Thirlwall's Z and World System (fwd)

Thu, 06 Feb 1997 15:46:31 +1100
Bruce R. McFarling (

Two more responses to the question of potential for mutual
ineraction of Post Keynesian economics: one optimistic, and a skeptical
rejoinder. First the optimistic response.


Bruce R. McFarling, Newcastle, NSW

Date: Mon, 03 Feb 1997 09:27:01 -0500 (EST)
From: Gernot Kohler <>
Subject: Thirlwall's Z and World System

Thirlwall's Z by: Gernot Kohler mini #41 Feb. 1997
and World System

[I extend my apologies to Professor Andre Gunder Frank for the rough tone
of the first half of another post of mine and repeat the opinion
expressed in the second half of the same post--namely, that it would be nice
if Post(-)Keynesians and World(-)System scholars could work together --
for example, on the development of an "Economic Programme" for the
democratic world party proposed in World System circles.
--- One solidarity is stronger than two solitudes.]

(Post Keynesian) Professor Thirlwall has a variable Z (world income)
which is useful in world system economics.

REFERENCE: A.P. Thirlwall,
_Growth and Development_. 5th edition.
London: MacMillan, 1994, p. 389-390.

Thirlwall argues, in his theory of balance-of-payments constrained
growth, that a country's aggregate income (Y) is constrained by the
country's balance of payments. Because of this constraint,
world income (Z) has an influence on national income Y, or:

y = f ( z, other )

in words, the growth rate of national income (y) is a function of the
growth rate of world income (z) and other variables. (For details, see
below, Appendix 1.)

By including Z (world income) as an independent variable in a model
explaining Y (national income), Thirlwall uses a world system variable
(mega-level, namely, Z) in order to explain a national variable
(macro-level, namely, Y). This leads to my:


Thirlwall's Z (world aggregate income) is the world-system equivalent
of Keynes's Y (national aggregate income).

Thirlwall uses Z as an independent variable. No harm is done if we
entertain the notion that Z could be a dependent variable. This leads to my:


Thirlwall's Z (world aggregate income) is to world system economics
(megaeconomics) what Keynes's Y is to macroeconomics -- namely,
the grand dependent variable ("the quaesitum", as Keynes calls it).

Rounding this out, we can add:


World income (Z) and its corresponding world GDP have several dimensions
which are of interest to both the World(-)System school and the
Post(-)Keynesian school, namely:

history of Z [apology to AGF for a cheap shot on this one]
politics of Z
magnitude of Z
distribution of Z
growth of Z
content of Z [ in the sense of,
"ecologically sustainable or not"]


I submit that Thirlwall's Z is an excellent analytic device for linking
World(-)System Theory and Post(-)Keynesian Theory (and, hopefully, some
action as well).

This linkage operation involves also a linking of two levels of analysis
(which is taken for granted in WS, but needs to be made explicit in PK).


Linking two levels of analysis is a familiar activity in economics --
as, e.g., when we speak of "the micro-foundations of macroeconomics" or,
in Keynes's et al. reversal, "the macro-influences on microeconomics".

Let's posit the existence of three levels of analysis, namely:


Thirlwall's Z facilitates a linkage between the mega-level (world
system level) and the macro-level (national system level). The causal
influences can run both ways. Thus, we can speak of:

(1) the macro-foundations of mega-economics, and
(2) the mega-influences on macro-economics

(i.e., nation-to-world and world-to-nation).

Thirlwall's theory implies #2 (mega-influence on macro), while Davidson's
and Harkness's theories of exchange rates imply #1 (macro-foundations of



Reference: A.P. Thirlwall, _Growth and Development_. 5th edition.
London: MacMillan, 1994, p. 389-390.

[The equation looks more elegant in the original.]

y = epsilon * (z) + (pd + pf - e) * [(1+eta+psi) / pi]


y growth rate of Y (domestic income)
z growth rate of Z (world income)

price changes:

pd change of average (domestic) price of exports
pf change of average (foreign) price of imports
e change of the exchange rate

(pd+pf-e) rate at which the real terms of trade
are changing


epsilon income elasticity of demand for exports
eta price elasticity of demand for exports

pi income elasticity of demand for imports
psi price elasticity of demand for imports

NOTE: Thirlwall's growth rate y is a postulated, longer-term y
which may differ from measured, annual y . In Thirlwall's
words: y is an "expression for a country's growth of income
consistent with current account equilibrium" (p. 390).



There is a small discrepancy between Thirlwall's Z and the Z which I
used in my discussion, as follows:

If "i" is the number of all countries in the world (presently,
approximately, i = 185 countries), then:

(A) Thirlwall's Z = sum (Y) for 1 to (i - 1)

(B) (my) all-inclusive Z = sum (Y) for 1 to i

The difference is one country. I include all countries; Thirlwall's
Z includes all countries less the exporting country. This is not stated
explicitly, but can be inferred from the fact that Thirlwall analyzes
exports/imports between one country and the rest of the world.
Thirlwall's "world income" (Z) actually means "rest-of-world income".

For a small economy, e.g., Mozambique, the difference between the
two definitions of Z is inconsequential. However, for a large economy,
e.g., USA, the difference is significant.

Whenever we study the exports/imports of a single country,
Thirlwall's Z applies. Whenever we study the world system, the
all-inclusive Z applies.



This posting has not (NOT) been financed by Z magazine, neither by the
Zapatista movement. The Z used in this posting is post-Keynes-ian, in as
much as Z follows upon Y and in as much as Professor Thirlwall is a Post
Keynesian. Furthermore, this Z is a clean, professional, Cambridge
University Z , absolutely hygienic.

Gernot Kohler
Oakville, Canada