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I am going to begin providing a restatement or paraphrase of, plus some commentary on, Earl Thompson’s important, but unpublished, paper “A Reformulation of Macroeconomic Theory.”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.
Uneasy Money 
David
But the deeper preferences behind the real rate of return on capital are simply time preference and the marginal efficiency of capital, i.e it is analogous to the Wicksellian natural rate. The Keynesian theory of interest, whether liquidity preference in the form of the speculators of the Treatise, or the more naive money demand of the GT, is a theory of the market rate of interest. To say that the market rate must vary as per the natural rate within the bounds of transaction costs is to presume that the economy has a tendency to automatically revert of S-I equilibrium with a smooth and ‘appropriate’ adjustment of real output and growth path, and with no involuntary unemployment, if not for some minor nominal rigidities.
It’s the kind of model which results in the dreary capital controversy debates, which I believe are quite irrelevant now that we live in a Jim Tobin-Fischer Black economy, where these transaction costs, asset specificity, capital heterogeniety etc. can all be priced in through a system of risk free return, systemic risk, and idiosyncratic risk.
So reformulating in the no-arbitrage conditions of modern finance, it is to assume the existence of a Fischer Black general equilibrium. And a Black GE necessarily ignores liquidity preference, even in the Tobin sense of liquidity preference as aversion to risk.
The Keynesian insight, which admittedly gets lost in IS/LM – as well as in the modern reliance on financial markets sorting out all our problems – is that the market for bonds has a life of its own, and rather than being bounded by the ‘real’ market for capital services, it might in some situations create the bounds on the market for capital services, where the resulting no-arbitrage condition and factor price equalization is achieved by a drop in output and unemployment.
The shape of the IS curve is irrelevant – indeed one can generate a Keynesian liquidity trap and involuntary unemployment with a horizontal IS curve – what maters is whether the LM curve is horizontal-ish, when the Keynesian claim dominates, or whether it is about 45 degrees or above, where the classical model dominates.
In this formulation, I would stick with the Leijonhufvud-ian disagreement with IS/LM, which is that shifts in one curve cannot be presumed to leave the other curve unchanged.
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To put it differently, here the various positions :
1) Neoclassical, including Thompson : There is a natural rate, and the market rates is bounded by this natural rate.
2) Cambridge Keynesian/ Post-Keynesian : There is a market rate, but it is uninteresting. There are multiple rates of capital return, so what is all this talk about a natural rate. The two are determined separately, and thus there are two price levels.
3) Fischer Black-ian : There is a market rate, and the market is right, so whatever the natural rate is, it can be inferred from the market rate.
4) Wicksell-Keynes-Tobin-Leijonhufvud : There are market rates and there are natural rates. The two may or may not be in accordance, depending upon the specific circumstance.
IS/LM is couched in Walrasian language, yes, so it misses the Marshallian point that it is trying to convey, namely the relative primacy of the adjustment mechanisms between interest rates and income.
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I don’t wish to be rude, but “Clearly in equilibrium these two alternatives must offer an equal advantage to the marginal investor in each of them”
just sounds, if you will pardon the expression, like ivory tower nonsense.
I mean, how on earth do you know if a new tractor (cap good) is the same as a bond ?
The “price signals” – the tractor price and interest rate – aren’t really that useful, given the huge uncertainty in the rate of return from the tractor
I think in the real world people have a wing and a prayer, rather then equilibrium logic
or am I just a clueless non economist who is missing hte point totally ?
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Ritwik, We are obviously engaged in a very abstract modeling exercise. But in this exercise, with a single homogeneous output that can be consumed or put to work as a factor of production, the real interest rate is determined entirely by the productivity of capital as an input, which in turn depends on how much labor is being applied, the more labor is applied, the greater the marginal product of capital. If labor is being withheld because of incorrect expectations of future wages, that qualifies, under Keynes’s own definition of the term, as involuntary unemployment. There is no Keynesian model, by the way, in which equilibrium does not correspond to S = I. The question is whether the level of output and income corresponding to that equilibrium is consistent with full employment. But the equilibrium condition is always S = I.
To get to the Fischer Black equilibrium in the Thompson model, you need a competitive money supply that ensures that there a predictable price (actually wage) level that eliminates the possibility of incorrect wage expectations. But that is not the monetary system Keynes or the Keynesians were assuming. Nor would a gold standard do the trick because of the possibility of unpredictable fluctuations in the value of gold owing to cyclical variations in the monetary demand for gold. Thompson actually shows that the standard LM curve may imply an unstable low-inflation equilibrium in which the economy is at risk of an unbounded deflationary contraction. I’ll be discussing that case in a subsequent post.
Whether the bond market has a life of its own that is disconnected from the market for real capital is an interesting question. Thompson was working with a pretty extreme version of the neoclassical theory of production and distribution, so there is certainly room to relax his assumptions, but most economists would be reluctant to explicitly adopt a model that is flatly inconsistent with neoclassical theory.
I wouldn’t say that the shape of the IS (or its analogue in Thompson’s model) is irrelevant. You get very different implications about the cyclical behavior of interest rates depending on the slope of IS.
About the natural rate, Thompson is perfectly consistent with Keynes. There are as many natural rates as there are levels of employment. The more employment there is, the higher the natural rate.
Ezra, Just so we are all clear, you are quoting Keynes, not me. Every business decision about undertaking any new investment project (buying a capital good) involves some estimate of the cash flow the asset will generate over time and then discounting it by an appropriate discount rate. That exercise generates some estimate of the present value of the capital good and, thus, governs how much the business is prepared to spend on acquiring the capital good. So the disconnect between everyday business decisions and the abstract theory so eloquently articulated by Keynes is not as outlandish as you suggest. On the other hand, I agree that the theory is operating at a very high level of abstraction. It’s ivory tower to be sure, but not necessarily nonsense.
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David
Interesting explanation of a drop in the natural rate being isomorphic to incorrect wage expectations. This is interesting, and does explain Keynesian unemployment, but I wouldn’t say it is consistent with Keynes, whose MEC should be exogenous to the model, rather than ‘wherever the labour supply curve wants it to be’.
In this model, the capital stock should go on accumulating smoothly, with changes in the output path resulting in different real rates of return. Investment could still vary a lot, as rates of return on capital are of the order of 10% or less, so a small dip in the accumulation of capital may be a large dip in investment. The Keynesian/Kaleckian fact has thus been explained, but the causality is reversed between spending and investment. The capitalist is not the master of his own fate – the worker is the master of his own fate!
Interesting also that a Black GE would require a competitive money supply. Here is Black postulating a competitive private-sector determined money supply, even in the presence of a monopoly issuer of currency/reserves :
“In the U.S. economy, much of the public debt is in the form of Treasury bills. Each week, some of these bills mature, and new bills are sold. If the Federal Reserve System tries to inject money into the private sector, the private sector will simply turn around and exchange its money for Treasury bills at the next auction. If the Federal Reserve withdraws money, the private sector will allow some of its Treasury bills to mature without replacing them” (From his wikipedia page, in a letter to Friedman in 1972)
Thus, Black has turned the tables around again – the market is right, so whatever are the wage/ output expectations that the market is telling you, through its decision to reflux or not, are ‘correct’. The natural rate, whatever it is, can be inferred from the market!
About IS/LM stability, I think you’d get an unstable equilibrium whenever the slope of the LM curve is lower than the IS curve. And any cyclical behaviour of interest rates is explainable, with almost any shape of the IS curve, as long as you allow both curves to fluctuate in the business cycle. The important bit if to remember which interest rate we’re taking about. Too often, we forget that we draw IS/LM in (Y, rb = real rate on bonds) space, and then start explaining the pro-cyclicality (or not) of rm = nominal rate on money. Federal funds are not bonds, they’re money. Similarly, an interest rate setting central bank does not make the LM curve horizontal, nor does an NGDP targeting central bank make the LM curve vertical.
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The more posts I read about IS-LM, the more I become convinced that “the Keynesian IS-LM model with which we are all familiar” doesn’t actually exist. It seems that no two people have the same model in mind. I’ve never regarded IS-LM as a one-period model; if it were, then of course the presence of an interest rate would be anomolous. At a minimum you need two periods, with the second being called the future or “the long run”, in which we may all be dead, but for which we must nonetheless plan. A property developer can only justify the huge cost of building a skyscraper on the assumption that it will continue to earn rents long after the builders have died.
In my world, IS-LM is the model Hicks constructed to enable students to get to grips with Keynes. When the student has read the GT the limitations of IS-LM are obvious enough. The big weakness is that almost any shock to the state of long-term expectations will shift both curves, since it will affect both the MEC schedule and the liquidity preference schedule. In that sense it’s usually better to think in terms of an explicit two-period model with sticky prices (and/or wages) in the first period. Such a model will always have an IS-LM representation, but everyone who looks at it will say: that’s not what I mean by IS-LM!
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David, great, thought-provoking post! Are you’re assuming a one-good model throughout your argument above? If you add heterogenous capital goods, the marginal productivity theory won’t work because you can’t determine the quantity of capital without recourse to the rate of interest or some other surrogate.
You write, “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.”
For Keynes, this is exactly backwards. Once the rate of interest is determined, investment proceeds until the MEC equals the interest rate (with adjustment for risk). Saving and investment are always equal given Keynes’s definition of income; the rate of interest doesn’t bring them into balance.
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Ritwik, Granted, the scope for MEC to vary is limited, but changes in inflation expectations imply changes in the yield from holding capital as opposed to consuming it, do that is one way to get the MEC to change. Moreover changes in expected inflation were explicitly mentioned by Keynes in the GT as a factor causing MEC to shift.
I don’t think I understand your second paragraph. I think that Black and Thompson were pretty close. On money, what Black missed was Thompson’s taxation argument for why bonds (which are not accepted for tax payments) are not perfect substitutes for currency.
Kevin, I agree with you that IS-LM has to be understood in the context of a two-period model, but the question is whether if we are in fact working with a 2-period model, IS-LM is a good representation of the relevant variables.
Greg, Thanks. Yes, it is a one-good model. That’s the only way to avoid the index number problem in measuring capital. Even a two-good model with one consumption good and one capital good becomes very much harder to work with. You are right that Keynes would argue that liquidity preference determines the interest rate and the rest of the economy adjusts, but unless you are in a liquidity trap, the interest rate must depend on non-monetary factors as well, so I think that Keynes was indulging in characteristic hyperbole in saying that interest is determined strictly by liquidity preference.
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Dear David
The post is indeed very illuminating. But I have one basic doubt. You are taking about fitting a neoclassical growth model into a framework of IS-LM which has nominal rigidities.Since in your growth framework wages equal marginal product, markets will always clear in this framework. Hence how is this suitable for explaining residual prductivity attributed to capital in a basic keynesian model with wage rigidity? I get the basic idea that IS-LM framework does not have any constraint that makes interet rate solution coming out of this framework convergent with that in asset allocation market, but can the neoclassical growth model can capture the basic flavour of keynesian rigidity?
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Indy, You say,
“Since in your growth framework wages equal marginal product, markets will always clear in this framework.”
Doesn’t Keynes also assume that workers receive wages equal to their marginal product? When you say that markets always clear, that’s only true in the sense of temporary equilibrium. But it is not a full equilibrium because workers’ wage expectations are overly optimistic. So while you call it market clearing, it might also be thought of as sticky wages. So I think that at a certain level, it does capture what we think of as a Keynesian phenomenon, albeit in a very abstract framework. The model in its simplicity may not be rich enough to be capture everything that we would like it to have.
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David, although Keynes did say wages equal labor’s marginal product, this seems inconsistent with other aspects of the GT. In particular, Keynes argued that firms and labor bargain over the nominal wage, which means that workers’ real wages will be determined “later” by the prices of wage goods, which neither workers nor entrepreneurs can possibly know in advance. In addition, firms don’t know how much output they can sell at the time they’re hiring. So, it would seem, to me at least, that wages would equal labor’s marginal product only by accident.
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“…wages would equal labor’s marginal product only by accident.”
Money wages will equal the value of marginal product if short-term expectations are fulfilled. That’s Keynes’s equilibrium condition, in effect. So of course it doesn’t imply full employment. It merely implies that the market for current output is in equilibrium.
It’s not an accidental state of affairs; if expectations are not being fulfilled then firms have an incentive to adjust output levels.
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Kevin, I don’t disagree. Perhaps I should have said that, although Keynes assumes in parts of his argument that expectations are fulfilled, the thrust of the GT is that, given the subject matter of these expectations, they are only likely to be fulfilled by accident, i.e., unlikely to be fulfilled.
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