Spatial economic performance of South African municipalities using the rank-size rule:

population size, GVA and municipal income

Hlabi MoruduPaper presented at the Isibalo Symposium for Evidence Based Decision

MakingeThekwini

12 -13 September 2013

Introduction

Seeks to highlight some statistics gaps in spatial policy formulation in South Africa

Seeks to illustrate, through use of a basic framework (from Zipf) potential scope for developing estimates to enhance spatial policy formulation in the country

Will see that if local municipality statistics are developed generally held economic notions (e.g. thriving local economies are associated with increased population sizes) may become perverse with the introduction of space/geography in policy formulation

National socio-economic models like RDP, GEAR, ASGISA, NGP & NDP use highly aggregated national data and remain severely hampered in terms of explicit geographical detail.

At municipal level: (a) Integrated Development Plans (IDP) , (b) Spatial Development Framework (SDF) and (c) Local Economic Development (LED) programs are drafted with major challenges on the availability of useful spatial socio-economic statistics.

Spatial statistics gaps

Not surprisingly, the overall IDPs, SDF and LEDs generally seem detached from national socio-economic models of growth.

Approach

Propose Zipf’s law as one of the frameworks that can be used to bridge statistics gaps between national modelling and local municipality planning

Zipf’s law suggests a clear geographical distribution of data, and applies with almost all variables (this study experiments with population, gross value added and municipal income data)

Zipf’s law, based on empirical findings worldwide, simply suggests: the largest city is ranked 1, the 2nd largest city is ½ the size of the largest city, the 3rd largest city is 1/3 the size of the largest city, and in general the nth largest city 1/n the size of the largest city.

Approach

More concisely, Zipf’s law is expressed as: Si = CRi –α [1]

where Si denotes the population, gross value added or income size of municipality i, C is a constant term, Ri is the rank of municipality i, and α is an exponential coefficient.

In log form, equation [1] becomes: log(Si) = C – αlog(Ri) + εi [2]

where εi is an independent random error term for municipality i. The unknown coefficient α in equation [2] is then estimated through ordinary least squares

If Zipf's law does not apply,

α < 1 suggests a more even distribution of the population, GVA or income among municipalities in the existing hierarchy of municipalities.

α > 1, the slope is steeper implying a less even distribution of the population, GVA or income among municipalities, from the largest to the smallest municipality

Approach

If Zipf’s law holds:

α = 1

Literature review on Zipf’s law

Rationale: classic works of von Thunen (1826), Christaller (1933), Losch (1954), Philbrick (1957), Berry (1964) on how cities are structured, and fit into a hierarchy of higher cities. There are typically many small cities, and few big cities.

Hsu (2008) hypothesizes the distribution of cities in central place theory is consistent with Zipf’s law, and proves it

Zipf’s law applies with almost every variable: Li (2000), Wheeler (2002), Kawamura & Hatano (2002)

Literature review on Zipf’s law

Author Variable Countries α estimates Rejected

Rosen & Resnick(1980) Population 44 countries 0,81-1,96

Soo(2004) Population 73 countries 0,7287-1,719 53

Nitsch(2005) Population 515 estimates 0,80-1,20 33,33%

Fujiwara et al(2008) Company assets France 0,881-0,891

Company sales France 0,885-0,907

Company employees France 0,982-1,008

Tanaka & Hatsukano(2011) Employees Cambodia 1,33

Rossi-Hansberg & Wright(2007) Employees US ≈1

Knudsen(2001) Population Denmark ≈1

Employees Denmark ≈1

Okuyama(1999) Company income in

Construction Japan 1,13

Electrical products Japan 0,72

Okuyama(1999) Employees in

Construction & electrical products Japan 1,2-0,7

Hinloopen & Marrewijk(2007) Ballasa index 166 countries

1970-1997 0,849-1,031

Per sector 0,394-3,420

Per country 0,366-3,710

Data usage

Data used:(a) population: Census 2001, Community Survey 2007, Census 2011*(b) GVA: Quantec estimates 2001 and 2007(c) Municipal income: the annual “Financial Census of Municipalities” (P9114),

excluding transfer payments (i.e. excl. subsidies and grants).(d) Observation units are municipalities and a case of the Greater Johannesburg

Tshwane Functional Region (GJTFR) is used in line with suggestions in Berry & Okulicz-Kozaryn (2012)

GJTFR α t-value R2 adjust

Census 2001 1,04 37,13 0,86

C Survey 2007 1,09 37,79 0,86

Census 2011* 1,06 35.52 0,84

GVA 2001 1,26 69,44 0,95

GVA 2007 1,25 57,25 0,93

Mincome 2006 1,52 56,51 0,94

Mincome 2010 1,43 80,15 0,97

Zipf’s law results

Other studies SA Country Subject Variable Data α

Krugell 2005 S Africa Cities Population Census2001 0,75

Naude & Krugell 2003 S Africa Cities Population Census2001 0,75

Soo 2004 S Africa Cities Population Census1991 1,36

Zipf’s law results

-2.0

-1.5

-1.0

-0.5

0.0

0.5

4

6

8

10

12

14

25 50 75 100 125 150 175 200 225

ResidualActual Zipf valuesEstimated (fitted) Zipf values

log(G

VA2007)

Resi

dual

Municipal rank

GVA

-.8

-.4

.0

.4

.8

8

10

12

14

16

18

25 50 75 100 125 150 175

ResidualActual Zipf valuesEstimated (fitted) Zipf values

log(m

unicipal in

com

e 2010)

Municipal rank

Resi

dua

l

Municipal Income

-2.0

-1.5

-1.0

-0.5

0.0

0.5

4

6

8

10

12

14

25 50 75 100 125 150 175 200 225

ResidualActual Zipf valuesEstimated (fitted) Zipf values

log

(GV

A2

00

7)

Re

sid

ua

l

Municipal rank

-2.0

-1.5

-1.0

-0.5

0.0

0.5

8

10

12

14

16

18

25 50 75 100 125 150 175 200 225

ResidualActual Zipf valuesEstimated (fitted) Zipf values

log(p

opulatio

n size

)

Residual

Municipal rank

Population

Zipf’s law results

Zipf’s law results: GVA 2007

Zipf’s law results: Municipal income 2007

Zipf’s law results: population 2007

Zipf’s law results

Spatial relationships: population, GVA and municipal income

It is generally expected that municipalities with improving economies should increase in terms of population ranking, and municipalities with deteriorating economies to decline in terms of population ranking.

For instance, an increase in GVA rank in the 2001-2007 period is expected to be associated with an increase in population rank over the same period; a decline in GVA rank is expected to be associated with a decrease in population rank.

Similarly, and reflecting the quality of municipal governance, municipalities with prospective increases in municipal income in the 2006-2010 period are expected to be associated with an increase in population rank.

Those with prospective decreases in municipal income are expected to be associated with a decrease in population rank.

The development of local municipality estimates, in this case using Zipf’s law, would expand comprehension of changing patterns e.g. as seen when one simultaneously considers the behaviour between population, GVA and MINCOME

Spatial relationships: population, GVA and municipal income

The data suggests a more complex relationship between population size and economic variables

Population GVA

Municipal Income

Spatial relationships: population, GVA and municipal income

Spatial relationships: population size, GVA and municipal income

Insignificant rank movement

Municipality Rank (pop, GVA, income)

GJTFR (0,0,0)

Nelson Mandela Bay (0,0,0)

City of Cape Town (1,0,0)

Msunduzi (1,0,1)

eThekwini (-1,0,0)

Emfuleni (-1,0,1)

Buffalo City (-1,0,-2)

Spatial relationships: population size, GVA and municipal income

(Pop) ↑ (GVA&Mincome) ↑

Municipality Rank (pop, GVA, income)

(examples) Dipaleseng (1,3,20)

Hantam (2,3,6)

Mbizana (3,20,21)

Ngquza Hill (3,39,45)

Kannaland (5,11,2)

Port St Johns (6,1,2)

Spatial relationships: population size, GVA and municipal income

(Pop) ↓(GVA, Mincome) ↓ Municipality Rank (pop, GVA, income)

(examples) Drakenstein (-1,-1,-2)

Thembelihle (-1,-3,-22)

Ubuntu (-1,-14,-9)

Karoo Hoogland (-1,-5,-5)

Matjhabeng (-2,-5,-3)

Spatial relationships: population size, GVA and municipal income

(Pop)↓ (GVA, Mincome) ↑ Municipality Rank (pop, GVA, income)

(examples) Mhlontlo (-1,11,20)

Greater Giyani (-2,12,13)

Kouga (-2,27,11)

Umzimvubu (-2,27,43)

Swellendam (-3,6,2)

Nquthu (-4,4,15)

Mandeni (-5,2,13)

Msinga (-6,14,2)

Spatial relationships: population size, GVA and municipal income

(Pop)↑(GVA, Mincome) ↓ Municipality Rank (pop, GVA, income)

(examples) Intsika Yethu (1,-1,-35)

Nokeng tsa Taemane (1,-10,-5)

Siyathemba (1,-5,-15)

Beaufort West (1,-5,-3)

Emalahleni-EC (2,-31,-30)

Naledi-NW (2,-28,-12)

Conclusions

Zipf’s law basically holds in the hierarchy of South African municipalities with regard to population size. There are however high concentrations of GVA & Income in major municipalities

The framework is robust in the sense that it is applicable to a wide range of variables – population size, GVA, municipal income and other variables where some data is available.

Zipf’s law can be used to develop spatial estimates that could bridge the statistics gap between national aggregate models and local municipality models

The framework provides scope to analyse complex spatial patterns that could previously, without local municipality data, be done

Thank you very much!