Hlabi Morudu Paper presented at the Isibalo Symposium for Evidence Based Decision Making

Spatial economic performance of South African municipalities using the rank-size rule: population size, GVA and municipal income HlabiMorudu Paper presented at the Isibalo Symposium for Evidence Based Decision Making eThekwini 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

Spatial statistics gaps 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. 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

Approach If Zipf’s law holds: α = 1 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

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

Data usage Data used: population: Census 2001, Community Survey 2007, Census 2011* GVA: Quantec estimates 2001 and 2007 Municipal income: the annual “Financial Census of Municipalities” (P9114), excluding transfer payments (i.e. excl. subsidies and grants). 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)

Zipf’s law results

Zipf’s law results GVA Population Municipal Income

Zipf’s law results Zipf’s law results: population 2007 Zipf’s law results: GVA 2007 Zipf’s law results: Municipal income 2007

Spatial relationships: population, GVA and municipal income 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 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.

Spatial relationships: population, GVA and municipal income The data suggests a more complex relationship between population size and economic variables

Spatial relationships: population, GVA and municipal income GVA Population Municipal Income

Spatial relationships: population size, GVA and municipal income

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

Thank you very much!

Hlabi Morudu Paper presented at the Isibalo Symposium for Evidence Based Decision Making