1. Measures of concentration 1.Comparable across industries 2.Comparable across spatial scales 3.Unbiased with respect to arbitrary changes to spatial classification 4.Unbiased with respect to arbitrary changes to industrial classification 5.Carried out with respect to a well-established benchmark 6.Allow to determine whether significant differences exist between an observed distribution and its benchmark Properties of an ideal index of concentration

2. Measures of concentration E = employment s = ratio i = sector i= 1,……., N j = region j= 1,……., M employment in sector i in region j total employment of region j total employment of sector i total employment in the country

3. Coefficient of specialization Coefficient of specialization of region j in sector i Localization coefficient (or Hoover-Balassa) Coefficient of localization of sector i in region j

4. Herfindhal index Index of Isard

5. The Gini Index The most popular index for measuring inequality Here we use it to evaluate the spatial concentration of a given sector in terms of employment Cumulative percentage of

6. Region 10.10.20.50.10.2 2 0.250.80.30.45 30.30.251.20.60.7 40.40.31.311

7. Index of Ellison y Glaeser All previous indexes are sensitive to industrial and spatial definitions The EG index has into account the size distribution of the establishments of each industry and fulfills the first property Exemple of EG: 75% of employment in the vacuum-cleaner industry is covered by merely four plants in USA The reference of EG is the distribution of employment if all plants in a sector were located randomly Let be N the number of plants in a sector and the percentage of employment across the plants of the sector

8. The correlation between the location choices of two plants l and k belonging to the same sector is an index: whereIf plant l in sector i is located in region j andotherwise If, location choices are independent, which corresponds to a random distribution of plants across space If, all plants in this sector are located together If the distribution of economic activity is the benchmark, the probability that a a given plant in sector i chooses to be located in region j is given by the relative size of this region with respect to the overall level of economic activity

12. EVIDENCE ON NEW ECONOMIC GEOGRAPHY S. Kim (1995) “Expansion of markets and the geographic distribution of economic activities: the trends in the US regional manufacturing structure, 1860-1987” Analyzes the evolution of specization and concentration of manufacturing in the long term - Externalities - H-O - Internal increasing returns A DESCRIPTIVE MODEL

13. Integration of US economy starts in 1860 and is completed by 1940s: Transportation costs: 1860-1890 Railway: by 1890 most railroad lines had converted their tracks to a standard gauge of 4'8.5” Miles built 30626 to 166703 Telegraph: Miles 50000 to 19382000 Price convergence: - Goods market: second half of 19th century - Interest rate early 20th century - Wages mid 20th century

14. Units of analysis: Spatial 9 Census divisions (internalize factor mobility and externalities) Industrial: 2 digits (21) (homogeneous technology and externalities) Specialization Localization

15. Specialization. Average of bilateral indexes

16. Localization. Average of Hoover-Balassa

17. First: trend due to half of sectors that increase weight Second: h-t sectors are no more concentrated than traditional sectors → ¿No externalities?

18. - Heckscher-Ohlin (Resources y raw materials) - Internal returns to scale Avarage number of workers per establishment Cost of raw materials/ Value added

19. Elasticities: Plant size 0.157 Raw material intensity 0.223

20. - Historical trends in U. S. regional specialization can be explained jointly by models based on scale economies and resources. - As transportation costs fell between 1860 and the turn of the twentieth century, firms adopted large-scale production methods that were intensive in relatively immobile resources and energy sources. - The rise in scale and the use of immobile resources caused regions to become more specialized. - As factors became increasingly more mobile and as technological innovations favored the development of substitutes, recycling, and less resource-intensive methods over the twentieth century, regional resource differences diminished. - The growing similarity of regional factor endowments and the fall in scale economies caused regions to become despecialized between World War II and today.

21. A STRUCTURAL MODEL Accessibility to markets and firm’s profit: a framework for the empirical analysis mill priceiceberg transport cost marginal cost elasticity of substitution/price elasticityquantity sold by the firm in s In the short-term with a given number of firms:

22. Total profits of r over all markets where is the Real Market Potential freeness of trade recall

23. Market potential and factors attraction (Head y Mayer, 2004) Location decision of firms between two locations i and j depends on → Carlton (1983) logit model Hypothesis: firms locate where markets accessibility is highest Sample de 452 Japanese branch plants localized in 57 regions from 9 EU countries in the period 1984-1995

25. Variable costs: wagesprice of other inputs (land, intermediates) Total factor productivity

26. Construction of the market potential: Problem: we do not have data ofand We need to proxy these two variables: we will do it with trade flows Trade flows estimated with a gravity equation:

27. Supply capacity of export country Market capacity of the import country Distance, border effect, same language National production minus exports

28. Regions from different countries Regions from the same country Intra-regional trade Share of GDP of s on national GDP of country S Potential built for 18 sectors (2 digits) each year

29. Production costs: 1. Labor costs observable (payroll sector /number of employees in the region) additionally: non labor costs (only vary across countries) Unemployment rate 2. Other costs non observable a. Capital cost affected by subsidies/taxes: - Corporate tax rate (only vary across countries) - Elegibility to benefit from Structural Funds (Objective 1) b. Control for land supply and price: - Area of the region

30. Evidence on clusters. 3 types: - Number of establishments in the two-digit industry region - Number of Japanese affiliates in the three-digit industry region - Number of affiliates owned by the same Japanese parent or members of same vertical keiretsu Possible efects of these clusters: - Lowering intermediates prices regional production networks - Share knowledge (non observable) - Clusters will form around the same exogenous sources of low input costs or high productivity Hypothesis: clusters form in areas with high market potential in the relevant industry The hypothesis would receive support if after controlling for market potential, the presence of same industry firms lowers the attractiveness of a region

32. Main results: Ambiguous with respect to RMP: - of RMP increases the probability of locating in the region in 3%-11% - “theory doesn’t pay” - Agglomeration variables the most important but, omitted variables?

33. ECONOMIES OF AGGLOMERATION

34.  Density generates costs Higher cost of land Greater congestion, higher commuting and transport costs  Population and economic activity are ever more concentrated in cities  There must be offsetting benefits Higher productivity for firms Higher wages for workers  Are these advantages due to agglomeration economies?  What are their scale and scope and causes?

35.  Why is it profitable for firms to concentrate employment? 1.Plant-level economies of scale  Plants produce more efficiently at a larger scale 2.Agglomeration economies  Plants produce more efficiently when close to other plants A.Urbanization economies when close to other plants in general B.Localization economies when close to other plants in the same industry

36. Economies of agglomeration are externalities A person who is making an economic decision, such as whether to produce more output, makes the decision on the basis of his own marginal costs and benefits, and ignores costs or benefits that affect others An example An industry in an urban area: demand, D and supply, S Made up of a large number of small, competitive firms Each of these firms has a lon-run average cost curve that has a minimum point at some level of output In the long run the output of the industry expands by adding more firms The long-run supply curve of the industry is the horizontal line S The market price is set equal to long-run average and marginal curve

37. Economy external to the firm but internal to the industry: The expansion of the industry output, through the addition of another firm, will lower the average costs for the other firms The price at which the firms in the industry will offer the good now drops to the lower average cost

38. MICRO-FOUNDATIONS OF AGGLOMERATION ECONOMIES Sharing. Matching. Learning.

39. 1. SHARING A.Sharing indivisible facilities  Simplest argument to justify the existence of a city  Example: ice hockey rink Expensive facility with substantial fixed costs Few individuals would hold a rink for themselves An ice hockey rink is a an indivisible facility that can be shared by many users  Factory towns

40. B. Sharing the gains form the wider variety of input suppliers that can be sustained by a larger final goods industry C. Sharing the gains from the narrower specialisation that can be sustained with larger production  Example: Dresses and Buttons  Some competing firms locate close to one another to share a firm that supplies an intermediate input (something one firm produces that a second firm uses as an input in its production process)  Buttons produced by one firm are used by a dressmaking firm

41.  Production of high-fashion dresses  Demand for dresses subject to the whims of fashion dressmaking firms must be small and nimble (ready to respond quickly to changes in fashion)  Varying demand for dresses causes varying demands for intermediate inputs (e.g., buttons)  Demand for buttons changes from month to month Important → not in the quantity demanded, but in the type of buttons demanded (e.g., one month square blue buttons with a smooth finish and the next month round pink buttons with a rough finish)  Production of dresses is subject to constant returns to scale

42.  Production of buttons  Subject to economies of scale. Use of indivisible inputs and specialized labour → Cost per button decreases as the quantity increases Scale economies large relative to button demand of individual dressmaker  Face time. A button for a high-fashion dress is not a standardized input. Requires interaction between dressmaker and button-maker Dressmaker must be located close to the button-maker  Modification cost. The dressmaker may incur a cost to modify the button to make a perfect match (e.g., to shave the edges of a square button to make it a hexagon)

43.  Average cost of buttons from the perspective of the dressmaker Point a → High cost for an isolated dressmaker Two reasons: - Low production of buttons - Button-maker produces only one type of button

44. Point f → Low cost for the each dressmaker in a cluster Two reasons: - Sufficient demand for buttons to exploit economies of scale - Larger demand for buttons allow specialization of button-makers

45.  Other example:  High-technology firms - Rapidly changing demand → Small innovative firms - Share suppliers of intermediate inputs (electronic components) - Not standardized inputs → Face time

46. Model of gains from diversity productive advantages of sharing a wider variety of differentiated intermediate inputs produced by a monopolistically competitive industry ↓ Aggregate returns to scale There are sectors In each sector, perfectly competitive firms produce goods for final consumption under constant returns to scale They use intermediate inputs, which are specific to each sector and enter into plants’ technology with a constant elasticity of substitution The higher the lower the elasticity of substitution

47. Intermediates produced in monopolistic competititon Production is expalined by: Increasing returns is the marginal productivity of laboris a fixed cost Profit maximizing price Long-term equilibrium

48. Number of firms in equilibrium: Applying normalizations: An increase in final production by virtue of sharing a wider variety of intermediate suppliers requires a less than proportional increase in primary factors

49. Gains from specialization 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 The number of tasks is fixed Each atomistic worker is endowed with one unit of labour. Any worker allocating an amount of time l(h) to perform task h produces Parameter of productivityIntensity of the gains from specialization

50. 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. L workers andtaskseach worker devotes of her unit labour to each of theshe performs

51. D.Sharing risk: labour pooling  Firms are subject to demand shocks  In each time period the demand for some firms grows and the demand for some other firms decreases  Unsuccessful firms will be firing workers at the same time that successful firms are hiring them  An agglomeration of firms facilitates the transfer of workers from unsuccessful firms to successful ones  The process occurs at the level of the firm, not the industry

52.  A simple model  The total demand at the industry level is constant, but the demand for each firm varies from year to year  For each firm there are two possibilities equally likely: a. High demand b. Low demand

53.  Isolated firm  A firm can be isolated  The isolated firm doesn’t face any competition for labour within its town  Labour supply is perfectly inelastic, fixed at 12 workers High demand for the product of the firm ↓ High demand for labour Equilibrium at point b → wage= $16 Low demand for the product of the firm ↓ Low demand for labour Equilibrium at point h → wage= $4

54.  Firm in agglomeration  Firms in agglomeration face competition for labour (labour supply perfectly elastic, horizontal line)  For every successful firm hiring workers, there is an unsuccessful firm firing them  Total demand for labour in the agglomeration is constant A firm can hire as many workers as it wants at the market wage High demand for labour ↓ Firm hires 21 workers (point d) Low demand for labour ↓ Firm hires only 3 workers (point j)

55.  Spatial equilibrium  Wage uncertain at the isolated site high demand w=$16, low demand w=$4 The two outcomes are equally likely: Expected wage (isolated firm) = 0.5 · $16 + 0.5· $4 = $10  To make workers indifferent between isolated site and agglomeration → w(agglomeration) = $10

56.  Firm gains from agglomeration  Expected profits will be higher in the agglomeration  Let’s suppose a firm moves from isolated site to agglomeration and then experiences one year of high demand followed by a year of low demand Good news when demand is high (w=$10 instead of w=$16, and can hire 21 workers instead of 12 workers) Higher profit Bad news when demand is low (w= $10 instead of w=$4) Lower profit

57.  Which is larger, the good news or the bad news? –Good news dominate because a firm in the agglomeration responds to changes in the demand for its product –Expected profit in agglomeration > Expected profit in isolated site (0.5 · adf) + (0.5· gjf) > (0.5 · abc) + (0.5 + ghi) (0.5 · $147) + (0.5 · $3) > (0.5 · $48) + (0.5 + $48) $75 > $48

58. 2. MATCHING. A.Improving the quality of matches between employers and employees  Usual assumption → workers and firms are matched perfectly  Each firm can hire workers with the skills the firm requires  In real world workers and firms are not always perfectly matched  Mismatches require costly worker training  A large city can improve the matching of workers and firms in the real world

59.  A simple model  Assumptions  Each worker has a unique skill described by a position or “address” on a circle with a one-unit circumference  There are 4 workers and skills evenly spaced on the circle  The address of a worker is the distance between her skill position and the “north pole” of the circle  Each firm enters the market by picking a product to produce and an associated skill requirement. S=1/8 S=5/8  Training costs. Workers incurs the cost associated to mismatch

60.  Competition for workers. Each firm offers a wage to any worker who meets its skill requirement Each worker accepts the offer with the highest net wage net wage = wage offered by the firm - training costs  Each firm will hire two workers

61.  Equilibrium  Each firm is the single employer in the skill interval surrounding its skill requirement Equilibrium with 4 workers (skill types) and 2 firms Equilibrium mismatch is 1/8 (workers at 0 and 2/8 work in firm at 1/8, so each worker has a skills gap of 1/8) Each firm pays a gross wage equal to the value of output produced by a perfectly matched worker. Net wage = Gross wage – Skills gap·Unit training cost Net wage = $12 – 1/8 · $24 = $9

62.  Introducing agglomeration  We represent an increase in the size of the labour force by increasing the number of workers on the unit circle Now we have 6 workers (skill types) and 3 firms enter the market Each worker has a mismatch of 1/12 Workers incur lower training cost Net wage increases Net wage = $12 – 1/12 · $24 = $10

63.  An increase in the number of workers decreases mismatches and training costs  The presence of a large number of workers attracts firms that compete for workers, generating better skill matches and higher net wages  This is an incentive for workers to live in large numbers in cities, so the attraction between frims and workers is mutual

64. 3. LEARNING The Obligatory Marshall Quotation When an industry has thus chosen a locality for itself, it is likely to stay there long: so great are the advantages which people following the same skilled trade get from near neighbourhood to one another. The mysteries of the trade become no mysteries; but are as it were in the air, and children learn many of them unconsciously. Good work is rightly appreciated, inventions and improvements in machinery, in processes and the general organization of the business have their merits promptly discussed: if one man starts a new idea, it is taken up by others and combined with suggestions of their own; and thus it becomes the source of further new ideas. Alfred Marshall. 1890. Principles of Economics. London: Macmillan. Book IV, Ch. X, § 3: The advantages of localized industries; hereditary skill.

65. Cost and output for an industry Dynamic agglomeration economies

66.  Three Types of Externalities (Glaeser et al. 1992) 1. Marshall-Arrow-Romer Local knowledge spillovers between firms in the same industry Specialization and concentration promote growth Local monopoly helps growth by internalizing externalities 2. Porter Innovation in competitive industry clusters with many small firms Specialization and fragmentation promote city growth Local competition requires firms to innovate or die 3. Jacobs Local knowledge transfers across industries Diversification and fragmentation promote city growth “Cross-fertilization” of ideas across different lines of work

67.  Evidence not conclusive  Glaeser et al. (1992) find evidence of Jacobs externalities explain the employment growth of sector-city  Henderson et al (1995) find that new industries appear in diverse cities but mature industries grow in specialized cities.

68.  Nursery cities (Duranton and Puga, 2001)  Consider a firm that is looking for the ideal production process for a new product  By experimenting with different processes, the firm will find the ideal process  Once found the ideal process, the firm will switch to mass production and start earning a profit  Question is: where should the firm experiment, in a diverse city or a specialized city?

69.  Cost and Benefits of both options (model)  First option → experiment in a diverse city and then move to a specialized city after discovering the ideal process  An experiment entails producing a prototype of the firm’s new product with a particular production process  Suppose there are six processes in the diverse city  Once the prototype from the ideal process is finished, the firm will immediately recognize that it has discovered the ideal process  Assume that it takes on average three years  Once discovered the ideal, the entrepreneur will move to a specialized city and start making profits

70. Cost of each prototype = $4 (losses of the firm each year of the 3 year) Year 4 the firm moves to specialized city. Moving cost = $7 Assume firm operates 6 years Last 3 years the firm earns a gross profit = $12 Firm’s lifetime profit is Net profit = Gross profit – Prototype cost – Moving cost Net profit = $36 – $12 – $7 = $17

71.  Second option → search for the process in the specialized city Advantage → lower prototype cost Each specialized city has the specialized inputs for one production process Suppose, prototype cost = $3 · 3 years = $9 Disadvantage → Higher moving cost The search for the ideal process would require moves from one specialized city to another An average of three moves, moving costs = $7 · 3 years = $21 Net profit = $36 - $9 - $21 = $6  Profit is lower when experimenting in specialized cities  Different roles of diverse and specialized cities

72. Establishment relocations in France, 1993-1996

73. Combes et al. (2005) Wage curve: wage as a function of the local labour force, w(N), is increasing in the size of the labour force reflecting agglomeration economies Cost of living curve: commuting, housing and other consumption goods Labour supply curve: indicates for any level of net wage, the amount of labour supplied in the area (here it is assumed perfect mobility)

74. DIVERSITY, SPECIALIZATION AND URBAN SIZE Cities of different size and productive specialization can be found in all the economies Specialized and diversified cities co-exist Medium size cities tend to be highly specialized in their production patterns, in terms of goods exported form the city All cities have a base of locally produced goods and services just for local consumption: housing, retail and personal services, business services, repairs and education and health services. (about 60% of total employment)

75. Two industries of similar size nationally (USA, 1987):  Traditional textile (excluding apparel)  High-tech instruments

76. Textiles Most metro areas have no employment None of metro areas > 1m even have 1% of employment in textile Most of specialized areas are medium-small

77. Instruments: Most metro areas have no employment Very large metro areas record small shares Some areas >1m. record shares that are almost 4% of local employment

79.  Model  Firms, in each sector, require both sector-specific inputs as well as business services for their headquarters  There are agglomeration economies in all sectors  Firms face a trade-off between spatial integration of both headquarters and production facilities and the spatial separation of these two functions  If firms decide to split, then both parts of the operation can fully benefit from the relevant agglomeration economies: Sector specific inputs for production Business services for headquarters  Spatial integration Firms manage the interaction between production facilities and headquarters more efficiently because of savings on communication costs But more expensive inputs due to crowding

80. 1.When communication costs high → split costly → low demand for labour from spatially disintegrated firms → firm will pay low wages 2.When communication costs low → separation efficient → cities specialized by function → each function benefit from specific agglomeration effects → headquarters will pay higher wages