NBER WORKING PAPER SERIES CITIES AND GROWFH: THEORY AND EVIDENCE FROM FRANCE AND JAPAN Jonathan Eaton Zvi Eckstein Working Paper No. 4612 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 January, 1994 Rios-Rull, and We thank Paul Beaudry, David Canning, Sam Kortum, Ed Prescott, Victor for constructive participants at presentations at Universitat Pompeu Fabra and Harvard University comments, M. Minni of INSEE for his helpfulness in providing data onFrench aggloneratioiiS Aditya Bhattacharjea, Yuval Nachtom, and Akiko Tamura for their excellent research and from assistance. Akiko Tamura constructed population data for Japanese urban agglomerations of NBER's research census figures on the population of Japanese cities. This paper is part those of the authors program in International Trade and Investment. Any opinions expressed are and not those of the National Bureau of Economic Research. NBER Working Paper #4612 January 1994 CITIES AND GROWI'H: THEORY AND EVIDENCE FROM FRANCE AND JAPAN ABSTRACT The relative distribution of the populations of the top 40 urban areas of France and Japan remained very constant during these countries' periods of industrialization and urbanization. Moreover, projection of their future distributions based on past growth indicates that their size- distributions in steady state will not differ essentially from what they have been historically. Urbanization consequently appears to have taken the form of the parallel growth of cities, rather than of convergence to an optimal city size or of the divergent growth of the largest cities. We develop a model of urbanization and growth based on the accumulation of human capital consistent with these observations. Our model predicts that larger Cities will have higher levels of human capital, higher rents, and higher wages per worker, even though workers are homogeneous and free to migrate between cities. Cities grow at a common growth rate, with relative city size depending upon the environment that they provide for learning. Jonathan Eaton Zvi Eckstein Department of Economics Tel-Aviv University Boston University Ramat Aviv 270 Bay State Road Tel Aviv 69978 Boston, MA 02215 ISRAEL and NBER CITIES AND GROWTH: THEORY AND EVIDENCE FROl FRANCE AND JAPAN Jonathan Eaton and Zvi Eckstein December 1993 I. INTRODUCTION A basic aspect of economic development is the movement of population from the countryside to cities.1 In this paper we consider the particular cases of France between 1876 and 1990 and Japan between 1925 and 1985, both of which experienced substantially increased urbanization during these periods of industrialization. 2 We consider the further issue of whether urbanization took the form of: (1) an increase in the population of larger cities relative to other cities ("divergent growth"), (2) the growth of smaller cities relative to larger cities ("convergent growth"), or (3) similar growth rates across cities of different sizes ("parallel growth"). We find that the evidence rejects the first hypotheses: Urbanization took the form of similar growth rates across cities of different sizes (with only slightly faster growth of large cities in tKuznets' (1966) historical data document the increased share of population living in urban areas during the economic development of a number of rich nations. Chenery and Syrquin's (1980)-cross—sectional evidence shows that the share of a nation's population that lives in cities rises with its per capita GNP. 2Between 1876 and 1990 the population of France grew from 36.9 million to 55.8 million, while the agglomeration of Paris grew from 2.6 million to 9.3 million. Between 1925 and 1985 Japan grew from 59.7 to 122.6 million people, while metropolitan Tokyo grew from 6.5 million to 26.5 million. Hence we are considering each country for a period in which the total population roughly doubled, while the population of the largest urban areas (as well as the other urban areas in our sample) approximately quadrupled. —2— Japan). We then develop a model of growth and urbanization consistent with this finding. We adopt a model of urban development in which urban growth is driven by the acquisition of human capital.3 We choose this approach because of the emphasis that a number of observers of urban development have placed on the role of human capital in the functioning of cities.4 Lucas (1988), in particular, specifically relates what his model identifies as the driving process of economic growth, the acquisition of knowledge and the externalities associated with it, to the forces that lead to the development of cities: It seems to me that the 'force' we need to postulate to account for the central role of cities in economic life is of exactly the sane character as the 'external human capital' I have postulated as a force to account for certain features of aggregate development. (1988, pp. 38—39) Nevertheless, this literature has so far not provided any formal link between the processes of economic growth and of urbanization. Going back at least to Adam Smith, analysts have thought about economic growth in terms of nations. This focus may partly reflect the availability of data at that level. But nation states typically correspond to single legal jurisdictions and, as posited by Ricardo, may best correspond to the domain of 3Work on the determinants of economic growth has attempted to explain the secular growth of per capita GNP in terms of (i) physical capital investment (Solow, 1956, Romer, 1986), (ii) the accumulation of human capital (Uzawa, 1965, Lucas, 1988), (iii) product and process innovation (Inada, 1969, Grossman and Helpman, 1991), and (iv) learning by doing (Arrow, 1962, Young, 1991). 4See, for example, the discussions in Jacobs (1969, 1984), Henderson (1988), Rauch (1991), and Glaiser, et al. (1992). Much of the urban literature has focused on the development of cities that specialize in the production of particular commodities (as in Henderson, 1988). Our approach, in contrast, focuses on cities that need not be specialized, whose productivity derives from the interaction of individuals with complementary forms of knowledge. —3— factor markets. For these reasons this choice of unit may be totally reasonable. Nevertheless, it remains an open question whether the driving forces of economic growth are primarily national in character, with the growth of cities following as a derivative, or whether the process of economic development can better be understood by focusing on some smaller unit, such as the city. The model we develop in this paper allows us to distinguish between local and national sources of growth. Our purpose here is to review some issues raised by the role of urbanization in economic growth, to examine some evidence, and to provide a simple analytic framework to relate the process of urbanization to economic growth. We do so by integrating two branches of literature, that on the endogenous determinants of economic growth, in particular the Lucas (1988) model of human capital accumulation, and that on circular cities, developed by Pines Hills (1967), Arnott (1979), Helpman and (1980), and Henderson (1987, 1988), among others. In Section II which follows we consider the basic empirical question of the extent to which the process of urbanization associated with development is primarily extensive, taking the form of the creation of new cities, or intensive, involving the growth of existing cities. Existing work on urbanization and growth (e.g., Niyao, 1987, Henderson, 1987), predicts that urbanization takes the form of the creation of new cities, whose size converges to an optimum city size.5 Hére we develop an alternative approach in which urbanization involves the parallel expansion of a given number of cities. 5Henderson's (1987) analysis relates new cities to new industries. The steady—state implication is that "the economy grows by churning out new cities at the rate of population growth." (p. 950). Glaiser et al. (1992), on the other hand, find that diversified cities tend to grow faster. -4- The question is analogous to the issue of "convergence" in economic growth. The hypothesis that urbanization is primarily extensive implies that city sizes should "converge," i.e., initially smaller cities should grow faster than larger cities. Our alternative model implies "parallel growth," that is, population growth rates that are independent of initial size, with growth raie3 converging to a common value. We examine this issue with data from 39 French urban areas (agglomerations) from 1876 to 1990 and for 40 Japanese urban areas for the period 1925 to 1985. The French data provide striking evidence in favor of parallel growth: The size distribution of cities remains virtually unchanged throughout the period. Moreover, we find little evidence either of "new" or of "dying" cities. Results for Japan also suggest evidence of parallel growth with some slight, statistically insignificant, additional concentration in large cities. In neither country do we find any support for the convergence or divergence hypothesis. We then develop, in Sections III, IV and V, a model of urbanization and growth consistent with the parallel steady—state growth of cities, but with possibly different short—term growth rates and changes in the ranking of individual cities. Section III presents a static model of a city. Land is a factor of production, and total productivity within a city declines with the distance of 6The notion that relative city size does not change even as urban populations grow relative to the population as a whole has an old tradition in the regional science literature. In particular, the "rank—order rule" asserts that the product of a city's population and its rank in population is constant across cities and time. Beckmann (1958), Rodwin (1970), and Henderson (1988) discuss the rule and its history. With the exception of the analysis in Henderson (1988), which concerns the growth of specialized cities, the rule does not appear to have played a role in current theories of urban growth. The rule does not appear to be mentioned, for example, in the Iandbook of legionat and Urban Economics (1987). —5— production from the city center. This last assumption is meant to capture in a simple way the contribution of urban agglomeration and proximity to productivity. In Section IV we make the model dynamic. We relate total factor productivity in a city to its average level of human capital, as in Lucas (1988). A basic characteristic of a city is the environment that it provides for acquiring human capital (which can either be city—specific or general in terms of its applicability). Cities are linked together in terms of how their human capital stocks contribute to learning, much as the human capital stocks of different countries jointly contribute to national pools of knowledge in Lucas (1993). The interaction of the human capital stocks of different cities implies that, in the long run, city populations will grow at common rates. Migration provides the link between the growth and distribution of human capital among cities and their relative populations. In Section V we analyze migration between cities of different relative levels of human capital. The model implies that cities where time spent acquiring human capital is more productive will have larger populations, higher wages, higher land rents, arid higher levels of human capital per worker, correlations consistent with the data.7 In Section VI we provide some concluding remarks. II. EVIDENCE ON DE1ELOP1ENT AND TILE SIZE DISTRIBUTION OF CITIES We have already mentioned that economic growth and urbanization are very parallel processes. We now consider the question of how cities of different TVe find a correlation between city population and wages and population and price level in our French data. Rauch (1991) finds a significant positive correlation between levels of human capital and city size in U.S. cities. Henderson (1988) discusses other evidence on the correlation of education levels and city size. -6- sizes grow during the process of development. One possibility is that urbanization occurs as new cities develop, and as smaller cities catch up with larger ones, in which case the size distribution of cities would become more even over time. At the other extreme, urbanization could take the form of the expansion of the largest cities, so that the size distribution would become more unequal. To examine this issue we look at historical data on urban agglomerations from France and Japan. Ve choose France for several reasons. First, since it is a high—income country we can observe the evolution of its urban structure during the process of industrialization. Second, it has constituted an intact nation—state more or less within its current borders throughout the industrial revolution. Third, its total land area was settled at the origin of the industrial revolution. Fourth, it is geographically large enough to contain a number of distinct, large metropolitan areas.8 Japan shares the first three characteristics but not the fourth. However, we have constructed data on agglomerations for Japan that seem to be consistent for the period under consideration. We have collected data on the population of 39 urban agglomerations in France for the years 1876, 1911, 1936, 1954, 1962, 1982 and 1990 (see Table A1).9 Our criterion for selection is a 1911 population of at least 50,000 inhabitants. Only two agglomerations (Grasse—Cannes—Antibes and Bethune) nt in our sample rank among the top 35 ciUes in 1990 (rank 17 and 19) in 1990. The smallest agglomeration in our sample (Hagondage) ranks 50 in 1990. Hence, 8Vhile Great Britain shares the first three characteristics, because of its much greater population density, metropolitan areas tended to blend into each other during the process of urbanization. We could not find historical data based on definitions of urban areas that remained consistent during the period of interest. 9The data are from INSEE, Annuaire StaU3tique de La France, various issues. —7— there are almost no new urban agglomerations since 1911 and no urban agglomeration has fallen drastically in its relative size, i.e., no city that was big (relatively) in 1911 has "died."° For Japan we have organized data for the largest 40 agglomerations from 1925 to 1985 for every 5 years (see Table A2). The definition of each agglomeration is not trivial. An appendix explains how agglomerations were defined and how the data were constructed.11 We included all agglomerations that had a population of at least 250 thousands in 1965. As in France, only a few (3) agglomerations not in the sample became marginally larger than those in the sample by the end of the period. But there is no "new" city in that every city in the top 30 cities in Japan in 1990 was in our sample. Similarly, none of the cities in the sample "died" in that none of the cities in the sample ranks below 50 in 1985. As we discussed in the introduction, the urban economics literature addresses the issue of new cities and the optimal size of a city (e.g., Henderson, 1988), both in static and dynamic contexts. The evidence from France and Japan is that there are new cities. Even the tourist cities in France, which may be viewed as new, existed and had a moderate size by the beginning of the 19th century. '°Moreover, the two towns that did grow substantially faster than the other cities and became agglomerations that rank among the top 20 in France are tourist centers with a significant loc3tional advantage. If the demand for leisure and tourism is highly income elastic then the substantial increase of French income per capita over the last 130 years can easily explain the high growth of these two cities. Since our focus is on aggrepte growth and the size distribution of cities that produce a common good, it seems reasonable to ignore those cities whose location led to higher growth due to a higher income elasticity of demand for their specialized product. l1The data are based on historical city population census data provided in rankeisu Showa-kokusei-Soran, vol. 1, in turn based on data from the Statistics Bureau of the Management and Coordination Agency of the Japanese Government. Akiko Tamura aggregated the city population data into data for urban agglomerations. An appendix discusses agglomeration definitions and aggregation procedures. -8- Lorenz Curve3 Using our French and Japanese samples of agglomerations we computed the Lorenz curves for population for each year in our sample for France and every second year for Japan. These are displayed in Figures 1 and 2 and in Tables A3 and A4. The French data demonstrate starkly how the size distribution of cities has not changed noticeably during the most spectacular period of growth of population, movement of population from rural to urban areas, and growth of income per capita. While the population of Paris nearly quadrupled during this period (while that of France as a whole did not quite double) its share of the total population of our sample of cities remained stable at 40—43 percent from 1876 to 1990. The change of ranking among the cities (up and down within the sample) is more frequent for small cities. That is, the relative size of a city in the sample is more stable among the largest cities. The Japanese Lorenz curves show a slight movement towards less equal distribution of size. The share of the larger cities went up and, in particular, Tokyo's share increases for the whole population as well as among the top cities. It is interesting to note that the Lorenz curve for France is the same as the Japanese Lorenz curves for the early years. ilence, the two countries, which are significantly different in their geographical structure, have a very similar size distribution of cities.L2 The stability of the Lorenz curve could be the consequence of any number of dynamic processes driving the population growth of individual cities. The most obvious possibility is that all cities on average grow at the same rate starting at different levels ("parallel growth"). Two possibilities are ruled '2The "rank—order rule" also implies stable Lorenz curves. However, this rule makes the largest city to be about 207. of the sample of 40 cities, while the largest city is in fact much bigger (30 7. for Japan and 40 Z for France).