Romer’s article on ‘mathiness’ triggered a debate in the economics blogs last year. I didn’t pay a great deal of attention at the time; that economists were using relatively trivial yet abstruse mathematics to disguise their political leanings didn’t seem a particularly penetrating insight.
Later in the year, I read a comment piece by John Kay on the same subject in the Financial Times. Kay’s article, published under the headline ‘Economists should keep to the facts, not feelings’, was sufficiently cavalier with the facts that I felt compelled to respond. I was not the only one – Geoff Harcourt wrote a letter supporting my defence of Joan Robinson and correcting Kay’s inaccurate description of her as a Marxist.
After writing the letter, I found myself wondering why a serious writer like Kay would publish such carelessly inaccurate statements. Following a suggestion from Matteus Grasselli, I turned to Romer’s original paper:
Economists usually stick to science. Robert Solow was engaged in science when he developed his mathematical theory of growth. But they can get drawn into academic politics. Joan Robinson was engaged in academic politics when she waged her campaign against capital and the aggregate production function …
Solow’s mathematical theory of growth mapped the word ‘capital’ onto a variable in his mathematical equations, and onto both data from national income accounts and objects like machines or structures that someone could observe directly. The tight connection between the word and the equations gave the word a precise meaning that facilitated equally tight connections between theoretical and empirical claims. Gary Becker’s mathematical theory of wages gave the words ‘human capital’ the same precision …
Once again, the facts appear to have fallen by the wayside. The issue at the heart of the debates involving Joan Robinson, Robert Solow and others is whether it is valid to represent a complex macroeconomic system (such as a country) with a single ‘aggregate’ production function. Solow had been working on the assumption that the macroeconomic system could be represented by the same microeconomic mathematical function used to model individual firms. In particular, Solow and his neoclassical colleagues assumed that a key property of the microeconomic version – that labour will be smoothly substituted for capital as the rate of interest rises – would also hold at the aggregate level. It would then be reasonable to produce simple macroeconomic models by assuming a single production function for the whole economy, as Solow did in his famous growth model.
Joan Robinson and her UK Cambridge colleagues showed this was not true. They demonstrated cases (capital reversing and reswitching) which contradicted the neoclassical conclusions about the relationship between the choice of technique and the rate of interest. One may accept the assumption that individual firms can be represented as neoclassical production functions, but concluding that the economy can then also be represented by such a function is a logical error.
One important reason is that the capital goods which enter production functions as inputs are not identical, but instead have specific properties. These differences make it all but impossible to find a way to measure the ‘size’ of any collection of capital goods. Further, in Solow’s model, the distinction between capital goods and consumption goods is entirely dissolved – the production function simply generates ‘output’ which may either be consumed or accumulated. What Robinson demonstrated was that it was impossible to accurately measure capital independently of prices and income distribution. But since, in an aggregate production function, income distribution is determined by marginal productivity – which in turn depends on quantities – it is impossible to avoid arguing in a circle . Romer’s assertion of a ‘tight connection between the word and the equations’ is a straightforward misrepresentation of the facts.
The assertion of ‘equally tight connections between theoretical and empirical claims’, is likewise misplaced. As Anwar Shaikh showed in 1974, is it straightforward to demonstrate that Solow’s ‘evidence’ for the aggregate production function is no such thing. In fact, what Solow and others were testing turned out to be national accounting identities. Shaikh demonstrated that, as long as labour and capital shares are roughly constant – the ‘Kaldor facts’ – then any structure of production will produce empirical results consistent with an aggregate Cobb-Douglas production function. The aggregate production function is therefore ‘not even wrong: it is not a behavioral relationship capable of being statistically refuted’.
As I noted in my letter to the FT, Robinson’s neoclassical opponents conceded the argument on capital reversing and reswitching: Kay’s assertion that Solow ‘won easily’ is inaccurate. In purely logical terms Robinson was the victor, as Samuelson acknowledged when he wrote, ‘If all this causes headaches for those nostalgic for the parables of neoclassical writing, we must remind ourselves that scholars are not born to live an easy existence. We must respect, and appraise, the facts of life.’
What matters, as Geoff Harcourt correctly points out, is that the conceptual implications of the debates remain unresolved. Neoclassical authors, such as Cohen and Harcourt’s co-editor, Christopher Bliss, argue that the logical results, while correct in themselves, do not undermine marginalist theory to the extent claimed by (some) critics. In particular, he argues, the focus on capital aggregation is mistaken. One may instead, for example, drop Solow’s assumption that capital goods and consumer goods are interchangeable: ‘Allowing capital to be different from other output, particularly consumption, alters conclusions radically.’ (p. xviii). Developing models on the basis of disaggregated optimising agents will likewise produce very different, and less deterministic, results.
But Bliss also notes that this wasn’t the direction that macroeconomics chose. Instead, ‘Interest has shifted from general equilibrium style (high-dimension) models to simple, mainly one-good models … the representative agent is now usually the model’s driver.’ Solow himself characterised this trend as ‘dumb and dumber in macroeconomics’. As the great David Laidler – like Robinson, no Marxist – observes, the now unquestioned use of representative agents and aggregate production functions means that ‘largely undiscussed problems of capital theory still plague much modern macroeconomics’.
It should by now be clear that the claim of ‘mathiness’ is a bizarre one to level against Joan Robinson: she won a theoretical debate at the level of pure logic, even if the broader implications remain controversial. Why then does Paul Romer single her out as the villain of the piece? – ‘Where would we be now if Solow’s math had been swamped by Joan Robinson’s mathiness?’
One can only speculate, but it may not be coincidence that Romer has spent his career constructing models based on aggregate production functions – the so called ‘neoclassical endogenous growth models’ that Ed Balls once claimed to be so enamoured with. Romer has repeatedly been tipped for the Nobel Prize, despite the fact that his work doesn’t appear to explain very much about the real world. In Krugman’s words ‘too much of it involved making assumptions about how unmeasurable things affected other unmeasurable things.’ So much for those tight connections between theoretical and empirical claims.
So where does this leave macroeconomics? Bliss is correct that the results of the Controversy do not undermine the standard toolkit of methodological individualism: marginalism, optimisation and equilibrium. Robinson and her colleagues demonstrated that one specific tool in the box – the aggregate production function – suffers from deep internal logical flaws. But the Controversy is only one example of the tensions generated when one insists on modelling social structures as the outcome of adversarial interactions between individuals. Other examples include the Sonnenschein-Mantel-Debreu results and Arrow’s Impossibility Theorem.
As Ben Fine has pointed out, there are well-established results from the philosophy of mathematics and science that suggest deep problems for those who insist on methodological individualism as the only way to understand social structures. Trying to conceptualise a phenomenon such as money on the basis of aggregation over self-interested individuals is a dead end. But economists are not interested in philosophy or methodology. They no longer even enter into debates on the subject – instead, the laziest dismissals suffice.
But where does methodological individualism stop? What about language, for example? Can this be explained as a way for self-interested individuals to overcome transaction costs? The result of this myopia, Fine argues, is that economists ‘work with notions of mathematics and science that have been rejected by mathematicians and scientists themselves for a hundred years and more.’
This brings us back to ‘mathiness’. DeLong characterises this as ‘restricting your microfoundations in advance to guarantee a particular political result and hiding what you are doing in a blizzard of irrelevant and ungrounded algebra.’ What is very rarely discussed, however, is the insistence that microfounded models are the only acceptable form of economic theory. But the New Classical revolution in economics, which ushered in the era of microfounded macroeconomics was itself a political project. As its leading light, Nobel-prize winner Robert Lucas, put it, ‘If these developments succeed, the term “macroeconomic” will simply disappear from use and the modifier “micro” will become superfluous.’ The statement is not greatly different in intent and meaning from Thatcher’s famous claim that ‘there is no such thing as society’. Lucas never tried particularly hard to hide his political leanings: in 2004 he declared, ‘Of the tendencies that are harmful to sound economics, the most seductive, and in my opinion the most poisonous, is to focus on questions of distribution.’ (He also declared, five years before the crisis of 2008, that the ‘central problem of depression-prevention has been solved, for all practical purposes, and has in fact been solved for many decades.’)
As a result of Lucas’ revolution, the academic economics profession purged those who dared to argue that some economic phenomena cannot be explained by competition between selfish individuals. Abstract microfounded theory replaced empirically-based macroeconomic models, despite generating results which are of little relevance for real-world policy-making. As Simon Wren-Lewis puts it, ‘students are taught that [non-microfounded] methods of analysing the economy are fatally flawed, and that simulating DSGE models is the only proper way of doing policy analysis. This is simply wrong.’
I leave the reader to decide where the line between science and politics should be drawn.