GROWTH RATE STABILITY IN THE KALDORIAN REGIONAL MODEL
| DOI | http://doi.org/10.1111/j.1467-9485.1978.tb01188.x |
| Author | R. J. Dixon,A. P. Thirlwall |
| Date | 01 February 1978 |
| Published date | 01 February 1978 |
Scottish
Journal
of
Political Economy,
Vol.
25,
No.
1,
February
1978
GROWTH RATE STABILITY IN THE
KALDORIAN REGIONAL MODEL
R.
J.
DIXON*
AND
A.
P.
THIRLWALLt
*
Victoria, Australia and
t
University
of
Kent at Canterbury
In their recent note
on
the model we developed of regional growth rate
differences (1975) on lines originally suggested by Kaldor
(1970),
Guccione
and Gillen (1977) claim that the stability of the single region system we used
for illustrative purposes is “only the result of the partial nature of the
analysis”. This is not
so.
Nor did we claim that stability for a single region
implies immediate stability for any number of interdependent regions. The
stability of our system, and the interregional (two region) system that
Guccione and Gillen develop, depends not on the number of regions but on
the parameter values assumed in the model which determines the roots of the
system. In our single region model instability is not excluded. The region’s
growth rate diverges from its equilibrium rate if the product of the Verdoorn
coefficient and the price elasticity of demand for its exports exceeds unity in
absolute value. We argued that with
a
Verdoorn coefficient of
0.5
and
a
price elasticity
of
demand for exports of between
1
and
2,
the system would
be stable. If the price elasticity exceeds two, with a Verdoorn coefficient of
0.5,
the single region system is unstable. Thus our model certainly does not
rule out instability. Reasonable parameter values and real-world evidence
suggests, however, that instability is unlikely. It is not usual to observe
a
region’s growth rate continually increasing through time or regional growth
rate
differences
diverging through time. It is more common to observe regions
growing at different (equilibrium) rates, which may, of course, cause per
capita income differences to widen and for unemployment rate differences to
persist or widen.
It is certainly interesting to develop the two region case’ but the demonstra-
tion of instability does not depend on it, nor is stability precluded. Guccione
and Gillen prove the point themselves by choosing parameter values for their
two region system which give characteristic roots
of
0.5
and
1.
For instability
the dominant characteristic root must be greater than unity. Since the
dominant root in their system is
1,
the growth rate
of
each region will remain
at its equilibrium level plus some constant. They thus demonstrate the point
that whether the system is unstable or not does not depend on the number of
The only difference between the solution
to
their model and
ours
is that the income
elasticity of demand
for
regions’ exports
(q)
enters explicitly in theirs. This may make the
condition
for
stability of the system more
or
less stringent depending on the regional values
of
~i.
The roots of the system may also be complex giving oscillations.
Received in ha1 form:
20
July
1977.
7 97
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