Krugman’s 45 Degree Rule

Recently, Paul Krugman reminded us of his “45 degree rule” on his blog Conscience Of A Liberal. This was a reference to his paper in 1989 which was a rediscovery of Thirlwall’s Law from 1979 [1] which states that the long run rate of growth of any country is constrained by the rate of growth of exports divided by the income elasticity of imports. Krugman rediscovered this law but interpreted the causality in the opposite way. This shouldn’t be surprising because in neoclassical economics, growth is explained by a production function and it is then difficult to interpret the causality in Thirlwall’s way. In an essay [2], John McCombie explains:

Krugman (1989) rediscovered Thirlwall’s Law, which he termed the 45-degree rule, as empirically ε/π = y/z or, when the (log) of the former is regressed on the (log) of the latter, the coefficient is unity or the slope of the line is 45-degrees. (Krugman provides some empirical evidence providing further confirmation of this empirical relationship). Like McCombie and Thirlwall (1994), he rules out sustained changes in the real exchange rate as a factor in bringing the balance of payments into equilibrium. Consequently, it is necessary to explain why the rule holds. The Keynesian explanation is that it is growth rates that adjust to maintain the balance of payments in equilibrium, but this is rejected by Krugman on “a priori grounds” that it is “fundamentally implausible.” He continues that “we all know that differences in growth rates among countries are primarily determined in the growth rates of total factor productivity, not differences in the rate of growth of employment; it is hard to see what channel links balance of payments due to unfavourable income elasticities to total factor productivity growth” (Krugman, 1989, p. 1037).

The Krugman article is instructive because it goes to the heart of the question about the direction of causation. Drawing on new trade theory, monopolistic competition, and the importance of increasing returns, he argues that faster growth leads to increased specialisation and the production of new goods for sale in overseas markets. Thus high “export elasticities of demand” are due to a dynamic supply side and rapid growth, rather than vice versa.

[x is the growth of the volume of exports, π is the domestic income elasticity of demand for imports, ε is the world income elasticity of demand for exports, and z is the growth of world income]

For a more forceful defence of Thirlwall’s Law, see McCombie’s paper.

In my opinion, the causality runs in both directions. However I am more sympathetic to Thirlwall and McCombie. And because the causality runs in both directions, there is still a balance-of-payments constraint. Complex economic dynamics still benefit richer nations and immiserate others. To an extent, this is already present in Kaldorian models. Growth brings in rise in productivity and this effects price competitiveness and hence beneficial to balance of payments generally. However, I also consider the income elasticity as being affected by growth at home and abroad.


  1. Thirlwall, A. P. (1979) ‘The Balance of Payments Constraint as an Explanation of International Growth Rate Differences’, Banca Nazionale del Lavoro Quarterly Review, March.
  2. McCombie, J.S.L. (2011) ‘Criticisms and defences of the balance-of-payments constrained growth model: some old, some new ‘, PSL Quarterly Review, vol. 64 n. 259 (2011), 353-392. (Can be previewed on Google Books here)

Leave a Reply

Comments are welcome, but not published—see comments policy. Required fields are marked *