DISCUSSION PAPER

Report No.: UDD-30

URBAN DEVELOPMENT IN BRAZIL

by

John Vernr.on Hienderson

February, 1983

Water Supply and Urban Development DepartmenitOperations Policy Staff

Thie World Bank

The World Bank doe, not accept responsibility for the vi ews expressed

herein nwrfhich are those of the authors and sh6uld not be attributed to the

World Bank or to its affiliated organizations. The findings, interpretationLs,

and conclusions are the results of research supported by the Bank; they do not

necessarily represent official policy of the Bank. The designations employed,

the presentation of material, and anv maps used in this document are solely

for thte convenience of the reader and do niot imply the expression of any

opin nion whatsoever on the part of the World Bank or its affiliates concarntnr

the legal status of any coLn.try, territory, city, area, or i-ts authorities, or

coacerning the deli-mitation of its boundaries, or national affiliation.

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John Vernon Henderson was a consultant with the Development EconomicsDepartment and the Urban Development Department. He is on the EconomicsFaculty at Brown University.

Research Project No.: 67213National Spatial Policies Research Project

ABSTRACT

This paper investigates various aspects of urban concentration, particu-larly those relating to disproportionate migration of highly skilledlabor into the larger cities. The empirical work is grounded in datafrom southern Brazil, a large region which is the most industrializedand urbanized area of the country. A model of ,the size and populationcomposition of cities was estimat:ed. The findings on the productionsize concerning urban concentration suggest that the nature of externaleconomies of scale in manufacturing cannot be used to explain the lackof activity specialization in metropolitan areas like Greater Sao Paulo.This suggests that constraints in capital and utilities markets mayinduce a more diversified mix of industries to locate in large centersthan would otherwise be the case, attracting a larger work force thanexpected. In addition, larger centers, with or without distortions atplay, appear to require large quantities of skilled labor, because ofthe nature of industries located there, because of the c...fficulty ofreplacing skilled with unskilled labor, and because agglomerationeconomies require relatively heavy use of skilled labor for theirexploitation. On the consumption side, highly skilled people areattracted to large urban centers because of the nature of big cityamenities, especially superior educational facilities. Those with fewskills tend to follow the highly skilled labor force to these urbanareas, since those locations (with larger concentration of highly skilledworkers) are thought to be intrinsically more desirable.

TABLE OF CONTENTS

Introduction . . . . .. . . . .. . . . . . . . . . . . . . .. . . 1

The M4odel . . . . . . . . . ..e.... , . . . . . . ... ...... 5

Demand Side and Production Aspects . . . . . . . . . . . . .. 6

Supply Side . . . . . . . . . . .. . . . . . . . . . . . . . . 7

Empicical Specifications and Results: Demand Side . . . . . . . . 10

Data . . . .. . . . . . . . . . . . . . . . . . . . . . . . . 13

Results . . . . . .. .. . . . . . . . . . . . . . . . . . . . 16

Empirical Specifications and Results: Supply Side . . . . . . . . 22

Population Amenities . . . . . . . .. . . . . . . . . . . . . 26

Price Variables . . . . . . . . . . . . . . . . . . . . . . . . 26

Local Public Services Set by the State Government ........ 27

Locally Determined Ptublic Services . . . . . . .. . . . . . . 27

Conclusions . . . . . . . . . . . . . . . . . . . . .. . . . . ... 29

Footnotes . . . . . . . . . . . . . . . . . . . .. . . .. . . . . 30

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . it 9

Appendix A ................................... ....... ........ 34

Appendix B . . . .. . . . . . . . . . . . . . . . . . . . . . . . 36

Economic development is usually associated with population move=ents from

rural areas and small towns into large cities, as the labor force shifts from

agricultural and cottage industry employment into modern manufacturing and

service provision. There is a major strain in the development literature

which analyzes aspects of this phenomenon (e.g. Harris and Todaro (1970),

Corden and Findlay (1975), Kelly and Williamson (1980), Miyao and Shapiro

(1979)). Implicit in this literature is the notion that the movements of interest

are not to smaller or medium size cities but to large cities or metropolitan areas.

Metropolitan areas have large labor pools., extensive formal vs. informal sectors,

and enforced minimum wages in the formal sector, while in smaller cities the

formal vs. informal distinction may disappear and minimum wage laws and other

regulations may not be enforced.

There is also a recognition in the development literature that migration may

be a multi-stage process of rural to small city, then smaller city to larger city

movements (Yap, 1976, 1977), with these later stages currently dominating the

migration patterns of various countries. This recognition is consistent with the

fact that the largest metropolitan areas of many LDC's are growing at extraordinar-

rates, which are also far in excess of the rates for smaller and medium size cities.

Thus the growing urban population of many countries is becoming more and more con-

Clentrated in just a few cities. These extraordinary growth rates and heightened

degrees of urban concentration present major problems for administration and plan-

ning for new public investments in urban infrastructure. Moreover, the implied

massive population relocations involve costly social upheavals and result in a

perhaps dubious quality of life in these largest metro areas.

These costs of adjustment may be a natural and efficient part of the development

process. On the other hand, the heightened degree of urban concentration may be un-

necessary -- an inadvertent result of other government policies. For example, the

largest metro area in a country could be growing at an extraordinary rate because

the population is attracted to the public serrvices provided there which are un-

avrailable or provided at inefficiently low levels in smaller cities and rural arcis

(e.g. modern, schools in a government controlled school system). T.n that case the

heightened concentration is a result of a misallocation of public resources and

involves unnecessary upheavals and leve's of urban infrastructure investments unde--

taken in rapidly growing metro areas.2 It is apparent that LDC officials believe

in some cases that the heighcened concentrations are inefficient, as evidenced by

the development of deconcentration policies and medium size city progras in

countries such as Brazil, Egypt, Mexico, and Thailand. Some of these 3programs

focus on deconcentrating' the provision of local public services.

There is a second aspect to these migration patterns which is overlooked

but may be even more serious. Although the urban-rural models tend to focus on

movements of rural or traditional sector laborers in response to minimum wages

legislated and applied to the formal industrial sector, the movements and the

population allocation to large cities is disproportionately higher in the high

skill occupations, where the minimum wage is not effective. For example, for the

country we will focus on, Brazil, the simple correlation between city size and

educational attainment of adults in a city is about 0.70 in our sample, whereas

the corresponding number for the U.S.A. is negative (-0.33).3

Whethet this disproportionate draining of high skill labor into the larger

cities is a natural part of the development process or whether it is an inadvertent

result of other government p6licies again is a.critical question. The draining means

that smaller towns are endowed with poorly educated public officials and where

relevant uneducated voters, as well as a labor force uaattractive to high skill

industries. This could represent a costly misallocation of resources or a neces-

sary but unpleasant aspect of the dev&'.opment process.

This paper investigates these aspects of urban conceniration, in the context of

Southern Brazil (see definition later), a large region which is the more industrial-

ized and developed area of Brazil. The region has recently emerged from a period of

rapid urban concentration into the metro areas of Grande Sao Paulo and Rio de Janeiro,

and now has a developed system of cities where all parts of the size distribution are

growing approximately equally. jIowever, the marks of the recent period of rapid con-

centration still dominate. Our data applies to 1970 and in that year Grande SAo

Paulo accounted for 71% of Brazil's total value added in transportation, 40% in

steel, and 35% in chemicals (almost the entire petrochemical sector); but it accounted

for less than 20% of Brazil's urbanized population.

In the context of a demand and supply model for city sizes and for population

composition, two sets of hypotheses are explored concerning the aspects of urban con-

centration discussed above. The first set of hypotheses deals with the production

aspects of cities. In terms of urban concentration, the urban population and labor

force may be concentrated in the largest cities, because production may become more

efficient in larger cities. External economies of scale in orodt,ction are now the

accepted basis for the existence of cities. Tlhse -,ale economies derive, for

example, from scale enhancing urban labor market efficiencies and the possibilitie',

3 -

for inter and intra industry specialization in the tasks which firms do. The

presence of e:cternal economies of scale, however, does not mean efficiency in-

creases with city size per se. That depends on the precise source and specifica-

tion of scale economies.

For any industry these scale efficiencies may derive from the benefits of

increases in eithdr city size per se (urbanization economies) or own industry

employment per se (localization economies). If they are urbanization economies

and derive from city size per se, we would expect the industry to want to locate

in larger cities. Larger cities or metro areas would then contain a diverse set

of industries (e.g. service activities) all benefiting from the general scale of

urban activity. If they are localization economies and derive from own industry

size, we would expect an industry to locate in smaller cities specialized in

primarily just that industrial activity, since there are no production benefits

to locating in larger cities and paying the associated higher *wage and land costs

(Henderson, 1974). So, for example, in the U.S.A. for industries displaying locali-

zation but not urbanization economies (Henderson 1982c), we have smaller urban

areas specialized in steel, autos, textiles, food processing, machinery, pulp and

paper, etc. If, for Brazil, external economies of scale are not related to city

size for those industries heavily concentrated in the largest metro areas, they

may be there because of possible government restrictions i. the capital and utilities

markets, limiting supplies outside major metro areas. If the spatial allocation of

capital and utilities had not been restricted, development might have been quite

different. For example, U.S.A. urban areas of size comparable to Grande Sao Paulo

do not have the concentrations of heavy manufacturing found there.

Turning to the skill composition of people in the larger cities, the high

concentration of high skill people may be based on skill requirements in the

production activities of cities. It may be more efficient to use more high

relative to low skill workers in production in larger compared to smaller cities.

There could be two reasons for this.

First, urban areas of different sizes typically have different industrial com-

positions and it may be that the types of industries found in larger urban areas re-

quire more hizh relative to low skill workers. This first reason only makes sense

if two conditions are met. First, skill requirements must be an operational con-

cept.. If, for example, high and low skill workers are highly substitutable in

production, then skill composition in an industry will vary widely in response to

small changes in relative wage diffe.-ncials. In -that case, skill requirements are

not really an operational concept. 'However, if high and low skill workers are

weak substitutes or complemdnts in production so the ratio of their employments -

is unresponsive to wage differentials, then skill requirements are an operational

concept. The second condition for skill requirements in industry to explain the

skill compositi.on of population of larger versus smaller urban areas is that

relatively high skill using industries tend to natuzally locate in larger versus

smaller urb:4L: areas due to scale economy and other considerations (see later).

The second reason underlying the skill usage hypothesis for larger cities

does not concern industrial cbmposition but focuses on the nature of scale eco-

nomies. External economies of scale could affect factors neutrally or they could

be biasad towards the use of high to low skill workers. If scale economies are

relatively high skill using, then that would increase the relative demand for high

skill labor in larger cities.

The second set of hypotheses are a versicm of the "bright lights" phenomenon.

In terms of general urban concentration, controlling for wages, housing costs, and

ubiquitous public services, households may prefer to live in larger compared to

smaller urban areas. We note two possible reasons for this in a developing country

context. The first involves a natural market phenomenon in a developing country.

For certain types of privately produced goods and services, large metro areas

provide a critidal level of scale for these goods to be produced and delivered.

As urban area size falls, these goods either start to become unavailable or their

effective costs rise dramatically. Examples might be retail outlets for imported

products and certain local durables, and services such as specialized medical care,

the arts, and specialized educational services.

A second reason why people rould prefer larger urban areas is that certain

public services are unavailable in smaller cities. Our measures of primary school

and urban infrastructure services reveal no biases towards large urban areas in

southern Brazil. However, for example, it is commonly stat-ed that good high schools

and colleges are only found in larger metro areas in Brazil. To the extent that it

is socially efficient to in fact provide such services in all cities, this would

represent a misallocation of resources, inducing families to unnecessarily emigrate

from smaller cities.

turning to the skill composition of the urban concentration in term.s of

these consumptior. aspects, it may be that high skill people concentrate relatively

more in larger metro areas because they have a greater preference for these market

goods and public services which are only readily available in large metro areas

(i.e., these goods have a high wealth elasticity of demand). Again to the extent

the spatial allocation of these goods is distorted by government policies, so

will the spatial distribution of high skill people be distorted.

To analyze and test these hypotheses, we outline a simple model of city

sizes and population composition, based on a situation where we divide people

into two skill categories. The model is phrased in terms of demand and supp'ly

curves, the characterisrics of which are explored econometrically.

1. The Model

The model is suimmarized in two demand and supply curve diagrams. In Figure

(la), city size (population), N, is plotted against wages to low skill workers, WLL

The demand for population by a city comes from the production aspects of the city

and the supply curve from the consumption aspects. In Figure (lb), population

composition, or the ratio of high to low skill people, NH/NLV is plotted against

the ratio of high to low skill worker wages, W 1l . Again, the demand and supply'HL

curves come from respectively the production and consumption aspects of cities.

We now examine the production and consumption aspects of cities to discuss in terms

of our hypotheses what factors generally shift these curves and determine their

elasticities.

WL HWL

S(A L,'". D(W LlN,L l,

N N(a) (b) N

NL

Figure 1

-6-

1.1 Demand Side and Production AsDects

We do not excplicitly estimate the demand curves in Figures (la) and (lb).

However, we do estimate the parameters of production which would determine

their basic characteristics, so here we explore the link hetween the produc-

tion model we estimate and the curves in Figures (la) and (lb). The popo\la-

tion demand functions are directly connected to labor force demand f-mctions through

labor force participation coefficients or functions. Given that, the tndustrial

demand for labor comes from two compcuents. One is the non-traded good c'mponent

(housing, retail and personal services) which appears in every city and is chaurac-

terized across cities by similar functions and parameters. The other is the ;

port good component which varies across cities as industrial composition varies

with urban specialization. -It is this latter component which we examine, since

it is the only component which varies in a consistent fashion across cities and

hence it is the component which determines the shifts and rotations in the demand

functions in Figures (la) and (lb). In Henderson (1974, 1982a), a complete model

is formally solved where the parameters of the production process for the export

sector determine the height and shape of the demand curve in Figure (la).

From Henderson, the demand for total labor in the export sector of the city

and hence in the whole city shifts up as the dearee of scale economies or capital

intensity of the export good the city is specialized in increases. Greater scale

or capital intensity allows the city to pay higher wages at any level of employment

(with sufficient scale the demand curve may even be upward sloping); and the effi-

cient city size where the marginal benefits of increasing city size (rising incomes)

just equal the marginal costs (rising costs-of-living) is raised. Thus, in Figure

(la), as industrial composiftion across cities changes to higher scale economy in-

dustries, the demand for N shifts up in N, WL space, controlling for w /WL~H L

Given industrial composition determines the height of the demand curve, what deter-

mines industrial composition?

The determination of industrial composition is beyond the scope of the

paper, but we outline a model of the process. There is a set of urban sites

in a region upon which cities can' form. Each site has a natural endowment

from the set of site characteristics -- access to various natural resoturce

deposits, access to coastal ports, climate, terra;.n, altitude, etc. Industries

compete for sites resulting in an equilibrium allocation where, for example,

steel type cities go to sites with acces- to limestone, coal or charcoal, and

-7-

iron ore, large service and international market oriented metro areas go to

coastal ports, and sites with low endowments of all characteristics remain

unoccupied until regional population anid the total number of cities becomes

very large. Thus, for any city in Figure (la), while the height of the demand

curve is determined by industrial composition, industrial composition will in

part be determined by the natural amenities or site attributes of the city's

location.

The hei8ht of the demand curve in the composition diagram and its slope

depend on skill requirements in production of the good a city is specialized in.

If high and low skill labor are poor substitutes or complements, demand for

skill composition (N IN ) will be unresponsive (inelastic) with respect toH L

relative price changes, WHE/W1L, controlling for wage levels W . Second, as

skill needs vary across industries, the demand curve will shift in NH/NL N W/WL

space as industrial composition varies. Finally, the curve may also shift with

city size changes, if urbanization economies are Hick's biased, or high relative

to low skill using (or vice-versa).

In the econometr.c section of the paper, we estimate these scale , Hicks'

bias, and substitutability/complementarity parameters for manufacturing industries

in Brazil, generally choosing industries which cities in Brazil do tend to spe-

cialize in.

1.2 Supply Side.

For the supply side we directly specify the equations for the curves in Figures

(la) and (lb). The equations are formally derived from consumer theory, in

Henderson (1982d). A basic assumption underlying the precise speciLication is

that similar skill people migrate across cities in our region in response to

utility diff-erences they can earn in different cities, so that in general utility

levels of similar skill people are equalized across cities in regional labor

markets. The bases for this assumption are as follows. The region of Brazil we

look at is well integrated in terms of communications and transportation; almost

any rural or village eidgrarLt faces a variety of cities he could move to within a

two-hour bus ride. All different sizes of towns seem to be growing on average a:

the same rates in all parts of our region, irregardless of subregional populatic-.

Finally, the assumption is in part tested and it is consistent with recent

empirical evidence. We note, however, that the assumption is not critical,

in that the qualitative interpretation of the econometric results is the same,

if utility levels are not equalized across cities and regional supply (migra-

tion) shifters are incorporated Lnto the model. 5

By examining low skill workers, we can specify the supply curve in Figure

(la) to be

(1) N = NL (L' NH/NL, D, tL; UL)

In Figure (la), holding the utility level of low skill workers at the going rate

in regional labor markets, UL, the supply curve is upward-sloping, or

ON/3WL > 0 in eq. (1). This states that holding utility constant, wages, WLL

must rise with city size to compensate low skill residents for increased housing

costs and disamenities associated with increases in urban area size. In the

absence of cost-of-living data we assume from the Alonso-Muth-Mills rent gradient

model that the cost of housing rises with city population, N. -

The other arguments in eq. (1) are supply shifters in Figuare (la). For

example, the ratio of high-to-low skill adults in a city, N INL is characterized

in our work as a consumer amenity for low skill people for reasons discussed in the

next paragraph. As an amenity, other things being equal, an increase in N IN inH L

a city raises potential utility of low skill people. However, given the going

utility level in regional markets UL, controlling for other arguments in eq. (1),

the potential rise in utility from the increase in N. NI causes people to migrate'H L

to the city. This rise in city size, N, raises costs-of-living and continues

until the benefit of the increased N IN is offset in terms of utility b'y increasedH L

costs-of-living. Thus, controlliag for utility and other variables, an increase in

an amenity in a city causes city size to rise, or acts as a supply shifter in

Figure (la). A decrease in an amenity causes the curve to shift back.

The ratio of high-to--low skill adults, NH/NL, is characterized Q5 an amenity

for low skill people for three reasons. An increase in this ratio m-.ay lead to

better local public decision making and administrative implementation (given a

-9-

population which in 1970 was about 40% effectively illiterate). It may also

lead to more fruitful interactions with state and federal government agencies

which confer favors on urban areas. Finally, the ratio may be a strong deter-

minant of amenities such as crime rates and better quality quasi-public services

puch as health care, wh-±,ch we do not have measures of.

Other supply shi.ters in eq. (1) are a vector of city amenities and public

services, AL, and D, distance of the city to the nearest coastal port. Fur

the latter, as D increases, the cost to a city of importing goods may rise,

raising costs-of-living for residents and causing the surply curve to shift

back in Figure (la). For AL, in the estimation to Tollow, the signs of the

coefficients of the components of AL in the city size equation Twill tell us

which components are amenities (positive sign) or disamenities (negative sign).

Then an increase in, say, disamenities in a city will cause its supply curve in

Figure (la) t-o shift back.

To analyze population composition and the supply curve in Figure (lb), we

look at both high and low skill adults. The supply curvte of the'ratio of high

to low skill people, NHINL, is specified to be

(2) H/ L =N (;H/WL, N, A1, AL, D: UH/U L)

U and U are the going utility levels of- respectively high and low skill workersH L

in regional X -1ity markets. Controlling for the ratio of these utility levels, the

supply curve NH/NL is upward sloping in WH/WL space, or 9(NH/NIN/3(W/WL) > 0.

Intuitively, as W /W rises and thus the (relative) wages of low skill workersH L

decline, NH INmust rise to compensate low skill people through increased amenities

(NH/NL) for their (relative) loss in utility caused by the (relative) low skill

wage declines. There is an implicit assumption here that increases in N IN

benefit low skill people more (defined by % increase in utility) than high skill

people. This assumption is consistent with stability o. equilibrium in the model

(Henderson 1982d). An intuitive notion is that w;hile increases in N./JT raiset. L

thepuli qalt;of life in a cil,, (e. g., crl e ra.-es) --:or low sk-i11 oeople, c;=-

- 10 -*

greater income of high skill people ensures high levels of many of these quality

of life items through personal consumption patterns alone (walled estates,

servants, private transportation, etc.).

In terms of supply shifters the arguments are-similar. An increase in

amenities to high skill people, A., raises N IN so that U/UL is maintained.

That is, to maintain U '/UL as , rises, which thus potentially raises the

relative utility level of high skill people, NH/NL rises to maintain UH/UL

(given N I/N is more of an amenity for low skill people). Thus; as A. rises,O H -L

the supply curve in N IN W /W space in Figure (lb) shifts out; and as A rises,H L'P H L

it shifts back.

For items which are amenities common to both groups of people such as city

size, N, the sign of the variable in eq. (2) determines which group benefits

most (measured by % increase in utility) from increases in the particular amenity.

Thus-, a(NH/NL)/IN > 0 implies N is either more of an amenity or less of a dis-

amenity for high relative to low skill people. Then increases in N would shift

the supply curve out in Figure (lb).

2. Empirical Specifications and Results

2.1 Demand Side.

For the demand side, we estimate production parameters for seven important

urban export industries, to determine scale effects and biases and substitutability/

complementarity among capital, high skill, and low skill labor. For the industries,

we picked 2- and 3-digit industries representing textiles,-primary metals, food

processing,-transport equipment, chemicals, machinery, and non-metallic minerals.

To estimate the relevant parameters, we employ a conventional trans-log specifi-

cation of the cost function. The specification we employ is quite general, but

we do impose some restrictions consistent with basic results from other work

(Henderson 1982b) based upon simpler specifications. First, we assume the firm

production is constAnt'returns to scale, but the industT`7 function with external

economies of scale is not. This allows us to estimate the unit cost function

(i.e., average cost function) rather than the total cost function. Second, rwe

assume external economies of scale are either localization economies measured 'by

own industry employmnent in an urban area or urbanization economies measured

here by urban population (a total employment measure yields identical results).

Based upon extensive experimentation we specify that it is the urbanization com-

ponent of scale effects which may be biased, and that the localization effects

are Hicks' neutral (leave the ratios of marginal products of factors unchanged).

Thus, the translog approximation (see, for example, Fuss and. McFadden (1978)

and Denny and Fuss (1974)) of the cest function is

(3) iog c = A + B /L + B log N + Z a log p.

2 1 z y.. log p. log p. + £ y log p. log N

c is average unit cost of production (value added), the Pi are factor prices of

capital and high skill and low skill workers, N is urban area population, and L

is own industry employment in the urban area. Variables are normalized so that

their values are centered near 1 to be consistent with the notion t:hat the

translog function is a second order Taylor Series expansion about the point where

vTariables equal 1 or their logs equal zero. The declining elasticity formula-

tion for own industry scale effects (1/L) is chosen on the basis of the extensive

work in Henderson (1982b) on the nature and extent of scale effects. The elasticity

is (3c/3L)(L/c) = -B1/L. Symmetry is imposed on eq. (3) so that yi. = and

the function must be linear homogeneous in..prices. Thus, if prices double, unit

costs double. This implies the following restrictions imposed during estimation:

(4) i ci 1, J y.. i YiN °

Applying Shephard's Lemma (which states that the derivative of the unit cost

function, c, with respect to an input price equals the demand for that factor) and

partially differentiating (3) we obtain factor share equations

(5) Si = a. + E y. lo-g p + iN log N.

Si = oL./TC where L. is tha quantitv of the - actor and TC are total- cos.sLi

of production as measured by total factor payments. Given the defnition Of S.

o S. = 1. Then, in estimation the number or independent share equations is the

- 12 -

number of factors minus one, because if we know all factor shares but one, we

can calculate the last by subtracting the others from one.

The economic parameters of interest to us are as follows. First, there are

the elasticities of substitution in production among capital, high skill, and

low skill workers. For any pair of inputs the partial elasticity of substitu-

tion is

(6) ai. = 1 + y. /(Si S.) i # j

where Yi; is measured in eqs. (3) and (5) and S. and S. are factor shares.

(ai =1 + y. /S2 - l/S.). We evaluate a.. at "representative" (average) values

for S. and S.. If a.. < 0, factors are complements not substitutes. To

understand the meaning of a.. we note that in economic terms

(7) a/S = n. /1j

where Ti. is the % change in the ith input when the price of-the jth input

rises, holding output and other input prices fixed. Thus, a.i < 0 implies com-2j

plementarity in the sense that if the price of an input rises its use and the use

of its complements falls, whereas the use of its substitutes rises.

Second, factor requirements of LL and L_ follow from the data. We looka

at the requirements for the industries in the same representative situation, each

evaluated at an urban population of 230,000, a capital opportunity cost of .25,

and compensation for high and low skill workers of 10 and 5 thousand pesetas

respectively (note these variables are normalized during estimation). From the

share equations

(8) L = PH a'L"LL ln (PL)+rLH ln (pH)+YLK ln (PK)+YLN ln(N)

i 7 PL lHH (pH)y LH ln (pL)+7HK ln (PK)+YH ln(N)

where p 1, and po are the prices of low and high skill wor"kers and capital.

Finally, we are concerned with non-neutraliyt of urbanization ecZn=Zias. These

are reflected in the values of y and y 'We calculateLN LN

- 13 -

(9) d l = (LL/LH) Y LNS - y SFL/,N d loagN L N

TiLH\l is the % increase in LL/L1 for a 1% increase (decrease) in city

size and is defined holding input prices fixed and evaluated Jor a repre-

sentative situation. Eq. (.9) will indicate whether urbanization economies

are high or low skill labor using,

[Given that stochastic components added to eqs. (3) and (5) will be con-

temporaneously related, we estimate eq. (3) and the t-wo factor share equations

for hign anid low skill workers jointly by Zellner's approach for estimating seem-

ingly unrelated regressions to achieve maximum likelihood estimates. This ignores

any problems of RHS variables being endogenous. Because the observations usually

pertain to three- or even four-digit industries within a city, it seems reasonable

to assume that industry disturbances at this level of disaggregation do not usually

affect city sizes and prices.]

To obtain estimates of the parameters necessary tc answer our questions we

only need to estimate eq. (5). Estimating eq. (3) also allows us to estimate

all the scale effects. The system of equations was estimated without and with

eq. (3). In all but one case, the parameters of eq. (5) were negligibly affected

by including ea. (3), so the full system is presented to also have estimates of6

all scale effects. For that one case the critical difference in estimates

is noted.

Data.

The basic data is from the 1970 Industrial Census of Brazil and variable

definitions are given in Table 1. The definition of high and low skill is based

on educational attainment. The two class division is between those with more than

primary school education (six or more years in Brazil) and those with primary school

or less. This is usually about a 1/4, 3/4 division of the adult population in the

South. Other divisions could have been obtained. But some early casual experi-

mentation indicated that our division was a reasonable one on the demand side and

was the only one possible on the supply side (once the data was ordered from the

Brazilian Census Bureau).

The data for hiah vs. low sk4ill wo-rkers are from the 1970 DemograDhic Census.

.;e obtained tabulations for full-time workNers for our urban areas giving the nu-wier

of workers in each education category by "two-digit" industry and giving the

- 14 -

average annual incomes by education and two-digit category. We used the figures

on relative numbers in each education category to divide total employees in the

Industrial Census for the corresponding industry into two education groups. We

used the figures on relative incomes (and numbers) of the two education grouips

to divide up total compensation and obtain an annual compensation for high and

low skill workers. For three-digit industries in the industrial Census we use

numbers on incomes and skill division from the relevant two-digit industries of

the Demographic Census. In doing so, we assume relative annual incomes equal

relative annual compensations for the two classes of workers and that the

numbers for two-digit industry divisions among high and low skill workers apply

to three-digit industries. We do not consider this latter problem to be serious:

in most cases in our urban areas one three-digit sub-industry accounts for almost

all two-diait employment.

Of the seven industries, two are two-digit industries (,non-electrical machinery

and food processing). The rest are three-digit industries except for traditional

chemicals and spinning and weaving. Traditional chemicals is a collection of three-

digit chemical industries primarily excluding petrochemicals. Sninning and weaving

is the four-digit natural fiber components of the three-digit spinning and weaving

category and omits the four-digit articifial fiber components. Detailed industries

(as opposed to just two-digit industries) are studied because they relate to a

more narrowl,y and well-defined product and technology. Also the Brazilians did

not censure for disclosure reasons at the three- and four-digit level (only at

the two-digit)!

For each industry, the sample is the urban areas in southern Brazil which had

employment in that industry and the unit of observation is the industry data for

an urban area. Tne data tapes cover 126 urban areas in South and South-Eastern

Brazil including the states of Minais Gerais, Espirito Santo, Rio de Janeiro, SGo

Paulo, Santa Catar•.na, and Rio Grande do Sul. This region exceeds the size of

France, both Germanys, and Spain combined. All urban areas over 20,000 in the

region in 1970 are covered with a few exceptions (inadvertently missed and later

discovered). The urban areas cover a regular size distribution and include s :;

major mnetroDol'tan areas and many major large cit es. Urb-n area definitions are

similar to Ur-anized Area definitions in the Unized States. First, reogracnh-a:-,

larger urban areas are comDosed of a number or "counties" (-.unici?ios) and small

urban areas one count7. The Demographic Census data relates to the urbanized 2c:u-

lation of these councies or groups of counties; about 10% of the population in the

counties of the sample is rural.

- 15 -

Table 1

PRODUCTION TECHNOLOGY

Sppi,aninq

Weaving,:Iron Norn-Elect. Auto Natural Food -

Ceramics Stew, Me4chinery Accessories Chemicals Fibers Processin'

a .38 .16 -. 12 . 4 7E.0 3 ]a -. 25 -1.54 -. 52LH

a 1.06 1.25 .48 .55 .48 1.02 .93.LK

aHK .59 .74 .64 1.25 .89 1.73 .83

YLN -.028 -. 029 -. 024 -. 036 -. 040 -. 023 -- -. 007

yHN .019 .013 .023 .031 .015 .004 .011

L/H,POP -. 16 -. 22 -.15 -.22 -. 24 -. 08 -. 09

L /L 5.25 3.37 2.45 1.93 1.92 5.28 3 76

E L(1000) -.04 -. 07 0 -.03 -. 02 -. 06 -.01

aLL -. 92 -1.36 -. 27 -1.70O -. 83 -. 46 -1.12

aHH -. 69 -1.67 -. 59 -2.37 -1.56 -.72 -1.43

a, -1.o84 -1 .63 -1.18 -1.43 -. 65 -1.00 -.91KK 1.84 -

a. This is the one industry where for this one parameter onlyestimating equations ( 3) and ( 5) jointly vs. equations ( 5 ) aloneyielded different results. The estimate in square brackets comesfrom estimating equations ( 3 ) alone.

- 16 -

.r.esul s .

The results for the estimated system of equations are presented in Appendi:C A.

Variable definitions are in Table 2. In the text we focus on the key re-sults in

Table 1 relating to our hypotheses presented earlier. Note in almost all cases

the economic parameters in Table 1 are based on statistically significant coeffi-

cients in Appendix A, Table A1.

City Size Demand Curve.

We hypothesized that the demand for population curve in Figure (la) shifts as

the degree of scale economies in production of the city's export good varies with

changes in specialization and industrial composition. We also hypothesized that if

scale economies are ones of local..zation for an industry (dependent on own emplov-

ment, not city size per se), the industry would tend to locate in a smaller- city

whose export sector was devoted primarily to producing just that good. If

economies were ones of urbanization .or an industry, then that industry might

gravitate towards majar metro areas.

These particular hypotheses are the subject of a detailed investigation in

Henderson (1982b). Our results tend to support the very strong conclusions of

that paper. However, given the degree of multicollinearity in eq. (3) amongst

the scale terms, the results here are weaker. Henderson (1982b) focuses just on

the nature of scale effects and ths technical specification is derived to minimize

multicollinearity. The specification in this paper is oriented to calculating sub-

stitutability/compleriientarity parameters. The results in this paper are as follows.

Scale economies (and also caDital intensities) varv across industries sug-

gesting the demand curve in Figure (la) varies across industries. With two

exceptions in Table Al in Appendix A, the coefficients of log N, 62' are insig-

nif-cant and of varied sign (the two which are significant at a low level are of

opposite sign). Apart from scale bias considerations, this would suggest that

urbanization effects in production are not important. In contrast, localization

economies are all positive and only one coefficient is negligible. eL in

Table 1 is the %O decline in unit costs for a firm with a 1%' increase in own

industry labor force, holding firm inputs fixed. .he numbers for - , as evaluat.ed

at 1000 em?loyees, are fairly large.

These results suggest, that just as in the U.S.A., we would not expect to

find most of these industries heavily concentrated in large metro areas. the

- 17-

Table 2

DATA DEFINI"TONS: COST FUNCTICNSVarLable Def ini tionc Total costs 'lavided by output. Output is value added defIned thesame was as Ln the U.S. Census. Total costs are total labor costs (wagesand salaries plus firm contributions to Social Security and private per.sior.,health and other plans) plus capital costs. Capital costs areK Yt pK. *K Is the capital stock and Is the response to the Census

qvtestion 'What are your equipment and structures worth today?" with theverbal explanation to the effect. 'That is, what could you get for them'oday if you sold them?" The Census claims they are getting what may be theecoanomists' dream number. a is defined below.L Average monthly employees in the industry (hours of work are not collected).N Urban area population.

PL Wage of low skill workers. This is calculated as average industrycompensat'Ion (see definition of c) mult-L.z'Isd by the ratio of averagereported annual income of wor-kers ln the industry with less than six yearsof schooling to average annual iAcome of all workers in the Industry. Theseannual income numbers are from t.e Demographic Census and are for full-timewo-rkers by rdo-digit industry.

pH Wage of high skill workers. Defined in corresponding fashion to PLP Opportunilty cost of capital calculated to be (0.23 + pt). 0.23.epresents Interest plus depreciation based for Brazil on a real rate

of return of 0.08 and a rate of exponential decay of 0.15. Obviouslythese numbers are arguable but can be defended based on numbers -n theliterature (U.S. numbers for decay, Braz iIan numbers for real rate ofreturr.). pt is the industry-urban area specLfic property tax rate and Iscalculated from industry property tax payments divided by K.TrypLcally pt = 0.02 but varLes qulte widely across space. Theresults are not sensitive to the choIce of Interest and deorecia-tion rates.

a. It Is the dream number if capLtal Is perfectly malleable si.nce adepreciated quantity of capital has the same value as the samequantity of new capLtal, and hence equals the cost of producing thesame quanti ty of capital. Value is also approximately proportio'nalto quantIty irregardless of age of the quantlty If non-malleablecapltal'is "InfIntitely" lived but decays expotentially. In th't case Ifyear n after the creation of K unitLs of capital, the quantItYLs Ke -n where 6 Is t'e rate of depreclatlcn and the valueIs w4O x fore un x ($+r) for a constant m.ar.inal product ofcapital ('p.P) over tL nme and r the rate of dlI:coun-. In a orehoss-shay model, however, for a given K,, age critcally affectsthe value of capital.

- 18 -

fact thait they are exceptiornally strong concentrations for several of them in

Grande Sao Paulo suggests that they have been induced there by restrictions in

the ca-,,ital and utilities markets in the hinterlands. This suggestion is explored

in detail in Henderson (1982b).

ComDos4ition Detrand Curve.

At the beginning of the paper we formulated hypotheses about why there was a

strong pos'tive correlation between educational attainment and city size. On the

demand side in Figure (lb), we hypothesized that the demand curve (NH/NL) may

generally shift out as city size increases. There were two reasons for this which

we explore econometrically.

Skill Recuirements.

Skill requirements for high-to-low skill labor mav increase with city size be-

cause higher skill industries may be more likely to locate in larger cities. In

order for this to be a useful notion, skill requirements must be-an operational

concept, so that high and low skill lab.or are not highly substitutable in

production. The strong evidence of the first panel in Table 1 states that

high and low skill labor are complements in production or else very weak

substitutes. This result was unexpected; but it is strong and persistent

under all reasonable specifications we could think of. (For example, if-

one does not like the cost of capital measure and would prefer to either assume

the cost of caDital varies stochastically across space or is a function of dist-

ance from major metropolitan areas and of urban area size, the complementarity

result and also the results concerning iL/g pop hold just as strongly. I

would also note that there are no peculiarities about the data; for example,

the simple correlation coefficient between compensation of high and low skill

workers in all manufacturing across urban areas is .58 which is quite reason-

able in this k.ind of estimation).

In summary,z, the results indicate that s'kill classes of labor are not sub-

stitutable and thus, skill requirements are an r:>erataiaonal crcept. This also

means chat the demand curves in Figure (lb) will be inelascic or the use of

high-to-low skill labor will not vary that much w,ich W. /w var-'at-ons. '.e alsoH dL

note the LL/L,, requirements as evaluated for a common set of variables varv

across industries by several fold, as indicated by the third panel of figures

in Table 1.

- 19 -

Returning to the original hypothesis, do increases in skill requirements by

industry type generally go along with increases in the size of city by industry

type, so that shifts out in the demand curve in Figure (lb) correspond to shifts

up in city size? To answer this question we would need an exhaustive list of

industries including service industries. We would have to rank them by require-

ments and compare that ranking with the size of the type of city these industries

tend to locate in. We cannot do this, but a casual comparison indicates a matching.

For a casual comparison, we took the 126 urban areas and classified them by

type: specialized cities where, say, more than 10% of the urban labor force was

in just one (usually three-digit) industry, agricultural service centers, metro-

politan areas, and government centers. About 1/2 of the 126 urban areas were

specialized in production of one manufactcred good and these were broken either

in.o 13 types (different manufactured goods) or 8-9 grosser classifications. Popu-

lation size for the 126 urban areas was regressed on dummy variables classifving

cities by type and "exogenous" variables such as distance to the coast and public

service levels per person. The dummy variables gave us a ranking.of sizes of di-

ferent types of cities.

In Table 3, we give the resulting ranking of the city types represented in

Table 1. Chemicals are not in the ranking because any large concentrations of

chemical employment are found in large diversified metro areas (typically the

government owned petrochemical industr-y). Tne cas;ual picture painted in Table 3

suggests that industry requirements for high relative to low skill labor may in-

deed rise, as the size of urban area type rises. That is, skill requirements

mesh with the supply side of the model. I would also note- that when city types

are ranked by population composition, the ranking by size in Table 3 is the

same as the ranking bv composition (N/NL).

- 20 -

TABLE 3

SIZE RANKINGS OF TYPES OF CITIES

Size Ranking LL/ , from Table 1

(Starting with Largest) (for CorresDonding Industry)

Transport type 1.93

Machinery type 2.45

Food type equal rank 3.76

Steel type 3.37

Spinning and Weaving type 5.28

Ceramics type 5.25

Scale Biases.

The notion that the demand curve in Figure (lb) generally shifts up with

city size is also supported by the second panel of results in Table 2. In most

cases there is strong evidence that external economies of scale are relatively

biased against low skill workers -- i.e., they are high skill using. The elas-

ticities of the ratio of low to high skill use with respect to urbanization effects

were all non-positive, controlling for wages. They are to my mind verv large

effects, stating that a 10% increase in city population causes a firm to decrease

its ratio of low to high skill workers by, say, 1% for the same factor prices and

firm level of output. Note, however, that althouYgh city size affects the use of

high relative to low skill workers, that does not mean it affects overall effi-

ciency. In general the. gains in efficiency for high slkill people cancel out

wizh the losses for low skill people.

- 21

The bias result suggests that even without slkill requirement considerations,

production in larger urban areas irn a developing country is biased towards

using high skill labor. 'Whatever are the source of scale effects such as

larger general urban labor markets and a greater opportunity for specialization

of industries and firms in their tasks within an urban area, they make high

skill workers more efficient relative to low skill workers. Perhaps this is not

surprising, considering that specialization in tasks and communications in labor

markets may go hand-in-hand with treater skills of workers.

Other Results on Cost Functions.

From Table 1, labor and capital are reasonably substitutable in production,

with both types of labor displaying similar degrees of substitutability with

capital. Own price effects are all negative as required for regularity and are

all of reasonable magnitude. Capital appears to be somewqhat more price responsive

than the other factors; this is also evidence that the cross-sectional approach of

estimating the long-run cost function (where capital inputs are price responsive)

is reasonable. Finally, we note that scale effects appear to be 'neutral with res-

pect to capital usag.

2.2 SuDnlv Side.

On the supply side in the empirical work, we estimate what factors will tend

to shift the supply curve out in Figure (la) -- i.e., what amenities do low skill

-eople value? Second, we estimate what factors will shift the composition NH/NL)

supply curve out in Figure (lb) -- i.e., what amenities do high relative to low

skill people value? In exploring the reason why high sk-ill people relatively tend

to concentrate in large cities, we will ask if the supply curve in Figure (lb)

shi'ts out with city size per se. It will turn out that there appear to be fas-

cinating interactions among population groups on the consumption side in Brazil.

To explore these questions, we estimate these supply functions directly.

The city size and composition equations (1) and (2) in empirical form with

stochastic components eN and £ included areN c

- 22 -

(la) L (L' NH/NL.' 7 AL, e )

(2a) =/NL N(N, WH/WL, AH, AL, D e C)

These are specified in double log form. We assume the disturbance terms are

identified and independently distributed about ze.o. (There was no evidence of

heteroscedasticity.) However, the disturbance terms across equations are con-

temporaneous related. Secondly, the RHS of both equations contain variables

which from Figures 1 and 2 are clearly endogenous, such as wages and city size

and composition. To de.al with these two aspects, equations (la) and (2a) are

estimated by Three Stuge Least Squares (3SLS).

The resul.ts must ba viewed as being tentative, hecause the set of amenity

and public service variables is quite limiter- relative toy say, U.S.A. data. This

means certain important variables mavybe missing in the equations. Second, for

the same reason, the list of instruments (see' Table 4) is limited and there might

be arguments about the exogeneity of some variables. In selecting instruments,

variables determined within the city are treated as endogenous, whereas as those

determined outside the city are treated as exogenous (e.g., school characteristics

set by the state).

For our data, variable definitions are given in Table 5 and the variables are

discussed as resul, are presented. All v:riables are from the 1970 Census, ex-

cept for road distance which is from 1970 maps. The sample has the same charac-

teristics as for the demand side. In the results presented, population composition

is measured in terms of relative numbers of high and low skill adults. The alter-

native noted iii Table 5 is to measure composition by relative numbers of hilgh aL:d

low skil.A 'juseholds as categorized by educational attainment of the household

head. Some of our variables in Table 3 relate to people and some to households.

We present the results for the adult composition measure here, primarily because

t,iey were more robust in moving to 3SLS. In general, the results are similar and

any major differences are notedl.

Results in. Table 4 are discussed by blocks of variables rather than equation

by eauation. We present OLS results along wi ;h 3SLS results. A'll this facilitates

the comDarison of what ameni:i'e2s and pu'- c services are valued by each skil'l grcu-.

Ln addi:ion to the corss-section results in ;he text, there are results based on

1960-70 comparisons in Appe4-dix B, Table B2. Those results are brieflv reviewed -n

-23-

TABLE 4CITY POPHlLATICN SIZE AND COMPOSITION

(All variahles except 0 and % N Waterare In ndtural logs.) L

SLze (N) CompositLon (N H/NL

OLS 3SLS 1 OLS 3SLS2

N IN, 2.202 2.732H (7.85) (6.86)

N .160 .195(9.19) (4.09)

L 1.366 1.588(3.08) (1.70)

W -.034 .435H L (.39) (.95)

-3 -3 -3 -3Port DLst -. 480x10 -. 534x1O .182 x10 .182x10(0) (1.17) (1.15) (2.05) (1.70)

Transf/ .103 .176Person (1.27) (1.15)

Teach. .769 .828Educ. (2.28) (2.03)

Pupil/ -.443 -.334Teach. (5.49) (4.18)

% N Water .135 -. 027L (.78) (.04)

% N Sewer -. 616 -1. 111(1.38) (.82)

Constant 6.733 6.380 -3.674 -4.854

N 126 126 126 126

Adj. R2

.42 .53

(absolute value,i of t-s.tAUstLcs Arc Ln parenLhe:ses)

1. InsLrus'snLs are 0, pupl-Learcher ratLo, .--tcher educ., meso rec7ton urbdnpopula2.on (excludtlnq our urbtn area), meso reaion toLa, norotlIac'on, uradnared t.x aiL- on LnriistriaL nronerty, federal qoven rent ^-.plcowent inurban 3reA, St.-Le dummies. .labor foro- aarnc'aLa,, r a1U1. orid 3vCrkcetennperature,. Meso reqlons ire dn .lLea such thht da StdLe. SUC.1 -is -lIUnoLSwould he dL:dt-i Ln'o 6-8 neso revions.

- 24 -

Table 5

VARIABLE DEFINITION: SUPPLY SIDE

Variable

N Urban population of urban area.

N /N- Ratio of high to low skill adults. Skill level isdetermined by whether the adult has six or more years ofschooling or has five or less years of schooling. The samebasic results (except for the wage variable in OLS work oneq. (4a) where the coef'icient becomes .. 132 (t = 1.18))occur if the variable,is defined by dividing householdsaccording to educational attainment of the household head.The data indicate that if anything women are favored byhigher primary school completion rates.

D Distance in kms. to nearest major coastal metro area.Coastal metro areas include Sao Paulo which is actually.about 100 kms. inland.

Transfer/Person Value-added tax revenues in manufacturing paid by the urbanarea divided by the urban population. 20% of these revenuesare automatically returned to local governments. Theserevenues are the primary source of intergovernmentaltransfers. W'e calculated the tax revenues from the 1970Census of Manufacturers.

W4 Average annual income of people in ith education group,based on incomes of individuals working full time inmanufacturing in an urban area.

Teacher Z-duc. Average education of all full-time school (not college)teachers in the urban area.

Pupil-Teacher Ratio Total people ages- 5-18 regularly attending a school in theurban area divided by total full-time school teachers.(Participation rates of people 5-18 in school varywidely.) For one state, we had the school system'spresumably more precise measure of oupil-teacher ratios.For that restricted sample of 46 urban areas, the OLSresults for eauation (4a) were similar to our results.

%N- Water The number of low skill households serviced by awater connection divided by total low skillhouseholds (as defined by education of the house-hold head). Water connection means water off apublic system piped into the house.

%NL Sewer See % NL water. A sewer connection means a connection toany type of sewage disposal system including a sectic tarn:or plpes running into a roadside public sewaae ditch on' ypartially covrered.

- 25 -

that Appendix and referred to on occasion in the text. A table of simple cor-

relation coefficients for the varia'hles in Table 4 is presented in Appendix B

also.

Due to space limitations, we focus on the first block of variables which

represent our mrAjor findings and limit the discussion of the remaining variables.

Population Amenities.

The population amenity in the city size supply equation in N, WL space forL

low s'kill people is population composition. The effect of this amenity is very

large and robust. It would suggest in a developing countrv context where low skill

people are at best barely literate that low skil people highly value the re-

source, public sector skills, and perhaps influence a. the state and federal govern-

ment level which higher skill people may bring to a city.

The population amenity in the composition supply equiation is city size and

the estimates indicate it is a strong robust effect. Urban area size clearly

appears to affect skill groups differentially, being much less of.a disamenity

[more of an amenity] to higa skill people. Both these amenity results are sup-

ported by the overtime comparison in Table B2..7

These two results suggest the following interaction between population com-

position and city size. High skill people are attracted to large urban areas ror

consumDtion Durposes to that under appropriate demand (industrial efficiency and

composition) conditions the ratio of high-to-low skill DeoDle rises with citv si-e.

Low skill DeoDle, while not valuing the Dositive amenity asoects of city- size

(relative to the negative cost-of-living and disamenity aspects), do value being

near high skill oeoDle, so thev flow to larger urban areas in large absolute

numbers (although not in large numbers relative to high skill people), to in 'act

help make large urban areas large.

Price Variables.

In both equations,'with one exception, the wage variables have the correct

sign. For the city size equatton, moving from OLS to 3SLS has what r,ight be t-he

anticicated imnact or zaising the elasticity, (assuming a negative correlat or.

between price and the supDly :unction error term, given a dcs-,ard sloning ce.

curve in Figure (la)). Controlling for amenities, our estimates suggest that o.r a

1% increase in wages, city size must rise by 1.6% before cost-of-living increases

- 26 -

and any direct disamenit-y effect of city size offset the wage benefits. The

1.6% elasticity is roughly consistenit with the (weak) coefficient of inter-

governmental transfers per person.8 This also implies that, controlling for

public services, transfers are used to lower local property tax rates to benefit

residents and do not just somehow "disappear".

Turning to the composition equation, again moving from OLS to 3SLS has the

effect of raising the elasticity of composition with respect to relative wages.

(The negative coefficient in the OLS results becomes positive if composition is

measured by households not people (see Table 4)). Allowing WH and WL to have

different coefficients (for example, by adding W to the ecuation) produced noL

gains or changes. As for equation (2a), the elasticity seems small.

The final "price" variable is distance to the nearest major port. It is

negative but statistically weak in the size equation, indicatilng the costs of

goods do rise with distance from the nearest major port. In the composition

equation it is positive, suggesting that the market basket of goods of high skill

people is less adversely affected than for low skill people in terms of the costs

of importing goods to a city from the coast.

Local Public Services Set bv the State Government.

We now 4urn to public service provision. We distinguish between public ser-

vices set by the state versus those set by the local government. Increases in

state set public services in a community represent a straight gain for tlhe com-

munity given they are finianced out of national or state revenues; and hence, they

should have positive coefficients in the size equation. The situation for locally

determined public services is different.

Our list of characteristics of state set public services included variables

related to the health, education, and transport system. The state also controls

police and fire protection. For the city size equation none of our variables

performed in any robust fashion with anticipated signs'. It simply appears that the

measures we had were not important characteristics of ser-vices to low skill people

and we do not present any results concerning them.

jiowever, for high skill people, from the comnosition equation it aDvears ;'a,

characterist-cs of the educational svstem are very important. This result is

robust and also is very strong in the overtime equat-ons in Appendix B. In USA

work, one would not find such gross measures as pupil-teacher ratios and average

- 27 -

education of the teachers to have impacts. However, in Brazil, the education

system by reputation is very bad in terrms of resources devoted to education in

various cities in various states; and it appears that high skill people are

strongly affected irn their migration decisions by this phenomenon. Finally,

we note that the rate of participation in the education system is not included

;.n the equations. Wole view that as an endogenous variable determined by the

characteristics of the school system and of the population of an urban area.

Locallv Determined Public Services.

Local governments in Brazil are quasi-democratic, with a locally elected

city council but appointed mayor. The local government has responsibility for

urban infrastructure and associat:ed zoning and land use planning -- roads, sewers,

water, public buildings, parks, EttC. Increases in these services while increas-

ing consumption benefits also raise local (property) taxes. Thus, in evaluating

the impact of increases in these services on consumer welfare and it-y size, we

must account for taxes. In general, if a local public good is optimally provided,

the marginal consumer benefits from increasing its level just equal the marginal

costs (increases in taxes), so that the net benefits from increasing its level are

zero. If marginal benefits exceed marginal costs then the net benefits from in-

creasing its level are positive, and vice versa when costs exceed benefiEs;

In the city size equation, given we have no information on local taxes,

inserting measures of local pvLblic services thus provide a test of whether services

are optimally provided. If services are not consistently overprovided or under-

provided, then in the estimat.ion to follow the coefficients for locally provided

public services will be zero. This could imply that localities have fiscal autonomy

over these services and that tehey satisfy the preferences of the representative low

skill person. If coefficie7nts are positive or negative, however, then this would

imply services are respectively consistently under or overprovided. In doing such

an analysis, wSe must control for differential local subsidies for these services

from the national or state governments, to avoid a problem of higher local public

service levels repreasenting cities able to get greater subsidy rates. The variable

on intergovernment transfer controls for the basic block of trans'fers.

lurning to the results, for the city size equation locally determined public

ser-vice variables are the ;0% orf low sk-ill households serviced bv water and sewer

connections. The results in Table 4 and also in Aopendix B for the overt-.me

- 28 -

equatiotis suggest weakly that sewer connectiors has a negative sign and hence

may be overprovided relative to what voters want. This might reflect coercion

on the part of state governments who were concerned with the "lack" of urban

infrastructure. Tne evidence on water connections suggest services are not

donsistently over or underprovided.

In summary for Section 2.2, the strenath of the work on the supply side lies

in the methodology and in the discovery of the strong population amenity effects

in a less developed country. I would note that in the course of our work, "better"

looking versions of (2a) and (4a) were obtained by either restricting the sample

(to cities under 1/2 million), or fiddling with the instrument list to bring in

more "endogenous" variables, or including variables I felt on reflection did not

belong. 9

3. CONCLUSIONS

We have estimated a model of the size and population compositLon of cities, so

as in part to explain urban concentration and the strong positive. correlation between

city size and educational attainment of the adult population.

Our findings on the production side concerning urban concentration are that

the nature of external economies of scale in manufacturing is such that we would

not expect to find these heavy manufacturing industries concentrated in large metro

areas. The fact that they are there suggests there are constraints in the capital

and utilities markets inducing firms to locate in the largest metro areas. Second

skill requirements in production are an important and viable consideration and

skill requirements appear to rise as city size type rises. Moreover, urbanization

economies in production appear to be high skill relative to low skill, using.

On the crnsumption side, high skill people are attracted to large urban areas

because of big city amenities. Low skill people are attracted to large urban

areas on the consumption side, not so much because of big city amenities, but

rather because of the presence of large relative numbers of high skill people.

In terms of local public services, a good educational system seemed to be important

Lor high but not low skill people.

in exDlaining the c,rrelation betw.een city size and populat-oa com-position,

the demand and suoly si-ds of che model in Figure (lb) seemed to neat v mesh to-

eth.er. 1 30Both demand and suaolvt curves displayed a .endencr co shif: ouc in

N/ WI/TW space as c- tsH H L paea iysize increases.

- 29 -

Footnotes

1. For example, for 1970-75 in Nigeria, Thailand, Bangladesh, and Zaire, the

average annual growth rates of the largest metro area were respectively

7.3, 5.3, 11.6, and 8.4%. For Brazil, Egypt, and Mexico, the rates were

5.0, 3.8, and 4.8%. See Dillinger (1979).

2. The efficient level of urban infrastructure investment per household rises

with city size.

3. In Brazil, the simple correlation coefficient between urbarn area size and

either average education or the ratio of high to low educational people is

between .65 and .70 (see Appendix B, Table B2) depending on the exact

variables, definitions and sample used. For the U.S.A., the corresponding

number tends to be negative. The U.S.A.. number corresponding to the +0.69

for Brazil in Table Bl is -.33.

4. This evidence suggests that real wages for equal skill people (nominal wages

deflated by costs-of-living) are approximately equalized across big and small

cities and urban and rural areas, suggesting people migrate to quickly eli-

minate real wage differentials (Williamson (1977), Thomas (1978), Henderson

(1980)).

5. Supply shifters can be incorporated into equation (2) in which case the

parameters of (2) then -reflect parameters of utility and cost-of-living

functions as well as the supply function. The directional impact of variables

remains unchanged.

6. The arguments for including equation (3) are that it incorporates more informa-

tion with which to estimate the parameters of (5) and allows us to estimate

more parameters. The arguments against incorporating (3) are that (3) is

subject to a high degree of multicollinearity and L in (3) may be viewed

as a RHS endogenous variable.

7. Note the population charai:teristics may be primary determinants of unobserved

endogenous amenities such as crime rates and pollution which are important in

U.S.A. work (Rosen, 1978). Note climate does not vary much in the region.

8. Raising the transfer measure bv one unit per person in fact only leads to an

increase in actual transfers of 0.2 units (see Table 5 definition). Thus,

the transffr coefzicient should be about 0.2 of the wage coefficient w.hnc-2.

rou-hl is (especially in. Col. 2 where all local public service variables ar:

endogenous).

- 30 -

9. Specifically omitted were measures of telephone and electrical connections

because thev are private goods in Brazil, measures of transDort service

such as existence of an airport because in the context I did not think it

was -lither a general consumer amenity or a good measure of air service, and

health measures such as infant dortality because the measure was for geogra-

phic areas also covering very large rural populations.

10. This neat meshing of demand side scale economy biases with the supply side

amenity wishes of the population could raise the suspicion that there may

be simultaneity biases in the cost function estimation. That is, LL/Ii falls

with population in part because of composition availability. To account .or

possible endogeneity of pT, XPX and N we tried 3SLS estimation for a few

industries in Table 1. The results are not worth repeating because we could

not predict values of RHS variables at the second stage with the instru-

ments available to us. However, amongst all the coefficients, it was the

bias coefficients which tended to survive in magnitude and significance.

- 31 -

References

1. Berglas, E. (1976), "Distribution-of Tastes and Skills and Provision of

Local Public Goods," Journal of Public Economics, 6, 409-423.

2. Borts, G. and J. Stain (1964), Economic Growth in a Free Market, New

York^: Columbia University Press.

3. Chipman, J.S. (1970), "External Diseconomies of Scale and Competitive

Equilibrium," Quarterly Journal of Economics, 84, 347-85.

4. Corden, W.M. and R. Findlay (1975), "Urban Unemployment, Intersectoral

Capital Mobility and Development Policy," Economica, 42, 59-78.

5. Denny, M. and M. Fuss (1974), "The Use of Approximation Analysis to Test

for Separability and the Existence of Consistent Aggregates,"

American Economic Review, 64, 404-417.

6. Dillin-er, W. (1979), "A National Urban Pattern Data File for 114 Couintries,"

IBRD, Urban and Regional Report #79-5.

7. Fuss, M. and D. McFadden (1978), Production Economics: A Dual Approach to

Theor-y and Applications, 2 volumes, Amsterdam, North-Holland Publishing

Company.

8. Harris, J.R. and M.P. Todaro (1970), "Migration, Unemployment, and Develop-

ment: A Two Sector Analysis," American Economic Review, 60, 126-142.

9. Henderson, J.V. (1980), "A Framework for International Comparisons of

Systems of Cities," World Bank, tUrban and Regional Report No. 80-3.

10. (1982a), "The Impact of Government Policies on Urban Con-

centration," Journal of Urban Economics, in press.

11. (1982b), "Urban Scale Economies in Brazil," Brown University,

Working Paper No. 82-13.

12. (1982c), "Efficiency of Resource Usage and City Size," Brown

University, Working Paper No.

13. Kelly, A.C. and J.G. Williamson (1980), L'odeAlng Urbanizat:.jon and Economic

Growth, Laxenburg, Austria: IIASA.

14. McKenzie, L.I. (1960), "Mtatrices with Dominant 'Diagonals and Economic Theory,"

Proceedin2s of a Sr-..osiui on Mathe2matical Methods in the Social Sciences,

Stan`ord University Press, Palo Al-o.

- 32 -

15. Miyao, T. and P. Shapiro (1.979), "Dynamics of Rural-Urban Mi.gration in a

Developing Country," Environment and Planninz A, 11, 1157-1163.

16. Rosen, S. (1978), "Wage Based Indexes of Urban Quality of Life," in

Current Issues in Urban Economics, P. Mieszkowski and M. Straszheim

(eds.), Baltimore: Johns Hopkins.

17. Thomas, V. (1978), "The Measurement of Spatial Differences in Poverty:

The Case of Peril," World Bank Staff Working Paper I#273.

18. Tiebout, C. (1956), "A Pure Theory of Local Public Expenditures,"

Journal of Political Economy, 64, 416-424.

19. Williamson, J.G. (1977), "Unbalanced Growth, Inequality, and Regional

Development: Some Lessons from American History" (mimeo).

20. Yap, L. (1976), "Rural-Urban Migration and Urban Underemployment in Brazil,"

Journal of DeveloDment Economics, 3, 227-243.

21. (1977), "The Attraction of Cities: A Review of the Migration Literature,"

Journal of DeveloDment Economics, 4, 239-264.

- 33 -

Appendi:;. A

Table Al

The Parameters of the Cost Function

Spin.

Iron & Non-Elect Auto Weave: Food

Cerai'ics Steel Machinery Accessories Chemicals Nat. Fib. Processing

A0 -. 297 -. 342 -. 373 X -. 851 -1.055 -. 2'53 -. 900

(2.10) (6.44) (6.48) (7.44) (12.69) (1.99'9) (12.43)

B1 42. 633 65. 994 3. 25 25. 900 21. 29 57. 448 10. 327(3.87) (3.00) (.35) (1.65) (1.39) (3.24) (1.08)

B, -. 075 -. 027 -. 061 .074 -. 120 -. 02S -. 018

(2.31) (.40) (1.65) (1.42) (2.52) (.70) (.46)

aL .531 .383 .599 .356 *4 1 .518 .422

(3.99) (5.22) (15.10) (3.97) (8.36) (5.19) (7.50)

a . 144 * 179 * 230 . 186 . 198 -. 021 . 124

(2.56) (4.95) (7.99) (2.81) (4.51) (.39) (4.67)

If .047 . 031 .194 . 011 .132 .165 - .096(.72) (.67) (6.48) (.15) (8.97) (3.20) (3.47)

-LH . 057 - 070 - 123 -. 051 - 094 -4 072 -. 167 5(2.04) (2.51) (5.81) (1.07) 1.55 (2.41) (6.63) (6.32)

r, H .070 .092 .151 .026 .087 .- 1 16 .900

(3.02) (3.57) (6.34) (.49) (2.22) (5.00) (8.84)

YLN -. 028 -. 029 - 024 -. 036 -. 040 -. 23 -. 007

(2.37) (2.16) (1.95) (2.04) (3.01) (1.89°) (o83)

yHN 019 .013 023 * 031 * 015 .004 .011(2.94) (1-.82) (2.21) (2.21) (1.05) (.48) (2.14)

N 27 36 58 22 30 51 109

SL .468 . 390 . 436 . 359 . 223 . 411 . 337

SH . 1 98 . 213 . 251 . 268 . 259 . 160 .1 6O

SK .334 .397 .313 .373 .518 .439 .497.K

yLK .010 . 039 -. 071 -. 060 - 060 002 -. 011

YHK -. 027 -. 022 -. 028 .025 -. 015 .051 -. 014

'f.< .009 . 016 .001 .005 .025 .019 -. 004

yKK .017 -. 017 .099 .035 .075 .053 .025

t-statistics are in parentheses.

(Table B3 conti nued on next Page.

-34

S. are factor shares. The final panel of coefficients are calculated

from the restrictions in equations ( 4). For these coefficients, the

standard error of estimate is .'var. - var.. + z cov. where13 1J

var.. and var.. are the variances of the other coefficients used to

calculate the residual coefficient and cov., is the covariance of the

other coefficients. In practice approximating the standard error of

estimate by ivarj. + var produces an estimate off by less than

15%. Thus for example, the standard error for yLK for ceramics is

2 2approximately V(.04 7/.7 2) + (.057/2.04) .071. The true number is

.062.

- 35 -

Append4x B

Table Bl

Simple Correlation -Matrix for City. Population

and CompositLon Variables (in lags)

N/N L Transf/ %NL NL wH/w Pupl/ TeacherHouse water sewer Teach Educ.

N .69 .36 -.11 -.02 .06 -.19 .33 .05 .14

NH/NL .29 -.08 -.16 .01 -.16 .29 -.27 .28

wL -.21 .14 .17 .10 -.07 .25 .07

D -.32 -.15 -.19 .06 -.06 .03

Transf/House .11 .27 -.01 .33 -.03

% N Water .S6 -.09 -.21 .31

% N Sewer -.16 .01 .00L

wH/wL -.02 -. 07

Pupil/Teach -.29

Using the 1970 and 1960 Demographic Ce.nsus for the sample of most 1960 urbanareas we looked at the determinants of the % change in city size and populationcomposition as a function of % change in independent variables. The results arein Table A2. In the city size equation the second panel of variables were meant tocapture productivity effects. We could not get income information for 1960. Thecoefficients in Table A2 are comparable in macnitude with those in Table 1 and thesigns arid strength of critical variables are consistent. However, for thecomposition equation the comparability of magnitudes is only possible because of thecontrol an growth of urban infrastructure represented by the sewer variable.without this variable the education coefficients soar to not believable magnitudes(for teacher education and pupil-teacher ratio respectively 12.976 tt = 4.63) and-2.444 (t = 2.77)).

- 36 -

Table B2City Poculation and Composition 1960-70 Comparisons

AN/N / L)/ L / L

a A N/*a .263NH/L (2.01)

% AN .282

(2.62)

A labor force 1;252participat4on (1.27)

% A % of pop. -8.000

adult (4.67)

% A % of employ. .040

in manufacturLng (.23)

Distance to port .571x10 -.460x10(1.50) (1.39)

% AN sewers -.062 .090L (1.77) (10.94)

% AN water .038L (.23)

% A Pupil-teacher -.720

ratio (2.74)

% A Teacher 1.550

education (1.74)

N 94 94

Ad. R2 .24 .70

a. This variable in the size ecuation -s defined by households not people(see Table 5). This occurred because this work was done early in theproject and the % AN water variable was not included. It was

Lnot possible to redo the work, at least at a reasonable cost. Theresults vor the size equation with % AN, water omitted are the sameessentially, for both definitions of populatlon composition.