When Keynes was Caught on Harrod's Knife Edge

March 8th, 2015
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Fixing the Economists Article of the Week
On Keynes' Short-Period Analysis and Harrod's Dynamics: A Reconciliation

by Philip Pilkington

When I first encountered the Harrod-Domar growth modelI never interpreted it as a long-period representation. It seemed to me such a strange characterisation and, I’ll admit, when I first approached the growth literature that arose out of it I was completely flummoxed.

Follow up:

Let us start with the most basic form of the model itself.


Where I is investment, s is the propensity to save and lower-case sigma is the potential social average productivity. In order for full employment to be maintained the rate of investment — that is, the left-hand side of the equation — must be equal to the propensity to save times the increase in productivity brought about by the increased investment.

If the left-hand side of the equation rises too fast investment will outpace the accumulation of productive capital being built and inflation will result. If the right-hand side of the equation rises too fast savings and productive capacity will increase too quickly and there will be unemployment.

If that is not intuitive enough for the reader consider this. Let us imagine that the growth rate of investment is 5% and the increase in productivity from the last round of investment is 10%. What then will the propensity to save have to be for an equilibrium growth path to be achieved? It will have to be 0.5, of course. This will ensure that half of the increase in productivity goes to consumption and half of it goes to the new investment expenditure that is coming online. (For more examples in this regard see Bill Mitchell’s excellent series of posts).

The manner in which I have just described the equation is how I always saw the model. The model did not tell us where the economy would be at any moment in time. It was just a framework through which to view the world intuitively. Yet after its publication the equation got completely misinterpreted. It began to be thought of as a long-run growth condition. And economists thought that the fact that there was no mechanism in the model for stabilising the left and right-hand side of the equations represented some sort of “problem” to be “solved”. This problem became known as “Harrod’s knife-edge”.

The first to make this mistake was the editor of the journal in which Harrod sought to publish: John Maynard Keynes. Actually, that is unfair to Keynes. The latter was a practical thinking man and he never felt that unsolved or open-ended equation was by necessity some sort of puzzle to be solved. But he did think that Harrod was referring to a long-run problem. In his correspondence with Harrod he wrote (all quotes are taken from Jan Kregel’s excellent paper ‘Economic Dynamics and the Theory of Steady Growth: An Historical Essay on Harrod’s ‘Knife-Edge”):

You have shown I think, that steady growth can only occur as the result of a miracle or intense design. But this is essentially a long-period problem, and steady growth a long-period conception. As I have said above I do not see that the theory has any application worth mentioning to the trade cycle. (p100)

Harrod was completely befuddled by this. He was entirely in agreement that the trade cycle was a short-period phenomenon but he saw his equation as capturing this. Again, he saw it as a tool that showed the conditions in which the economy diverged from a steady state. Harrod was not viewing the equation as some sort of little model of the economy that had to be solved but rather as a tool with which we approach the real world. Kregel summarises in his paper:

Even if the trend did not describe any actual state in the cyclical process, it could still provide an outline for the analysis of the forces that acted to produce cyclical fluctuation. The formulation of the requirements for the existence of a steady trend rate was not meant to imply that such a rate was likely to be achieved in practice. Yet it could provide a reference point to show why steady growth did not exist, i.e. why cycles occured in the real world with such regularity. (ibid)

To me this was always what Harrod’s equation was saying. I found it intuitively hard to see it any other way. When others criticised it for not having a stability condition (when I first studied growth theory) I thought at first I was the idiot and I didn’t understand the equation. But it turns out my intuition was correct.

Understood correctly Harrod’s growth model is a fantastic addition to macroeconomics. And, to me at least, it provides the sort of framework that shuns completely any silly, ‘Kingdom Come’ notion of the so-called “long-run” trajectory path of an economy. A path that only exists in the Wizard of Oz-style fantasies of the economists themselves.

The whole thing got even worse when Bob Solow picked up Harrod’s equation and thought it to be a long-run condition. Solow then tried to argue that flexible wages and prices would lead to a long-run equilibrium result. But even getting away from the question of whether wages and prices are flexible in the long-run, Harrod is talking about the short-run. He is giving us an intuitive sense of how income and potential income diverge from one another. The picture of a capitalist economy that he gives is the same one that Keynes put forward in his letter to Harrod where he wrote:

The maintenance of steady growth is at all times an inherent improbability in conditions of laissez-faire. (p100)

What Keynes unfortunately failed to realise was that Harrod’s equation gave us a tool to make precisely that case. But growth theory unfortunately soon became a field of silly people trying to prove long-run equilibrium results and, in doing so, convincing themselves that they had said something of relevance about the real world.

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