Tyler Cowen recently posted a diatribe against the idea monetary policy should be conducted by setting the interest rate target of the central bank at or near the natural rate of interest. Tyler’s post elicited critical responses from Brad DeLong and Paul Krugman among others. I sympathize with Tyler’s impatience with the natural rate of interest as a guide to policy, but I think the scattershot approach he took in listing, seemingly at random, seven complaints against the natural rate of interest was not the best way to register dissatisfaction with the natural rate. Here’s Tyler’s list of seven complaints.

1 Knut Wicksell, inventor of the term “natural rate of interest,” argued that if the central bank set its target rate equal to the natural rate, it would avoid inflation and deflation and tame the business cycle. Wicksell’s argument was criticized by his friend and countryman David Davidson who pointed out that, with rising productivity, price stability would not result without monetary expansion, which would require the monetary authority to reduce its target rate of interest below the natural rate to induce enough investment to be financed by monetary expansion. Thus, when productivity is rising, setting the target rate of interest equal to the natural rate leads not to price stability, but to deflation.

2 Keynes rejected the natural rate as a criterion for monetary policy, because the natural rate is not unique. The natural rate varies with the level of income and employment.

3 Early Keynesians like Hicks, Hansen, and Modigliani rejected the natural rate as well.

4 The meaning of the natural rate has changed; it was once the rate that would result in a stable price level; now it’s the rate that results in a stable rate of inflation.

5 Friedman also rejected the natural rate because there is no guarantee that setting the target rate equal to the natural rate will result in the rate of money growth that Freidman believed was desirable.

6 Sraffa debunked the natural rate in his 1932 review of Hayek’s *Prices and Production*.

7 It seems implausible that the natural rate is now negative, as many exponents of the natural rate concept now claim, even though the economy is growing and the marginal productivity of capital is positive.

Let me try to tidy all this up a bit.

The first thing you need to know when thinking about the natural rate is that, like so much else in economics, you will become hopelessly confused if you don’t keep the Fisher equation, which decomposes the nominal rate of interest into the real rate of interest and the expected rate of inflation, in clear sight. Once you begin thinking about the natural rate in the context of the Fisher equation, it becomes obvious that the natural rate can be thought of coherently as either a real rate or a nominal rate, but the moment you are unclear about whether you are talking about a real natural rate or a nominal natural rate, you’re finished.

Thus, Wicksell was implicitly thinking about a situation in which expected inflation is zero so that the real and nominal natural rates coincide. If the rate of inflation is correctly expected to be zero, and the increase in productivity is also correctly expected, the increase in the quantity of money required to sustain a constant price level can be induced by the payment of interest on cash balances. Alternatively, if the payment of interest on cash balances is ruled out, the rate of capital accumulation (forced savings) could be increased sufficiently to cause the real natural interest rate under a constant price level to fall below the real natural interest rate under deflation.

In the Sraffa-Hayek episode, as Paul Zimmerman and I have shown in our paper on that topic, Sraffa failed to understand that the multiplicity of own rates of interest in a pure barter economy did not mean that there was not a unique real natural rate toward which arbitrage would force all the individual own rates to converge. At any moment, therefore, there is a unique real natural rate in a barter economy if arbitrage is operating to equalize the cost of borrowing in terms of every commodity. Moreover, even Sraffa did not dispute that, under Wicksell’s definition of the natural rate as the rate consistent with a stable price level, there is a unique natural rate. Sraffa’s quarrel was only with Hayek’s use of the natural rate, inasmuch as Hayek maintained that the natural rate did not imply a stable price level. Of course, Hayek was caught in a contradiction that Sraffa overlooked, because he identified the real natural rate with an equal nominal rate, so that he was implicitly assuming a constant expected price level even as he was arguing that the neutral monetary policy corresponding to setting the market interest rate equal to the natural rate would imply deflation when productivity was increasing.

I am inclined to be critical Milton Friedman about many aspects of his monetary thought, but one of his virtues as a monetary economist was that he consistently emphasized Fisher’s distinction between real and nominal interest rates. The point that Friedman was making in the passage quoted by Tyler was that the monetary authority is able to peg nominal variables, prices, inflation, exchange rates, but not real variables, like employment, output, or interest rates. Even pegging the nominal natural rate is impossible, because inasmuch as the goal of targeting a nominal natural rate is to stabilize the rate of inflation, targeting the nominal natural rate also means targeting the real natural rate. But targeting the real natural rate is not possible, and trying to do so will just get you into trouble.

So Tyler should not be complaining about the change in the meaning of the natural rate; that change simply reflects the gradual penetration of the Fisher equation into the consciousness of the economics profession. We now realize that, given the real natural rate, there is, for every expected rate of inflation, a corresponding nominal natural rate.

Keynes made a very different contribution to our understanding of the natural rate. He was that there is no reason to assume that the real natural rate of interest is unique. True, at any moment there is some real natural rate toward which arbitrage is forcing all nominal rates to converge. But that real natural rate is a function of the prevailing economic conditions. Keynes believed that there are multiple equilibria, each corresponding to a different level of employment, and that associated with each of those equilibria there could be a different real natural rate. Nowadays, we are less inclined than was Keynes to call an underemployment situation an equilibrium, but there is still no reason to assume that the real natural rate that serves as an attractor for all nominal rates is independent of the state of the economy. If the real natural rate for an underperforming economy is less than the real natural rate that would be associated with the economy if it were in the neighborhood of an optimal equilibrium, there is no reason why either the real natural rate corresponding to an optimal equilibrium or the real natural rate corresponding to the current sub-optimal state of economy should be the policy rate that the monetary authority chooses as its target.

Finally, what can be said about Tyler’s point that it is implausible to suggest that the real natural rate is negative when the economy is growing (even slowly) and the marginal productivity of capital is positive? Two points.

First, the marginal productivity of gold is very close to zero. If gold is held as bullion, it is being held for expected appreciation over and above the cost of storage. So the ratio of the future price of gold to the spot price of gold should equal one plus the real rate of interest. If you look at futures prices for gold you will see that they are virtually the same as the spot price. However, storing gold is not costless. According to this article on Bloomberg.com, storage costs for gold range between 0.5 to 1% of the value of gold, implying that expected rate of return to holding gold is now less than -0.5% a year, which means that the marginal productivity of real capital is negative. Sure there are plenty of investments out there that are generating positive returns, but those are inframarginal investments. Those inframarginal investments are generating some net gain in productivity, and overall economic growth is positive, but that doesn’t mean that the return on investment at the margin is positive. At the margin, the yield on real capital seems to be negative.

If, as appears likely, our economy is underperforming, estimates of the real natural rate of interest are not necessarily an appropriate guide for the monetary authority in choosing its target rate of interest. If the aim of monetary policy is to nudge the economy onto a feasible growth path that is above the sub-optimal path along which it is currently moving, it might well be that the appropriate interest-rate target, as long as the economy remains below its optimal growth path, would be less than the natural rate corresponding to the current sub-optimal growth path.

“We now realize that, given the real natural rate, there is, for every expected rate of inflation, a corresponding nominal natural rate.”

Did you mean here that the real natural rate (whatever the usefulness of such concept) is independent of the rate of inflation? Although that might be the case in simple models, it would not be generally true. If inflation expectations rise with an equal increase in the nominal rate, the payment rate (coupon rate?) on some financial assets will rise. But for many assets, the payment rate will be fixed, so the value of the asset will fall instead. This has distribution consequences and potential real effects, notwithstanding that those real effects might not appear in simple representative agent models.

“First, the marginal productivity of gold is very close to zero. If gold is held as bullion, it is being held for expected appreciation over and above the cost of storage. So the ratio of the future price of gold to the spot price of gold should equal one plus the real rate of interest.”

Probably something basic, but why not:

“So the ratio of the future price of gold to the spot price of gold should equal one plus the cost of storage plus the real rate of interest.”

David,

I understand why you prefer to use the Fisher Equation as the basis for your discussion, however, as argued here, http://www.creditcapitaladvisory.com/2014/09/04/swedish-perspective-equilibrium-level-interest/ the Fisher Equation is more useful if an economy works as the model assumes it should. Ie that investment will continue to be made until the rate of return on capital equals the cost of capital. But there is very little evidence that this is indeed the case in most industries, with the possible exception of industries such as apparel with very low barriers to entry.

Hence the way our economy currently functions does not accord with your assumption that at any moment there is some real natural rate toward which arbitrage is forcing all nominal rates to converge. (Eg. Retail sector 5% ROC vs rating agencies 50% ROC) – Regulatory systems largely prevent this kind of stuff happening, although if we did have perfectly efficient markets then I would certainly agree with your point.

For every expected rate of inflation (given any real natural rate) there is a corresponding nominal natural rate only if the return on capital converges with the cost of capital. We can understand quite a lot about what is happening in the economy from the bond market – but it doesn’t tell you what the return on capital minus the cost of capital is from which estimates of the marginal productivity of capital can be generated. That is determined from aggregating up company accounts information as Wicksell implied in Interest and Prices, an idea subsequently developed by Myrdal in Monetary Equilibrium.

Empirical analysis shows that the marginal return on capital has been rising since 2011 (chart 2 in link) – which in turn has driven future profit growth and equity valuations. Hence I disagree with your statement that between 2011 and 2014 “At the margin, the yield on real capital seems to be negative.” There may well be a case that for 2015 we might see this happen but the data wont be out until 2016.

From my perspective, Tyler’s point that the natural rate is not helpful for monetary policy is more related to the fact that our economic system does not operate with the equilibrating tendencies (due to lack of efficient markets) that economic models would like it to operate on.

‘“We now realize that, given the real natural rate, there is, for every expected rate of inflation, a corresponding nominal natural rate.”

I am struggling a bit with the concept of a “nominal natural rate” as it seems to depend upon an objectively measured “expected rate of inflation”. Firstly, expected by whom ? Secondly , even if everyone shared the same expectations about future prices then (unless all prices are expected to rise by exactly the same amount) you have a problem of how you extract a single expected rate of inflation from a set of prices that are expected to change relative to each other between now and the future.

So: If the “nominal natural rate” cannot be calculated, the real natural rate cannot be calculated either since you don’t know what to subtract from the nominal to get to the real.

Moving back to the barter economy model: If current exchange rates between commodities are expected to differ from future exchange rates between commodities then I think you have a similar problem of identifying a “unique real natural rate toward which arbitrage would force all the individual own rates to converge.”. In this situation there would be a different interest rate for each commodity. Arbitrage would indeed tend to lead these different own-rates to align with each other to reflect underlying expectations about future expected relative prices. There may be one (or more?) set of own-rates that would be consistent with a certain employment level, inflation as measured by a specific basket of goods using a single commodity as numeraire etc. But in a dynamic situations where relative “prices” are going to change I do not see how any amount of analysis could help us to identify the one “real” from the multiple “nominal” natural rate of interest that exists in that economy.

“If gold is held as bullion, it is being held for expected appreciation over and above the cost of storage. So the ratio of the future price of gold to the spot price of gold should equal one plus the real rate of interest.”

There could also be some sort of growing convenience yield on gold held, like there is on oil, in which case the futures price would fall below the spot price.

http://jpkoning.blogspot.ca/2014/11/golds-rising-convenience-yield.html

Rob Rawlings

I would agree with you that, if we allow for the relative price of commodities to vary over time, there is no absolute real rate of interest. Each commodity has a “nominal” own rate, just as monetary assets have their individual own rates. To specify a real rate of interest we need to specify a particular basket of commodities, which is inevitably arbitrary.

However, if we represent all the individual own rates as a vector then, in the model in question, it is supposed that for any given rate of time preference, there is a unique vector relating to the required employment level. We can think of this vector itself as representing the natural rate or we can pick an arbitrary basket of commodities and use that to define our natural rate.

That’s the theory anyway. But I tend to agree with David here that however well-defined, it’s nearly useless.

How can commodities be of any use in calculating an interest rate?

The difference between spot and forward prices for commodities is given by interest rates AND a host of other factors which are specific to each commodity, viz. supply and demand conditions through time. Heck there are times when the spot and forward price are in backwardation.

Keynes identified four factors which determine own interest rates. The extent to which the commodity produces a yield, it’s cost of storage and carrying, its rate of wastage, its degree of liquidity (liquidity premium). (He argued that what distinguished money as a means of exchange and a store of value over commodities in general was that its liquidity premium far exceed its carrying/storage costs/wastage costs and the reason that interest rates are given by money S/D and not commodity own rates of interest.)

Neoclassicals argue that the natural rate of interest is given by the saving and investment schedules. Given flexible prices/wages, then theoretically the CB can’t do anything about the (real) natural interest rate, it can only move nominal rates – unless it can cause shifts in the S and I schedules. Perhaps it does this by causing expectations to shift, which is somewhat a circular argument – how can it cause expectations to shift if it doesn’t directly control the natural rate?

Paul Krugman doesn’t even want to go near the theoretics, preferring to ask whether rates are being kept artificially low to which he answers a no.

Where I said the difference between spot and forward prices for commodities is given by interest rates I should have said given by time preference – if looking at it from a Neoclassical point of view.

@Nick,

Thanks. I agree with what you say.

Keynes knew that if money was kept scarce that market interest rates could be held too high to have full employment (by the oligarchs who control the money supply)

and if liquid money supply increased it would cause lower interest rates and drive money towards jobs creating investment…… the multipliers being determined by where the money was invested

keeping fed funds rate low is a way to increase availability of money driving rate banks can charge lower (to ultimately have more go into spending and other investment)

until the market interest rate balances the marginal efficiency of capital(return on investment)

the marginal efficiency of capital depends on income ie aggregate demand

so with low demand states one could see a point where you couldn’t drive the interest rate any lower

Keynes did not think monetary policy would always be adequate to attain full employment either

but he certainly had the idea of interest rate having a relationship to full employment

which was always his goal

I have read where people have ACCUSED certain economists of literally believing there is a certain number that represents THE natural rate of interest for all conditions

I have never actually seen any economists say that there is such a rigid number

so its a concept

its related to monetary policy…….you can get some intuitive idea of it from the hick diagram

buts its a concept

and one conclusion you can draw from it is that when its gets low and appears to cross into negative territory you’ve reach the point where monetary policy is no longer useful

so you need something else to increase that investment and spending so we can increase income and employment till we achieve full employment

like fiscal policy

(so I think the concept is useful)

Debunking the natural rate of interest

Comment on ‘The Well-Defined, but Nearly Useless, Natural Rate of Interest’

Wicksell has always been well aware of the fact that economists are confused confusers “… when it is a matter of finding the cause of general changes in the price of commodities, and especially the influence on those of credit and the institutions regulating credit, some maintain that cheap and easy credit, in other words, a low rate of interest, will tend to increase the amount of means of payment in circulation and the demand for goods and this will tend to increase the general level of prices; while others maintain the contrary, that cheap credit means the same things as cheaper costs of production and so tends to lower the level of prices, not to raise it; and naturally … there is no lack of more moderate opinion between the two extremes, eclectics who say that the influence of credit on prices is sometimes in one direction, sometimes in another and is sometimes nil.” (quoted in Deane, 1983, p. 8, see also 2013).

It can even be said that economic analysis consists essentially of kicking any problem around in the realm between true and false, where, as Keynes said, “… nothing is clear and everything is possible” (1973, p. 292), without ever arriving at a final true/false conclusion. Hicks is exemplary for how to deal with manifest contradictions “As far as I can make out, there are relevant and important senses in which all these statements are each of them right and each of them wrong.” (1939, p. 184)

Inconclusiveness is the very characteristic of political economics. Theoretical economics is different, it aims at clear-cut answers. This presupposes that the formal apparatus of analysis is consistent. “The highest ambition an economist can entertain who believes in the scientific character of economics would be fulfilled as soon as he succeeded in constructing a simple model displaying all the essential features of the economic process by means of a reasonably small number of equations connecting a reasonably small number of variables.” (Schumpeter, 1946, p. 3)

Standard economics never got close to this ‘simple model’. Roughly speaking, the two main approaches, the Walrasian and the Keynesian, are both defective, that is, they cannot explain how the monetary economy works (2015). The ultimate reason is that standard economics is not built upon a set of acceptable premises or axioms. Walrasianism is based on the concepts of constrained optimization and equilibrium. Both premises are methodologically unacceptable.

So, what does the correct ‘little apparatus’ look like? Generally speaking, it is based upon a set of axioms that do not contain any Walrasian or Keynesian propositions. The replacement of obsolete premises amounts to a paradigm shift.

As a matter of principle, analysis must always start with the most elementary case. This is the pure consumption economy. The theory of interest has to be developed out of the objectively given properties of the most elementary economic configuration. That is, to begin with there are two firms; one produces the consumption good and the other money/credit. This firm is also called the central bank and it stands for the banking industry as a whole. For a start, only the household sector takes up credit. There is no investment in the pure consumption economy and by consequence no investment financing.

Under the objective condition of zero profit in both firms we have Pc=Wc/Rc, the price of the consumption good is equal to unit wage costs, and Ja=Wb/Rb, ditto for the rate of interest on the asset side of the central bank’s balance sheet. If wage rates are set equal for simplicity then we have Ja/Pc=Rc/Rb, that is, the real interest rate is objectively determined by the production conditions in both industries.

In the investment economy things are a bit more complex. Normally, the household sector is the lender and the business sector is the borrower. Accordingly, one has two rates of interest Ja and Jl. The interest rate on the asset side Ja denotes what business has to pay, the interest rate on the liability side Jl denotes what the household sector is paid. Under the zero profit condition there is a fix relationship between the two rates. The central bank, though, is in principle free to set any configuration of Ja and Jl. A very interesting limiting case is Jl=0.

Now, the employment equation for the investment economy reads as follows

From this equation follows inter alia:

(i) An increase of the expenditure ratio rhoE leads to higher employment.

(ii) Increasing investment expenditures I exert a positive influence on employment.

(iii) An increase of the factor cost ratio rhoF=W/PR leads to higher employment. This implies that an increase of the average wage rate W relative to price P and productivity R leads to higher employment (2015).

What remains to be done, is to establish how the expenditure ratio depends on the deposit rate rhoE=f(Jl) and how investment depends on the lending rate I=f(Ja). These two functions inserted give the general relationship between employment, prices, and the two interest rates.

Conclusion: if the functional relations f(Jl) and f(Ja) are reliable and if the price mechanism works such that rhoF is roughly constant then the central bank is in the position to establish full employment by fine-tuning the two interest rates.

Wicksell’s natural-rate mechanism implies the equalization of saving and investment (Blaug, 1998, p. 621). It has already been shown in previous posts that this equality/equilibrium never occurs, neither ex ante nor ex post. And this in turn means that the concept of the natural rate has been fallacious from the start.

Egmont Kakarot-Handtke

References

Blaug, M. (1998). Economic Theory in Retrospect. Cambridge: Cambridge University Press, 5th edition.

Deane, P. (1983). The Scope and Method of Economic Science. Economic Journal, 93(369): 1–12. URL http://www.jstor.org/stable/2232161.

Hicks, J. R. (1939). Value and Capital. Oxford: Clarendon Press, 2nd edition.

Kakarot-Handtke, E. (2013). Confused Confusers: How to Stop Thinking Like an Economist and Start Thinking Like a Scientist. SSRN Working Paper Series, 2207598: 1–16. URL http://ssrn.com/abstract=2207598.

Kakarot-Handtke, E. (2015). Major Defects of the Market Economy. SSRN Working Paper Series, 2624350: 1–40. URL http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2624350.

Keynes, J. M. (1973). The General Theory of Employment Interest and Money. The Collected Writings of John Maynard Keynes Vol. VII. London, Basingstoke: Macmillan.

Schumpeter, J. A. (1946). The Decade of the Twenties. American Economic Review, 36(2): 1–10. URL http://www.jstor.org/stable/1818192

David,

Thinking of an interest rate as a time relative price between money now and money later (or apples now and apples later) misses the big picture.

In a barter economy, it is unlikely that person would be concerned with lending apples now to receive apples later (aka an “own rate of interest”). Instead a person would likely lend apples now for some other good (a choo choo train?) later.

The whole point of a system of credits and debits is to overcome the differences in production schedules between different goods – it takes the apple picker 6 months to obtain apples, it takes the choo choo train builder two years to build a new train, it takes the skyscraper builder eight years to design and build the new skyscraper.

And so the statement:

“At any moment, therefore, there is a unique real natural rate in a barter economy if arbitrage is operating to equalize the cost of borrowing in terms of every commodity.”

That seems only possible if all commodities (goods) have the same or similar production schedules. Otherwise, a term premium kicks in for the difference in production time between various goods. I as an apple picker will lend apples to the train builder at one interest rate reflecting the 1 1/2 year difference in production time between apples and trains. I as an apple picker will lend apples to the skyscraper builder at another interest rate reflecting the 7 1/2 year difference in production time between apples and skyscrapers.

David,

I have been reading your paper (with Zimmerman) on the Sraffa/Hayek debate on the natural rate of interest.

Your paper seeks to significantly weaken Sraffa’s attack on Hayek, Sraffa having argued that Hayek’s idea of the natural rate of interest is “incoherent” because there is no unique commodity own rate.

In the paper, you endeavour to debunk Sraffa’s argument by using Lachman’s (Capital and It’s Structure 1956) argument that markets will work to eliminate the differences between commodity own rates in a barter economy.

In a later paper, Lachman (1986) seems to shift this slightly to argue that:

“This does not mean that the actual own-rates must all be equal, but that their disparities are exactly offset by disparities between forward prices.”

This to me does not make sense. I wonder if you could explain it?

He went on to talk about a “third kind of equilibrium” which was equally confusing, going on to say that only some of the own rates should equalize.

Being thoroughly confused by all this I thought I would actually look at some markets and see what was going on there. I had a look at the LME’s closing markets for the 5/11 for various metals. Using the closing buyer’s quote for cash and the December 2016 quote, I calculated the following own rates for the following metals:

Aluminium – 1.0377

Copper – 0.9936

Lead – 1.0276

Nickel – 1.0046

Zinc – 1.0398

As you can see there is quite a disparity in the money own rates. (This can’t be explained in terms of storage and handling costs as these metals are similarly packaged in billets – although I believe nickel is generally packaged as pellets – and even stored in the same warehouses.)

Not only did Lachmann argue that money own rates would equalize so did Keynes (p. 227-228 of GT), as you point out in your paper.

Lachman (1956) himself also asked the question – can the rate of interest become negative? – to which he responded no, for rates set in both a barter and monetary economies.

As can be seen from the above list, the copper own rate contradicts this.

Returning to your paper, you put forward Keynes comments regarding his rejection of his Treatise of Money treatment of the rate of interest as an argument to blunt Sraffa’s attack. I think you have drawn a very long bow here indeed.

In Chapter 17 of the GT, Keynes was making a case for why the money interest rate has its own peculiar characteristics independent of commodity own rates and why money rates rather than commodity rates influence output and employment, that’s why he repudiated his Treatise treatment of the natural rate of interest. To use Keyne’s discussion in the way you have in your paper seems to be inappropriate.

The irreparable unreality of all ‘real’ models

Comment on ‘The Well-Defined, but Nearly Useless, Natural Rate of Interest’

Keynes had a great methodological insight “In 1933, Keynes wrote a short contribution to a Festschrift for the German economist Arthur Spiethoff. He there attacked classical economists for not providing an adequate monetary theory. He then embarked upon the development of what he termed a monetary theory of production, a theory in which the interdependence of money and uncertainty, and their effects on economic behavior, could be properly investigated.” (Fontana, 2000, p. 40)

Keynes’s insight has been that the proper subject matter of economics is the monetary economy. Many economists have not got this point until today but still maintain that the ‘real’ economy is the real economy. It is definitively not.

And for one simple reason: the phenomenon of profit cannot appear at all in a ‘real’ economy (2011b). Because of this all ‘real’ models miss the essence of the market economy and are a priori worthless. This includes approaches like Ricardo, Sraffa, or RBC. This is Keynes’s lasting contribution to the advancement of theoretical economics: all ‘real’ models have to go out of the window because they are deeply and irreparably flawed.

The real-word economy manifests itself in the interaction of real and nominal variables. Because of this, the theory of saving, investment and interest has to be developed within the framework of what Keynes called the ‘monetary theory of production’.

The real time-travel, i.e. inventory accumulation/decumulation, is entirely disconnected from the nominal time-travel, i.e. saving/dissaving (2013). And, most important of all, saving/dissaving is intimately connected with loss/profit. This connection is obviously of overriding importance, yet it is entirely missing in the familiar theories of interest.

The crucial point is that the representative economist does not understand what profit is (2011a). Because of this the theory of interest is false by implication. The worst blunder consists of conceptualizing the natural rate as a real magnitude and in the rather futile attempt to derive interest from an apples-now-apples-later time preference model.

Egmont Kakarot-Handtke

References

Fontana, G. (2000). Post Keynesians and Circuitists on Money and Uncertainty: An Attempt at Generality. Journal of Post Keynesian Economics, 23(1): 27–48. URL http://www.jstor.org/stable/4538713.

Kakarot-Handtke, E. (2011a). The Emergence of Profit and Interest in the Monetary Circuit. SSRN Working Paper Series, 1973952: 1–22. URL

http://ssrn.com/abstract=1973952

Kakarot-Handtke, E. (2011b). When Ricardo Saw Profit, He Called it Rent: On the Vice of Parochial Realism. SSRN Working Paper Series, 1932119: 1–19. URL http://ssrn.com/abstract=1932119

Kakarot-Handtke, E. (2013). Settling the Theory of Saving. SSRN Working Paper Series, 2220651: 1–23. URL http://ssrn.com/abstract=2220651