Mathiness, Growth and Increasing Returns

The following was originally posted on Ecological Headstand in October, 2012 under the title, Endogenous Growth Theory and Ecological Unequal Exchange: linkage, displacement and deflection of 'diminishing returns'. Paul Romer's rant on mathiness has provoked a response from Lars Syll regarding the issue of increasing returns to scale, which I discussed in this post.

What the late Stephen G. Bunker wrote bears repeating:

The crucial difference between production and extraction is that the dynamics of scale in extractive economies function inversely to the dynamics of scale in the productive economies to which world trade connects them.

Rather than repeat what Bunker wrote, though, I'm going to cite, later, a longer piece by Nicholas Kaldor from his 1985 Hicks Lecture that makes a somewhat similar point. But first, I want to present some background on an old debate and a 'new' theory.

In December 1926, The Economic Journal published an article by Piero Sraffa dealing with "that difficult branch of economic theory" -- the theory of increasing returns. Over the next five years it published responses from Cecil Pigou, G. F. Shove, Lionel Robbins and Allyn Young and, in March 1930, a symposium on the topic by D. H. Robertson, Sraffa and Shrove.

Almost exactly 60 years later, in October 1986, The Journal of Political Economy, published Paul D. Romer's "Increasing Returns and Long-Run Growth," an important contribution to so-called New Growth Theory. Romer took his cue explicitly from Young's 1928 paper, "Increasing Returns and Economic Progress" and although he mentioned the precedents of Adam Smith's pin factory and Alfred Marshall's distinction between internal and external economies, he skipped over the rest of the debate in which Young's contribution had appeared.

Critics have argued that Romer's usage of increasing returns and external economies is not faithful to Young's formulation, in that it "overlooked Young's emphasis on the reciprocal relations between the division of labor and the feed-back into aggregate demand as a requirement for growth," "neglected Young's categorical rejection of the usefulness of Walrasian general equilibrium models" and wrested "Marshall's microeconomic concepts of internal and external economies out of his theory of value and price to serve as a basis for amending constant return production functions to exhibit increasing returns for the macroeconomy" (Rima 2004, 181-182).

My concern here is with a more conspicuous omission in Romer's analysis -- the distinction between increasing returns as characteristic of manufacturing and diminishing returns as dominant in agriculture and extractive industries (Young 1928, 528-529). The words "agriculture," "land" and "rent" do not appear in Romer's 1986 article. When Romer mentions diminishing returns, it is only in the context of research activity or the limiting assumptions of classical conventional growth models. But diminishing returns is a specific limitation, not a generality that can be indiscriminately "offset" by increasing returns. In a lecture given at Harvard in 1974, "What is Wrong with Economic Theory," Kaldor explained that "it is the income of the agricultural sector, (given the "terms of trade") that really determines the level and the rate of growth of industrial production, according to the formula:"

Or, in prose, economic growth depends on either a relative reduction in the income of agriculture or increased demand from agriculture for industrial products. And, of course, increased demand from agriculture implies increased agricultural production, which at some point confronts the problem of diminishing returns. In his 1985 Hicks Lecture, Kaldor explained the inverse dynamics of scale between industrial and agricultural areas, parenthetically, in terms of the "differing manner of operation of perfect and imperfect competition":

The basic requirement of continued economic growth is that the various complementary sectors expand in due relationship with each other -- that is to say that general expansion is not held up by "bottlenecks" in key sectors. However, in the course of time, under the influence of technical progress, both of the natural-resource saving and labour-saving kind, the requirements of expansion may become considerably modified. In the manufacturing sector which becomes more important as real incomes rise, there are considerable economies of scale, as a result of which manufacturing activities are subject to a "polarization process" -- they are likely to develop in a few successful centres, and their success has an inhibiting effect on similar developments in other areas. The realisation of these economies of scale normally requires also that numerous processes of production which are related to each other are carried out in close geographical proximity.

As a result different regions experience unequal rates of growth of output and of population. The industrial areas experience a growing demand for labour which may involve immigration from other areas once their own surplus labour is exhausted. Technological development in primary production on the other hand, tends to be more labour-saving than land-saving, so that the growth of output may go hand in hand with a falling demand for labour; and though output per head may grow fast in real terms, the level of wages will tend to remain low (and may even be falling) as a result of a growing surplus population. Since labour cost per unit of output is the most important factor in determining selling prices (at any rate under competitive conditions) the low wages prevailing, in terms of industrial products, will mean that the terms of trade will move unfavourably to primary producers, which may be the main factor, along with the low coefficient of labour utilisation, for their state of "under-development" characterised by low standards of living. The important contrast -- which I regard as a major factor in the growing inequality of incomes between rich and poor countries -- resides in the fact that the benefit of labour saving technical progress in the primary sector tends to get passed on to the consumers in the secondary sector in lower prices, whereas in the industrial sector its benefits are retained within the sector through higher wages and profits. (The main reason for this difference lies in the differing manner of operation of perfect and imperfect competition.)

Kaldor's parenthetical explanation suggests more than it reveals. Sraffa's 1926 discussion is the key to unpacking why Kaldor specifies perfect competition as characteristic of primary production and associates imperfect competition with manufacturing industry. The key determinants, in that view, are the shapes of the firms' supply curves (increasing or diminishing returns) and the nature of external economies.

Externality and Ecological Overshoot

Marshall's notion of "external economies" has gone through a series of modifications to become today's "externalities." Pigou extended the concept beyond Marshall's industrial agglomerations and distinguished between “incidental uncharged disservices” and "incidental uncompensated services." The former became known as negative externalities and the latter as positive externalities, although typically it is the negative environmental externalities that are referred to simply as externalities. There is a seeming but misleading symmetry to the two terms and a similarly illusory quality of reciprocity within each of them. When a disservice is uncharged or a service is uncompensated there is a presumption that there might otherwise have been a "whom" to charge or to compensate and that the missing invoice could have been denominated in currency. In other words, the charging and compensating would appear to be a financial transaction between two parties, both of whom must be assumed to be legal persons. In reality, the services or disservices performed may (or may not!) be extremely indirect and the parties affected incredibly diffuse, both in space and time. Mundane examples of factory soot and laundry hanging out to dry may be more mystification than illumination.

In the case of the external economies of increasing returns and diminishing returns, respectively, although they function inversely to one another it is a double inversion that ultimately produces parallel incentives to firms in manufacturing and agricultural or extractive industries. In other words, while firms in the manufacturing center are routinely considered to be the beneficiaries of external economies that generate increasing returns in the sense that they receive uncompensated services, firms in the extractive periphery may also benefit from the externalization of diminishing returns in that they are able to avoid being charged for the environmental disservices they inflict. In effect, the cost of diminishing returns is first displaced to poor regions where it is then deflected onto society and the environment. Unequal exchange thus takes place, that is to say, in the global external economies, "behind the back", so to speak, of formal monetary transactions.