Testing the Stability of a Production Function with Urbanization as a Shift Factor
| Published date | 01 November 1999 |
| Date | 01 November 1999 |
| Author | Suzanne McCoskey,Chihwa Kao |
| DOI | http://doi.org/10.1111/1468-0084.0610s1671 |
TESTING THE STABILITYOF A PRODUCTION
FUNCTION WITH URBANIZATION AS A SHIFT
FACTOR
Suzanne McCoskey and Chihwa Kao
I. INTRODUCTION
Urban economists have long been attempting to answer the question of why
cities exist. In particular, recent research has focused on the idea that cities
capture some sort of agglomeration economies ± production in urban areas
bene®t from some increasing returns to scale which are not present in rural
environments. Urban economists have gone further to separate these
agglomerations into two categories: localization economies (economies of
scale present because of industrial clustering in cities) and urbanization
economies (economies of scale present because of the overall size of city).
Localization economies are external to the ®rm but internal to the industry.
Most of the articles dealing with output and urbanization have focused on
urbanization economies and not localization economies.
Given that urban structure is hypothesized to in¯uence output levels
another related question is how urbanization affects economic development:
what is the role of urbanization levels in developing and developed
countries? A long-running debate in development economics has been
whether developing countries have become over-urbanized. In Moomaw
and Shatter (1993) the debate is characterized as that between the tradition-
alists as represented by Todaro's works, for example Todaro (1995) which
claims that less-developed countries are over-urbanized, and the modernists
as represented in the work of Wheaton and Shishido (1981), which claims
that large cities are necessary to realize economies of scale. Unfortunately,
there are not many empirical studies which look at this question. Exceptions
are Moomaw and Shatter (1993, 1996). Further, the empirical research in
the literature is either based on cross-section studies or very limited panels
which are unable to capture truly the dynamic nature of the question.
The main idea of the dynamic model we use in this paper comes from the
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, SPECIAL ISSUE (1999)
0305-9049
671
#Blackwell Publishers Ltd, 1999. Published by Blackwell Publishers, 108 Cowley Road, Oxford
OX4 1JF,UK and 350 Main Street, Malden, MA 02148, USA.
Address for correspondence: Suzanne McCoskey, Department of Economics, United States
Naval Academy, 121 Blake Rd., Annapolis, MD 21402. E-mail: mccoskey@nadn.navy.mil. The
authors would like to thank Jack Strauss and a co-editor, Anindya Banerjee, for their helpful
comments as well as two anonymous referees. Thanks also to the participants in the Eighth
International Conference on Panel Data.
neoclassical growth literature which sets out a dynamic optimization
problem for the economic individual constrained by some production func-
tion. An example of this theory is given by Lucas (1988) and his attempts to
explain economic growth in developed and developing countries. His paper
is not among those concerned with the convergence theories of growth such
as the article by Barro (1991). Rather it solves models with utility
maximization given production constraints where human capital, learning
by doing and comparative advantage in trade drive growth. He also alludes
to, though never solves, an example where cities could cause growth by
capturing certain agglomerations in production. This is the background
philosophy for the model presented below: urbanization as a potential
engine of growth. Although the model presented here does not solve the
consumer maximization problem set out in Lucas, it does set out a
production function which, if properly speci®ed, could enter a growth model
as a pertinent constraint. Further, it can be used to estimate individual cross-
section urbanization agglomerations.
Section 2 of this paper presents the Cobb ±Douglas production function
model used in the paper. In this model urbanization is added as a shift
factor. Section 3 presents the empirical results of the paper distinguishing
between the dynamic results on the model including non-stationary vari-
ables, and the results from cross-section regressions. In particular, we apply
the panel unit root test given by Im, Pesaran and Shin (1997); test of the null
of cointegration in panel data from McCoskey and Kao (1998); and
procedures for estimating long-run relationships from Pesaran and Smith
(1995). Section 4 offers concluding notes.
II. THE MODEL
The model proposed here uses a Cobb± Douglas production function1which
restricts the sum of exponents on capital and labor to one. The production
function is de®ned for each country and each year:
yi,tAi,t(Ui,t)ëi(Kâi
i,tN1ÿâi
i,t), (1)
where yi,tis GDP for country iin time period t,Ui,tis the percent of the
population living in an urban area, Ki,tis capital stock, and Ni,tis the
number of workers. Ai,tis the speci®cation for technology and is the
element which introduces a stochastic element into the model. Technology
and urbanization levels in this model both act as shift factors. Technology
includes both a possible intercept and trend term:
Ai,teáiäitåi,t:(2)
1The Cobb± Douglas speci®cation is the standard production speci®cation used to estimate
urban agglomerations in the urban literature. For example, see Henderson (1988, p. 34).
672 BULLETIN
#Blackwell Publishers 1999
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