dimou urban hierarchies and city growth in the balkans

7/30/2019 Dimou Urban Hierarchies and City Growth in the Balkans

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http://usj.sagepub.com/content/46/13/2891The online version of this article can be found at:

DOI: 10.1177/0042098009344993

2009 46: 2891 originally published online 4 September 2009Urban StudMichel Dimou and Alexandra Schaffar

Urban Hierarchies and City Growth in the Balkans

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contradicted Zipfs law (Moriconi-Ebrard,1993; Gurin-Pace, 1995; Glaeser et al., 1995;Krugman, 1996; Eaton and Eckstein, 1997;Fujita et al., 1999; Dobkins and Ioannides,2000; Cuberes, 2004; Anderson and Ge, 2005;Soo, 2005; Ye, 2006). However, when focusingon the shifts in urban hierarchies over time,a more dynamic approach is required, withregard to both the nature and causes of citygrowth (Black and Henderson, 2003; Gabaixand Ioannides, 2004; Bosker et al., 2006).

Urban Hierarchies and City Growth inthe BalkansMichel Dimou and Alexandra Schaffar

[Paper first received, February 2008; in final form, September 2008]

Abstract

This paper uses empirical evidence from the Balkan peninsula during the 19812001period, in order to study the dynamic patterns of a conflict-affected city-sizedistribution. By examining the time variations of the Pareto exponent on the onehand and by exploring cities relative growth patterns and intradistribution mobilityon the other, the paper shows that city growth dynamics follow a hybrid pattern,where city size filters the effects of external shocks. City-size dynamics thus seem morecomplex than that predicted by random growth or endogenous growth theories. Inthe Balkan peninsula, during the 19812001 period, medium-sized city demographicshave resisted external shocks due to conflicts, redrawing of national frontiers andinstitutional upheaval better than large conglomerations. However, this does not lead

to convergence towards a steady city size.

1. Introduction

Over the past two decades, many studies haveattempted to test the empirical validity ofZipf s law in different regions and countries.By using various methods for estimatingthe Pareto exponent (Gabaix and Ioannides,2004; Gabaix and Ibragimov, 2006; Dimouand Schaffar, 2007), these studies have al-lowed the comparison of different urbanlandscapes and have either confirmed or

0042-0980 Print/1360-063X Online 2009 Urban Studies Journal Limited

DOI: 10.1177/0042098009344993

Michel Dimou is in the University of Runion, CERESUR 29, Rue Czanne, Saint Pierre, La Runion,97432, France. E-mail: [email protected].

Alexandra Schaffar is in the IREMIA, University of Runion and LEAD, University of Toulon, 29 RueCzanne, Ravine des Cabris, La Runion, 97432, France. E-mail: [email protected].

46(13) 28912906, December 2009

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2892 MICHEL DIMOU AND ALEXANDRA SCHAFFAR

By using empirical evidence based on Balkan

peninsula data for the period 19812001, this

paper studies the dynamic patterns of urban

hierarchies within a particularly unstable dem-

ographic, institutional and political region,mainly due to the collapse of communist

regimes and the splitting-up of the former

Yugoslavia. Over this period, the peoples of the

Balkans saw their national frontiers redrawn,

as a result of conflicts generated by ethno-

centric impulses, leading to vast migrations

both within the region and out of it.1 Among

these migrations were the movements of

300 000 people from Bulgaria to Turkey inthe 1980s, 200 000 people between Serbia and

Croatia during the SerbCroat war of 1991,

1 300 000 between the various republics in the

former Yugoslavia during the Bosnian war

(199295), 180 000 between Serbia and

Macedonia in 1995 and over 400 000 between

Albania and Greece in the 1990s (Economou

and Petrakos, 1999; Petrakos and Totev, 2001;

Venderburie, 2005; Domenach et al., 2005).

In addition to these internal movements, there

was an exodus from the Balkan region, with

over 2 million people leaving over the past

20 years, mainly for western Europe (Hovy,

2005). In the long-term, these migrations have

resulted in contrasting demographic trends

in the Balkan peninsula with, initially, an in-

crease of its population, from 50.610 million

in 1981 to 53.687 million in 1991, followed by

a decrease to 49.676 million in 2001 (WorldBank, 2006).2

Taking these changes into account leads one

to a certain number of questions, when study-

ing the evolution of the Balkan peninsulas

urban hierarchies. Firstly, how did the Balkan

city-size distribution vary over the period

studied? Did it follow Zipfs law or not?

Secondly, is the growth of Balkan cities a

random or a deterministic process, sensitiveto city-size effects? In the former case, heavy

political upheaval should lead to permanent

changes in city-size distribution, while in the

latter case, these events may have temporary

effects on the distribution but size remains

the fundamental explanatory factor for city

growth.

The main hypothesis of this paper is thatcity size does matter when it comes to city

growth dynamics, but not in such a critical

way as predicted by some recent theories. The

consequences of temporary random shocks

on Balkan urban growth, due to political,

social and institutional unrest, are different

according to the size of the cities. Medium-

sized cities have resisted these shocks better

than some large conglomerations, which havesuffered from demographic volatility.

The paper is organised as follows. Sections 2

and 3 investigate the theoretical aspects by

presenting first random growth and then

endogenous urban growth theories which

link city dynamics to size. Section 4 treats the

methodology and data specification for

the Balkan region. Section 5 gives informa-

tion on the time variations of the Pareto

exponent for the Balkan city-size distribution.

Section 6 investigates urban growth and

focuses on the shifts in the Balkans urban

hierarchies, using tests for non-stationarity

in city size and Markov transition matrices.

The last section concludes.

2. Random Growth Theories

Random growth theories consider that citygrowth is a stochastic process which, in the

steady state, produces, for large cities, a rank

size distribution that obeys Zipf s law. These

theories follow Gabaixs (1999) basic model,

developed under the very restrictive hypoth-

eses of a growing population, free labour

mobilityalthough only for young people

and constant returns to scale technologies.

The growth of cities appears to be a ran-dom walk process, linked to randomly dis-

tributed exogenous shocks, which generate

urban amenities in a multiplicative way.

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URBAN HIERARCHIES IN THE BALKANS 2893

These amenity shocks are either policy shocks(related to the level of taxes, to pollution, tothe quality of public and municipal servicesand infrastructure such as roads and schools,

or to environment protection measures) ornatural and historical shocks (due to naturalcatastrophes, wars, diseases or poor harvestsin less developed economies), but Gabaixalso considers the possibility of industry-specific productivity shocks in bigger cities.All these amenity shocks subsequently modifya citys household utility function.

If ait is the level of amenities for city i, a

household whose consumption level is c, hasa utility function u(c) of the form

u(c) = aitc

If the levels of amenities ait are independentand identically distributed and if the wagein cityi is wit, then, in equilibrium, all utilityadjusted wages will be the same for all cities

aitwit= ut

Then, considering the probabilityof deathand that only young people migrate, once intheir life, the growth it of cityis

it t it f u a=

1( / )

with S it the normalised size of cityi in period t

S St

iti

ti

+ +=1 1

As the distributions of amenity levels ait areindependent of the initial size Sit, the citygrowth variables it+1 are also independentacross city sizes, with a distributionf() . Thismeans that each cityi has the same expecteddemographic growth rate it+1 1.

The average normalised size is constant

( )iN tiS= =1 1 , which requires that

E() = 1i.e. 0

1

=f d( )

IfGt(S) is the tail distribution of city sizes attime t, the equation of motion for G, in thesteady state, is

G S G S f d( ) ( )=

0

Gabaix (1999) argues that a distributionsuch as G S S( ) /= satisfies this equation,provided Zipfs law holds. This means that,beyond a certain size threshold, city growthdynamics obey Gibrats law and producea Pareto ranksize distribution of cities.

Cordoba (2006 and 2008) extends Gabaixsapproach, by arguing that when Zipfs lawholds, not only the growth rates of cities butalso their variance are independent of size(Gabaix and Ioannides, 2004; Cordoba, 2008).3

In order to test the random growth hypoth-esis, Ioannides and Overman (2003) pro-duced a non-parametric estimation of urbangrowth, by using a sample of large metropol-itan areas in the US from 1900 to 1990. They

found that the growth process of US citiesobeys Gibrats law and hence scale effects playno determining role in city growth dynamics.Following Ioannides and Overmans work,Rossi-Hansberg and Wright (2007) also intro-duced a model able to predict random urbangrowth. Under some particularly restrictiveconditions, such as the elimination of physicaland human capital, they considered thatcity-size growth depends upon randomlydistributed productivity shocks, specific to alocalised industrial sector or group of firms.In their model, the expected urban growthrate and variance still remain independent ofthe size of cities, which confirms Gibrats law.However, Rossi-Hansberg and Wright (2007)admit that this does not necessarily result inZipfs law, because of the short-term effectsof the exogenous productivity shocks which

may, on the contrary, lead to deviations froma Pareto distribution.

At the opposite end of the spectrum, anumber of empirical studies have sought to



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test Gibrats law on time-series data for citiesof different sizes. Working on theoreticalissues previously raised by Bessey (2002),Garmestani et al. (2005) found evidence for

significant clustering and discontinuity incity-size distribution on a regional scale inthe US between 1890 and 1990, which contra-dicts the hypothesis of Zipf s law. By plottingthe normalised city sizes versus their long-term growth rates, Garmestani et al. (2007)revealed departures from Gibrats law, withsmaller towns growing significantly fasterthan larger ones.

When dealing with conflict-affected distri-butions, Davis and Weinstein (2002) supposedthat each city undergoes, in a permanentbut random process, isolated shocks whichresult in a relocation of labour. This producesa temporal instability in the slope of the dis-tribution of city sizes. Davis and Weinsteinstudied the case of a country which experiencedthe most powerful shocks to city-size evolutionduring the 20th centurynamely, Japan

which suffered the Allied bombing of itscities during World War II. They found thatthese bombings had significant but tem-porary effects and that, after about 15 years,the Japanese cities returned to their initial,pre-war positions in the national ranksizedistribution. This seriously contradicts therandom growth model predictions.

Bosker et al. (2006) initially reached asomewhat different conclusion, because theyfound that the memory effects of the Alliedbombings on the demographic dynamics ofGerman cities were much longer than claimedby Davis and Weinstein. They showed thatthe smaller cities, which were relatively un-affected by the bombings, have significantlyand permanently moved to a higher positionwithin the ranksize distribution of Germancities since the war. Sharma (2003) reached

an almost identical conclusion when studyingthe effects of the shock of the 1947 partitionof India and Pakistan, with respect not onlyto the cities sizes but also to the cities relative

growth during the 20th century. However,unit root tests on the growth of each citys sizefrom 1925 to 1990, led both Bosker et al. andSharma to reject Gibrats law in 75 per cent

and 87 per cent of the cases for, respectively,the German and Indian samples.

3. Endogenous Urban GrowthTheories

The endogenous urban growth theories areprincipally based on Hendersons models(Black and Henderson, 1999 and 2003;

Henderson, 2004; Henderson and Wang,2007). Quite unlike the theories mentionedearlier, those of endogenous urban growthassume that cities differing sizes dependon firms location choices, when comparingthe advantages and drawbacks of each city.Firms concentrate geographically in orderto take advantage of conglomeration effects,linked either to specialisation (MAR exter-nalities) or to diversification (Jacob external-

ities), but suffer, on the other hand, fromdiseconomies due to congestion and the costsof commuting.

Following this theoretical framework, Eatonand Eckstein (1997) and Black and Henderson(1999, 2003) developed models in which thesize of a city depends on parameters such asscale externalities and human capital con-centration. Using Barro and Sala-i-Martinsmodel, Eaton and Eckstein have studiedthe dynamics of French (18761990) andJapanese (192585) city-size distribution dur-ing the 20th century. Although they workedon small samples (which included the 40largest metropolitan areas), they developedMarkov transition matrices, showing that thek largest cities in each country maintainedtheir ranking over the entire reference period,which means that city growth is parallel,

rather than convergent or divergent.Black and Henderson (1999) developed a

Lucas model, in which urban size is a func-tion of the conglomeration effects due to



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the presence of human capital externalitiesand localised information spillovers. Theyassumed a closed urban system, with twotypes of cities, no appearance of new cities

and free movement of households for whomthe migratory choices depend on the stockof human capital in each city. Black andHenderson considered that urban growth isexclusively linked to the growth in humancapital in each city.

If is the weighted elasticity of the sizeof a city as a function of its human capital(between the cities of types 1 and 2), then

= ( ) + ( ) 1 1 2 21 2 1 2

where, is the ratio of human capital perworker between cities 1 and 2; 1 and 2 arethe levels of the scale economies in each typeof city, linked to the total volume of localisedinformation exchange; and 1 and 2 are theelasticity rates of the sizes of cities 1 and 2 totheir respective stocks of human capital.

Black and Henderson (1999) consideredthat there are two possible steady states.In the first one (= 1), the ratio of humancapital per worker between a city of type 1and one of type 2 remains constant overtime. In the steady state, the adjustment tospecific isolated shocks within a sector oreven a group of individual firms is almostspontaneous and the cities experience parallel

growth given by

n

n

n

n

h

h

A

1

1

2

2

1 12 2= = =

where, n1 and n2 are the growth rates of citiesof types 1 and 2;is the anticipated rate offuture household growth; is the elasticityof substitution between products;and h/h isthe constant growth rate of the human capital.

Black and Henderson extended this ap-proach to allow new cities to enter the system.The entry rate of new cities of types 1 and 2

also depends on the growth rate of the humancapital, given by

m

m

m

m gh

h1

1

2

2

12= =

where,m1 andm2 are the numbers of new cities;and g is the countrys demographic growthrate.

One can easily show that urban growth isequal to the national demographic growthminus the rate at which new cities appear

n

ng

m

m=

In the steady state, cities differ by their ratioof human capital per worker and by theirsize, while featuring the same growth ratein human capital and therefore in theirpopulations. The number of cities increasesonly ifg> h/h.

In the second case (< 1), Black andHenderson considered that the human cap-ital converges towards a stationary level and,as a result, the cities also converge to an op-timal size. In the steady state, urban growthis fuelled solely by new cities entering thesystem.

By using this model, Black and Henderson(1999) test the nature of urban growth, while

including the heterogeneity of cities throughdifferentiated stocks of human capital. Inan initial work on the evolution of the dis-tribution of US cities between 1900 and 1990,the two authors found that the average sizeof the cities increased under the impetus oftechnological changes and human capitalaccumulation, but also that the smaller citiesgrew faster than the large ones, hence leadingto a convergence of urban dynamics towards

an optimal city size. However, by relaxingsome hypotheses, in particular the strong re-lationship between urban growth and the role



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of education, to which the growth in human

capital was almost exclusively linked, Black

and Henderson (2003) found, in a more re-

cent work, that US cities exhibited parallel

growth patterns over the same period.Some authors have tested the existence of

parallel urban growth by using sample data

from other countries. Sharma (2003), Bosker

et al. (2006), Delgado and Godinho (2007)

and Dimou et al. (2008) all reject the hy-

pothesis of parallel growth for cities, in the

urban systems of India, Germany, Portugal

and China respectively.

4. Methodology and Data Issues

This paper tests urban growth patterns in

one of Europes most agitated regions, which

features a complex urban landscape, char-

acterised by continuous political reconstruc-

tion and vast migratory movements. We

therefore consider the Balkan peninsula to

be a single global urban system rather than

the sum of different national or regional

urban sub-systems. When it comes to data

collection, however, some problems occur,

since the definition of a city varies through

space and time.

Cheshire (1999) considers three criteria for

sampling: the number of cities, the size of cities

and a conglomeration threshold above which

the sample represents a fixed proportion of

the countrys population. The first criterionpresents some problems because, in small

countries, a city of rankn might be simply a

village, whereas in a bigger country, it could

be a substantial conglomeration. The third

criterion is also worrisome because it is

strongly biased by the degree of urbanisation

in each country. Lastly, the second criterion

has the disadvantage of introducing samples

of differing sizes for countries. Nevertheless,this seems realistic because large countries

generally have a greater number of cities than

small ones.

In our sample, we retained all cities with

over 20 000 inhabitants, which is one of the

lowest city-size thresholds used in ranksize

studies. City data series go from 1981 to 2001,

which broadly represents the period before,during and after the crisis in the former

Yugoslavia and the collapse of the commu-

nist regimes, hence allowing one to measure

their effects on the Balkan urban hierarchies.

Data were principally provided by the World

Gazetteerdatabase and completed, for some

missing years, by data from the national

statistical offices.4 This means that for Bosnia,

Croatia and the Yugoslavian Republic ofMacedonia, Serbia and Slovenia, the data

are regional from 1981 to 1991 and national

afterwards. For Greece, a grouping of com-

munes into urban units was carried out in

1993. A set of suburban communes in the

two biggest metropolitan areas, Athens and

Thessalonica, was included in this group-

ing during the census of 2001. To make the

data homogeneous and comparable, we

have therefore also pooled the data from

1981 to 1991 to agree with the presentation

used in this country after 1993. Finally, the

European part of Turkey was not included

in this study, as Istanbul mainly attracts in-

ternal migration from the eastern part of the

country and features different demograph-

ic and sociological characteristics which

would have skewed the ranksize distribu-

tion of cities throughout the whole Balkanpeninsula.

As a result, the nine regions/countries

selected are relatively homogeneous from

a demographic point of view (the biggest,

Romania, has 21 million inhabitants, while

the smallest, Slovenia has barely 2 million).

(See Figure 1.) One can easily see in Table 1

how contrasting demographic changes,

during the 19812001 period, have influencedour sample. Among the 316 cities of over

20 000 inhabitants in our 2001 sample, 16 are

in Albania, 21 in Bosnia, 42 in Bulgaria, 23 in



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Table 1. Evolution of cities in the Balkan peninsula

Smallest size

city Si

Number of

cities in 1981

Variation

1981/91

Number of

cities in 1991

Variation

1991/2001

Number of

cities in 2001

Si > 100 000 49 0.183 58 0.017 59

Si > 50 000 116 0.232 143 0.021 146

Si > 20 000 269 0.131 302 0.051 316

Source: World Gazetteer database.

Figure 1. The Balkans in 2001

Source: Eurocartes, 2006.

Croatia, 20 in Macedonia, 38 in Greece, 82 inRomania, 16 in Slovenia and 58 in Serbia.

From a methodological point of view, wehave performed two complementary analyses.

First, we focused on the evolution of theranksize distribution of the cities, between1981 and 2001, through the study of the timevariations of the Pareto exponent. We used



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the Gabaix and Ibragimov (2006) correction,which eliminates the bias in ordinary leastsquares regression when applied to smallfinite samples, as is the case here. This involves

replacing the traditional ranksize model withthe rank model

ln lnR S

=

1

2

with the approximate true standard error of

the estimated coefficient given by 2n

(Kratz and Resnick, 1996; Gabaix andIbragimov, 2006; Dimou and Schaffar,2007).

In order to have complementary informa-tion on the distribution patterns, we alsoused Rosen and Resnicks (1980) quadraticmodel, where a value significantly differentfrom 0 indicates a departure from a Paretodistribution

ln ln (ln )R S Sj j j= + + 2

Secondly, we investigated urban growthpatterns. Initially, we tested for stationarity incity size. We considered that a citys sizes aregenerally correlated over time, because of thedurability of the publically owned equipment,houses and real estate investments. If ln(Sit)is the logarithm of the population of a cityiat time t, then the size of a city is a first-orderautocorrelation process such as

ln ln, ,S Si t i i t it = + 1

where, i, t is the first-order regression co-efficient; and itan isolated shock at time t.

This means that an isolated shock, leadingto a single migration process, should have

significant and durable effects on a citysdemographics, as advocated by the randomgrowth theories. In order to test the longevityof the effects of such a shock on a citys popu-lation, we performed a unit root test (Sharma,2003; Chen and Fu, 2007).

In the work discussed next, we havehighlighted the relative growth of cities bystudying the changes that occur in the distri-

bution patterns of the city sizes. We have useda Markov transition matrix, which is a con-venient method to model fluidity and toexamine substantial intradistribution mob-ility (Black and Henderson, 2003).

5. Time Variations of the ParetoExponent

Urbanisation in the Balkans increased dur-

ing the 19812001 period: from 45.2 percent of the population in 1981, the urbanpopulation increased to 55.5 per cent in 1991and 59.7 per cent in 2001, while, at the sametime, the total population of the peninsuladeclined because of war and migration,mainly during the second decade (Table 2).This means that the urbanisation processwas a genuine phenomenon between 1981and 1991, but only a statistical one between1991 and 2001, mainly due to a decrease intotal population. This is underlined by thefact that the average city size increased by

Table 2. Descriptive statistics on the urbanisation of the Balkan peninsula

1981 1991 2001

Urbanisation rate 0.452 0.555 0.597

Sample size (number of cities) 269 302 316Average city size (number of inhabitants) 85 051 98 658 93 916

Standard deviation (number of inhabitants) 165 505 239 642 236 014

Median city size (number of inhabitants) 42 031 45 362 42 097



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10 per cent during the first decade, but stag-nated and even decreased between the 1991peak (98 658 inhabitants) and 2001 (93 916inhabitants).

Table 3 shows the evolution in the ranksizedistribution of the cities between 1981 and2001, by estimating the values of the Paretoexponent for the three reference periods.One can note some significant features. First,the Pareto exponent was significantly higherthan 1 over the whole period, which meansthat the Balkan peninsula is a rather poly-centric region; this seems a normal result, as

the capitals of each country are distinct eco-nomic and political centres. In Table 4, onecan see that, among the 10 biggest cities in thepeninsula in 2001, eight are capitals.

Secondly, the Pareto exponent decreasesmonotonically from 1981 to 1991, which

means that the Balkan city-size distributiontends to become more hierarchical. This isprobably due to the progressive collapse ofcommunist regimes which led to more relaxed

policies towards migration and resultedin higher urbanisation and demographicconcentration in big cities. However, underthe shocks of war, institutional breaking-upand insecurity, this progression stopped andthe Pareto exponent stagnated during the19912001 period, as people seemed to stayin medium-sized cities more than in largerconglomerations.

Thirdly, the observed distributions donot follow Zipfs law for any year of the ref-erence period. This is also confirmed by thesignificantly positive value of the quadraticterm in Rosen and Resnicks model, theresults of which are given in Table 5.

Table 3. Pareto coefficient for the distribution of the Balkan cities according to their size(19812001)

Estimation

Year Sample size

Pareto exponent

S.D.

()

1981 269 1.231 0.106

1991 302 1.181 0.096

2001 316 1.195 0.094

Table 4. The ten biggest cities in the Balkan peninsula

Rank

in 2001

Rank

in 1981 City Size in 2001

Average annual growthrate 19812001

(percentage)

1 1 Athens (GR) 3 187 734 1.18

2 2 Bucarest (ROM) 1 926 334 0.32

3 3 Sofia (BUL) 1 138 950 0.07

4 4 Belgrade (SER) 1 120 092 0.14

5 6 Thessaloniki (GR) 800 764 1.53

6 5 Zagreb (CRO) 691 724 0.28

7 7 Scopje (FYROM) 467 257 0.68

8 9 Sarajevo (BOS) 380 000 0.889 19 Tirana (ALB) 343 058 3.02

10 10 Plovdi (BUL) 341 464 0.59

Source: World Gazetteer database.



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Finally, when comparing the density kernelsof 1981, 1991 and 2001, one recalls the un-

balanced and contrasting patterns of theBalkan peninsulas urban hierarchies duringthis period (Figure 2). The 1991 curve exhibitsa lower apex and a wider base than that of1981, which supports the idea that urbangrowth leads to a more unbalanced ranksizedistribution of cities. However, the 2001 plotshows a slight return towards the previoussituation, which can be explained by a stopin migratory movements and stronger dem-

ographics in medium-sized cities, as men-tioned earlier.

6. Urban Growth Patterns in theBalkans

In order to test urban growth patterns, we firstperformed a unit root test. The augmentedDickeyFuller test (ADF) for examining the

instability of the size of a cityi takes the form

ln ln, ,S Si t i i t it ( )= + 1

where, i = i 1We consider two hypotheses: H0 :

i = 0 (i = 1) is the instability hypothesis,where cities sizes are not stationary, versusthe alternative H1 : i < 0 (i < 1), where thelogarithms of cities sizes converge to a con-stant value in the steady state. Following Chenand Fu (2007) and Dimou et al. (2008), weused a specification where the constant

and the linear term itaccount for the upwardtrend and kjis the number of the lagged differ-

ence term for cityi

= + +

+ +

ln ln

ln

,

, ,

S t S

p S

it i i i i t

ij i t j i t

j

ki

1

We carried out the ADF test for 112 cities,for which we had complete time-series be-tween 1981 and 2001. Among them, 87 had

significant unit roots at the 10 per cent level,which led us to reject stability in 77 per centof the cases. It was the same for the wholeurban population of the peninsula (1.015).Table 6 provides additional information forsome cities.

The results of the ADF test strongly rejectH0 and show that most cities sizes in theBalkan peninsula are not stationary. Sharma(2003) and Bosker et al. (2006) have pointed

out, however, the weakness of the unit root testas a diagnostic aid, when applied to a singleequation for a short time-series. Althoughunit root tests on samples with large Ncanimprove a models diagnostic capacity, as inour case, we have used the Im et al. (2003)panel method, which includes cities that donot reject unit roots, to improve the power ofour unit root tests.

The Im et al. test value confirms the previousresults as the hypothesis of non-stationaritycannot be rejected at the 10 per cent level. Thismeans that cities do not converge towards a

Table 5. Rosen and Resnick's quadratic regression on the distribution of the Balkan citiesaccording to their size, 19812001

Student test

YearSample

sizeEstimation (H 0): = 0

() () 1 Alpha 0

1981 269 0.787 0.090 0.035 0.004 8.750 0.000 Yes

1991 302 0.761 0.086 0.034 0.004 8.500 0.000 Yes

2001 316 0.705 0.096 0.036 0.004 9.000 0.000 Yes



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unique steady size and therefore we cannotconfidently reject the random growth hypoth-esis. However, even if city sizes evolve in a non-

stationary way, common factors that affectcity growth may still have a different impact,according to size. We have studied relativeurban growth and intradistribution mobility

in the Balkan cities during the 19812001period, to test such a hypothesis.

We proceeded by dividing the relative size

distribution of the cities into five discretegroups, at the date t, with cut-off points de-fined exogenously with the following bounds(see Table 7)

Figure 2. Kernel densities of the ranksize distribution of the Balkan cities, 1981, 1991 and2001

Table 6. Unit root test for the logarithms of sizes of some cities of the Balkan peninsula

City ADF test City ADF test

Athens (Gr) 0.754 Banja Luka (Bos) 0.344

Bucharest (Rom) 2.197 Ruse (Bul)a 4.098

Beograd (Ser) 2.547 Iraklion (Gr) 0.789

Thessaloniki (Gr) 0.823 Podgorica (Ser) 1.387

Zagreb (Cro) 1.365 Volos (Gr) 1.628

Tirana (Alb) 0.129 Botosani (Rom)a 3.035

Iasi (Rom) 2.043 Suceava (Rom) 1.761

Costanza (Rom)a 2.987 Kumanovo (Fyr) 0.439

Ljubliana (Slo) 1.314 Durres (Alb) 0.078

Novi Sad (Ser) 1.998 Targu Jiu (Rom) 0.859Patras (Gr) 1.653 Elbasan (Alb) 0.513

Pitesti (Rom) 0.993 Haskovo (Bul) 1.014

Pristina (Ser) 1.568 Bitola (Fyr) 1.722

a Values rejected at the 5 per cent level.



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(1) between the threshold entry point of our sample ( = 20 000) and+( )/4 where is the average city

size;(2) between +( )/4 and +( )/2;(3) between +( )/2 and the average

city size ;(4) between and 2; and(5) greater than twice the average city size.

The slight differences between the definitionof these cut-off points and the ones most oftenused in regional studies literature (Eaton and

Eckstein, 1997; Dobkins and Ioannides, 2000;Bosker et al, 2006) are due to the specificityof the Balkan city-size distribution and to thechoice of our samples threshold.

Letftbe the vector of distributional sharesfor each group. By assuming that thisdistribution follows a homogeneous first-order stationary Markov process, ft evolvesover time according to

f f Mt t+ = 1

where,Mis the transition matrix of existingcities from time t to t+1. Each element mijof the transition matrix corresponds to theprobability that a city goes from group i atmoment t to group jat moment t+1. Eachmij is estimated by the maximum likelihoodmethod

,m

n

nij

it jt t

T

itt

T=

+=

=

11

1

1

1

where, nit,jt+1 is the number of cities movingfrom group i at moment t to group j atmoment t+1 and nit the number of cities in

group i in year t. Standard errors are given by

=

=

( )m m

n

ij ij

itt

T

1

1

1

Following Bosker et al. (2006), we haveestimated, for the Balkan city-size distribu-tion, the 10-year transition matrix from1981 to 1991, which corresponds to a period

of moderation in the communist regimesconstraints on migration and to a gradualopening-up to a market economy, prior towar and political unrest. Results are given inTable 8.

The transition matrix illustrates the trendof the Balkan urban hierarchies during thisperiod: in almost all the categories, citiesmoved up a category, with the exception of

the last one but this is a limitation in the ex-planatory power of the matrix, as it is upperbounded. Institutional reforms and eco-nomic changes have clearly positive effects onurbanisation. Although we previously rejectedstationarity in city size, medium-sized citiesgrew faster than the bigger ones, during this10-year period.

Next, we turn to the period of the formerYugoslavias crisis and failing communist

system in order to study their impact on thedistributional patterns of city size. Table 9presents the transition matrix for the19912001 period. First of all, one can note

Table 7. Discretised city size distribution in the Balkan peninsula

1981 1991 2001

f1 < < + ( )S 4 0.40 0.38 0.43

f2 + ( ) < < + ( )4 2S 0.21 0.24 0.20

f3 + ( ) <


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that the diagonal probabilities have muchhigher values than in the preceding period.This means that temporary shocks due towar, ethnic tensions and massive migratorymovements did not produce instability inthe city-size distribution, but had an op-posite effect, which is a rather unexpectedresult. However, the descending off-diagonaltransition probability patterns exceeded the

ascending patterns of the previous decade,which is mostly due to the overall decreasein population in the peninsula.

More importantly, the diagonal probabil-ities for the medium city-size categories arehigher than for larger ones. This means thatstability is higherand demographic up-heaval lowerfor small and medium-sizedcities than for larger conglomerations, moreaffected by external shocks due to war and in-stitutional and political change. Once again,size seems determinant in explaining dif-ferent cities demographics, but no simplistic

conclusion can be drawn (such as parallel orconvergent growth).

When looking at the whole period, theMarkov matrices show that the city-size dis-tribution in the Balkans displays no tendencyto completely flatten (spread) or to converge(collapse to a common city size). Nevertheless,different city-size categories feature specificgrowth trends, which means that size does

matter when characterising urban growth.This means that the intradistribution mobil-ity of cities follows different trends, accordingto the period and size category. Medium-sizedcities grew faster during the 1980s and resistedexternal shocks during the 1990s better thanlarge conglomerations.

7. Conclusion

One of the limitations of a study such asthis is that a 20-year period is very short formeasuring the effects of external shocks on

Table 8. The 19811991 Markov matrix

1991

f1 f2 f3 f4 f5

1981

f1 0.852 (0.101) 0.148 (0.101) 0 0 0f2 0.095 (0.057) 0.625 (0.087) 0.275 (0.104) 0 0

f3 0 0.088 (0.044) 0.500 (0.156) 0.412 (0.106) 0

f4 0 0 0.100 (0.070) 0.609 (0.119) 0.291 (0.055)

f5 0 0 0 0.059 (0.026) 0.941 (0.100)

Note: Standard deviations in parenthesis.

Table 9. The 19912001 Markov matrix

2001f1 f2 f3 f4 f5

1991

f1 0.926 (0.075) 0.074 (0.075) 0 0 0

f2 0.080 (0.053) 0.906 (0.110) 0.014 (0.062) 0 0

f3 0 0.072 (0.026) 0.894 (0.112) 0.024 (0.013) 0

f4 0 0 0.133 (0.066) 0.850 (0.050) 0.017 (0.031)

f5 0 0 0 0.159 (0.082) 0.841 (0.022)

Note: Standard deviations in parenthesis.



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the city-size distribution. Moreover, politicaland institutional upheaval in the Balkans isnot finishedalthough it is only currentlyoccurring in some specific provinces, such as

Kosovowhich means that we can observeshort-term effects for long-term institutional,demographic and political disturbances.

Although this reduces the robustness ofthe interpretation, it does not prevent usfrom delivering some interesting conclu-sions about urban dynamics within conflict-affected city-size distributions. Recent paperson this issue all admit that short-term results

should be handled with care, but they also pro-vide evidence that the information providedrelating to short-term and long-term trendsmay be different and complementary for citydemographic analysis.

This papers findings can be summarisedas follows. The Balkan city-size distributiondoes not obey Zipf s law, over the whole periodof our study. The Pareto coefficient follows avariable trend, declining from 1981 to 1991,

then stagnating. Cities relative growth ratesand intradistribution mobility show thatcity growth dynamics follow a hybrid pat-tern, where city size filters the effects ofcommon external shocks. City-size dynamicsthus seem more complex than predictedby random growth or endogenous growththeories. Finally, during the 19812001 period,medium-sized cities demographics resistedexternal shocks due to conflicts, redrawingof national frontiers and institutional up-heaval better than large conglomerations.This does not, however, lead to convergencetowards a steady city size.

Notes

1. From a six-country region in the 1980s, theBalkans became a nine- and then ten-country

region in less than a decade. In this study,Montenegro appears as a province of Serbia,since our data analysis stops in 2001 andMontenegro only gained independence in2006.

2. The Balkan region includes Albania, Bosnia,Bulgaria, Croatia, Macedonia, Greece, Romania,Serbia and Slovenia. We do not take into con-sideration the European part of Turkey.

3. In a similar model, Duranton (2002) tried tomodel the micro-foundations of the stochasticprocess which leads, through product prolif-eration and local spillovers, to a ranksize dis-tribution of cities obeying Zipfs law. Underthe assumption of monopolistic competition,free labour movement and a fixed number ofcities, Duranton considers that the locationof innovation, over time, is a random processwhich depends on external shocks linked,amongst other things, to the R&D policies in

each city. This results in a process of randomurban growth, but does not necessarily produceZipfs law.

4. The Institute of Statistics of Albania, the Agencyfor Statistics of Bosnia, the National StatisticInstitute of Bulgaria, the National StatisticService of Greece, the State Statistical Officeof FYROM, the National Statistical Office ofRomania, the Statistical Office of Serbia andMontenegro, the Statistical Office of Slovenia,the Yugoslavias Federal Statistical Office.

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