Urban and Regional Report No. 81-16

Polarization Reversal

in the State of Sao Paulo, Brazil

David J. Keen

and

Peter M. Townroe

July 1981

Urban and Regional Economics DivisionDevelopment Economics Department

The World BankWashington, D.C. 20433

This report was prepared under the auspices of the National Spatial Po1liciesin Brazil Research Project (RPO 672-13) as NSP Working Paper No. 6. Theviews reported here are those of the author, and they should not be inter-preted as reflecting the views of the World Bank or its affiliated organi-zations. This report is being circulated to stimulate discussion andcomment.

Urban and Regional Economics DivisionDevelopment Economics Department

Development Policy StaffThe World Bank

Washington, D.C.

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1. "Polarization reversal" is the term given to the turning point in

the spatial pattern of growth and development in a nation when continuing

relative concentration ceases and urban deconcentration or spatial decen-

tralization commences. The term was first used in 1977 (Richardson, 1977),

although the phenomenon has been of interest for many years. It is linked

to the ideas of "counter-urbanization't and regional dispersal remarked

upon and studied in the United States and other developed countries (e.g.,

Berry and Gillard, 1977; Vining and Kontuly, 1978). However, the partic-

ular usage of the term "polarization reversal" (PR) hitherto has been in

the context of less developed nations. The focus of this paper is on those

LDC's with fast growth rates of population which are reaching a t-rnsitional

stage in their pattern of economic development as well as a change in direc-

tion of their spatial developmente

2. The paper briefly discusses why a PR turning point may be anticipated

as the economy of a nation grows and the urban system develops. We then

review the relatively few studies which have attempted to measure the PR

turning point. Our survey of these studies finds that polarization reversal

is an ambiguous term. There is no agreed definition. Out of our examin-

ation of possible indices of PR and of alternative definitions of the core

and the periphery emerges a new and narrower definition of PR. This

definition and the earlier measures are then considered in the context

of the State of Sao Paulo in Brazil. We find that the State of Sao Paulo

underwent increasing polarization of urban population from 1950 through

1970, but that a PR turning is evident in the nineteen seventies. This

may well be the first documented example of polarization reversal in an LDC.

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A. The Onset of Polarization Reversal

3. Why does "polarization reversal" (PR) occur? What conditions

bring about this change in the spatial pattern of economic growth and

urban development in a national system of cities? For initial simpli-

city here, we may think of an economy which is effectively a single city

region, with a large primate city and a surrounding scattering of smaller

cities stretching away into a rural hinterland. We may then use as a

working definition of PR that provided by Richardson (1977): the point

at which the growth rate of the secondary cities located outside the core

comes to exceed that of the primate metropolitan center. This definition

of PR allow a continuing urban concentration in absolute terms where the

population of the primate city is greater than that of the secondary cities

combined; but it has the virtue of distinguishing the process of polarization

from the state of primacy. This distinction is a cornerstone of this paper

and is the prime reason for conducting the discussion of the urbanization

process in terms of PR rather than (more traditionally) solely in terms

of relative degrees of primacy. Further definitions of PR will be discussed

in the next section of the paper.

4. One way to think about the reasons behind relative urban decon-

centration in an economy is to look for the dual of those factors encour-

aging changes towards greater urban concentration. However, the interest

here is in the turning point between the two sets of pressures. This

turning point may be brcught about by increases or decreases in the

-3-

intensity of certain social and economic forces initially promoting

concentration. At a given level, the interaction between these forces,

and with forces promoting deconcentration, is such as to move the confi-

guration of changes in the urban system from one direction to another.

Or, the turning point is brought about by changes in direction of certain

of these forces, sufficient to swing round the combined effects of all

the forces. Alternatively, new forces enter the system. The underlying

issue is that of changes in the relative advantages of different locations

for the performance of economic activity.

5. Changing opportunities in geographical space come with economic

development. Alonso's (1980) five bell shaped curves are useful in order

to analyze changes in our primate city region economy. The curve we are

interested in, geographical concentration, interacts with the other four.

The rate of increase of material output rises, then decelerates and slows,

in the course of which the complexity of the national economy greatly in-

creases in the range of products manufactured and the capacity and variety

of the full supporting social and economic infrastructure. This develop-

ment both changes the demands made upon spatial relationship in the economy,

and upon the potential for a response to be made to those demands. Simi-

larly, the stages of the demographic transition, pushing the rate of pop-

ulation growth along its bell shaped curve, have a clear impact on city

growth and on urban concentration. The curve of social or income in-

equalityportrays a more indirect pre3sure on urban development, a pressure

that perhaps deserves greater research attention. Rural incomes mray be

much lower than urban incomes, thus failing to promote rural market centers.

Very unequal incomes within the large cities influence residential densities,

accessibility of work places, and shopping development, as well as family

-4

size and motives for migration. In spatial terms, it links closely wi.th

the fourth curve, that of regional inequality. The divergence and sub-

sequent convergence of per capita incomes of region in an economy has been

discerned in terms of backwash and spread effects by Myrdal (1957) or

polarization and trickledown by Hirschman (1958), as well as demonsteated

empirically by Williamson (1965). (See review by Ternent, 1976).

The causal mechanisms behind the curve of regional inequality are closely

related to geographical concentration. In particular, both the geogra-

phical spread of development in a country away from the central city

and convergence of regional per capita incomes involve rising levels of

education and shifts in attitudes and expectations which encourage the

diffusion of information and innovations and foster entrepreneurship and

tie capacity to become involved in the complexities of a modern indus-

trial society.

7. Alonso's five bell shaped curves are not symetric; they differ

from country to country and. they will not necessarily be coincidental

in their upper turning points in any one country. They nevertheless

reflect underlying processes of socialand economic development which should

not be forgotten when we search for more direct reasons for the arrival

of PR. These direct factors fall into two groups: one group operating

in the dominant city and the other group within the hinterland.

8. Within the city, the central metropolis, continuing growth may

bring about increases in congestion, in crime and pollution, and in

infrastructure deficiencies. Or the marginal costs of infrastructures

and services start to rise. There is actually very little evidence for

the onset of these ills being a function of size or even growth per se,

rather than being a function of inadequate urban management; or of a

-5-

failure to correctly price negative externalities; or of direct geografical

limits to expansion (mountains, lakes, etc.) (Renaud, 1979). Each of

these factors encourages producer decentralization from the city and/or

discourages consumer and worker in-migration, thus bringing on PR. All of

these factors have been widely discussed in the literature (Ternent, 1976;

Richardson, 1977; Renaud, 1979). The existence of such factors in a

given city is one reason why a judgement may not be reached a priori

on whether PR is a "good" or a "bad" thing for the economy of a country.

9. The above factors reinforce more overt market processes which

are a function of urban size and growth. One such market process involves

the value of land. Urban economic theory teaches us to expect the value

of land per unit in the aggregate to rise as the size of the city rises.

The owner of a given plot initially at the periphery of the city will

find his plot becoming relatively more central as the city grows, and

therefore as an asset its value will rise faster than prices in general.

Its rise in value will also be proportionate to rises in the value of the

output of the city. As long as the core city is increasing the value of

its output per unit of land faster than other cities, land owners in the

core city benefit. However, this rise in relative land values works against

the introduction of new land extensive activities except at the edge of

the city (or except as in part a land investment or speculation) and against

the in situ expansion of existing land extensive activities. Deconcentration

is thereby promoted. The effect is reinforced by the development in the

economy of more land intensive activities (e.g. in the service sector),

encouraging therefore an outward movement of land extensive activities

(many sectors in manufacturing).

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10. The pressures in the labor markets work somewhat differently. If

metropolitan growth results in residential environmental deterioration,

higher taxes and larger journeys to work, then would be in-migrants are

deterred and existing residents became prospective out-migrants; unless

compensation is avai.lable in the form of higher rewards from employment.

Employers may be able to pay these higher rewards if they themselves are

'benefitting from metropolitan externalities and economies of agglomeration;

or if they are in a dominant market position to pass forward the higher

costs to the consumer. As the city grows and the economy develops to-

wards European or North American levels, the office sectors, particu-

larly government, may begin to outbid manufacturing for labor. Employers

not able to pay the higher rewards are encouraged to move to the sub-

urbs or to a secondary city. In labor abundant countries these pressures

are reduced if a steady flow of poor in-migrants with low expectations

holds down the bidding price. This is where issues of income distri-

bution may become important, because the monetary/non-monetary trade-

off in the migration decision of the poor in-migrant will take a very

different form than that of the affluent skilled or professional pros-

pective out-migrant.

11. The advantages for a resident or for an existing company or for

new investment of remaining in the city as it grows in size may cease

to rise in an absolute sense. Absolute advantages for in-migrants to

the city may also stabilize as the city increases in population. How-

ever before this failure to rise further, or even a deterioration, is

acted upon, the possiblitZ of an alternative location must exist. This

is where we bring in a second set of factors influencing PR. The possi-

bility of an alternative location for the resident will normally mean the

guarantee or prospect of employment in a secondary city, access to public

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services of some national standard, and not more than a small fall in real

income (depending upon the size and rate of discount of the relevant

transaction costs). Similarly, for the company, outward movement from

the metropolis will normally only be regarded as possible if the centers

for deconcentration have the relevant infrastructures, services and

communications network. For the resident, the migrant, the existing

company or the new investment, location or relocation to a secondary

city therefore rests on prerequisites before a calculation of balance

of advantage is undertaken.

12. Prerequisites are not absolutes in these forms of locational

behavior, but they form a base upon which locational choices are made

by trading off the .elative advantages of the central metropolis against

those of one or more of the secondary cities. If the information is

available, a company for example will compare relative land values,

transport costs and wage-levels just as the resident will compare relative

house prices, journey to work costs and income levels. Changes in the

aggregate pattern of choices will induce PR.

13. Migrants from the primate city or hinterland areas may be

attracted to jobs created in a secondary city not only from an outward

movement of firms from the core but also from an increase in income levels'

in the hinterland of the secondary cities as well as from locally generated

economic growth within the city. Changes in the pattern and value of

agricultural production or in the extraction of minerals could foster

secondary city employment growth. Growth may also come from improvements

in the publicly provided infrastructura base of roads, power, water, com-

munications, and industrial sites. A further improvement affecting the

productivity of local firms would be in the educational level of the

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secondary city labor force. With the increased population and aggregate

income coming from economic development, a secondary city would cross addi-

tional thresholds of the minimum market size necessary for locally produc-

ing those goods and services consumed by residents and firms in the city

and its hinterland. One must note, however, that in both the primate

city and the secondary cities specific sets of PR inducing factors rely

upon the "absorptive capacity" of each local community for economic

growth. This capacity of the loca'. infrastructure to accomodate

growth will limit the contribution any one secondary city can make to

the onset of PR (Linn, 1979).

14. Recognizing these two groups of factors moving an urban system

towards PR, we can now turn to the direct influence of changes in public

policies. Policies which protect or promote a designated sector of in-

dustry implicitly protect or promote those urban centers in which the

industry is located. If the industry is spatially concentrated, the

subsidy or tariff will have a spatially biased result. Location poli-

cies for state owned enterprise can have a similar impact on urban develop-

ment patterns. Policies which seek to promote metropolitan decentralization

and/or lagging region development will normally have PR, or an acceleration

of the reversal once started, as a prime strategic objective. These

policies commonly have carrots and sticks Ln the investments used plus some

form of favored public sector infrastructure programming for the desig-

nated reception areas of decentralizing industry (Townroe, 1979).

15. A further policy change which may bring PR closer in our city

region economy is any improvement in the fiscal standing of mmnicipal

authorities in the secondary cities. At early stages of development,

the major industrial metropolis typically receives a net fiscal transfer

-9-

per head and per unit of output from the rest of the economy. Political

clout and rising public service costs may maintain this differential as

the city grows. If local tax revenues are dependent upon property values

or on industrial output and powers to borrow are limited, the public

authorities in a secondary city have little ability to foster local

industry or attract in new investment. They are dependent upon a central-

ized approach to decentralization. And yet, in general, the least pri-

mate uX*ban systems around the world tend to occur in countries with a

federal system of government (Henderson, 1980).

16. The political concerns with PR come from several directions simul-

taneously. They come from a desire to promote development in lagging

regions and rural hinterland; or from worries about the economic and

social costs of a city or region which appears to be.getting too large or too

dominant or which is growing too fast. The concerns are with the balance

of private and social costs and benefits and with issues of equity as

well as efficiency. The quality of economic understanding underlying these

concerns has frequently been questioned (Alonso,1968; Richardson, 1977;

Renaud, 1979; Townroe, 1979). Nevertheless the politician will be in-

terested in the timing of PR; and then whether and in what ways PR should

be encouraged and fostered. To answer these questions in any one nation

we need to return to consider alternative definitions and measures of PR.

B. The Measurement of Polarization Reversal

(i) Some problems of definition.

17. In offering a definition of PR based upon relative urban growth

rates, Richardson (1977) viewed the onset of PR as the commencement of

10 -

a persistent tendency for a few secondary cities to grow faster than

the primate metropolis. The urban system moves through a sequence of

central city polarization, then inter-regional deconcentration, and then

inter-regional decentralization. Eventually this pattern will be repeated

for the large and small cities in the core region and the more peripheral

-regions. However this fairly loose formulation leaves open the choice

of numeraire, and provides an inadequate distinction between city

growth and regional growth.

18. Population growth of secondary cities relative to tha core city

is not the only measure of PR used in the literature. Richardson (1977)

also suggests studying the spatial concentration of industry as a possible

maasure of PR. Renaud (1977) studied population growth and migration in his

study of PR in Korea. He also used the changing spatial concentration

of gross regional product and regional per capita incomes as measures.

Linn's examination of PR in Colombia (1979) used gross regional product,

income and investment. Comparisons between studies are made difficult

by the different indicators used. Considerable ambiguity is introduced

to the use of the term polarization reversal. For example, does the phe-

nomenon refer to the concurrent reversal in a trend of spatial concentration

of population, industry and income? Or is it possible to have PR if only

the distribution of population exhibits deconcentration from the core,

while incomes are not converging or industry deconcentrating? If the

timing of industry deconcentration leads income convergence which in

turn leads population deconcentration, at what point does PR begin?

19. Although the leads and lags in the various possible indicators

are of interest in their own right, this paper uses population as the

sole measure of PR. Population estimates are often available on an

annual basis, are comprehensive over space, and have a high level of

spatial disaggregation. Employment and income data for LDC's in particular

tend not to have these advantages. Analysis of changes in employment may

be clouded by differences in production technology and productivity

between cities. However, movement of population in those societies

allowing freedom of migration would be direct evidence of changing

economic advantages over space. There are also strong policy concerns

with population size of primate cities and so population seems the most

appropriate single measure.

20. Using relative population changes alone as the measure of PR does

not eliminate amabiguity in the definition of PR. A further difficulty

arises in specifying the geographical boundaries of both the area of

concentration and the area of relatively slower growth or even decline,

or in other words the core and the periphery. To illustrate the pro-

blem, imagine our small country as before (Jamaica perhaps ar El Sal-

vador) with a relatively large primate city, a ring of subu. 's and

industrial satellites around the central city, and an agricultural hinter-

land with a number of smaller secondary cities. The minimum boundary of

the core could be that of the large central city. This would lead how-

ever to a relatively rapid growth of thesuburbsbeing interpreted as PR.

The effect would be heightened if the resident population of the central

city should decline, as has happened for example in London. Polarization

reversal in our small country has to be concerned with the balance between

- 12 D

the secondary cities in the hinterland and the core, which will include

both the central city and its suburbs. This suggests that some functional

definition, such as the labor market area or commuting shed, is a better

definition of the core region.

21. The difficulty of finding an appropriate definition of the core

grows as the structure of the core becomes more complex as many previously

self-standing urban centers are absorbed into one large matropolitan agglo-

meration. A functional approach delimiting the boundaries of the core

over time would be to include a town or city in the core when it became

functionally linked to the core. If a town was outside a defined corn-

muting shed in a subsequent time period, the population of the town

would be attributed to the periphery in the former period and to the

core in the latter. The alternative is a fixed boundaries approach

for which the outer limits of the core region are defined for the latest

time period and used for preceeding time periods regardless of the changes

in functional relationships between cities over time.

22. Although the functional approach better matches the theory of

urban growth and development, the fixed boundary approach is more prac-

tical. There are few consistent time series such as commuting patterns

on functional linkages between cities. These data are typically available

for the latest time period only. Even if linkage data were available

over time, there would be a danger of creating an artificial jump in the

core population from one time period to the next as the boundaries of the

core are extended. Administrative annexation by the government of the

central city poses a similar problem. This problem is especially im-

portant to any definition of PR which relies on comparing relative growth

rates of population between twc, time periods.

13 -

23. Further problems emerge once we move away from our small primate

country example. If our primary concern is with the processes of spatial

development which lead to the acceleration and then deceleration of the

growth of large metropolitan areas, aud we have a large country with

several major cities, then there are two alternatives for measurement.

One is to follow the approach used by Barat and Geiger (1973) in Brazil

and to study each major center with its hinterland independently of the

other regions. The results will make possible a generalization as to

whether or not PR has taken place within city regions. 'hL%e other is

to regard the various dominant cities as collectively forming the core,

and then make comparisons with growth in the periphery summed across the

city regions. Both approaches are weakened if we cannot regard the com-

plete country as being encompassed within the limited number of city

regions.

24. Richardson's (1977) original usage of the term PR was expressed

in terms of the regions of a country, although the indicators were

reflecting relative c growth rates. This usage reflects past empi-

rical work on regional inequalities of regional economic development,

set up in terms of a core and a periphery (Friedmann, 1966). The causal

processes involved however are essentially urban and have to do with the

factors discussed in the previous section of the paper such as the pull

of agglomeration economi-es. One approach in a large county with a pri-

mate but not dominant city size distribution might be to dist.inguish four

areas in examining spatial concentration: (a) the primary core or the

metropolitan area of the largest city, (b) a secondary core of other

large cities above a clear size break in the urban size distribution,

- 14 -

except where a city is clearly a functional satellite of the primary

core, (c) the primary periphery or the hinterland of the primary core,

and (d) the secondary periphery, the balance of the nation.

25. A further analytical issue is whether to study thi total pop-

ulation of areas or regions or only the urban population. This is

critical in order to distinguish between a study of urbanization, or

Berry's 1978 "counterurbanization" and PR. As Falk (1978) points out,

studying the growth of total population of a highly urbanized core region

and a predominately rural periphery is very close to just studying urban

vers.us.rural population growth. It introduces the danger of losing sight

of vigorous growth of secondary cities in a periphery dominated by rural

decline. Clearly, if an unambiguous definition of "rural" is available

from the agency responsible for collecting population statistics, then

an urban definition is superior to use of total population, at least

up until the stage in economi.c development when "rural" may be regarded

as "low density urban" rather than as being distinctively different in

incomes, birth and death rates, access to modern private and public

services, as well as other characteristics.

(ii) Indices of reversal.

26. Once these preliminary definitional issues have been settled,

there remains the question of how to measure the onset of polarization

reversal. Studies of urban concentration and deconcentration have used

a number of different summary indices. Those from the major studies

are listed in Table One. There are three groups of indices shown in

this table. Indices no. 1-5 all compare the core region with all the

periphery cities as a group. These indices change as the relationship

between the aggregate urban populations of the core and the periphery

fable One: Iidlces of Relative GeograEhllc-al Concentration

No. Index Example Fornula

I Shtare of Population in Core (Primacy Ratio) Richardson (1977), P /LPHera (1978). Linn (1979) C

2 Rate of Change of Shiare of Populatioin in Core (_____ (P /P )-(P P)

3 Share of Population Growth Captured by Core Hera (1978), Linn (1979) (P ct+l-P c)/(EPt +-P t)

4 Difference in Average Annual Population Modified from Dillinger growth rate P - growth rate PCrowtli between Core and Peripihery (1978) c P

5 Difference in Absolute Population Growthbetween Core and Periphery (P -P )-(P -P )c,t+l c,t p,t+I p.t

6 Conparlson of Average Annual Population Modified from Linn (1979). growth rate P.ize I - growth rate PGrowth Rates between Core and Secondary City Falk (1978)Size Classes

7 Number of Secondary Citiea Growing Modified from Richiardson Number of cities for which growthFaster than the core (1980) rate Pl> growth rate P

8 Difference ln Average Annual Growth Ratsa Dillinger (1978) (growth rate P ) - (growth rate P +P+P +P 1between tthe Core and the Total Core plus3 Next Largest Cities .

9 4 City Primacy Ratio Owen and Witton (1973) p /p I P 3 PRenaud (1979) c c

10 10 City Primacy Ratio Linn (1979) p/ c*P2 ....* 10

11 Urban Deconcentration Indlx (UD) lenderson (1980) r 21Uheaton and Shishido (1981) UD (P /E P)]

Notation: Average annual growthl rate - t n - I

P t Urban population in core in year tc,t

P t-n- Urban population In periphery in year t+n

LP -p +Pc p

P - Urban population of ith largest city

Psize i Urban population of city size class I

Note that not all indices originally used urban population.

- 16 -

changes. Indices no. 6-10 compare the core with subsets of the cities in

the periphery. Finally, the Urban Deconcentration Index compares all

cities with one another. This index will change if one secondary city

grows relative to another, even without change in the aggregate urban

populations of the core and the periphery.

27. These indices can yield contradictory results. To illustrate

possible inconsistancies, imagine a nation in which the core region is

growing faster than cities in the periphery on average, but small peri-

pheral cities are growing faster than the core. Index 1, the share of

urban population in the core, would increase auggesting further polarization.

Indices 2-5 which measure .ae relative absolute or rates of changes in

population of the core and periphery could increase or decrease depend-

ing on the relative growth in the previous period. Declines in these

indices would suggest PR. Index 6 would show that one size class of

peripheral cities, smaller cities, was growing faster than the core

region. In addition, Index 7 would indeed show a persitent tendency

for some secondary cities to grow faster than the core. Whether these

two indices alone indicate PR is unclear. Indices 8 and 9 compare the

core with the next three largest cities and would increase for the city

region, thus showing further polarization. A similar comparison of the

ten largest cities, Index 10, may show no change. The UD Index, however,

would increase, suggesting PR. This hypothetical example demonstrates

that the answer depends upon the index used as much as the underlying spatial

trends. Which index will be most relevant to the concerns of spatial policy?

28. It becomes clearer how each index relates to PR if we introduce

a simple model of polarization. Alonso's (1980) bell shaped curve of

geographical concentration, shown in Figure One, serves as the basis of

- 17 -

this stylized model. Note that Alonso expressed concentration as a function

of economic development. We have modified this relationship by replacing

level of economic development by time with the assumption of a strong link

between development and passage of time. As shown by the solid line,

polarization, defined as the concentration of the urban population in the

metropolitan core, increases over time until reaching a peak. After

reaching this peak, polarization decreases over time. Alonso cautions

that very little is known about the right hand side of the bell. Polarization

may just reach a certain level and stabilize, or stabilize only when all

the urban population is in the core region. Future empirical research

on the spatial development of both developed and less developed countries

will contribute to understanding the patterns of population concentration

after a turning point is reached.

29. Two additional concentration functions may be added to Alonso's

original model in order to identify specific states of polarization.

The dashed line in Figure One represents the rate of change of concen-

tration and the third line pot-trays the share of population growth

captured by the core region over time. The rate of change of polarization

peaks at Point A in Figure One corresponding to the inflection point in

the absolute concentration curve. At Point B, the proportion of growth

going to the core region equals the aggregate share of population in the

core. At ..this point, change in polarization, the dashed line, is zero.

30. From this model we can now suggest a definition of PR and intro-

duce some related terms. Assuming these curves properly reflect the

underlying model of other research workers-who have considered urban

concentration, polarization reversal may be defined as Point B in Fig-

ure One, the point at which the concentration of the urban population in

the core begins to decrease. This is-measured by Index 1, the primacy

- 18 -

Figure One

A Model of Polarization

.^ Rate of chargeConcentration or Rin the concen-urban population in the tration of urba!core and the share of . iurban population growth popa ncore.in the core.maximum

LMaximum

'4' 0?-I

Equality. - --.. -

Point A Point, B Tme

r,

Key

Concentration of absolute urbanpopulation in core.

,I - Rate of change in concentration ofpopulation in core.

7 Share of population growth capLturee-by core.

- 19 -

ratio. It may also be defined by the point at which Index 3, the share

of growth captured by the core, equals the value of Index 1; or by Index 4,

the difference in growth rates between the core and periphery, becoming

equal to zero. If concentration only stabilizes after Point B, this

would not be PR but may be defined as polarization stabilization. This

can also be measured by Indices 3 and 4. Point A in Figure One may be

defined as the point of reversal in the rate of polarization. Index 2

increases before this point and decreases after this point.. We must

caution, however, that the model in Figure One is a very stylized

representation of population concentration. There may be many points

of reversal in the rate of polarization over time as the rate of con-

centration increases and decreases with economic growth and development.

There is therefore the possibility of two or more points of polarization

stabilization, reversal in the rate of polarization and even PR.

31. The remaining indices cannot be used to define the PR turning

point, but maybe very useful to determining the underlying spatial

changes related to PR. Comparison of growth rates of different city

size classes over time, for example, will identify the types of cities

bringing about PR.

B. Polarization Reversal in the State of Sao Paulo, Brazil

(i) Development of the State of Sao Paulo.

32. Use of a single state of a country as the area of analysis for

PR would not be recommended for most countries since the state boundaries

would not encompass the relevant city region. The well developed city

system and the size of the State of Sao Paulo in Southeast Brazil make it

an exception to this rule. The State has 25 million residents, about the

same population as Canada, Yugoslavia, or Colombia. The State is also phy-

- 20 -

sically large, approximately the same size as the United Kingdom or West

Germany. Sao Paulo is the largest industrial concentration in South Amer-

ica and has almost one half of the industrial employment of Brazil. The

State is also a rich agricultural region as well with coffee and sugar

cane as major crops.

33. With a population of 12.6 million in 1980, Metropolitan Sio

Paulo is the second largest LDC city in the world after Mexico City.

The Metropolitan Area covers six thousand square kilometers over an

approximate radius of fifty kilometers. The city of Siao Paulo forms

the center of the Metropolitan Area and isalso the capital of the State.

The city of Sio Paulo is fifty kilometers and 2700 feet in elevation

from the port city of Santos to the south. The fringe areas of the

Metropolitan Area are generally hilly and sparsely populated. The

1980 Demographic Census shows nine million people living in the central

city (as defined by 1950 boundaries) and 2.7 million residents living

in the immediately surrounding municipalities. An additional one million live

in outer suburbs within the Metropolitan Area. Population trends are

further detailed in Table Two.

34. Thehinterlandof the State extends six hundred kilometers to

the northwest of Metropolitan Sao Paulo. Nine urban agglomerations within

150 kilometers of the Metropolitan Area account for 3.6 million of the

State's population. Other cities and rural areas within 150 kilometers

total 2.2 million population as shown in Table Two. The area outside

this inner region encompasses most of the rural population of the State.

Cities in this region are distributed in a well developed central place

pattern and are: linked by an extensive highway network radiating from

Metropolitan Sao Paulo.

- 21 -

Table Two

Total and Urban Population for Areas of theState of Sao Paulo 1950-1980

(Population in Millions)

Areas within Total Population Urban Population (b)the State(a) 1950 1960 1970 1980 1950 1960 1970 1980

Metropolitan Sao Paulo 2.7 4.8 8.1 12.6 2.3 4.5 7.9 12.3

City of Sao Paulo 2.2 3.8 6.2 9.0 2.1 3.7 6.2 8.9

Builtup Fringe 0.3 0.7 1.4 2.7 0.2 0.6 1.4 2.5

Outer Suburbs 0.2 0.3 0.5 1.0 0.1 0.1 0.4 0.9

Hinterland 6.5 8.2 9.6 12.4 1.7 3.0 4.8 7.6

Large City Inner Region 0.9 1.4 2.2 3.6 0.6 1.1 2.0 3.4

Other Inner Region 1.1 1.3 1.6 2.2 0.3 0.4 0.7 1.2

Outer Region 4.5 5.5 5.8 6.6 0.8 1.4 2.1 3.0

State of S'ao Paulo 9.1 13.0 17.8 25.0 4.0 7.5 12.1 19.9

Notes: (a) Areas have constant boundaries corresponding to boundariesexisting in 1950. Metropolitan Sao Paulo as defined byDavidovich and Lima (1975). "Inner Region" includes allareas within 150 kilometers of the Metropolitan Area plusall of the Paraiba Valley. "Large City" refers to nineurban agglomerations.

(b) Urban population is urban population as defined by the -

Brazilian Demographic Census for Municipios with 20,000 ormore inhabitants in 1970 or cities within urban agglomerations.

Source: Fundacao IBGE. Censo Demografico 1950, 1970;Censo Preliminar. 1960,1980.

22

Table Three

Average Annual Growth Rates of Total and Urban Population forAreas of the State of Sao Paulo 1950-1980

(Growth Rates in Percent)

Areas within Total Population Urban Population (b)the State (a) 1950-60 1960-70 1970-80 1950-60 1960-70 1970-80

Metropolitan Sao Paulo 6.1 5.4 4.4 6.8 5.8 4.6

City of Sao Paulo 5.7 5.0 3.7 6.1 5.1 3.8

Builtup Fringe 9.3 7.6 6.4 10.8 8.1 6.2

Outer Suburbs 4.4 '6.1 6.7 9.2 9.7 9.6

Hinterland 2.4 1.6 2.6 5.8 4.8 4.8

Large City Inner Region 4.6 4.6 5.1 5.9 5.5 5.8

Other Inner Region 2.1 2.1 3.2 5.2 4.6 5.3

Outer Region 2.0 0.6 1.3 5.9 4.2 3.6

State of Sao Paulo 3.3 3.2 3.5 6.4 5.4 4.7

Notes: (a) Areas have constant boundaries corresponding to boundariesexisting in 1950. Metropolitan Sao Paulo as defined byDavidovich and Lima (1975). "Inner Region" includes allareas within 150 kilometers of the Metropolitan Area plusall of the Paraiba Valley. "Large City" refers to nineurban agglomerations.

(b) Urban population is urban population as defined by theBrazilian Demographic Census for Municipios with 20,000 ormore inhabitants in 1970 or cities within urban agglomerations.

Source: Fundacao IBGE. Censo Demografico 1950, 1970;Censo Preliminar, 1960, 1980.

- 23 -

35. Table Three illustrates two different patterns of population

change: suburbanization and relative deconcentration. The first

pattern becomes evident when comparing urban population growth rates

of the city of Sio Paulo, the built up fringe area, and the outer sub-

urbs of the Metropolitan Area. The rate of growth was highest in the

close-in suburbs in the nineteen fitties and highest in the outer

suburbs after 1960. The growth rate of the City of Sao Paulo decreased

consistently over this period.

36. The deconcentration trends are shown by comparing Metropolitan

Area growth with hinterland growth. Growth rates of inner region cities

have remained steady since 1950 while the growth of the core has declined

- the point where both large and smaller cities in the inner region

grew at a faster rate than the Metropolitan Area.

37. To put the growth rates in Table Three in perspective, the annual

rate of growth of total population for Brazil as a whole fell from 3.0

percent between 1950 and 1960, to 2.9 percent from 1960 and 1970, and

2.5 percent during the last decade. The State of S-o Paulo grew faster

than the nation during each of these periods. Growth of the frontier

states of Brazil - the North, Center-West, and South - was greater than

that of Sao Paulo since 1950 except for the nineteen seventies in the

case of the South region. Thus the national pattern of spatial changes

was a relative shift from the Northeast and the cther Southeastern States

towards Sao Paulo and the Brazilian frontiers. Merrick and Graham (1979),

Goodman (1975), Katzman (1977), and Fox (1975) all discuss these inter-

regional trends.

(ii) Data sources.

38. The data used for this analysis is urban population for each

municipio from the Brazil Demographic Censuses for 1950 and 1970 and

- 24 -

from the Preliminary Censuses for 1960 and 1980. A municipio roughly

corresponds to a county in the U.S. Population data are those

present in 1950 and 1960, and those resident for 1970 and 1980.

39. The Demographic Census defines urban populations for the "urban"

and "suburban'" areas of the administrative seat of each municipio and

other villages within the municipio. An urban center by this definition

may be as small as a few hLmdred people. We have redefined urban pop-

ulation to only include municipios with over 20,000 urban population

in 1970. The Census defined urban populations of municipios under

20,000 urban population are not included in our analysis except for the

three modifications that follow.

40. Municipio boundaries changed from 1950 and 1980 due to creation

of new municipios out of existing municipios. Our analysis treats these

Tmnicipios as if they were never created by attributing; their urban pcp-

ulation to the original municipios. In other words, the origin municipio

of each newly created municipio is identified and the urban population of

the new municipios is added to the municipio from which they were created,

thus keeping the municipios constant at 1950 boundaries.

41. A second modification. is grouping several linked municipios toge-

ther to form urban agglomerations where there is spatially contiguous

urban growth. The State Secretary of Planning and Economic Affairs (1980)

grouped central cities, satellite cities, and suburbs to form eight urban

agglomerations. We further modified this list to ersure that the boundaries

of these agglomerations are constant from 1950 to 1980. We also added a

nitrth agglomeration defined by Ablas and Azzoni (1978).

42. A final modification is an adjustment of urban population to correct

- 25 -

for the underclassification of urban population and overclassification

of rural population in some rapidly growing municipios in 1960, 1970,

and 1980 (see Altman, 1980). These changes reduced wide fluctuations in

the rural population of the municipios based on an assumption of straight

line decline of rural population in rapidly growing municipios.

(iii) Indices of urban concentration.

43. Analysis of the urban concentration indices shows increasing

polarizaticn in the State of Sao Paulo from 1950 through 1970 but polar-

ization reversal between 1970 and 1980. As shown in Table Four, the

share of urban population in the ?Metropolitan Area declined from 62.4

percent to 61.9 percent between 1970 and 1980. Index 2, the change in

concentration, was negative for the last period, and the percentage of

growth captured by the core fell to 61.0, almost one percentage point

below Index 1. Since the rate of population growth was greater for

hinterland cities than the core, Index 4 was negative for 1970 to 1980.

These four indices show JR taking place around 1970.

44. The ten year interval between demographic censuses in Brazil

makes it difficult to identify the precise timing of PR in the State

of Sao Paulo. It is not clear from the PR indices whether PR took place

before or after 1970. Population projections for 1980 by municipio esti-

mated by the Sao Paulo based Fundagao Sistema Estadual de Analise de

Dados (SEADE) shed more light on this issue. Based on data on the location

of births and deaths in the early nineteen seventies and 1960 to 1970

demographic changes, SEADE made forecasts for 1980 which over estimated

Metropolitan Sao Paulo population and underestimated the population of

secondary cities. When then PR indices were calculated using these

- 26 -

Table Four

Principal Indices of Polarization Reversal

No. Index 1950 1960 1970 1980

1 Percent of UrbanPopulation in Core 58.0 60.2 62.4 61.9

1950-60 1060-70 1970-80

2 Change in Percent of 2.2 2.2 -0.5Urban Population inCore

3 Percent of Urban 62.8 65.5 61.0Population GrowthCaptured by theCore

4 Difference in Average +0.97 +0.97 -0.22Annual PercentPopulation Growthbetween Core andPeriphery (Core-Periphery)

- 27 -

population estimates, increased polarization was found for 1970 to 1980.

Thus, migration trends must have changed in the middle to later nineteen

seventies to account for the difference in research findings resulting

from using the 1980 data. This is good evidence that PR took place

between 1970 and 1980.

45. The first index in Table Five demonstrates that the measure of

PR has to be based on relative growth not absolute growth. Index 5,

the difference between the absolute population growth of the core and

the periphery was not only positive between 1970 and 1980, but essentially

remained constant from the previous period.

46. The spatial trends uaderlying PR in the nineteen seventies are

further explained by Index 6 in Table Five. Average annual growth rates

of cities over 100,000 population between 1970 and 1980 were more than

one percentage point higher than the growth rates for smaller cities. It

was the growth of these large cities that brought about PR. Index 6

also demonstrates that-PR did not arise out of a sudden increase in

secondary city growth rates, since these rates are fairly constant by

city size class between 1960 and 1970; and 1970 to 1980. Rather, PR

resulted from a decline in the growth rate of Metropolitan Sao Paulo.

Whether this can be explained by reverse migration from the core to the

secondary cities or redirection of migration patterns is not clear.

Further analysis of the 1980 Demographic Census will shed more light

on the factors behind PR in the State of Sao Paulo.

47. The results for Index 7, the number of cities growing faster

than the core, are consistent with those for Index 6. Twenty five

cities experienced higher growth rates than the Metropolitan Area

between 1970 and 1980, up from fifteen in the previous period. An

- 28 -

Table Five

Descriptive Polarization Reversal Indices

NO. Index 1950-60 1960-70 1970-80

5. Difference in Absolute +877 +1603 +1602Population Growthbetween Core andPeriphery (in 000)

6. Comparison of Average (a)Annual Population Growth Rates(a

Number

MetropolitanSao Paulo 6.8 5.8 4.6

Secondary Cities

- 20000-50000 45 5.6 4.0 4.1

- 50000-100000 14 6.2 4.9 4.3-100000-250000 9 6.0 5.2 5.3-250000+ 2 5.5 5.3 5.4

7J Number of SecondaryCities GrowingFaster than theCore (n-70) 21 15 25

8. Difference in AverageAnnual Percent GrowthRates between the Coreand the Total of Coreplus 3 Next LargestCities +1.43 +0.43 -1.25

1950 1960 1970 1980

9. 4 City Primacy Ratio 0.846 0.862 0.868 0.853

10. 10 City Primacy Ratio 0.761 0.778 0.786 0.77Q

11. Urban Deconcentration 2.92 2.72 2.53 2.57Index

(a) City size classes defined by the urban population of cities in 1970.Cities do not move from one class to another over time.

29 -

average of three out of four cities in che inner region, extending

roughly 150 kilometers from Metropolitan Sao Paulo, grew faster than

the core from 1970 to 1980.

One out of five cities located beyond 150 kilometers grew faster than

Metropolitan Sao Paulo. These high outer region cities tended to

be larger cities. These patterns are consistent with a model of spatial

change in which population growth diffuses both by distance away from

the core and down the urban hierarchy within the periphery region.

48. The remaining indices in Table Five are less useful to under-

standing the components of PR. Indices 8 and 9 show that up to 1970,

the Metropolitan Aree, grew faster than the next three largest cities,

but after 1970, this pattern was reversed. A similar comparison of the

core with the nine next largest cities, Index 10, shows the same results:

increasing concentration in the core from 1950 to 1970 and a decrease

from 1970 to 1980. The Urban Deconcentration Index compares all cities

with one another with smaller values revealing greater inequality in

population between cities. This index decreased between 1950 and 1970,

but increased from -1970 and 1980. The two primacy indices returned to

pre 1960 levels by 1980 but the UD Index showed only a small change from

1970 to 1980, suggesting greater equality among the largest cities in the

State but less equality between the largest and the smallest cities.

C. Summary

49. This paper removes many ambiguities surrounding polarization

reversal. After a brief review of factors that may work to bring about

PR, the study narrows its examination of PR to urban population only

- 30 -

and defines the core and periphery regions. Starting with a list of

potential PR indiced culled from past studies of urban concentration,

we defined the principal index of PR as the proportion of urban pop-

ulation in a city region that is in the core region. This definition

and the definitions of polarization stabilization and reversal of the

rate of polarization are based on Alonso's (1980) model of urban con-

centration.

50. Using these definitions we found that PR took place in the

State of Sao Paulo between 1970 and 1980. This may be the first docu-

mented case of polarization reversal in an LDC.

51. The study is limited, however, to spatial changes in distribu-

tion of the aggregate population and does not encompass components of

this change such as migration treands. We also do not link PR in the

State of Sao Paulo to other changes associated with economic develop-

ment. Further research may identify the importance of such factors as

the large investment in the coxmnications, transportation, and elec-

tricity networks in the periphery in inducing PR in the State of Sao

Paulo. Thus, this paper is a first step toward additional research on

population concentration in the State of Sao Paulo and other city regions

of less developed countries. The approach to modelling PR presented

here will also be useful as a base for further discussion of what is

meant by polarization reversal and how it may be measured.

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