2012). Cross-fertilization in externalities and sorting of industries. The benchmark model assumes in- dustries are characterized by simple specifications of externalities, which potentially lead to urban specialization. In an innovative paper, Helsley and Strange (2014) explore cross-fertilization among industries in a generalized fashion. It explores equilibria and optima where cities may be of mixed employment or non-specialized, and there can be a hierarchy of non-specialized. The paper focuses on how under self-organization specialized cities are not just over-sized but may have poor compo- sitions of output. The paper is summarized in the chapter by Behrens and Robert-Nicoud (2015) in this volume. Some key results are as follows. Pareto efficient size cities where different city types have a plurality of own type population but an optimal mix of other worker types can never be stable equilibrium city compositions and sizes. In an equilibrium, own type workers will want to agglomerate further with own type workers in some types of cities, compared to the optimum. If it is efficient for all cities to specialize when complementarities are weak, we have the usual problem of equilibrium over-sized specialized cities under self-organization. However we can also have an equilibrium with specialized cities when the optimum would dictate mixing. And when we do have mixing, compositions and sizes are inefficient. For policy makers, the issue of how to enact optimal or second best policies and institutions is not covered in the paper, but the challenge is there.9 9We note two comments on the model. The first is based on the specification of cross-industry externalities. There are I types of workers where any type is employed in the corresponding industry of that type. Output per worker in sector i in city j is a function of the vector of the number of workers in different sectors in the city, nj, such that output per worker in sector i in city j is gi(nj). The comment is that the authors assume not just that there are localization and urbanization economies where ∂gi/∂nij > 0 and ∂gi/∂nkj > 0, but there are complementarities 45 4.2 Dynamics in the Urban Hierarchy So far the models we have presented are basically static, or, at best, stationary state models. To examine the rapid changes in urban systems which occur with economic development, we need models of the dynamics of the urban hierarchy. Such models are limited in number and many were reviewed in earlier handbook chapters (Gabaix and Ioannides, 2004; Henderson, 2005). Given that, we take a different expositional approach in the first part of this sub-section. We start by interweaving a discussion of empirical relationships about the dynamics of the urban hierarchy with a brief review of some key models which sought to explain certain patterns in the data. These have to do with growth of city sizes and numbers over time and the stability of the size distribution of cities over time. We then turn to a more recent focus on why production patterns of individual cities and cities across the urban hierarchy change with time. There we return to the format of presenting empirical relationships and then models that relate to them. 4.2.1 Facts and Concepts Concerning the Size Distribution of Cities Growth in city sizes. In general over the last centuries cities have been growing in population size. To see this for a more recent time period for which there is good data, Henderson and Wang (2007) take all metropolitan areas in the world from 1960-2000, divide by mean size in any time period to get a relative size distribution, and define a relative cut-off point so that the minimum to mean size is stable over time. They call this the relative size distribution. Within this distribution absolute mean (and median) size doubled from 1960 to 2000 worldwide. There are two explanations for why city sizes are increasing over time, given size is determined by a trade-off between scale economies and diseconomies. First is that scale economies are increasing relative to diseconomies. Black and Hender- son (1999a) have an endogenous growth model where economic growth is fuelled by human cap- ital (‘knowledge’) accumulation. In that model, human capital externalities interact with scale economies at the local level to enhance overall economies of agglomeration. They correlate differ- ential growth rates of U.S. cities with differential growth rates of local human capital. There is similar modelling work by Rossi-Hansberg and Wright (2007) on growth in city sizes. Recent work by Desmet and Rossi-Hansberg (2009) has a more nuanced approach, involving the endogenous where ∂2gi/∂nkj∂nij > 0 which is a special assumption without empirical validation. Second they only fully solve for self-organization equilibria. How equilibria would look with optimizing developers who can cross-subsidize worker- types within different types of cities is less clear, as is what institutions or policies would be required to achieve optima. 46 evolution of scale externalities as part of their work focusing on transition dynamics. An alternative to increasing scale externalities as the explanation for increasing city sizes is that diseconomies have dissipated with technological progress. The Alonso-Muth model emphasizes the decline in commuting costs as a driver of city spread. But it could also be the basis of increasing city sizes, with an eye to the technological revolutions of the last 120 years – the development of transit systems, the invention of the automobile and the construction of the multi-lane high speed highways systems with rays and rings for cities. Empirical work by Duranton and Turner (2012) supports this idea. Finally in thinking outside the traditional models, growth in human capital per person may be associated with better technologies and management techniques in planning of cities and in managing urban diseconomies. Although we have two reasons for city sizes to be increasing, that does not mean there will be necessarily a shrinking number of cities. In Black and Henderson (1999a) and Rossi-Hansberg and Wright (2007), city numbers may also increase with national population growth, as long as the rate of national population growth exceeds the growth rate of individual city sizes. These papers assume a fully urbanized world. Growth in city numbers in developing countries is also driven by urbanization, or the move out of agriculture as discussed in Section 2.1. Stability of the relative city size distribution and size ranking of larger cities. City size distributions for countries are remarkably stable over time, and some argue that they are either globally (Gabaix, 1999) or locally (Eeckhout 2004; Duranton 2007) approximated by a Pareto distribution and thus obey Zipf’s Law. Henderson and Wang (2007) illustrate this stability for the world size distribution from 1960 to 2000. Black and Henderson (2003) and Harris-Dobkins and Ioannides (2001) show this similarly for the U.S. over many decades. To be clear, these exercises look at just cities, not at the spatial transformation of the universe of space as described in Section 3. Theoretical modelling pioneered by Gabaix (1999) and modelled more fully by Rossi-Hansberg and Wright (2007) and Duranton (2007) argue that stochastic processes in particular contexts such as ones that obey Gibrat’s Law generate a stable size distribution of cities over time approximated by Zipf’s Law. A potential problem is that these models also have all cities transiting continuously through the size distribution of cities, in partial contrast to the next fact. Evidence suggests that the biggest cities historically tend to remain the relatively biggest cities in a country over long periods of time. There is little move downwards out of the top rung of cities in a country (Eaton and Eckstein, 1997; Black and Henderson, 1999b, 2003). Eaton 47 modestly. This shift to the hinterlands is correlated with the extensive investment in highways and telecommunications Korea undertook in the early 1980s to service hinterland areas. The overall dispersion of manufacturing is also consistent with manufacturing becoming a mature industry, as discussed in Section 3.1. A. Share of Seoul in Kyonggi Province (National Capital Region) 1970 1980 1983 1993 Population 62% 63% 67% 61% Manufacturing Employment 76% 61% 45% 30% B. Share in National Manufacturing Employment 1983 1993 Seoul, Pusan and Taegu Metro Areas 44% 28% Satellite Cities of Seoul, Pusan and Taegu Metro Areas 30% 30% Other Cities, Rural Areas 26% 42% Source: Henderson, Lee and Lee (1991) and related calculations. Table 4.3: Stages of Decentralization in Korea For China, Table 4.4 shows the decline in shares of areas defined as core urban counties of metropolitan areas in 1990 in national manufacturing employment from 1995 to 2008. New urban counties are on the periphery of these 1990 urban cores, or are the new suburbs. Their employment shares more than double. But hinterland towns labelled as county towns also see a modest rise in their shares. Note the high concentration of services in the original urban cores in 2008 (we do not know the 1995 numbers for services), far in excess of their shares of either population or manufacturing employment. Share of “Nation” Industry Services Population Share of Nat. Share of Nat. Share of Nat. Industry Emp. Services Emp. Population 1995 2008 2008 2000 Urban Counties in Both 1990 and 2000 52% 41% 58% 28% New Urban Counties 6.2% 13% 6.3% 5.5% County Towns 18% 22% 12% 18% Other Rural Counties in 2010 24% 24% 24% 48% Source: Authors’ own calculations. Table 4.4: Stages of Decentralization in China 50 Desmet, Ghani, O’Connell and Rossi-Hansberg (2013) show a corresponding trend in India, looking at the growth of manufacturing vs. service employment in districts where they are initially concentrated versus in districts where they are not. The time period is short, 2000-2005, but still the patterns are striking. As illustrated in Figure 4.3, they fit locally a trend with error bands; and, as the trend moves to higher density districts with fewer observations, the error bands widen. For manufacturing there is strong mean reversion whereby districts with high densities in 2000 grow much more slowly, than districts with low densities in 2000. The pattern for services is quite different. High density districts on average have higher growth rates than at least the middle density districts. At the upper end, growth rises with density. Overall this suggests decentralization of manufacturing as in the Korean and Chinese case, while services are concentrating even more in the high concentration districts found in the biggest cities. −. 4 −. 3 −. 2 −. 1 0 .1 An nu al G ro w th 0 2 4 6 8 Manufacturing Density 2000 (logs) Source: Authors’ calculations based on NSS and ASI Manufacturing Density 2000−2005 (a) Manufacturing −. 1 −. 05 0 .0 5 .1 .1 5 An nu al G ro w th 0 2 4 6 8 Services Density 2001 (logs) Source: Author’s calculations based on NSS Services Density 2001−2006 (b) Services Figure 4.3: Decentralization of Manufacturing and Centralization of Services in India Modelling industry movement across cities. The facts presented in the previous section concern churning and the general turn-over of industries in cities, changes in the degree of special- ization in the urban hierarchy, and patterns of industry movements across the urban hierarchy. We outline a model that deals with churning per se and then review a variety of relevant models that deal with industry movements across the hierarchy Churning. Duranton (2007) adapts the Grossman-Helpman quality ladder model to an urban setting, with the aim of presenting a model of the following facts. Cities are slow to change their relative sizes; the overall size distribution of cities is remarkably stable; and industries move quickly across cities, with cities changing production patterns. In the Grossman-Helpman quality ladder 51 model, there are a fixed set of consumer goods but they can be produced with ever increasing quality. Quality is a ladder process where there is one current best quality j̄(z, t) for sector z at time t. Research by research firms is on-going to improve that quality. Eventually that research leads in sector z to an advance discovered by one research firm. That firm then gets the (non-transferable) patent to produce that product and focuses on production activities, enjoying monopoly rents in production in industry z until there is the next move up the ladder. Only the research firm that discovers the latest quality level produces the product, pricing so as to exclude potential lower quality producers. Duranton adds an urban component. He assumes a fixed given number of cities, each specialized in the production of a different first-nature good, assumptions which anchor cities so that none can disappear, or become unpopulated. The action lies in second-nature goods which innovate and are completely footloose. Duranton makes two key assumptions. Production must occur in the place where a winning research firm makes a discovery. Production requires information from the research firm which can only be transmitted locally, such as through hiring the former research workers of the winning firm to be involved in production. Second, in order to be productive, all research firms focused on innovating in z must be located in the current city where z is produced. If all innovations, as in Grossman-Helpman, are within the own industry, then production would never move. Duranton introduces cross-industry innovation. The cumulated expenditure λk(z) by research firm k focused on innovation z has a probability βλk(z) of inducing a winning move up the quality ladder in industry z, but also a probability γλk(z), γ < β, of inducing a winning innovation in industry z′. The probability of an innovation in industry z is βλ(z) + γ ∑ z 6=z′ λ(z′), where λ(z) is the cumulated expenditures of all research firms focused on innovation in z. If a research firm working on z happens to make a winning innovation in z′, the production of z′ moves to the city where this firm is located, generating churning. In the steady state, there are several key results. First, there is industry churning: the location of production for second-nature products with footloose production will change over time driven by cross-industry innovation.10 Second, the innovation process leads to a stable size distri- bution of cities that locally approximates Zipf’s Law, so that the size distribution of cities remains time invariant. Third, however, there is motion for individual cities. Bigger cities which (by acci- dent) have accumulated innovations and production will lose and gain sectors over time, but in net 10An older heuristic version of this was that traditional producers and their nearby research firms become ‘com- placent’ and new locations do the innovation. 52 being constructed? We simply don’t have research which deals with such questions at a city or national scale. In this section we focus on two types of policies for which there is recent research and are fundamentally spatial in nature. A first policy concerns the causal effects of transport infrastructure investments linking cities and regions, as well as locations within cities, on urban form and city growth. A second policy concerns urban, or what we will label as big-city, bias in the allocation of public resources and operation of markets. 4.3.1 Transport Investments and Technological Change Modelling suggests that transport infrastructure investments are responsible for changing patterns of specialization and growth of towns and regions observed in the data. This is the subject of a chapter in this handbook by Redding and Turner (2015) and our coverage is brief. An old debate concerns the effect on hinterland towns of improved linkages to the national centers of economic activity: linkages offer better access to markets but remove protection from outside competition for local producers. Donaldson’s work on historical India (2014), based on the Eaton-Kortum (2002) model, suggests that transport investments lowering costs of trade between locations benefit essentially all cities or regions by allowing them to specialize in production of goods for which they have more of a comparative advantage and to shed production of others and import them as transport costs fall.12 For our purposes the key is increased specialization on a wide scale basis, consistent with the data on China and Korea we reviewed above. In the NEG models pioneered by Krugman (1991) transport improvements on a cruder scale lead first to centralization and specialization of the ‘core’ region in manufacturing, consistent with the above analysis. But further improvements (“at a later stage of development”) can lead to decentralization of manufacturing to periphery regions if core regions become congested (Puga 1999), as suggested by recent U.S. data. In the simple NEG models, specialization and concentration are intertwined. Transport investments also have strong effects on within-city decentralization of industry. In the U.S., historically, goods moved across cities by rail, being shipped from terminals in or near city centers to other cities. Transport within the city to rail terminals by for example horse-drawn wagons was very expensive so firms tended to cluster around the rail terminal in the city center. With the development of trucking and then the highway system, Meyer, Kain and Wohl (1965) 12Empirical work on China is less conclusive. Faber (2014) and Banerjee, Duflo and Qian (2012) reach opposite conclusions on the effect of transport improvements on the fortunes of hinterland areas that are ‘treated’ with transport investments versus those that are not. 55 argue that the construction of ring roads in cities in the 1950s and 1960s permitted various types of manufacturing to decentralize from urban cores to suburban areas with cheaper land and to then ship to rail sidings and suburban terminals by ring roads. For China, in a corresponding phase during the 1995-2008 period, Baum-Snow, Brandt, Henderson, Turner and Zhang (2013) show that rails and rings roads causally led to decentralization of manufacturing within Chinese cities. 4.3.2 Urban and Political City Bias There is a development literature based on the two-sector model (e.g., see Ray, 1998, for a synopsis) which talks about biases and/or policy distortions in labor or capital markets nationally that favor the urban sector and may draw in excessive numbers of migrants to cities. Alternatively, there may be migration restrictions such as China’s hukou system that restrain the extent of rural-urban migration. Here we turn to a related version of biases, where one, or more generally, larger and politically connected cities, are favored, relative to other cities and the rural sector. As we will see, favoring a certain city may make that city either larger or smaller than it otherwise would be. As reviewed by Henderson (1988) and Duranton (2008), the standard modeling of the effects of political bias assumes that favored cities are larger than they would be in the absence of favoritism. There is a system of cities in an economy of different types and equilibrium sizes. Under a developer regime, cities tend to operate near the peak of their inverted-U shape real income curves, at sizes where real incomes across different types of cities for a representative worker are equalized. In national labor markets, any one city faces a horizontal labor supply curve at that going real income. A city that is favored in capital markets or with special public services has an inverted-U that is shifted up — it can pay higher real income/utility at any size. If capital is subsidized to the city, that raises the marginal product of labor a competitive firm can pay. With unrestricted immigration, the size of the favored city expands beyond the peak of its inverted-U. The equilibrium is the point down the right-hand side from the peak where city real income equals the going real income in national labor markets in other non-favored cities. The implication is that, in a free-migration equilibrium, the benefits of favoritism are dissipated through increased commuting costs, or increased city disamenities more generally, as city size expands beyond the peak potential real income point. Empirically Ades and Glaeser (1995) and Davis and Henderson (2003) examine indirect evidence. As hinted at by the title of the Ades and Glaeser paper (“trade and circuses”) there seems to be a clear bias towards capital cities in many countries, especially pre-democratization. 56 Relative to their economic position, they are much larger than other cities, indicating a bias towards investing in capital cities. Other indirect evidence for China as a more specific example is in Au and Henderson (2006b) who infer differential rates of return to the urban versus rural sector and for different types of firms within the urban sector. Direct evidence is harder to find. While papers generate fiscal numbers showing higher per capita public expenditures in different classes of cities, it is hard to distinguish if that is bias, or if it simply that it is efficient for public sectors to be larger in bigger cities, with their greater congestion and environmental issues. Capital markets where we expect an efficient allocation equalizes rates of return across cities can provide more ready documentation. Jefferson and Singh (1999) estimate higher rates of return to rural compared to urban based firms in the early 1990s in China. Cai and Henderson (2013) show that rates of return to capital in China not only differ by firm type (lower for state owned firms) but by city type. All types of firms in political cities like Beijing on average are favored (earn lower rates of return) than in ordinary prefecture level cities in China. Figure 4.4 shows the distribution of returns for private sector firms in ordinary prefecture cities versus the three main provincial level and heavily politically favored cities in Eastern China, Beijing, Shanghai and Tianjin. 0 .1 .2 .3 .4 D en si ty -4 -2 0 2 4 ln((Output-Input)/Capital) Private Firms in East Provincial Cities All Firms in East Provincial Cities Private Firms in Non-Provincial Cities kernel = epanechnikov, bandwidth = 0.1851 Figure 4.4: 2007 Distribution of After Tax Value Added Divided by Net Asset Value (as proportional to the returns on capital) 57 distribution, and finishing with its upper tail — the cities. When addressing the question of how an economy’s spatial organization changes with de- velopment, the literature has often analyzed the long-term patterns of today’s developed countries, notably the U.S. Undoubtedly the past spatial development of the U.S. holds valuable lessons for today’s developing countries, so that this strategy is often both useful and appropriate. At the same time, today’s world is different from the one faced by the U.S. and other developed countries in the 19th and the 20th century. For example, the increasing impact of trade may imply that some countries can urbanize without industrializing. Traditionally the paucity of geographically disaggregated data has limited the extent of empirical analysis on developing countries. However, the rapidly increasing availability of data, together with GIS tools, is changing this. In fact, as this chapter has made clear, the last decade has seen a growing number of empirical studies using data from developing countries. 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