city size distributions and economic development

City Size Distributions and Economic DevelopmentAuthor(s): Brian J. L. BerryReviewed work(s):Source: Economic Development and Cultural Change, Vol. 9, No. 4, Part 1 (Jul., 1961), pp. 573-588Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/1151867 .Accessed: 28/01/2012 13:57

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CITY SIZE DISTRIBUTIONS AND ECONOMIC DEVELOPMENT*

Brian J. L. Berry University of Chicago

Students of urbanization have recognized two kinds of city size distributions: rank-size, 1 according to which the distribution of cities by population size class within countries is truncated lognormal;2 and primate, whereby a stratum of small towns and cities is dominated by one or more very large cities and there are deficiencies in numbers of cities of intermediate sizes. 3 Rank-size regularities have been associated with the existence of integrated systems of cities in economically advanced countries, 4 whereas primate cities have been associated

* This paper is designed in part as an example of the potential uses of the data brought together in the Atlas of Economic Development (Chicago, 1961). The author wishes to thank its author, Norton Ginsburg, for his constructive criticisms.

1. John Q. Stewart, "Empirical Mathematical Rules concerning the Distribu- tion and Equilibrium of Population, " The Geographical Review, Vol. 37 (1947), pp. 461-485; George Kingsley Zipf, National Unity and Disunity (Bloomington, 1941); and the same author's Human Behavior and the

Principle of Least Effort (Cambridge, 1949).

2. A statement which is valid when a variable exponent is allowed. See Martin J. Beckmann, "City Hierarchies and the Distribution of City Size," Economic Development and Cultural Change, Vol. 6 (1958), 243-248; Brian J. L. Berry and William L. Garrison, "Alternate Explanations of Urban Rank-Size Relationships, " Annals, Association of American Geog- raphers, Vol. 48 (1958), 83-91; Herbert A. Simon, "On a Class of Skew Distribution Functions, " Biometrika, Vol. 42 (1955), pp. 425-440; and J. Aitchison and J. A. C. Brown, The Lognormal Distribution (Cambridge, 1957). The truncated lognormal is used here rather than the Yule distribution because both are similar in form and because subsequent analysis is facilitated by use of lognormal probability paper. See also the discussion of E. N. Thomas, "Additional Comments on Population-Size Rela- tionships for Sets of Cities, " paper read to Symposium on Quantitative Methods in Geographic Research, Chicago, 1960, and to be published in the Proceedings.

3. Mark Jefferson, "The Law of the Primate City, " The Geographical Re- view, Vol. 29 (1939), 226-232. Here we use the term "primate" in a sense somewhat different from that of Jefferson, but in accord with the discussion in UNESCO, "Report by the Director-General on the Joint UN/ UNESCO Seminar on Urbanization in the ECAFE Region, " Paris (1956), for example.

4. Zipf, National Unity... and Human Behavior..., op. cit.; Brian J. L. Berry, "An Inductive Approach to the Regionalizati-n ofEconomic Devel- opment, " in Norton Ginsburg, ed., Essays on Geography and Economic Development, Department of Geography, University of Chicago, Research Paper Number 62 (Chicago, 1960), pp. 78-107; and UNESCO, op. cit. See also the studies of Beckmann, op. cit., and Berry and Garrison, op. cit., both of which argue for compatibility of Christaller-Lbsch type hierarchies and rank-size distributions of city sizes.

- 573 -

574 CITY SIZE DISTRIBUTIONS AND ECONOMIC DEVELOPMENT

with overurbanization and superimposed colonial economies in underdeveloped countries or with political-administrative controls in indigenous subsistence and peasant societies. 5 Questions as to the empirical reality of rank-size distributions have been raised, however. 6 Likewise, the idea of a primate city was not developed with Asian dual economies in mind. 7 There seems to be a need for detailed investigation of the whole question of the relations of city size distributions and economic development. Such an investigation is the purpose of this paper. The study will draw upon previous theoretical investigations of rank-size, ° and upon a detailed analysis of the relative economic development of countries. 9 It will not be concerned with systems of cities defined in terms of functional char- acteristics, 10 but simply with the distribution of cities by size within countries and with the economic development of these countries as ascertained in a principal components analysis of multiple indices to economic development.

The plan of the paper is as follows: (a) to describe the city size distributions of as many countries as seem necessary for purposes of this analysis and to compare them with indices of urbanization and primacy included in the Atlas of Economic Development;11 (b) to describe the relative economic development of these countries; and (c) to compare the materials presented in the first two sections in an attempt to test the hypothesized relationship between city size distributions and economic development. A model of city size distributions is for- mulate d.

5. UNESCO, op. cit., refers to the over-urbanization of Asian economies because ofT~) excessive in-migration, and (2) superimposition of limited economic development of a colonial or semi-colonial type, creating dual economies and primate cities which contrast with systems of cities in the west. It was reported that primate cities have paralytic effects upon the development of smaller urban places and tend to be parasitic in relation to the remainder of the national economy.

6. C. Stewart, "The Size and Spacing of Cities, " The Geographical Review, Vol. 48 (1958), 222-245, argues that there are marked divergences from Zipf's rank-size rule that in any country the nth ranking city has a population of I/nth that of the largest city because (i) for 72 countries in the world and (ii) for major political divisions within the six largest countries the theoretical 1.0: 0. 5: 0. 33: 0.25: 0.20 ratios of the sizes of the five largest cities are not found. Using Sweden and Denmark as his examples, and four time periods for each, he argues that there is, instead, an S- shaped distribution of towns by size (pp. 230 and 231). The comments of F. T. Moore, "A Note on City Size Distributions," Economic Development and Cultural Change, Vol. 7 (1959), 465-466, on Zipf's limiting case are also germane.

7. Jefferson, op. cit.

8. Beckmann, op. cit.; Berry and Garrison, op. cit.; Simon, op. cit.; C. Stewart, op. cit.; and Thomas, op. cit.

9. Berry, op. cit.

10. The paper is not concerned with central place systems and the like in the sense of Walter Christaller, Die zentralen Orte in SUddeutschland (Jena, 1933); and August Losch, Die raumliche Ordnung der Wirtschaft (Jena, 1944), trans. W. H. Woglom and W. F. Stolper, The Economics of Loca- tion (New Haven, 1954); or in the sense of rural-urban relationships as discussed by N. Rashevsky, Mathematical Theory of Human Relations (Bloomington, 1947).

11. Norton Ginsburg, Atlas of Economic Development (Chicago, 1961), Part 8, "A Statistical Analysis, " by Brian J. L. Berry.

ECONOMIC DEVELOPMENT AND CULTURAL CHANGE 575

The City Size Distributions

Figures 1-6 contain best-fitting curves to 38 city size distributions. These 38 were selected simply on the basis of convenience of access to data. In each the plot is of cumulative frequencies on lognormal probability paper, so that if a city size distribution is lognormal it assumes the form of a straight line. Data are listed in Appendix A. The cumulative frequencies obtained were for cities with populations exceeding 20, 000 and the cumulation proceeded over six size classes: 20,000-50, 000; 50, 000-100,000; 100,000-250,000; 250,000-500,000; 500, 000-1, 000, 000; and over 1, 000, 000 to 100 percent at the population of the largest city. As the list of countries in Appendix A suggests, all world regions except Africa are well-represented; under-representation in that continent results because very few African countries have many cities with populations exceeding 20, 000. Since we only have comparable urbanized area statistics for cities exceeding 100, 000 in population (see Appendix note), the statistics used refer to "city proper" populations.

Thirteen of the 38 countries have lognormally-distributed city sizes (Fig- ures 1 and 2). The higher one of the thirteen curves appears in the graph, the greater the percentage of small cities in the country concerned. The steeper the slope of a curve, the smaller is the largest city. Among the thirteen are both very large countries such as China and very small countries such as Switzerland. The smaller the country, the steeper is the curve. The thirteen also include both highly developed countries like the United States and underdeveloped countries like Korea. The lower the degree of economic development, the steeper is the curve and the greater the percentage of large cities in the country concerned. It is noticeable that countries with long urban traditions such as India and China and highly developed countries such as the United States and West Germany have very similar city size distributions.

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40 1 E 50 100 200 500 O CITY SIZE IN THOUSANDS

Figure 1. Seven lognormal (rank-size) distributions.

576 CITY SIZE DISTRIBUTIONS AND ECONOMIC DEVELOPMENT 99.9

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30 1 D 50 100 200 500 o CITY SIZE IN THOUSANDS

Figure 2. Lesser developed countries may also have lognormal city size distributions

There are fifteen countries with primate city size distributions (Figures 3 and 4). Note the shape of the curves: lognormally-distributed lesser city sizes are followed by a gap because cities of intermediate size are absent, and then by a rapid cumulation to a primate city or to several primate cities. Mex- ico, for example, has lognormally-distributed city sizes up to an urban population of 250, 000, and then a considerable gap followed by a primate capital city of over a million people. In the case of Ceylon the gap comes earlier, and the capital is smaller. In Japan the gap comes later and indicates absence of cities in the size bracket 500, 000 to 1, 000, 000; in this case there are several larger cities. The gap need not be a void, but a considerable deficiency of cities of intermediate size, as in the examples of Spain and Sweden. Thailand and Guate- mala are limiting cases in which the lower lognormal distribution is absent; instead, a few cities with between 20, 000 and 50, 000 people are followed by a considerable gap and a single large primate city. All fifteen countries are small, and they range from underdeveloped Thailand through countries with dual and peasant economies to Denmark and the Netherlands, with highly specialized agricultural economie s.

Nine countries have city size distributions intermediate between lognormal and primate (Figures 5 and 6). All display some primacy, but none are without cities of intermediate size. Some, such as Norway and Canada, approach lognormal. Others are almost primate, for example, Malaya and Pakistan. In the cases of Australia and New Zealand the deficiency is not in cities of middling size, but in smaller cities. Figure 6 also includes the special case of England and Wales, with primate cities grafted on top of a complete lower lognormal distribution. These intermediate cases again include countries of a variety of sizes and at a variety of levels of development.

What do these differences in city size distributions mean? We can begin to make sense out of them--and to refute some myths--if we compare them with two indices of the nature and degree of urban development, an index of urbanization and an index of primacy.

ECONOMIC DEVELOPMENT AND CULTURAL CHANGE

/, / A Urug If -- / /A Uruguay

B Peru *~- - - ~ C Guatemala

D Mexico E Dominican Republic F Thailand G Japan H Ceylon

500 CITY SIZE IN THOUSANDS

Figure 3. Eight primate distributions

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A Greece B Austria C Spain D Denmark E Netherlands F Sweden G Portugal

500

Figure 4. More developed countries may have primate distributions

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Figure 6. Three additional intermediate distributions, plus the special case of England and Wales

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Relationship to Degree of Urbanization

The Atlas of Economic Development12 includes a map showing the world pattern of urbanization (Figure 7). Countries are shaded in this map according to the percent of their population in cities of 20, 000 and more people, and are divided into six classes of urbanization for convenience of mapping. In Table 1 we cross-classify 37 countries according to these six categories of urbanization and the three categories of city size distribution.

Table 1. Urbanization and City Size Distributions

Degree of City Size Distribution urbanization Rank size Intermediate Primate

Most 4 2 5 2 2 2 1 3 1 2 3 4 4 2 3 5 2 1 3

Least - - -

None of the 37 countries falls within the "least urbanized" category because in this group very few countries possess more than a couple of cities with populations exceeding 20, 000. A chi-square test shows the arrangement of countries in the cross classification to be not significantly different from an arrangement which could have arisen at random. Therefore we conclude that there is no relationship between type of city size distribution and the degree to which a country is urbanized. Countries with lognormal city sizes and low urbanization include China, India, Korea, Poland, and Brazil, whereas countries with primate cities and high degrees of urbanization include Spain, the Netherlands, Denmark, Sweden, Japan, and Uruguay. Australia and New Zealand are the most urbanized of the intermediate cases. All of these countries deviate from the commonly hypothesized but nonexistent relationship between urbanization and rank-size regularities.

Relationship to an Index of Primacy

The Atlasl 3 also includes an index of primacy which is very similar to that used by Jefferson, 14 namely, the ratio of the population of the largest city in a country to the combined population of the first four cities (Figure 8). In Table 2 we cross classify 37 countries according to city size distribution and six classes of this primacy index. There is an obvious relationship: countries with the lowest primacy indices have rank-size city sizes, and countries with the highest have primate city size distributions. But there are also anomalies: Spain, the Netherlands, Sweden, and Japan have primate distributions yet low primacy indices, because they have more than one large city above the intermediate city size gap; countries which combine a high primacy index and a primate distribution have only one large primate city. This anomaly reflects a deficiency of the Atlas index: it only indicates primacy when a country has a single primate city. Intermediate Australia, New Zealand, Canada, and Yugoslavia also have low primacy indices because they have more than one large city, yet all display some primacy if their entire city size distributions are studied.

12. Ginsburg, Atlas..., op. cit.

13. Ibid.

14. Jefferson, op. cit.


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Table 2. Primacy and City Size Distributions

Degree of City Size Distribution primacy Rank size Intermediate Primate

Most 8 2 1 1 2 3 1 2 1 4 1 2 5 6 2

Least 4 4 2

If the deficiencies of the primacy index are taken into account in an inter- pretation of Figure 8, however, the map throws light on the differentiation of city size distributions we have exposed. Countries which have until recently been politically and/or economically dependent on some outside country tend to have primate cities, which are the national capitals, cultural and economic centers, often the chief port, and the focus of national consciousness and feeling. Small countries which once had extensive empires also have primate cities which are on the one hand "empire capitals" (Vienna, Madrid, Lisbon, etc. ) and on the other hand centers in which such economies of scale may be achieved that cities of intermediate size are not called for. Countries with more than one large city are either, like Canada, Australia, and New Zealand, effectively partitioned into several city-regions dominated by very similar primate cities or, like Sweden, Spain, the Netherlands, and Japan, have several large specialized cities which are complementary rather than duplicative. Countries with the lowest degrees of primacy, and therefore with lognormally distributed city sizes, include many of those with considerable industrialization, but also those with long urban traditions and histories of urbanization.

A Model of City Size Distributions

Given the above evidence, a simple graphic model may be proposed which places the several types of city size distributions on a scale between the limiting cases of primacy (e. g., Thailand) and lognormality (e. g., the United States). The model is presented in Figure 9.

A rationale for the model comes from the work of Simon, 15 who showed that lognormal distributions are produced as limiting cases by stochastic growth processes. Berry and Garrison16 argued that, as a limiting case, a lognormal distribution is a condition of entropy, defined as a circumstance in which the forces affecting the distribution are many and act randomly. This contrasts with other distributions which are simpler in that they are produced by fewer forces.

We assume that primacy is the simplest city size distribution, affected by but few simple strong forces. Thus, primate cities are either orthogenetic political and administrative capitals, heterogenetic capitals of the emerging na- tions, or empire capitals (we use the terms orthogenetic and heterogenetic in the original sense of Redfield and Singer, realizing that they are subject to debate).

At the other extreme, rank-size distributions are found when, because of complexity of economic and political life and/or age of the system of cities many forces affect the urban pattern in many ways.

15. Simon, op. cit.

16. Berry and Garrison, op. cit.


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Figure 9. A developmental model city size distributions (for explanation see text)


Intermediate distributions are arranged on the assumed scale from primacy to lognormality. Three intermediate sub-categories are evident: those with more small cities than the primate, those with more medium-sized cities, and those with more large cities. In addition, two stages in the intermediate progres- sion from primate to rank-size are pictured.

The model in effect proposes a major hypothesis: increasing entropy is accompanied by a closer approximation of a city size distribution to lognormality. Common sense leads to several sub-hypotheses: fewer forces will affect the urban structure of a country (a) the smaller is that country, (b) the shorter is the history of urbanization in the country, and (c) the simpler is the economic and political life of the country and the lower its degree of economic development. The converse of each sub-hypothesis also follows.

In the simple orderly cases most cities perform essentially the same set of functions, whether political and/or concerned with rudimentary economic activities. As complexity increases so do urban functions--political, as centers on transport routes, as specialized centers of primary or secondary economic activities, or as central places performing tertiary economic functions. At the highest levels of development a country will contain many specialized cities performing one or the other or several of these functions, and viewed in the aggre- gate, a condition of entropy will obtain.

The limited data available from the previous discussion seem to bear out several of the sub-hypotheses. Countries with rank-size distributions include urban-industrial economies (Belgium, United States), larger countries (Brazil), and countries with long histories of urbanization (India and China). Intermediate distributions nearest rank-size characterize countries which are larger (Canada) and have both primary and secondary commercial specialities (Australia and New Zealand), or at least have considerable commercialization in their economies. The more primate of the two intermediate stages is found in small countries engaged in primary production of relatively few commodities (Austria, Sweden, Netherlands, Denmark) or with some commercialization superimposed on a subsistence or peasant agricultural system in dual economies (Ceylon, Mex- ico, Dominican Republic). Primacy characterizes small countries with simple subsistence economies (Thailand), or is associated with the presence of an empire capital (Portugal).

What of the relationship to degree of economic development, the major topic of this paper? This is explored in the following section.

Relative Economic Development of 95 Countries

The author recently completed a principal components analysis of a data matrix comprising the ranks of 95 countries on each of 43 proposed indices to economic development. 17 The results of this analysis are available elsewhere, and hence will be reviewed only briefly here. Principal components analysis re- duced the dimensions of variation of the data matrix and revealed an extremely simple structure comprising only four basic patterns that differentiated among countries just as well as the original 43 indices and accounted for 92. 8 percent of the sum of squares of the data matrix. The analysis also produced scores for each country on each basic pattern. 18

17. Berry, op. cit.; and Ginsburg, Atlas.. ., op. cit.

18. Ibid.


The First Pattern

Indices of accessibility, transportation, trade, industrialization, urbanization, and national product differentiated among countries in the same way. Thus, when redundancies were eliminated by the statistical analysis, these indices collapsed to form the first basic pattern accounting for 84.2 percent of the total sum of squares. This pattern was identified as a technological scale. The urbanization index used was the index pictured in Figure 7. Thus Figure 7 pro- vides an approximate map of the world pattern of countries on the composite technological scale.

The Second Pattern

A second basic pattern was produced by collapse of indices relating to the population of countries to the demographic scale. These indices included birth, death, infant mortality, and population growth rates, population densities, and so forth.

The Third Pattern

In the third pattern countries with considerable external relations but low national income (e. g. , countries located in Latin America, or colonial territories) were contrasted with countries with the converse (e. g., the Soviet bloc).

The Fourth Pattern

A fourth pattern pointed out a group of large countries with persistently high per capita indices and low per unit area indices, and a group of small countries with the opposite. Canada, the United States, and the USSR were included among those in the first group, while Hong Kong, Lebanon, Israel were included in the second.

A Scale of Economic-Demographic Development

The first two patterns are of most interest here. If they are used as the abscissa and ordinate of a graph and the scores of countries on each are used to locate countries in this graph, a scale of economic-demographic development of countries results. Figure 10 presents this as scale A. Note the linearity of the distribution, the continuum of countries (i.e., there are no groups of countries on the basis of economic development), and the inversion of technological and demographic scores such that a "developed" country ranks high in terms of technology (high national product, etc. ) and low on the basis of demographic charac- teristics (low infant mortality rates, etc. ).

City Size s and Economic Development

Thirty-seven city size distributions have been classified on the basis of the four stages in the model pictured in Figure 9. Using a different symbol for each of the four stages, the 37 countries have been plotted on the scale of economic-demographic development. Results are shown in Figure 10 part B. If type of city size distribution is related to economic development the symbols representing a particular kind of city size distribution should cluster in this graph. It is readily apparent that no clusters occur; therefore it may be con- cluded that different city size distributions are in no way related to the relative economic development of countries. Rank size is not the culmination of a pro- cess in which national unityl9 is expressed in a system of cities. Primacy is not confined to lesser developed countries. We do not find in economic

19. Zipf, National Unity... and Human Behavior..., op. cit.


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Figure 10.

A. Distribution of 95 countries on a scale of economic-demographic development. Ordinate is a technological scale, abscissa is a demographic scale. Countries with the highest level of development are at bottom right and least developed countries are at top left (see text for explanation).

B. Countries classified by city size distribution. Star is lognormal, star in black circle is primate, diamond and circle are intermediate, former nearer lognormal, latter nearer primate.


development a ready explanation of variations in city size distributions on a scale from simple structure (primacy) to entropy (lognormality).

Conclusions

There are no relationships between type of city size distribution and either relative economic development or the degree of urbanization of countries, although urbanization and economic development are highly associated. It appears that there is a scale from primate to lognormal distributions which is somehow tied to the number and complexity of forces affecting the urban structure of countries, such that when few strong forces obtain primacy results, and when many forces act in many ways with none predominant a lognormal city size distribution is found. Simplicity was associated with indigenous political and administrative controls exercised from orthogenetic primate cities, with dual or multiple colonial economies and controls exercised from heterogenetic primate cities, and with empire capitals, in all cases also combined with small countries. Note that in most instances of primacy these statements apply only to the primate cities themselves, for the system of smaller urban centers is generally distributed lognormally. Complexity was associated with specialized economies, but also with countries which have strong urban traditions and long histories of urbanization, and was found in countries of every size.

CITY SIZE DISTRIBUTIONS AND ECONOMIC DEVELOPMENT

Appendix A. Data on City Size Distributions

Country

Canada United State s

Brazil Dominican Republic Ecuador Guatemala Mexico Nicaragua Peru Salvador

Number of Cities, A B C

1 5

2

1 2 13 23

3 1 1 1

1

1

by Size Cl D

7 65

8

1

3 1 2 1

assa E F

9 38 126 377

20 100 1 3 1 4

3 9 29 2 4 4 5 1 3

Austria Belgium Denmark England and Wales Finland France Germany, West Greece Italy Netherlands Poland Rumania Spain Sweden Switze rland USSR Yugoslavia

Australia New Zealand

1 2

1 3

1

4 1 1 7 1 3 3

1

9

3 10

6

1 1 4 1 2 1 4

1 1 1

2 20 28 2

1

2 South Africa

Egypt Turkey

Ceylon China India Japan Korea, South Malaya Pakistan Thailand

2 1

9 5 5 1

1 1

18 4 1

2 1

2

2

1 20 13 18

3

1

3 2 2

55 2

19 30

1 18

9 12

7 17

1 4

84 4

2 2

6

7 3

60 49 62

6 2 8

2 12 5 39 1 13

87 220 3 9

39 46 166

3 18 54 236 20 54 17 64

8 -

28 99 8 12 4 9

6 18

1 16 1 5

7 11

9 11

6 94 93

118 11

2 9

6 132 352 273

36 11 63 14

a. Size classes are as follows: A--over one million; B--500, 000 to 1,000, 000; C--250, 000 to 500, 000; D--100, 000 to 250,000; E--50, 000 to 100,000; and F--20, 000 to 50,000.

Note: These data are culled from a variety of sources (see International Urban Research, The World's Metropolitan Areas, Berkeley and Los Angeles, 1959, Appendix) and apply to the early 1950's. Where a dash (-) occurs, it means that this cell could not be filled; countries in this circumstance have not been plotted in the earlier lognormal distributions.

588

city size distributions and economic development

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