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Innovation and agglomeration: Two parables suggested by city-size distributions: Comment
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Japan and the World Economy 7 (1995) 391 393
the
ECONOMY
Innovation and agglomeration: Two parables suggested by city-size distributions: Comment Vernon
Henderson
*
Brown University and NBER, Providence, Rhode Island, RI 02912, USA
Paul Krugman's paper is a stimulating attempt to bring various diffuse concepts together to bear on the issue of spatial agglomerations. I have three sets of specific comments.
1. Rank size rule The rank size rule has been studied over time and across countries in dozens of articles. A serious overview is provided in the paper of Rosen and Resnick (1980) in which they look at 44 countries. In general and on average, the rank size rule simply does not hold. Typically the exponent ct, in the relationship Rank = Co(Urban Area Population)-" is significantly less than 1. For example in a standard undergraduate text, O'Sullivan (1993) estimates for the 396 urban areas in the USA in 1990 an ~ of 0.905 with a standard error of 0.005. While ~ in some sense is close to the rank size rule assumption of 1, in another sense, with a power series, 0.905 involves a large deviation from 1. For example, rather than rank times population being a constant, rank times population declines against rank exponentially according to Rank,Population = C 1Rank-o.1 The vast literature on the subject makes it clear that empirical investigation of the rule is very sensitive to issues of sampling. One should not simply pick subsamples as Krugman does (i.e. 130 of 396 urban areas or 10 of 130 edge cities) and be casual about what defines a city's size (i.e. political units versus geographic units).
* Tel.: 401-863-1000. 0922-1425/95/$09.50 © 1995 - Elsevier Science B.V. All rights reserved S S D I 0922-1425(95)00022-4
392
V.. Henderson~Japan and the World Economy 7 (1995) 391-393
2. Self organization Fujita and Ogawa (1980) examine spatial self-organization, or spatial agglomeration of atomistic agents, in a full blown spatial model, with consumers, firms, commuting, economies of scale and externalities, rent gradients and hence explicit consumption of land by businesses and residents. They show that ("stable") multiple equilibria may exist in any region of parameter space, so that businesses may agglomerate (i.e. "self-organize") into one, two, three or more business districts. The model is rich enough that, with three business districts, business districts need not be of identical size. To put Krugman in the context of this well-developed literature, he works with a reduced form version of Fujita and Ogawa, without rent gradients or business use of land. His final spatial allocations in any simulation correspond to one of Fujita and Ogawa's possible (Nash) equilibria. Krugman starts with firms almost uniformly distributed across a fixed number of locations and then allows flows of firms among these locations. He implicitly assumes, we all start with too many rather than too few occupied locations (clearly this is not a model of pioneering new locations). Krugman uses "history" (i.e. the initial arbitrary spatial allocation) along with the mechanical adjustment (flow) mechanism to choose one of the possible multiple equilibria in a Fujita-Ogawa type of model. Two items are important to note. First, Krugman's model is not dynamic in the sense of there being economic growth or forward looking decision making. He is simply using a mechanical model to give a role for history in determining static spatial allocations. Second, the model is a reduced form, and thus appears more like a simple mathematical model from physics rather than from economics. But, as Fujita and Ogawa show, there can be a complete underlying economic structure to the reduced form. So the reduced form is not a problem in this context.
3. Large agents In a series of recent articles by Rauch (1993), Henderson and Slade (1993a), and Helsley and Strange (1993), the urban economics literature has moved in the direction of considering the role of "large" agents, or entrepreneurial land developers in organizing urban agglomerations. The role of entrepreneurs in land markets is critical. Imagine trying to analyze market structure in industrial organization without a role for entrepreneurial firm owners and managers. Market structure, ~ la Krugman, would be determined by workers self-organizing (atomistically regrouping) across a historically given number of firms, with no role for new firms or for entrepreneurs to strategize in attracting workers. Industrial organization, as we know it, would not be a subject matter in economics.
V. Henderson~Japan and the World Economy 7 (1995) 391 393
393
In land markets today, developers act on an enormous scale, even beyond the Levittowns of early residential suburbs. Consider Garreau's edge cities such as Reston VA, Irvine CA, Tyson's Corners VA, Yaohan Plaza NY, or Rariton Center NJ. These are entities controlled by a single development agency, comprising millions and millions of square feet of office space and tens of thousands of workers and/or residents. Land use is tightly controlled within these edge cities. Capacity (office space) is chosen initially and over time strategically. Similarly location is chosen strategically vis-a-vis the historical central city and nearby existing and potential edge cities. As analyzed in Henderson and Slade (1993) and Henderson and Mitra (1994), strategic choices are made to maximize profits, in the context of competing with a passive central city with its historically given capacity and location and in the context of possibly precluding entry of other potential nearby edge cities. Mitra (1994) examines phased-in development in the presence of dynamic externalities and Helsley and Strange (1993b) formally consider the impact of stochastic elements. In the context of Fujita and Ogawa and of Krugman, land developers may minimize the role of history in terms of the actions of atomistic agents. They impose their own organization on space and may narrow the set of possible equilibria. Of course they are influenced by history and they themselves create their own history. After all, decades or centuries ago, a developer played a critical role in the formation and development of the entities we now treat as passive central cities!
References Fujita, M. and H. Ogawa, 1980, Equilibrium land use patterns in a non-monocentriccity, Journal of Regional Science 20, 455-475. Helsley,R.W. and W.C. Strange, 1993a,City formation with commitment,regionalscienceand urban economics, forthcoming. Helsley, R.W. and W.C. Strange, 1993b, City developers and efficiency,UBC mimeo. Henderson, J.V. and E. Slade, 1993,Developmentgames in non-monocentriccities, Journal of Urban Economics 34; 207-229. Henderson, J.V. and A. Mitra, 1994, The new urban landscape: developers and edge cities, Brown University mimeo. Mitra, A. 1994, Dynamic externalities and industrial relocation, Brown University mimeo. O'Sullivan, A., 1993, Urban economics,(Irwin, Homewood, IL). Rauch, J., 1993, Does history matter only when it matters a little, Quarterly Journal of Economics CVI II, 843-867. Rosen, K.T. and M. Resnick, 1980, The size distribution of cities, Journal of Urban Economics 8, 165 186.
Japan and the World Economy 7 (1995) 391 393
the
ECONOMY
Innovation and agglomeration: Two parables suggested by city-size distributions: Comment Vernon
Henderson
*
Brown University and NBER, Providence, Rhode Island, RI 02912, USA
Paul Krugman's paper is a stimulating attempt to bring various diffuse concepts together to bear on the issue of spatial agglomerations. I have three sets of specific comments.
1. Rank size rule The rank size rule has been studied over time and across countries in dozens of articles. A serious overview is provided in the paper of Rosen and Resnick (1980) in which they look at 44 countries. In general and on average, the rank size rule simply does not hold. Typically the exponent ct, in the relationship Rank = Co(Urban Area Population)-" is significantly less than 1. For example in a standard undergraduate text, O'Sullivan (1993) estimates for the 396 urban areas in the USA in 1990 an ~ of 0.905 with a standard error of 0.005. While ~ in some sense is close to the rank size rule assumption of 1, in another sense, with a power series, 0.905 involves a large deviation from 1. For example, rather than rank times population being a constant, rank times population declines against rank exponentially according to Rank,Population = C 1Rank-o.1 The vast literature on the subject makes it clear that empirical investigation of the rule is very sensitive to issues of sampling. One should not simply pick subsamples as Krugman does (i.e. 130 of 396 urban areas or 10 of 130 edge cities) and be casual about what defines a city's size (i.e. political units versus geographic units).
* Tel.: 401-863-1000. 0922-1425/95/$09.50 © 1995 - Elsevier Science B.V. All rights reserved S S D I 0922-1425(95)00022-4
392
V.. Henderson~Japan and the World Economy 7 (1995) 391-393
2. Self organization Fujita and Ogawa (1980) examine spatial self-organization, or spatial agglomeration of atomistic agents, in a full blown spatial model, with consumers, firms, commuting, economies of scale and externalities, rent gradients and hence explicit consumption of land by businesses and residents. They show that ("stable") multiple equilibria may exist in any region of parameter space, so that businesses may agglomerate (i.e. "self-organize") into one, two, three or more business districts. The model is rich enough that, with three business districts, business districts need not be of identical size. To put Krugman in the context of this well-developed literature, he works with a reduced form version of Fujita and Ogawa, without rent gradients or business use of land. His final spatial allocations in any simulation correspond to one of Fujita and Ogawa's possible (Nash) equilibria. Krugman starts with firms almost uniformly distributed across a fixed number of locations and then allows flows of firms among these locations. He implicitly assumes, we all start with too many rather than too few occupied locations (clearly this is not a model of pioneering new locations). Krugman uses "history" (i.e. the initial arbitrary spatial allocation) along with the mechanical adjustment (flow) mechanism to choose one of the possible multiple equilibria in a Fujita-Ogawa type of model. Two items are important to note. First, Krugman's model is not dynamic in the sense of there being economic growth or forward looking decision making. He is simply using a mechanical model to give a role for history in determining static spatial allocations. Second, the model is a reduced form, and thus appears more like a simple mathematical model from physics rather than from economics. But, as Fujita and Ogawa show, there can be a complete underlying economic structure to the reduced form. So the reduced form is not a problem in this context.
3. Large agents In a series of recent articles by Rauch (1993), Henderson and Slade (1993a), and Helsley and Strange (1993), the urban economics literature has moved in the direction of considering the role of "large" agents, or entrepreneurial land developers in organizing urban agglomerations. The role of entrepreneurs in land markets is critical. Imagine trying to analyze market structure in industrial organization without a role for entrepreneurial firm owners and managers. Market structure, ~ la Krugman, would be determined by workers self-organizing (atomistically regrouping) across a historically given number of firms, with no role for new firms or for entrepreneurs to strategize in attracting workers. Industrial organization, as we know it, would not be a subject matter in economics.
V. Henderson~Japan and the World Economy 7 (1995) 391 393
393
In land markets today, developers act on an enormous scale, even beyond the Levittowns of early residential suburbs. Consider Garreau's edge cities such as Reston VA, Irvine CA, Tyson's Corners VA, Yaohan Plaza NY, or Rariton Center NJ. These are entities controlled by a single development agency, comprising millions and millions of square feet of office space and tens of thousands of workers and/or residents. Land use is tightly controlled within these edge cities. Capacity (office space) is chosen initially and over time strategically. Similarly location is chosen strategically vis-a-vis the historical central city and nearby existing and potential edge cities. As analyzed in Henderson and Slade (1993) and Henderson and Mitra (1994), strategic choices are made to maximize profits, in the context of competing with a passive central city with its historically given capacity and location and in the context of possibly precluding entry of other potential nearby edge cities. Mitra (1994) examines phased-in development in the presence of dynamic externalities and Helsley and Strange (1993b) formally consider the impact of stochastic elements. In the context of Fujita and Ogawa and of Krugman, land developers may minimize the role of history in terms of the actions of atomistic agents. They impose their own organization on space and may narrow the set of possible equilibria. Of course they are influenced by history and they themselves create their own history. After all, decades or centuries ago, a developer played a critical role in the formation and development of the entities we now treat as passive central cities!
References Fujita, M. and H. Ogawa, 1980, Equilibrium land use patterns in a non-monocentriccity, Journal of Regional Science 20, 455-475. Helsley,R.W. and W.C. Strange, 1993a,City formation with commitment,regionalscienceand urban economics, forthcoming. Helsley, R.W. and W.C. Strange, 1993b, City developers and efficiency,UBC mimeo. Henderson, J.V. and E. Slade, 1993,Developmentgames in non-monocentriccities, Journal of Urban Economics 34; 207-229. Henderson, J.V. and A. Mitra, 1994, The new urban landscape: developers and edge cities, Brown University mimeo. Mitra, A. 1994, Dynamic externalities and industrial relocation, Brown University mimeo. O'Sullivan, A., 1993, Urban economics,(Irwin, Homewood, IL). Rauch, J., 1993, Does history matter only when it matters a little, Quarterly Journal of Economics CVI II, 843-867. Rosen, K.T. and M. Resnick, 1980, The size distribution of cities, Journal of Urban Economics 8, 165 186.