Agglomeration diseconomies are most associated with the development of which us region?

4.5.2 Agglomeration and urban inequality

Agglomeration economies affect all talents to the same degree in the previous subsection. This is counterfactual. Using individual data, Wheeler (2001) and Baum-Snow and Pavan (2012) estimate that the skill premium and the returns to experience of US workers increase with city size.62 A theoretical framework that delivers a positive relationship between city size and the returns to productivity is provided in Davis and Dingel (2013) and Behrens and Robert-Nicoud (2014b). We return to the latter in some detail in Section 4.5.3. To the best of our knowledge, the assignment mechanism similar to Rosen's 1981 “superstar effect” of the former—with markets suitably reinterpreted as urban markets—and the procompetitive effects that skew market shares toward the most productive agents of the latter are the only mechanisms to deliver this theoretical prediction.

To account for this, we now modify (4.26) as follows:

(4.55) y(t,Lc,Fc)=AcLca+ϵt,wheret∼N(μt,σt).

These expression differ from (4.51) and (4.52) in two ways. First, y is log-supermodular in size and talent in (4.55) but it is only supermodular in (4.51): “simple” supermodularity is not enough to drive complementarity between individual talent and city size. Second, talent is normally distributed and we assume that the composition of talent is constant across cities—that is, Fc = F for all c.

As before, our combination of functional forms for earnings and the distribution of talent implies that the distribution of earnings is log-normal and that the city Gini coefficient is given by (4.53). The novelty is that the standard deviation of the logarithm of earnings increases with city size, which is consistent with the empirical finding of Baum-Snow and Pavan (2014):

(4.56)σyc=σtϵlnLc.

Combining (4.53) and (4.56) implies that urban inequality increases with city size:

(4.57)∂GiniLc,Fc∂lnLc=∂GiniLc,Fc∂σyc∂σyc∂lnLc=σtϵ2 ϕσyc2>0,

where the second expression follows from (4.56). From an urban economics perspective, agglomeration economies disproportionately benefit the most talented individuals: the urban premium increases with talent. From a labor economics perspective, and assuming that observed skills are a good approximation for unobserved talents, this result means that the skill premium increases with city size.

Putting the pieces together, we assume finally that city size and individual talent are log-supermodular as in (4.55) and that the talent distribution is city specific as in Section 4.5.1:

(4.58)y(t,Lc,Fc)=AcLca+ϵt, wheret∼N(μtc,σtc ).

Then the relationship between urban inequality and city size is the sum of the size and composition effects:

dGini Lc,FcdLc= ∂GiniLc,Fc∂L c+∂GiniLc,Fc ∂σctdσctdLc=2ϵLcσtc 1+lnLcdlnσtc dlnLcϕσyc 2,

where the second equality follows from (4.54), (4.57), and (4.58). Both terms are positive if dσtc/dLc > 0. The solid line in the left panel in Figure 4.5 reports the empirical counterpart to this expression.63

2.6.3 The urban rat race

Another agglomeration effect can be shown to follow from the different incentives possessed by urban residents. Specifically, cities can either inspire or require hard work of their residents, a kind of urban rat race. Rosenthal and Strange (2002) consider this issue by looking at the connection between agglomeration and work behavior. The paper begins by looking at the facts: urbanization is shown to be positively related to work hours for full-time workers in professional occupations, even after controlling for individual worker attributes and for occupational fixed effects. However, that pattern largely disappears after controlling for the localization of the worker's occupation. In addition, the pattern is never present among non-professional workers.

To investigate the source of these effects, two simple models are specified: a selection model in which hard working individuals choose to locate in an active professional environment, and an urban rat race model in which proximity to workers of a similar type causes individuals to work longer hours. If the intrinsic taste for hard work persists over time, then the selection model implies that workers of all ages should work longer hours in agglomerated environments. In contrast, the rat race model is based on the idea that competition encourages individuals to work longer hours when it is important to be noticed. This effect is likely most pronounced among young professionals who have the most to gain from reputation building.

The paper employs differencing methods to test for the presence of these effects using 1990 Census data on full-time workers. For professional workers in their 30's (defined as “young”) and 40's (defined as “middle-aged”), work hours are longer in locations where the density of employment in the worker's occupation is high. No such effect is present for non-professional workers of any age. Adding controls for the proximity to rivals with whom the worker is most likely to compete – defined as individuals who earn a similar wage in the national wage distribution for the worker's occupation – does not change this result. Findings based on this specification also indicate that both young and middle-aged professional workers work longer hours in areas with a high concentration of individuals in their professions. In addition, young professionals are found to work longer hours when both rivals are present and the rewards to advancement are high. Absent such potential rewards, the presence of rivals does not differentially affect the work habits of young versus middle-aged professionals. It should also be noted that these results are robust to controls for occupation fixed effects and also the concatenation of occupation and MSA fixed effects (over 6000 fixed effects in all). On the whole, this work confirms the long held belief that cities attract industrious workers. The research also seems to identify an overlooked aspect of the urbanization–productivity relationship, that cities encourage hard work.

17.5.1 Theory

The key implication of agglomeration economies for tax competition models is that economic activities, even if mobile in terms of the institutional setting, may be de facto immobile because in order to remain competitive firms need to locate at the industry cluster. Hence, policy makers can tax agglomerations without necessarily jeopardizing their tax base. This mechanism has been analyzed extensively in “ new economic geography” models, featuring agglomeration equilibria in which a core region hosts the entire mobile sector that is subject to agglomeration forces while the periphery hosts some of the immobile industry only (Ludema and Wooton, 2000; Kind et al., 2000; Baldwin and Krugman, 2004; Krogstrup, 2008).45 The key insight of this literature is that agglomeration forces make the world “lumpy”: when capital (or any other relevant production factor) is mobile and trade costs are sufficiently low, agglomeration forces lead to spatial concentrations of economic activity that cannot be dislodged by tax differentials, at least within certain bounds. In fact, agglomeration externalities create rents that can, in principle, be taxed by the jurisdiction that hosts the agglomeration. Moreover, decentralized fiscal policy can itself reinforce agglomeration tendencies when scale economies in the production of publicly provided goods make the locus of agglomeration even more attractive (Andersson and Forslid, 2003).46 The core-periphery outcome, however, is quite extreme, particularly when considered at the scale of a city. It is therefore important to note that agglomeration economies need not be as stark as in the core-periphery case to reduce the intensity of tax competition. Borck and Pflüger (2006) show that local tax differentials can also be generated in models that produce stable equilibria with partial agglomeration, and where the mobile factor therefore does not derive an agglomeration rent.

While the mobility-reducing effect of agglomeration economies and the attendant attenuation of horizontal tax competition have been the most talked about policy insights generated by the new economic geography, the very same models in fact can generate the opposite result: knife-edge situations in which a very small tax differential can trigger large changes in the spatial distribution of the tax base. In those configurations, agglomeration economies in fact add to the sensitivity of firm location to tax differentials because one firm's location choice can trigger further inflows and thus the formation of a new cluster. In such configurations, agglomeration economies exacerbate the intensity of tax competition (Baldwin et al., 2003, Result 15.8; Konrad and Kovenock, 2009). A similar result is found by Burbidge and Cuff (2005) and Fernandez (2005), who have studied tax competition in models featuring increasing returns to scale that are external to firms, with firms operating under perfect competition. In these models, individual firm mobility is not constrained by agglomeration economies, and governments may compete even more vigorously to attract firms than in the standard tax competition model.

These results are essentially based on two-region models. In models featuring multiple regions, subtler differences emerge. Hühnerbein and Seidel (2010), using a standard new economic geography model, find that the core region might not be able to sustain higher tax rates in equilibrium if it is itself subdivided into competing jurisdictions. Similarly to the model of Janeba and Osterloh (2013), therefore, their model implies that tax competition puts particular pressure on central cities, which compete over mobile tax bases with other central cities as well as with their own hinterlands.

Such geography models hold particular promise for the analysis of tax policies within cities, given that production factors are highly mobile at that spatial scale and that agglomeration economies have been found to decay steeply over space (Rosenthal and Strange, 2004). If we focus on the scenario whereby locally stable clusters have already formed, such agglomeration forces could reduce race-to-the-bottom-type competitive pressures on local tax setting and thus make decentralized taxation efficient. It has furthermore been shown that decentralized tax setting can act as a mechanism of undoing inefficient spatial equilibria, where industry clusters are initially locked in a suboptimal location (Borck et al., 2012). Moreover, agglomeration economies may make decentralization more politically feasible, as they likely favor larger, central jurisdictions, thus giving central municipalities an advantage where in asymmetric models without agglomeration forces they generally are found as losing out from decentralization.

The potential importance of agglomeration economies for urban public finance, therefore, is hard to overstate. However, firm-level agglomeration economies are not the only force that shapes intracity geographies. As we discussed in Section 17.4.1.2, endogenous population sorting can lead to the geographically central municipality not being the economic center.47

5.7.3 Case studies

Some specific mechanisms of agglomeration economies can be assessed through case studies of firms or industries for which the nature of possible density effects are known and can be specified.

An interesting structural attempt to evaluate the importance of agglomeration economies in distribution costs is proposed by Holmes (2011). The study focuses on the diffusion of Wal-Mart across the US territory and considers the location and timing of the opening of new stores. These new stores may sell general merchandise and, if they are supercenters, they may also sell food. When operating a store, Wal-Mart gets merchandise sales revenues but incurs costs that include not only wages, rent, and equipment costs, but also fixed costs. These fixed costs depend on the local population density as well as the distance to the nearest distribution center for general merchandise and, possibly, the distance to the nearest food distribution center. Higher store density usually goes along with shorter distance from distribution centers. When opening a new store, Wal-Mart faces a trade-off between savings from a shorter distance to distribution centers and cannibalization of existing stores. The estimation strategy to assess the effects of population density and proximity to distribution centers is the following. The choice of consumers across shops is modeled and demand parameters are estimated by fitting the predicted merchandise and food revenues with those observed in the data. An intertemporal specification of the Wal-Mart profit function taking into account the location of shops is then considered. In particular, this function depends on revenues net of costs, which include wages, rent, and equipment costs as well as fixed costs. For a given location of shops, net revenues can be derived from the specification of demand, where parameters have been replaced by their first-stage estimators. To estimate parameters related to fixed costs, Holmes (2011) then considers the actual Wal-Mart choices for store openings as well as deviations in which the opening dates of pairs of stores are reordered. Profit derived for an actual choice of store openings must be at least equal to that of deviations. This gives a set of inequalities that can be brought to the data in order to estimate bounds for the effects of population density and distance to distribution centers. It is estimated that when a Wal-Mart store is closer by 1 mile to a distribution center, the company enjoys a yearly benefit that lies in a tight interval around $3500. This constitutes a measure of the benefits of store density.

The benefits from economies of density in agriculture related to the use of neighboring land parcels are evaluated by Holmes and Lee (2012). When using a particular piece of equipment, a farmer can save on setup costs by using it across many fields located close to each other. Moreover, if a farmer has knowledge of a specific crop, it is worth planting that crop in adjacent fields, although this may be at the expense of reducing the crop diversity that can be useful against risks. The analysis is conducted on planting decisions in the Red River Valley region of North Dakota, for which there are a variety of crops and years of data on crop choice collected by satellites. More precisely, the focus is on quarter sections which are 160-acre square parcels. These sections can be divided into quarters of 40 acres, each designed as a field. The empirical strategy relies on a structural model where farmers maximize their intertemporal profit on the four quarters of their parcels, choosing for each quarter the extent to which they cultivate a given crop (rather than alternative ones). Production depends on soil quality and the quantity of investment in a particular kind of equipment useful to cultivate the specific crop but which has a cost. It is possible to show that because of economies of density arising from the use of the specific piece of equipment on all quarters, the optimal cultivation level for a crop on a quarter depends not only on the soil quality of this quarter but also on that of the other quarters. The specification can be estimated and parameters can be used to assess the importance of economies of density. Results show that there is a strong link between quarters of the same parcel. If economies of density were removed, the long-run planting level of a particular crop would fall by around 40%. Two-thirds of the actual level of crop specialization can be attributed to natural advantages and one-third can be attributed to economies of density.

Measuring the Spatial Distribution of Economic Activity

Urban theory predicts that agglomeration economies give firms an incentive to locate in large metropolitan areas even though the cost of land and labor is higher in cities. How spatially concentrated is the actual distribution of employment? Do large cities attract new firms? Are firms attracted to cities that already have a concentration of jobs in the same industry? Several methods have been proposed to study the spatial distribution of employment in urban areas. Of these, the most common are the Herfindahl and Gini indexes, and a new method proposed by Ellison and Glaeser (1997). These measures require the researcher to first specify a unit of analysis, such as counties or zip codes. Let zi denote region i's share of national employment in a given industry, and let n be the number of regions under consideration. Then the Herfindahl index is given by

(3)H=∑i=1nzi2 .

The index ranges from 1/n to 1. Complete concentration— all employment in an industry in one region—implies that H = 1 because zi = 0 for all but the one region in which zi = 1. Completely diversified employment implies that zi = 1/n for each region, which implies that H=∑i=1n1/n2=1/n. That the Herfindahl index is simple to compute is its advantage. Its disadvantage is that it compares the actual spatial distribution of employment to an unrealistic counterfactual of complete homogeneity. Whereas the lowest possible value of H, 1/n, implies that each region has exactly the same employment share, it is unreasonable to expect a small region such as Cheyenne, WY, to have a similar share of an industry as New York or Denver.

Due to this disadvantage of the Herfindahl index, a more commonly used measure of employment concentration is the Gini coefficient. As a simple example, suppose that we want to measure geographic concentration across five regions in the manufacturing sector. The first region is the largest, accounting for 60% of all employment. The remaining four regions each have 10% of total employment. Sorted from lowest to highest, the cumulative shares are 10, 20, 30, 40, and 100%. Manufacturing employment is more dispersed than the total: each region accounts for 20% of manufacturing employment. Figure 1 is a graph of the cumulative manufacturing employment shares against the cumulative shares of total employment. If manufacturing employment were just as dispersed as total employment, then the plot of manufacturing shares would follow the 45° line—the dotted line in Fig. 1. The area between the two lines is the Gini coefficient. The area is zero if manufacturing and total employment are equally dispersed. The Gini coefficient equals 0.5 if all employment is in one region since the plot of the cumulative share of manufacturing then follows the x axis, while the area under the 45° line is simply 0.5 by construction.

Ellison and Glaeser propose an index that formally incorporates random firm locations—a “dartboard approach”—as the alternative. They begin by defining a gross geographic index for a given industry within the manufacturing sector, G = ∑i(si − xi)2, where si is the share of the industry's employment in region i, and xi is manufacturing's share of total employment in the region. Thus, G measures the extent to which the industry's employment shares differ from the overall distribution of manufacturing employment. Ellison and Glaeser show that the expected value of G is (1 − ∑ixi2)H when the distribution of firms is completely random, where H is the Herfindahl index for the industry. Using this result, they define the following index:

(4)γ=G−1−∑ixi2H1−∑ixi2H

High values of G indicate that an industry is more spatially concentrated than expected given the overall spatial distribution of manufacturing employment.

If firms' location decisions are driven by internal scale economies alone, then there is no reason to expect that the distribution of the industry's employment should be different from the overall distribution of manufacturing jobs, and γ is close to zero. Localization economies imply clustering, and γ > 0. Ellison and Glaeser find that the U.S. automobile, carpet, and computer industries are highly concentrated spatially, whereas soft drink bottling, manufactured ice, and concrete products are not.

5.5.2 Empirical Magnitude of Urban Benefits and Costs

We have seen that agglomeration economies are essential to understand why cities exist at all, and their magnitude fundamentally affects city sizes and patterns of firm and worker location. Thus, quantifying agglomeration economies has been a key aim of the empirical literature in urban economics, especially in recent years.

Agglomeration economies imply that firms located in larger cities are able to produce more output with the same inputs. Thus, perhaps the most natural and direct way to quantify agglomeration economies is to estimate the elasticity of some measure of average productivity with respect to some measure of local scale, such as employment density or total population. This elasticity corresponds to parameter σ in the model just presented. In early work, Sveikauskas (1975) regressed log output per worker in a cross-section of city-industries on log city population and found an elasticity of about 0.06. More recent studies have obtained estimates of around 0.02–0.05, after dealing with three key potential problems in the original approach.

The first problem is that measuring productivity with output per worker will tend to provide upwardly biased estimates of σ, since capital is likely to be used more intensively in large cities. To address this concern, recent contributions focus on total factor productivity, calculated at the aggregate level for each area being considered or, more recently, at the plant level. A particularly influential contribution using this approach is that of Henderson (2003), who estimates total factor productivity using plant-level data in high-tech and machinery sectors for the United States.

A second concern when estimating agglomeration economies is that productivity and city size are simultaneously determined. If a location has an underlying productive advantage, then it will tend to attract more firms and workers and become larger as a result. Following Ciccone and Hall (1996), the standard way to tackle this issue is to instrument for the current size or density of an area. The usual instruments are historical population data for cities and characteristics that are thought to have affected the location of population in the past but that are mostly unrelated to productivity today. The logic behind these instruments is that there is substantial persistence in the spatial distribution of population (which provides relevance), but the drivers of high productivity today greatly differ from those in the distant past (which helps satisfy the exclusion restriction). Most studies find that reverse causality is only a minor issue in this context and that estimates of σ are not substantially affected by instrumenting (Ciccone and Hall, 1996; Combes et al. 2010). An alternative strategy to deal with a potential endogeneity bias is to use panel data and include city-time fixed effects when estimating plant-level productivity, to capture any unobserved attributes that may have attracted more entrepreneurs to a given city (Henderson, 2003).31 Finally, Greenstone et al. (2010) follow an ingenious quasi-experimental approach. They identify US counties that attracted large new plants involving investments above one million dollars as well as runner-up counties that were being considered as an alternative location by the firm. They find that, after the new plant opening, incumbent plants in chosen counties experience a sharp increase in total factor productivity relative to incumbent plants in runner-up counties.

A third concern with productivity-based estimates is that agglomeration economies are not the only reason why average productivity may be higher in larger cities. As in Melitz and Ottaviano (2008) or Syverson (2004), the large number of firms in larger cities may make competition tougher, reducing markups and inducing less productive firms to exit. In this case, higher average productivity in larger cities could result from firm selection eliminating the least productive firms rather than from agglomeration economies boosting the productivity of all firms. Combes et al. (2012b) develop a framework to distinguish between agglomeration and firm selection. They nest a generalized version of the firm selection model of Melitz and Ottaviano (2008) and a simple model of agglomeration in the spirit of Fujita and Ogawa (1982) and Lucas and Rossi-Hansberg (2002). This nested model enables them to parameterize the relative importance of agglomeration and selection. The main prediction of their model is that, while selection and agglomeration effects both make average firm log productivity higher in larger cities, they have different predictions for how the shape of the log productivity distribution varies with city size. More specifically, stronger selection effects in larger cities, by excluding the least productive firms, should lead to a greater left truncation of the distribution of firm log productivities in larger cities. Stronger agglomeration effects, by making all firms more productive, should lead instead to a greater rightwards shift of the distribution of firm log productivities in larger cities. If firms that are more productive are also better at reaping the benefits of agglomeration, then agglomeration should lead not only to a rightwards shift but also to an increased dilation of the distribution of firm log productivities in larger cities.

Using a quantile approach that allows estimating a relative change in left truncation, shift, and dilation between two distributions and establishment-level data for France, Combes et al. (2012b) conclude that productivity differences across urban areas in France are mostly explained by agglomeration. They compare locations with above median employment density against those with below-median density (results are almost identical when comparing cities with population above or below 200,000). The distribution of firm log productivity in areas with above-median density is shifted to the right and dilated relative to areas below median density. On the other hand, they find no difference between denser and less dense areas in terms of left truncation of the log productivity distribution, indicating that firm selection is of similar importance in cities of different sizes. Their results show that firms in denser areas are thus on average about 9.7% more productive than in less dense areas. Put in terms of σ, this implies an elasticity of 0.032. However, the productivity boost of larger cities is greater for more productive firms, so the productivity gain is 14.4% for firms at the top quartile and only of 4.8% for firms at the bottom quartile.

For estimating the empirical magnitude of σ, an alternative to comparing establishments’ productivity across cities is to compare workers’ wages instead. As shown in Equation (5.42), from the point of view of workers, higher wages in larger cities are offset by higher house prices. Looking at the spatial equilibrium from the point of view of firms, Equation (5.39) shows that for firms to be willing to pay higher wages to produce in larger cities, there must be productive advantages that offset the higher costs. Thus, comparing wages across cities of different sizes also allows us to quantify the magnitude of agglomeration economies. This approach is used by Glaeser and Maré (2001), Combes et al. (2008), Combes et al. (2010) and De la Roca and Puga (2012), among others. A key concern when interpreting the existence of an earnings premium for workers with similar observable characteristics in larger cities is that there may be unobserved differences in worker ability across cities. Following Glaeser and Maré (2001), a standard way to tackle this concern is to use panel data for individual workers and introduce worker fixed effects. Compared with a simple pooled ols regression, a fixed-effects regression reduces the estimate of σ by about one-half (Combes et al. 2010). This drop in the estimated elasticity when worker fixed-effects are introduced is sometimes interpreted as evidence of more productive workers sorting into bigger cities. However, De la Roca and Puga (2012) argue that the drop is mostly due to the existence of important learning advantages of larger cities. A pooled ols regression mixes the static advantages from locating in a larger city, with the learning effects that build up over time as workers in larger cities are able to accumulate more valuable experience, with any possible sorting. Introducing worker fixed-effects makes the estimation of agglomeration economies be based exclusively on migrants, and captures the change in earnings they experience when they change location. This implies that an earnings regression with worker-fixed effects likely is expected to provide an accurate estimate of σ, capturing the static productive advantages of larger cities. Recent studies find the estimated value of σ thus estimated to be around 0.025 (Combes et al. 2010; De la Roca and Puga, 2012). At the same time, to more fully capture the benefits of larger cities, we should also study learning effects. We return to these below.

As we have seen, equilibrium and efficient city sizes are the result of a trade-off between agglomeration economies, as measured by σ, and urban crowding costs, as measured by γ. While there is now a large literature estimating the value of σ, the elasticity of urban productivity advantages with respect to city size, much less is known about γ, the elasticity of crowding costs with respect to city size. Combes et al. (2012a) develop a methodology to estimate this and apply it to French data. As highlighted by the monocentric city model studied in Section 5.2, house prices within each city vary with distance to the city center offsetting commuting costs. House prices at the city center capture the combined cost of housing and commuting in each city, so they are a relevant summary of urban costs. Combes et al. (2012a) use information about the location of parcels in each city and other parcel characteristics from recorded transactions of land parcels to estimate unit land prices at the center of each city. They then regress these estimated (log) prices at the center of each city on log city population to obtain an estimate of the elasticity of unit land prices at the center of each city with respect to city population: 0.72. Multiplying this by the share of land in housing (0.25) and then by the share of housing in expenditure (0.23), yields an elasticity of urban crowding costs with respect to population of 0.041.

Hence, existing empirical estimates suggest that the difference between the crowding costs elasticity γ and the agglomeration elasticity σ is small, perhaps 0.02 or less.32 This has some interesting implications. On the one hand, optimal city sizes as given by Equation (5.49) should be highly sensitive to changes in agglomeration economies and productivity. On the other hand, mild deviations from optimal city sizes as described by Equation (5.49) should have only a small economic cost. This in turn means that it may be important to better account for migration costs when studying cities: with free mobility small productivity shocks may have large consequences for city sizes, whereas if mobility costs are important migration may only weakly respond to shocks, since the net effect from changes in agglomeration benefits and crowding costs achieved by moving may be small.

4.2.2 Thick market for intermediate inputs

A second possible explanation for agglomeration economies centers on the availability of specialized intermediate inputs. Concentration of specialized industrial production can support the production of non-tradable specialized inputs. The agglomeration economy in this case is generated by the sharing of inputs whose production is characterized by internal increasing returns to scale. This explanation is likely to be particularly relevant for firms that utilize intermediate inputs that are both highly specialized and non-tradable. Consider, for example, an industry where production crucially depends on the availability of specialized local producer services, such as specialized repair services, engineering services, venture capital financing, specialized legal support, or specialized shipping services. To the extent that these services are non-tradable—or are costly to deliver to distant clients—new entrants in this industry have an incentive to locate near other incumbents. By clustering near other similar firms, entrants can take advantage of an existing network of intermediate inputs suppliers. In equilibrium, cheaper, faster or more specialized supply of intermediate goods and services makes industrial clusters attractive to firms, further increasing the agglomeration. This concentration process will go on up to the point where the increase in land costs offsets the benefits of agglomeration.

While this idea has been around for a long time, the first to formalize it are Abdel Rahman and Fujita (1990), who propose a model where final goods are tradable, but intermediate inputs are non-tradable and are produced by a monopolistically competitive industry. In the model, firms that locate in dense areas share a larger and wider pool of intermediate inputs suppliers, while otherwise similar firms that locate in rural areas share a smaller and narrower pool of intermediate inputs suppliers. This difference generates agglomeration advantages because an increase in the number of firms in an area results in a wider local supply of inputs and therefore in an increase in productivity.

The evidence in Holmes (1999) offers direct support for the input sharing hypothesis. Using data on manufacturing plants, he documents that manufacturing establishments located in areas with many other establishments in the same industry make more intensive use of purchased intermediate inputs than otherwise similar manufacturing establishments in areas with fewer establishments in the same industry. Notably, this relationship only holds among industries that are geographically concentrated. Spatial proximity has limited impact on geographically dispersed industries.

Building on an idea first proposed by Rosenthal and Strange (2001), Overman and Puga (forthcoming) provide an alternative test of this hypothesis by relating measures of geographic concentration for each industry to industry-specific measures of the importance of input sharing. They find support for the notion that the availability of locally supplied inputs is an important empirical determinant of industrial clusters.

Ellison et al. (forthcoming) propose an alternative approach to the one taken by Rosenthal and Strange (2001) and Overman and Puga (forthcoming). They seek to understand the mechanics of the agglomeration process by focusing on how industries are coagglomerated. Different agglomeration theories have different predictions about which pairs of industries should coagglomerate. For example, if input markets are important, then firms in an industry should be observed to locate near industries that are their suppliers. On the other hand, if labor market pooling is important, then industries should locate near other industries that employ the same type of labor. Ellison, Glaeser and Kerr find evidence that input-output dependencies, labor pooling and knowledge spillovers are all significant determinants of agglomeration, but input-output dependencies appear to be empirically the most important channel.

3.1.2.3 Between-industry interactions.

Between-industry interactions (or urbanisation economies) depend on overall activity in an area. The impact may vary across activities. For example, access to final demand will depend on the overall population but will matter more for industries that sell a high proportion of their output to final consumers. Local public goods provision can also depend on overall size, as can cost linkages and technological spillovers. In some theories, where CES preferences (or technology) mean that variety increases utility (or efficiency), diversity matters rather than overall size. Jacobs (1969) also claims that many technology spillovers depend on diversity. Urbanisation diseconomies, including congestion effects, occur if firms compete for the same factors (e.g. land) or customers.

Do between-industry interactions provide a third source of differences between the EU and other areas? As before, contractual arrangements, labour market institutions, anti-trust laws and intellectual property rights could all play a role. Another more realistic possibility is that institutional differences concerning land use and local taxation may change the nature of urbanisation diseconomies. Again, we have little idea if these possibilities are realities.

2.6 Location Externalities and Agglomeration Economies

The significant property of location externalities and agglomeration economies is embedded in the access measures presented. We call the impact on residents and visitors that a resident in a neighborhood, either a household or a firm, induces on other agents in the same neighborhood, a location externality. This impact may be of different types, such as socioeconomic, religious or ethnic, attraction or exclusion, nuisance, or production opportunities, which could be induced by explicit (personal contacts) or implicit (attitudes) interactions. When such an effect is associated with the increment on density, this type of location externality is called an agglomeration economy.

To appreciate this property, consider the elemental interaction benefit given by Eq. (2.9) and its aggregation across interaction purposes given by

(2.12)bni= ∑p∈ΓVnpi=∑p∈ Γ1μnpln(∑j∈I eμnpVnp(qj,cij))

where we recall that the direct aggregation of benefits accrued by the same agent is legitimate if these benefits are measured in terms of utility.

Let us examine the impact of a new agent on the city by increasing the population from N to N+1. We identify the newcomer's activity and its location with a single index j0 because each agent or activity has a unique location. Define I′=I∪{j0}, which considers that the newcomer adds a new location in the space by either expanding the city or by augmenting the density without changing the city limits. Then, the new benefit is

(2.13)bni′=∑p∈Γ 1μnpln(∑j∈I′ eμnpVnp(qj′,cij′))

where μnp recognizes that the variance of the destination choice behavior depends on the agent and the trip's interaction purpose. We observe that the new agent has two impacts on the interaction benefits of every agent in the city: (1) an additional positive term in the inner sum (it is positive because exponentials are strictly positive), which is a direct interaction effect, and (2) a change in the utility at each alternative destination Vnp(qj′,cij′) because of the change in quality due to agglomeration economies and in transport costs due to a change in congestion, from Vnp(qj, cij) to Vnp(qj′,cij′). The second impact represents the externality effect on the interactions.

To analyze these changes, we differentiate Eq. (2.13):

(2.14)dbni′=∑p∈ΓPnpij0Vnpij0+∑p∈Γ∑j∈Ij0 Pnpij(∂Vnpij∂qjdqj+∂Vnpij∂cij dcij)

where the utility Vnpij = Vnp(qj, cij) is defined such that ∂ Vnpij∂qj≥0 (quality attracts trips) and ∂Vnpij∂cij≤0 (congestion cost deters trips). The first term is the direct benefit of the potential interaction with the new agent in the city, with Pj0/npi∂Vnp∂ N=Pnpij0Vnpij0 because the variation in utility is the final utility in this case where there is no previous interaction with the newcomer. The second term represents the induced change in utilities by agglomeration economies generated by the presence of j0 in the neighborhood Ij0, which represents a change in the interaction benefits between agent n and all other agents j∈Ij0.

The induced effect on utilities represents location externalities, and it is the effect that a new agent introduces on the density and diversity of activities in the neighborhood, which is perceived by all citizens as a change in the potential interaction in that neighborhood. Observe that location externalities in Eq. (2.14) include a large number of potential direct and indirect impacts: (1) agents traveling and interacting directly with j0, represented by the first term in the equation, (2) agents traveling and interacting with other agents in the neighborhood and benefiting indirectly via agglomeration economies induced by j0, represented by the second term in the equation, and (3) residents in the neighborhood of j0, represented in Eq. (2.14) when i is the neighbor of j0, which is an indirect benefit induced by agglomeration economies that occurred without travel.

These impacts can be analyzed more closely according to the classical definition of agglomeration economies as a density effect. We have argued that the new agent increases the density in the neighborhood of location j0, which has an impact on the perceived attraction utility of all the locations in this neighborhood, thus affecting the neighborhood quality. Here, we simply define neighborhood as the area affected by a new agent at j0, but it is important to recognize that the size of this area and the magnitude and sign of the change in quality depend on who the new agent is and the magnitude of its activity at j0, i.e., it matters if the newcomer activity is a retail or a manufactory firm and if it is a large or small activity. Additionally, the increase in density may also increase congestion in general, again depending on the type of the new agent. This can be represented denoting the density in the neighborhood Ij0 by ρj0 and rewriting the change in the traveler's utility as a result of the change in density:

(2.15)dbni ′=∑p∈ΓPnpij0Vnpij0+∑j∈Ij0 ∑p∈ΓPnpij(∂Vnpi∂qj∂qj∂ρj0 +∂Vnpi∂cij∂cij∂ρj0)dρj0

where ∂qj∂ρj0 is the positive or negative change in attraction, and ∂c ij∂ρj0≥0 is the change in the congestion cost.

The sign of the combined effect of density on attraction and congestion is ambiguous, but to understand the net impact, we must consider the significant role of the interaction probability in Eq. (2.15). Indeed, the probability Pnpij weighs the term in brackets in a way that increases with utilities (when positive attraction outweighs congestion) and decreases with costs (when congestion costs outweigh attraction, or attraction change is negative). In fact, it is interesting to recognize that this adjustment on probabilities with externalities represents the agent's rational rule of choosing the interaction option that filters in favor of the highest benefit options for its benefit. Such a selection process induces that, on average, location externalities are positive, despite the increment in congestion, which is avoided as much as possible by travelers as the probabilities dictate. Additionally, this net positive effect increases with the size of the neighborhood Ij0 (number of terms of the outer sum of the externality), which depends on the type of the new agent (e.g., consider the size of the neighborhood impacted by a new shopping center vs. a new household residence) but also on the density in this neighborhood ρj0 because the greater the density, the larger the number of agents in the neighborhood impacted by the newcomer.

This analysis considers a simplified model of interactions because it does not recognize trip tours, i.e., chains of trips, but more complex transportation demand models could be considered to arrive at similar conclusions.

Therefore, noting that density on average increases with urban population N, we foresee that location externalities increase with the city's population size. Thus, on average, benefits of urban agents increase with the city size as

(2.16)bni=a+g(N)

where a is the direct benefit, and g(N) are the location externalities. This conclusion recognizes the existence of agglomeration economies associated with interactions in cities and explains its origins on a microscale. It is important to note that, as we have shown, these per capita economies are embedded in the economically sound definition of accessibility measures and emerge from the location externalities that new agents introduce on the travelers' utility. Additionally, we observe that the direct benefit in small cities, represented by the constant a in Eq. (2.16), is relatively larger than the externality compared with large cities.

Notice that the g(N) factor may not be observed when comparing access measures of cities of different sizes in the same country if they have been derived from travel demand models developed independently for each city. This is because, as we noted, access values are relative measures affected by an unknown scale parameter, which is different for each demand model, i.e., different for each city. This difficulty is overcome, however, with a nation-wide travel demand model that combines inner and intercity trips in which access measures have a common scale parameter.

We have purposely introduced the effect of density on the notion of accessibility, which links the microscopic definition of accessibility as an individual's perception of interactions with a mesoscale variable of the system such as density. The purpose is to provide a clear interaction between two scales of the model and therefore model the aggregation process between these scales.

2.3 Sharing the gains from individual specialisation

The micro-economic foundations for urban agglomeration economies presented in the previous section capture a plausible motive for agglomeration. However, they have been subject to two main criticisms. First, they seem somewhat mechanical: a larger workforce leads to the production of more varieties of intermediates, and this increases final output more than proportionately because of the constant-elasticity-of-substitution aggregation by final producers. Second, any expansion in intermediate production takes the form of an increase in the number of intermediate suppliers and not in the scale of operation of each supplier.21 That is, an increase in the workforce only shifts the extensive margin of production.

Adam Smith's (1776) original pin factory example points at another direction: the intensive margin instead of the extensive margin of production. In the pin factory example, having more workers increases output more than proportionately not because extra workers can carry new tasks but because it allows existing workers to specialise on a narrower set of tasks. In other words, the Smithian hypothesis is that there are productivity gains from an increase in specialisation when workers spend more time on each task.

To justify this hypothesis, Smith gives three main reasons. First, by performing the same task more often workers improve their dexterity at this particular task. Today we would call this ‘learning by doing’. Second, not having workers switch tasks saves some fixed costs, such as those associated with changing tools, changing location within the factory, etc. Third, a greater division of labour fosters labour-saving innovations because simpler tasks can be mechanised more easily. Rosen (1983) also highlights that when acquiring skills entails fixed costs it is advantageous for each individual to specialise her investment in skills to a narrow band of skills and employ them as intensively as possible.22

In an urban context, these ideas have been taken up by a small number of authors [Baumgardner (1988), Becker and Murphy (1992), Duranton (1998), Becker and Henderson (2000), Henderson and Becker (2000)].23 The exposition below follows Duranton (1998). The rest of the literature is discussed further below.

2.3.1 From individual gains from specialisation to aggregate increasing returns

Consider a perfectly competitive industry in which firms produce a final good by combining a variety of tasks that enter into their technology with a constant elasticity of substitution (ε + 1)ε just as intermediates entered into Equation (1) of Section 2.2.24 The main difference with the previous framework is that only a given set of tasks may be produced. Specifically, with tasks indexed by h, we assume that h ∈[0,

], where

is fixed. This assumption plays two roles. It formalises the idea that final goods are produced by performing a fixed collection of tasks. It also leaves aside the gains from variety explored earlier as a source of agglomeration economies. Thus, aggregate final production is given by

(13) Y={∫0n¯[x(h) ]1/(1+ɛ)dh}1+ɛ.

Each atomistic worker is endowed with one unit of labour. Any worker allocating an amount of time l(h) to perform task h produces

(14)x(h)=β[l(h)]1+θ,

units of this task, where β is a productivity parameter and θ measures the intensity of the individual gains from specialisation. Note that l(h) can be interpreted as a measure of specialisation, since the more time that is allocated to task h the less time that is left for other tasks. This equation corresponds to (2) in the previous framework. As in Equation (2), there are increasing returns to scale in the production of each task. However, the source of the gains is different. Here the gains are internal to an individual worker rather than to an intermediate firm (to be consistent with the learning-by-doing justification given above) and they arise because a worker's marginal productivity in a given task increases with specialisation in that task.

Workers’ decisions are modelled as a two-stage game.25 In the first stage, workers choose which tasks to perform. In the second stage, workers set prices for the tasks they have decided to perform. We consider only the unique symmetric sub-game perfect equilibrium of this game. Whenever two or more workers choose to perform the same task in the first stage, they become Bertrand competitors in the second stage and receive no revenue from this task. If instead only one worker chooses to perform some task in the first stage, she will be able to obtain the following revenue from this task in the second stage:26

(15)q(h)x(h)=Yɛ/(1+ɛ)[x(h) ]1/(1+ɛ)=Yɛ/(1+ɛ)β1/(1+ɛ)[l(h)] (1+θ)/(1+ɛ).

This revenue is always positive. Thus, a sub-game perfect equilibrium must have the property that no task is performed by more than one worker. Furthermore, if θ < ε (which we assume is the case), then marginal revenue is decreasing in l(h). Thus, a subgame perfect equilibrium must also have the property that every task is performed by some worker. Combining these two properties implies that there is a unique symmetric sub-game perfect equilibrium in which each and every task is performed by just one worker. Given that there are L workers and

tasks, this implies that each worker devotes L/

of her unit labour endowment to each of the

/L tasks she performs. Substituting l(h) = L/

into Equation (14), and this in turn into Equation (13), yields aggregate production as

Like (7), this equation exhibits aggregate increasing returns to scale. However, note that the extent of increasing returns is driven by the gains from labour specialisation as measured by θ and not by ε, the elasticity of substitution across tasks as in equation Equation (7) (since

is fixed).27 In this model, an increase in the size of the workforce leads to a deepening of the division of labour between workers, which makes each worker more productive. Put differently, there are gains from the division of labour that are limited by the extent of the (labour) market.

This aggregate production function can be embedded in the same urban framework as above. If we normalise

= 1, efficient city size is now equal to N* = θ/((2θ + 1)τ). Again, the efficient size of a city is the result of a trade-off between urban agglomeration economies (this time driven by the specialisation of labour) and urban crowding.