Sraffian Economics

One of the most fascinating schools of thought out there is Sraffian economics. It has had a big impact on historical debates but has relatively few modern adherents, and though it is often associated with Keynesianism it is surprisingly different. I want to offer a comment on Sraffian economics and why I ultimately see it as a negative enterprise: a tool for critiquing economic theory rather than a basis for explanation or prediction of the real economy. This blog will be unusual for the ‘pluralist showcase’ series because it is primarily theoretical rather than empirical, but Sraffian economics has made me reflect on the purpose of theory and how much it can affect empirical investigations. It was also sparked by an email I received from a blogger named Robert Vienneau introducing his new book on Sraffian economics, which details the technical ins and outs of the framework about as comprehensively as anyone could imagine.

Sraffian economics is a school of thought which is (unsurprisingly) associated with the economist Piero Sraffa. Sraffa produced a number of lasting contributions including his seminal 1926 critique of perfect competition; a famous review of Friedrich Hayek’s ill-fated 1931 book Prices and Production; and a full collection of the works of the classical economist David Ricardo. His own framework was presented in his 1960 magnus opus Production of Commodities by Means of Commodities and was clearly influenced by his previous contributions. Sraffa presented an alternative way of viewing the economic system which played a huge role in the famous Cambridge Capital Controversies (which is this post is ostensibly not about!) and went on to spawn an entire school of economics.

Classical economists like Ricardo, Smith, and Marx had always focused on the reproduction of society: has society produced enough to keep itself going? Economically, this can be formulated as whether industries (as well as labour) have sufficient inputs to produce the same level of output they did in the previous year, or to “self-replace” as Sraffa put it. To illustrate this, imagine that the economy only produces iron and wheat, and each of these require only iron and wheat to be produced. Let’s say 280 quarters of wheat and 12 tons of iron are used to produce 400 quarters of wheat; while 120 quarters of wheat and 8 tons of iron are used to produce 20 tons of iron. According to Sraffa, a year’s worth of production can be expressed as:

280qr. wheat + 12t. iron—> 400 qr. wheat

120 qr. wheat + 8t. iron—> 20 t. iron

You can see here that the amount of wheat and iron produced is just enough to allow production to continue into next year, because the total inputs add up to the total outputs. The farmer can keep 280 quarters of his wheat and trade the other 120 with the mining company, while they can keep 8 tons of their iron and trade the remaining 12 with the farmer. It follows that the exchange ratios – prices – must be 120 quarters wheat for every 12 tons of iron, or to simplify 10:1 wheat to iron.

It is possible to extend this to however many products you can think of, including labour and an allowance for profits or ‘surplus’. Mathematically this just entails the use of matrix algebra, which is conceptually simple even if computationally tricky. Sraffa also extended his system to include things like fixed capital, natural resources, essential versus non-essential commodities, and cases where there are multiple techniques for producing the same thing (in the above example, each commodity can only be produced one way).

Sraffa showed that his framework has a number of intriguing properties, all of which are completely contrary to the neoclassical approach. First was that the split between wages and profits was determined outside the system, rather than having any relationship to productivity. Sraffa thought that this showed the distribution of income was a matter of political power rather than objective economic conditions. Second was that prices were determined by the requirements of production – above, the economy had to keep producing 20 tons of iron and 400 quarters of wheat to self-sustain – rather than being related to supply and demand. These are both dramatic conclusions, but the third aspect of Sraffa’s framework is probably the most controversial: reswitching.

Neoclassical economics assumes a ‘production function’, where output is made from a combination of capital and labour using a production technique. Given this method of production, a higher rate of profit will induce capitalists to invest more in their production technique. This is simple and intuitive, but it’s also totally wrong. Sraffa showed using complicated mathematical examples a technique which is optimal for firms when profit rates are low becomes suboptimal when profits rise, only to once again become optimal when profits rise even higher. In other words, a technique having a higher rate of profit could result in capitalists moving away from the technique! Robert Vienneau’s aforementioned book (which unfortunately I am not able to share with you) details all manner of contrary cases, showing mathematically that reswitching arises in various shapes and sizes.

Unlike other aspects of Sraffa’s framework, reswitching can be tested empirically and maybe this is why it has been the focal point of the debate. Most empirical tests have failed to find confirmatory evidence for reswitching, which has become the main refrain of those few mainstream economists who are aware of Sraffian economics. However, Vienneau references a couple of recent examples which demonstrate that reswitching exists in the real world. Zonghie and Schefold (2006) show that it is demonstrated in about 4% of cases, while Zambelli (2017) uses a different technique and data to show that it is much more prevalent, occurring in a majority of cases. Another example which makes reswitching seem less esoteric is when higher wages actually result in the hiring of more labour, which Vienneau relates to modern empirical findings that the minimum wage does not reduce employment.

What’s the Point of All This?

Usually in this series I would present the evidence in a little more detail and leave it there. But Sraffian economics and the debates surrounding it throw up some interesting questions about how we use evidence and theory in social sciences and I’d like to explore them. An interesting part of the Zonghie and Schefold paper is where they note that methods of production may be selected for reasons outside either neoclassical or Sraffian economists: for example, the benefits of firms associating together and copying one another’s techniques (think Silicon Valley) could fix industries at a certain technology even if reswitching were optimal according to the theory. It was for this reason that Joan Robinson viewed empirical tests of reswitching as futile:

“Nothing could be more idle than to get up an argument about whether reswitching is likely to be found in reality. Even if there was such a thing as a pseudo-production function, there would be no movement along it to pass over switchpoints, and furthermore, in reality, there is no such thing as a pseudo-production function.”

In order to truly test reswitching we would need to precisely estimate the production function, be confident enough that its properties held for the period under examination, then test whether the predicted pattern of production technique held or not in the face of independent fluctuations of profits and wages. This is simply too much to ask of the data in social sciences, so the aforementioned ‘tests’ amount to little more than looking for oddities in the economy. The bottom line is that whatever we observe is probably some incomprehensible combination of neoclassical mechanics, reswitching, agglomeration, bounded rationality, and plenty of other things outside our purview. We should not be surprised that empirical results are mixed depending on the choice of technique, nor should we expect them to be otherwise.

There’s no denying that Piero Sraffa was a genius. But given these complications I wonder about modern attempts to turn his framework into a positive basis for economic enquiry. There are methodological objections one could make to Sraffian economics: for one, the condition that the economy reproduces itself may have intuitive or even moral appeal, but interpreted straightforwardly it is obviously wrong. Society does not reproduce itself completely or even approximately: firms and industries vanish; organisations and families face cutbacks; and people pass away. In this the Sraffian condition of reproduction reminds me of the equilibrium condition of neoclassical economics, where markets or even the whole economy are presumed to settle at an unchanging point over the long run. This tendency is not observed in real markets where price, quantities, and products are constantly changing; or in entire economies, which are beset by fluctuations.

Sraffa’s conclusion that prices are not set by demand and supply has also been criticised on the grounds that he doesn’t allow them to. For example, the Austrian economist Robert Murphy once wrote:

“Despite his interesting approach and clever results, Sraffa does not succeed in overthrowing marginal value theory. Rather than replacing the modern focus on subjective decisions made on the margin, Sraffa simply assumes them away. For example, in the simplest case of a subsistence economy, Sraffa just takes it for granted that the people in this economy will continue to produce 400 quarters of wheat and 20 tons of iron every period, forever. But why should they do this? Suppose the people don’t like iron or wheat! Or, more to the point, suppose the people discover a better use for their stocks of iron and wheat than to simply make more iron and wheat. How are the people supposed to break out of their subsistence mode in Sraffa’s world?”

Murphy is right that Sraffa’s system excludes consumer preferences at its base, but he frames his critique as a limitation of Sraffian economics in particular rather than of economic theory in general. We could equally charge that while Sraffian economics assumes away consumer preferences and demand, both neoclassical and Austrian economics assume away the issue of social reproduction and subsistence. All of these tend to assume away Marxist class struggle, or Keynesian liquidity preference. Such features may have some importance for explaining the world, but that importance cannot be established by theories (mathematical or otherwise) which assume their centrality while omitting the others. Murphy states that there is ideological appeal to the notions espoused in Sraffian theory, especially as the idea that profits and wages are arbitrary, not a reward for productivity is endorsed by labour unions. Once again he is correct, but less introspective how ideology might affect his support for Austrian economics.

This is why I ultimately view Sraffian economics as a negative enterprise. I am not the first person to emphasise the subtitle of his book: ‘Prelude to a Critique of Economic Theory’.  Neoclassical economists have proven that they can create a vast mathematical edifice with some appealing features and have used it to derive both scientific predictions and policy implications. Sraffa showed that he too could create such an edifice, only this time the predictions and policies were completely different. Sraffian economics has also been used to critique the Marxist labour theory of value, showing its status as a potent weapon for illustrating logical possibilities contrary to those assumed by other approaches.

When empirical tests are too uncertain to resolve these difficulties, how do we choose which method is best? Maybe economic theories are more like philosophical frameworks than we like to think and these differences can never be resolved. But if we are to try we need to talk about values, assumptions, and methodology – all things that mainstream economists like to avoid. In this sense Sraffa’s contribution was both smaller and larger than his adherents often claim. Smaller because it cannot form the basis of a positive framework for understanding the real economy. But larger because it has shown that many high-level tests of theoretical frameworks – especially in macroeconomics – may not do what they are purported to do, and economists cannot escape asking deeper questions about the frameworks they use.