As promised in my previous post, I am going to begin providing a restatement or paraphrase of, plus some commentary on, Earl Thompson’s important, but unpublished, paper “A Reformulation of Macroeconomic Theory.” It will take a number of posts to cover the main points in the paper, and I will probably intersperse posts on Earl’s paper with some posts on other topics. The posts are not written yet, so it remains to be seen how long it takes to go through it together.
The paper begins by identifying “four basic difficulties in received [i.e., Keynesian] theory.” In this post, I will discuss only the first two of the four that are listed, the two that undermine the theoretical foundations of the IS-LM model. The other two problems involve what Earl considered to be inconsistencies between the implications of the IS-LM model and some basic stylized facts of macroeconomics and business cycles, which seem to me less fundamental and less compelling than the two flaws he identified in the conceptual foundations of IS-LM.G
The first difficulty is that the Keynesian model assumes both that the marginal product of labor declines as workers are added and that every worker receives a real wage equal to his marginal product. Those two assumptions logically entail the existence of a second scarce factor of production – call it capital – to absorb the residual between total output and total wages. But even though investment as a category of expenditure is a critical variable in the Keynesian model, the status of capital as a factor of production is unacknowledged, while the rate of interest is determined independently of the market for capital goods by a theory of liquidity preference and the equality between savings and investment. A market for bonds is implicitly acknowledged, but, inasmuch as Walras’s Law allows one market to be disregarded, the bond market is not modeled explicitly. The anomaly of an interest rate in a static, one-period model has been noted, but the inconsistency between the conventional Keynesian model IS-LM model with the basic neoclassical theory of production and factor pricing has been glossed over by the irrelevant observation that Walras’s Law allows the bond market to be excluded, as if the bond market were a proxy for a market for real capital services.
How can the inconsistency between the Keynesian model and the neoclassical theory of production and distribution be reconciled? The simplest way to do so is to treat the single output as both a consumption good and a factor of production. This amounts to treating the single output as a Knightian crusonia plant. If used as a consumption good, the plant is purchased and consumed; if used as a factor of production, it is hired (implicitly or explicitly) at a rental price equal to its marginal product. The ratio of the marginal product of a unit of capital to its price is the real interest rate, and that ratio plus the expected percentage appreciation of the money price of the capital good from the current period to the next is the nominal interest rate. This is a basic property of intertemporal equilibrium. The theory of liquidity preference cannot contradict, but must be in accord with, this condition, something that Keynes himself recognized in chapter 17 of the General Theory and again in his 1937 paper “The General Theory of Employment.”
It is worth quoting from the latter paper at length, as Duncan Foley and Miguel Sidrauski did in their important 1970 article “Portfolio Choice, Investment, and Growth,” cited by Thompson as an important precursor to his own paper. Here is Keynes:
The owner of wealth, who has been induced not to hold wealth in the shape of hoarded money, still has two alternatives between which to choose. He can lend his money at the current rate of money-interest or he can purchase some kind of capital asset. Clearly in equilibrium these two alternatives must offer an equal advantage to the marginal investor in each of them. This is brought about by shifts in the money prices of capital assets relative to money loans. The prices of capital assets move until, having regard to their prospective yield and account being taken of all those elements of doubt and uncertainty interested and disinterested advice, fashion, convention, and what else you will, which affect the mind of the investor who is wavering between one kind of investment and another. . . .
Capital assets are capable, in general, of being newly produced. The scale on which they are produced depends, of course, on the relation between their costs of production and the prices which they are expected to realize in the market. Thus if the level of the rate of interest taken in conjunction with opinions about their prospective yield raise the price of capital assets, the volume of current investment (meaning by this the value of the output of newly produced capital assets) will be increased; while if, on the other hand, these influences reduce the prices of capital assets, the volume of current investment will be diminished.
Thus, Keynes clearly recognized that the volume of investment could be analyzed as the solution of a stock-flow problem with a given cost of producing capital assets in relation to the current and expected future price of capital assets. The solution of such a problem involves an equilibrium in which the money rate of interest must equal the real rental rate of capital services plus the expected rate of appreciation of capital assets. But nothing in the IS-LM model constrains the rate of interest to satisfy this condition.
Earl sums up this discussion compressed into a single paragraph at the beginning of his paper as follows:
An inconsistency thus appears within the received [i.e., IS-LM] theory once we recognize the necessity of a market for the services of a non-labor input, a recognition which amounts to adding an independent equilibrium equation without adding a corresponding variable.
In other words, the IS-LM model implies one interest rate, and the neoclassical theory of production and distribution implies another, and there is no new variable defined that could account for the discrepancy. Earl goes on to elaborate in a long footnote.
Numerous authors have pointed out the inconsistency of Keynesian interest theory with neoclassical marginal productivity theory. But they have not seen the need for the extra equation describing equilibrium in the capital services market, and thus they have not regarded the inconsistency as a direct logical threat to Keynesian models. Rather, they have unfortunately been satisfied, at least since the classic paper of Lerner, with a conjecture that the difference in interest rates vanishes when there are increasing costs of producing capital relative to consumption goods. The error in this conjecture, an error first suggested by Stockfish and fully exposed very recently by Floyd and Hynes, is simply that increasing costs of producing investment goods will not generally permit the interest rate determined by marginal productivity theory to vary in a Keynesian fashion.
In other words, the negative-sloping IS curve will be replaced by a corresponding (FF) curve, representing equilibria in the labor and capital-services markets, that is upward-sloping in terms of interest rates and price levels. The footnote continues:
A legitimate way to account for the difference in interest rates would be to follow Patinkin in assuming the presence of “bonds” which receive the “rate of interest” referred to in the standard theory, a rate of interest which differs from the money rate of return on real capital because of positive transactions costs in the process of lending to owners of capital. But received macroeconomic theory would still be inconsistent with marginal productivity theory because of arbitrage between the two interest rates, where the transactions costs in the process of lending to owners of capital will determine the relationship between the rates. This arbitrage would provide a constraint on the behavior of the bond rate which . . . is generally not satisfied in standard formulations.
The point here is that the interest rate on bonds is not determined in a vacuum. The interest rate on bonds is an epiphenomenon reflecting the deeper forces that determine the rate of return on real capital. Without an underlying market for real capital, the rate of interest on bonds would be indeterminate. Once the real rate of return of capital is determined, the rate of return on bonds can vary only within the limits allowed by the transactions costs of lending and borrowing by financial intermediaries. The footnote concludes with this observation:
Finally, there would be no difference in interest rates, and no extra equation, if the implicit market excluded with Walras’ law in a Keynesian model were simply a capital services market. However, this interpretation of a Keynesian model is inconsistent with the rest of the model.
What Thompson means here is that suppose we had a complete theoretical description of an economy consistent with the neoclassical theory of production and distribution, and we also had a complete description of the Keynesian expenditure functions for consumption and investment. It would then be legitimate, in accordance with Walras’s Law, to exclude the market for capital services, rather than, as Thompson proposes to do, to exclude the expenditure functions. If so, what is all the fuss about? And Earl’s answer is that in order to render the Keynesian income-expenditure model consistent with the excluded market for capital services, we would have to modify the Keynesian income-expenditure model into a two-period framework with an explicit solution for the current and expected future price level of output, implying that the expected rate of inflation would become an equilibrating variable determined as part of the solution of model. Obviously that would not be the Keynesian IS-LM model with which we are all familiar.
I hope this post will serve as a helpful introduction to how Thompson approached macroeconomics. The next post in this series (but not necessarily the next post on this blog) will discuss the concept of temporary equilibrium and Keynesian unemployment.