GROWTH RATE STABILITY IN THE KALDORIAN REGIONAL MODEL: THE CHARACTERISTIC ROOTS
| DOI | http://doi.org/10.1111/j.1467-9485.1978.tb00247.x |
| Author | William Gilleny,Antonio Guccione |
| Date | 01 June 1978 |
| Published date | 01 June 1978 |
Scottish
Journal
of
Political Economy,
Vol.
25,
No.
2, June 1978
GROWTH RATE STABILITY
IN
THE
KALDORIAN REGIONAL MODEL: THE
CHARACTERISTIC ROOTS
ANTONIO GUCCIONE
AND
WILLIAM
GILLEN
University
of
Windsor
In their reply to our comment (1977) on
“A
Model of Regional Growth-Rate
Differences on Kaldorian Lines” (1975), Dixon and Thirlwall have clarified
most of the issues sufficiently that they should now be left for the reader to
decide. However, there remains one technical error on
a
very essential point.
In our note we showed that, when the model is expanded to two regions, the
characteristic root upon which stability depends
is
increased. Perhaps we
should have been more explicit in pointing out that the relevant root con-
tinues to increase as the number of regions is expanded. Dixon and Thirlwall
seem to believe that, since we obtain a largest root of one, we have not shown
that instability results for reasonable values of the parameters. However, for
given parameter values, the root increases as the number of regions is ex-
panded. For example, it is enough to add a third region to obtain
a
char-
acteristic root of
1.25
(and in general, there is an increase of
0-25
for each
additional region) provided each area has the same “reasonable parameter
values” used in Dixon and Thirlwall’s example. We emphasize that the para-
meters are reasonable, that is they do not violate Dixon’s and Thirlwall’s
beliefs on what values are plausible. Clearly the example is rather artificial in
the sense that
all
regions have the same parameter values, but it provides an
appropriate counter-example to Dixon and Thirlwall’s statement “The stab-
ility of our system, and the interregional (two region) system that Guccione
and Gillen develop, depends not on the number
of
regions but on the para-
meter values assumed in the model which determines the roots
of
the system”.
In conclusion, the fact that explosive long run regional growth rates are
not usually observed cannot be explained simply by imposing reasonable
parameter values on the model. The explanation may be found in Dixon
and Thirlwall’s “product innovation” or in our suggested labour supply
constraints, or in Kaldor’s notion that the Verdoon effect may not be opera-
tional at high levels of growth: “There are also important diseconomies
resulting from excessive rates of growth in industrial activities in particular
areas.
. .
and these at some stage should serve to offset the technological
economies resulting from faster growth” (1970, p.
344).
REFERENCES
DIXON,
R.
and THIRLWALL,
A.
P.
(1975).
A
model of regional growth rate differences
on
GUCCIONE,
A.
and
GILLEN,
W.
J.
(1977). Growth rate stability in the Kaldorian regional
KALDOR, N. (1 970). The case for regional policies,
Scottish
Journal
of
Political Economy,
Kaldorian lines.
Oxford
Economic Papers,
July, pp. 201-214.
model,
Scottish
Journal
of
Political Economy,
June, pp. 175-176.
November, pp. 337-348.
Date
of
receipt
of
final
manuscript: 23 February 1978.
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