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HOW TO MEASURE ECONOMIES OF AGGLOMERATION
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Measures of spatial 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
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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
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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
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Herfindhal index Index of Isard
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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
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Region 10.10.20.50.10.2 2 0.250.80.30.45 30.30.251.20.60.7 40.40.31.311
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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 specialization and concentration of manufacturing in the long term - Externalities - H-O - Internal increasing returns
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Units of analysis: Spatial 9 Census divisions (internalize factor mobility and externalities) Industrial: 2 digits (21) (homogeneous technology and externalities) Specialization Localization
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Specialization. Average of bilateral indexes
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Localization. Average of Hoover-Balassa
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First: trend due to half of sectors that increase weight Second: h-t sectors are no more concentrated than traditional sectors → ¿No externalities?
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- Heckscher-Ohlin (Resources y raw materials) - Internal returns to scale Avarage number of workers per establishment Cost of raw materials/ Value added
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Elasticities: Plant size 0.157 Raw material intensity 0.223
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- 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.
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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
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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
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Plant Herfindahl Ranking Spatial Gini Ranking Ellison & Glaeser Ranking Leather & Leather Products0.025350.07410.05001 Textile Mill Products0.0018190.017170.01532 Instruments & Related Products0.008390.021960.01373 Rubber & Miscellaneous Plastics Products0.0041120.016380.01224 Lumber & Wood Products0.0023180.0143100.01205 Fabricated Metal Products0.0008200.0123140.01156 Printing & Publishing0.0025160.0129120.01047 Furniture & Fixtures0.0028140.0129130.01018 Primary Metal Industries0.017460.025650.00839 Paper & Allied Products0.0066100.014790.008110 Industrial Machinery & Equipment0.0025170.0085180.006011 Food & Kindred Products0.0039130.0088160.004912 Chemical & Allied Products0.005110.0086170.003613 Apparel & Other Textile Products0.0027150.0061190.003414 Stone, Clay, & Glass Products0.012970.0142110.001315 Electrical Material & Equipment0.011980.005120-0.006916 Other Transportation Material0.054540.03713-0.018417 Electronic Equipment0.064530.010815-0.057418 Motor Vehicles0.101620.02614-0.084019 Computer & Office Equipment0.239110.04592-0.253920
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Rosenthal and Strange (2001) “Determinants of agglomeration” High level of concentration indicative of agglomeration economies but also other explanations. R&S objective: to evaluate the degree to which agglomerative externalities explain inter-industry differences in spatial concentration. They regress Index of Ellison-Glaeser on proxies of sources of agglomeration Fourth quarter 2000
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Variables Controls for natural advantage and transportation costs Energy per $ shipment Natural resources per $ shipment Water per $ shipment To the extent that industries concentrate because of a desire to locate close to the sources of their energy, natural resources, and water realted inputs, expectation of positive coefficients of these variables Inventory per $ of shipment (Transportation cost). 1.Value of the end-of-year inventories divided by the value of shipments 2.Data on actual product shipping costs by industry not suitable: industries with high transport rate locate so as to minimize distances to their markets and the related shipping costs. 3.Industries that produce highly perishable products face high product shipping costs per unit of distance. 4.With multiple markets, less agglomeration. Conversely for non perishable
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Controls for agglomerative externalities Sharing Manufactured inputs per $ of shipment Nonmanufactured inputs per $ of shipment Manufactured: Larger economies of scale Greater industry specificity Expectation: non-manufactured less impact on agglomeration Learning Innovations per $ of shipment Innovations defined as the number of new products advertised in trade magazines in 1982, the only year for which such data are available
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Matching If matching is possible, an industry benefits by agglomerating because it is better able to hire workers wiyh industry-specific skills. It is difficult to identify industry characteristics that are related to the specialization of the industry’s labour force Three proxies: Net productivity (Value of shipments less the value of purchased inputs divided by the number of workers in the industry) Management workers/ (Management workers+ Production workers) % of workers with doctorates, Master’s degree, and Bachelor’s degree
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Strategy: They estimate equations for concentration measures at three different levels of spatial detail: State County Zipcode Does different sources operate at different spatial scales?
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Results Natural advantage and transportation costs Natural advantage (except energy). Significant at state level Inventories. Significant at state level (Industries with output that is costly to transport are more likely to locate close to their markets → less agglomeration) Sharing Manufactured inputs. Significant at state level Nonmanufactured inputs. Negative coefficient and significant at state level A reliance on manufactured inputs contributes to agglomeration A reliance on service inputs does not (constant returns to scale and not industry specific → available everywhere)
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Matching Net productivity. Significant at the three levels Managerial share of workers. Significant at county and zipcode level Master’s degree. Significant at the three levels Learning Innovations. Significant at zipcode level Reliance on manufactured and naturally occurring inputs and the production of perishable products serve to increase the importance of shipping costs in firm location That, in turn, positively affects state-level agglomeration but has little effect on agglomeration at lower levels Knowledge spillovers positively affect agglomeration at highly localized levels Reliance on skilled labor affects agglomeration at all levels
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MEASURING ECONOMIES OF AGGLOMERATION Agglomeration economies imply that firms located in an agglomeration are able to produce more output with the same inputs 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
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MODELING APPROACHES Production Function The most natural and direct way to measure economies of agglomeration Fundamental challenge is to find data on all inputs The easiest to find: - Employment/Hours of work The rest not so easy: - Physical capital - Land - Materials (purchased by the firm not made by the firm)
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Measures of A (s sector, c city) - Size of employment (nº de firms) from firm’s industry in the city (economies of localization) - Size of employment or population of the city (economies of urbanization) - Employment density - Measures of specialization of city in sector or - Measures of industrial diversity of the city
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Wages Assumption: In competitive markets Even without perfect competition, in more productive locations, wages will be higher Economies of agglomeration Higher productivity Higher wage Microdata on wages increasingly available
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Births of new establishments Assumption: Entrepreneurs seek out profit-maximizing locations and are disproportionately drawn to the most productive regions Economies of agglomeration Higher productivity Higher profit Location decision No need of data of purchased inputs New establishments are largely unconstrained by previous decisions Decisions are made taken as exogenous the existing economic environment
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Employment Growth Assumption: Agglomeration economies enhance productivity and productive regions grow more rapidly as a result Economies of agglomeration Higher productivity Shift labor demand Employment growth Data on employment easily available
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DETERMINANTS OF LOCAL PRODUCTIVITY We will see how can be derived an estimable equation relating productivity/wage and agglomeration economies, taking as a departure point a production function We assume a firm j Located in r Operating in sector s Using labor in quantity And other factors Production function given by: is the proportion of labor in production is a Hicks-neutral factor augmenting technology level is the efficiency level of workers
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Profit of the firm: is the quantity exported to region b, is the mill price set in region b net of the marginal cost of intermediate inputs, is the average unit value, net of the cost of the intermediate inputs is the wage rate is the cost of inputs other than labor and intermediate inputs is the value added of the firm (Value of production minus cost of intermediates)
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Applying FOC and rearranging terms: By plugging the second expression into the first, we obtain: By aggregating: is the number of firms in region r and sector s
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In which region is the marginal productivity of labor the highest? The equation shows that wages are directly proportional to workers’ efficiency, This has to do with workers’ endowments but not with space Still we have through which agglomeration effects show up A higher, because of high demand, weak competition or cheap intermediates, positively affects wages and worker attraction contributing to a higher degree of agglomeration in the region. captures the effects transmitted through other factor prices. When production factors have a low supply elasticity (e.g., land), prices will be higher in agglomerated areas, which pushes down the wage rate and are affected by pecuniary externalities that work through market mechanisms
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Technological externalities are taken into account through Regions with easy circulation of information and/or high concentration of skilled workers are likely to benefit from more productive technologies, then higher wages. Conversely, transport congestion or pollution worsen productivity and wages Alternatively, if data related to value-added and capital stocks are available:
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ECONOMETRIC ISSUES We regress the total factor productivity, average labor productivity or nominal wage on the employment or population density. We can use logs to interpret the coefficient directly as an elasticity where Estimating the above equation is equivalent to estimate: Implicit assumption: Density affects wage level through: the local level of technology, ; the output price, ; the prices of other inputs, ; the local efficiency of labor, Not able to determine through which variables. Only the net effect of density is identified But this still relevant for policies designed to concentrate or disperse activities
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Omitted variables 1.Skills Differences of skill across space partly explain productivity differentials Not controlling for average regional skill levels labor skills are randomly distributed across regions and captured by the error term If skill controls are not introduced: If denser areas are more skilled, the effect of density will be overestimated
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2.Intra and Inter-sectorial externalities Wage varies by region and sector but density only varies by region Industrial mix should be controlled Industrial mix is important where: output is sold to a small number of industries inputs used are industry specific it affects the level of productivity through price effects specialization index captures intraindustry externalities For interindustry externalities, an “industrial diversity” variables is included (Herfindhal index)
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3.Natural amenities and local public goods Amenities: Naturals: favorable climate, coast-line location, presence of lakes and mountains, natural endowments in raw materials Man-made: the result of public policy like leisure facilities (theaters, swimming pools,…) or public services (schools, hospitals,…) Local Public Goods → benefits reaped by local consumers LPG can be used by firms: Transport infrastructures, research laboratories, job training centers LPG can affect productivity of production factors If randomly located → captured by Problem: Supply of LPG greater in areas characterized by concentrated activity (public policy decisions) Consequence: overestimation of density effect
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But amenities may have additional effects On the supply side: If a region has amenities that attract population → Upward pressure on demand for housing → Pushing up rents On the demand side: Higher land rents → Higher cost for firms → Substitute other production factors, labor, for land → Marginal productivity of labor decreases → Drop in wages If natural amenities are more abundant in heavily populated regions (e.g., leisure facilities) the effect of density is underestimated
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4.Effects of interaction with neighboring regions Some form of density market potential 5.¿Using fixed effects? If available a panel of industries and regions, it is possible to use fixed effects to control for omitted variables We need to make the assumption that during the panel period, the omitted we want to control for are constant. For example, amenity and public good endowments
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Endogeneity bias OLS estimates are biased when some explanatory variables are correlated with the residuals of the regression. These variables are said to be endogenous Assume that a given region experiences a shock observed by economic agents but overlooked by the researcher: Positive shock → some correct decisions made by the regional government that increases productivity Negative shock → an increase of oil price negatively affects regions with intensive use of oil If shocks are localized and affect the location of agents: Positive shocks may attract workers to the affected region where wages are increasing Negative shocks may expel workers from the affected regions
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Shocks can have effects on the attraction of regions Impact on activity Impact on employment density Inverse causality: Shocks → → attraction/expulsion of workers → Increase/Decrease of density Low mobility of factors weaker bias However, still endogeneity bias through creation/destruction of jobs
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Most common approach to address the problem: Instrumental variables technique finding variables (instruments) correlated with the endogenous variable but not with the residual 1. The first step is regressing the variable we consider endogenous on the chosen instrument. Ciccone & Hall (1996) are the first to take into account the problem of endogeneity in this context. They use as an instrument past density. Instrumental regression: This provides us with a prediction of density: where is the OLS estimator for
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2. The density in the initial regression is replaced by its predicted value ( is instrumented) which uncorrelated with the residuals since the instrument is by construction exogenous: The OLS estimate of the equation no longer suffers from endogeneity bias Crucial point: assumption of exogeneity of the instrument Assumption: there is persistence in agglomeration but there is no correlation between past employment density and present productivity shocks Nevertheless a long lag is not a sufficient condition: The source of a shock may be linked to unobserved factors that persist over time
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