http://monetaryrealism.com/the-general-theory-of-employment-interest-and-money-chapters-11-and-17

]]>I qualified my penultimate comment with the hope that it would be my last. Since I’ve returned to looking at the GT for the first time in a while, I thought I’d try to improve my explanation with a further summary. I’m not so much rejecting your argument in doing this. In fact, I’m not sure I fully follow your argument. I suppose instead I’m more playing Devil’s Advocate in the affirmative, because I’m attempting to understand and believe how Keynes could be correct, without the contradiction you describe.

I also noticed this in your post:

“Eventually, I hope to write a paper exploring more deeply Keynes’s apparently contradictory thinking on the Fisher equation.”

So here I go again.

Chapter 11 describes the dynamic by which the MEC declines as output increases – until the MEC falls to the level of the interest rate or below, when production ceases. There is no decomposition of total return in Chapter 11 – just an annuity of prospective Q’s which he refers to as “yield”.

I think it is important to note upfront that the MEC refers to a different “thing” than the interest rate. One refers to anticipated return from purchasing a newly produced capital asset. The other refers to the anticipated return from lending the same amount of money rather than purchasing a new capital asset. This difference is roughly that of the difference between new investment (investment as in a GDP measure) and a bank loan for example. In fact, the difference can be viewed as that corresponding to the profit margin of a company borrowing money from the bank to acquire a new real investment. They are two different “things” measured on two different sides of the balance sheet or two different lines on the income statement. Whether or not they become equal in measure at some point in the process doesn’t change this fact. It happens that they are equal in measure when “equilibrium” is reached – when the MEC falls to the level of the interest rate. But that they are not equal in measure at other times just emphasizes that they refer to a different “thing”.

And that’s my best guess as to the context in which Keynes makes this statement:

“The mistake lies in supposing that it is the rate of interest on which prospective changes in the value of money will directly react, instead of the marginal efficiency of a given stock of capital.”

It is easy to understand how a change in the expected rate of inflation (i.e. a change in the value of money) will affect the MEC directly. He emphasizes the broader context for this analysis in his lead up:

“The most important confusion concerning the meaning and significance of the marginal efficiency of capital has ensued on the failure to see that it depends on the prospective yield of capital, and not merely on its current yield.”

Thus, the anticipated revenue from the prospective annuity of Q’s will change because of a change in expected inflation over the full time period. And so the MEC is subject to change.

But it is not evident at all how the same thing directly changes the interest rate. There is no similar direct visualization of this measure changing – especially not when it is understood that the MEC and the interest rate are two different “things”.

That said, I find the following difficult to understand (as I think you did):

“It is difficult to make sense of this theory as stated, because it is not clear whether the change in the value of money is or is not assumed to be foreseen. There is no escape from the dilemma that, if it is not foreseen, there will be no effect on current affairs; whilst, if it is foreseen, the prices of existing goods will be forthwith so adjusted that the advantages of holding money and of holding goods are again equalised, and it will be too late for holders of money to gain or to suffer a change in the rate of interest which will offset the prospective change during the period of the loan in the value of the money lent.”

Whatever he means there, I don’t think it’s critical to the general point of your post or my response here. My best guess is that he may be referring to a fixed rate of interest for a fixed term that is locked in when money is borrowed to purchase a capital asset. The MEC can change throughout the life of the investment for a number of reasons, including changes in the expected value of money. But the nominal interest rate will not change in the case where it is contractually fixed at the outset. But this is all really beside the main point here, which is about a potential contradiction in his thinking about the Fisher equation.

Moving onto Chapter 17, he makes the case for why the money interest rate on money is “the” significant interest rate. But the more critical connection to the Fisher equation is his demonstration of how the “own rate” of interest for a given commodity can be translated to a rate of interest on the same commodity expressed in terms of a second commodity.

So, for example, if the own rate of interest on wheat is ‘x’, and the rate of appreciation of wheat in terms of money is ‘a’, then the wheat rate of money interest (as he calls it) is (x + a).

(He calculates this as if it were a simple linear + translation, but in fact there is a small element of compounding involved.)

Such a translation adapts easily to the case of covered interest parity:

For example:

Suppose the US interest rate is x.

And suppose the expected appreciation of the US dollar is ‘a’ in Canadian dollar terms.

Then the corresponding prospective all-in return available to Canadian investors from US interest rates is (x + a).

And this is exactly the same calculation that would be evident through covered interest parity and covered interest arbitrage, were a Canadian investor to sell Canadian dollars spot in exchange for US dollars received, to receive the US interest rate, and to buy Canadian dollars forward in exchange for US dollars paid. The full result is an all-in Canadian dollar rate of interest (in effect) on an investment that internally pays an interest rate in US dollars. As a result of arbitrage, this all-in Canadian rate should be at least roughly equivalent to the pure Canadian interest rate.

This covered interest parity example corresponds to the Keynes framework whereby a US dollar standard might be translated/converted to a Canadian dollar standard, for purposes of measuring the interest rate on a US dollar investment.

None of this seems to be inconsistent with Chapter 11. Covered interest parity can be viewed as a particular case of interest rate standard conversion. This is separate from the dynamic whereby an MEC converges to its respective interest rate in the context of a given interest rate standard, as described in Chapter 11.

Keynes in Chapter 11 was really questioning the idea of a Fisher decomposition being applied directly to the interest rate standard, rather than to the MEC – this being in an assumed interest rate standard circumstance. The fact that the Fisher decomposition rises to the surface in the conversion of one interest rate standard to another in Chapter 17 is a separate analytical point, not contradicting the MEC/interest rate relationship described in Chapter 11.

The Fisher relationship requires the Chapter 17 ‘a’ factor in the context of the Keynes framework. And as I said earlier, this ‘a’ factor does not exist in respect of a standard measured in terms of itself – which in fact is the case that is applicable throughout Chapter 11, where Keynes invokes his criticism of Fisher. But the ‘a’ factor is critical in Chapter 17, because it involves the conversion of standards.

]]>Look forward to that – if you find the time to respond.

Or sometime later.

No problem.

Very much appreciate your ongoing posts.

It’s a genuine inspiration for me to try and understand this thing called economics.

It’s a timeless effort in that sense.

]]>Insofar as covered interest arbitrage between two different currencies is concerned, the chapter 17 framework adapts to that.

For example, the case of wheat can be analogized as if wheat is a foreign currency.

As a starting point, from chapter 17:

“Let us suppose that the spot price of wheat is £100 per 100 quarters, that the price of the ‘future’ contract for wheat for delivery a year hence is £107 per 100 quarters, and that the money-rate of interest is 5 per cent; what is the wheat-rate of interest? £100 spot will buy £105 for forward delivery, and £105 for forward delivery will buy 105/107 × 100 (= 98) quarters for forward delivery. Alternatively £100 spot will buy 100 quarters of wheat for spot delivery. Thus 100 quarters of wheat for spot delivery will buy 98 quarters for forward delivery. It follows that the wheat-rate of interest is minus 2 per cent per annum…

So in that example,

The money rate of wheat interest is 7 per cent

The money rate of money interest is 5 per cent

Which means that the wheat rate of wheat interest is (2) per cent

The referenced transaction:

Buy 100 units of spot wheat for 100 £

Sell 100 units of spot wheat in exchange for 98 units of forward wheat

(I.e. lend 100 units of wheat and earn wheat interest of (2) per cent on 100 units of wheat.)

Receive 98 units of wheat at forward maturity.

Convert 98 units of wheat to £

100 units of wheat at that point is worth 107 £, so 98 units of is worth roughly 105 £

So an initial investment of 100 £ becomes 105 £

Which is the same return as on 100 £ at the money rate of interest on money

Now think of the £ as the domestic currency, and wheat as the foreign currency. The fully hedged interest rate from £ to the foreign currency and back is 5 per cent, which is the same as the domestic currency £ interest rate.

This is covered interest arbitrage. Substituting US dollars for wheat while assuming realistic relationships for interest rate and foreign exchange markets in £ and US dollars would result in a similar representative calculation.

Not only is this perspective derivable from Keynes’ discussion of “own rates” of interest on commodities such as wheat, but he refers to such an adaptation specifically in this paragraph from chapter 17:

“It may be added that, just as there are differing commodity-rates of interest at any time, so also exchange dealers are familiar with the fact that the rate of interest is not even the same in terms of two different moneys, e.g. sterling and dollars. For here also the difference between the ‘spot’ and ‘future’ contracts for a foreign money in terms of sterling are not, as a rule, the same for different foreign moneys.”

Again, I think his overall framework hangs together, and I see no contradiction with anything said earlier in Chapter 11. All that was said there was that a change in inflation expectations acts directly on the MEC but not necessarily on the interest rate. Analogizing wheat as a foreign currency, and interpreting the return in MEC terms, the forward price differential on either wheat or the US dollar factors directly into that MEC calculation – but such a decomposition obviously and necessarily and logically appears nowhere in the assumed £ interest rate standard. I think Keynes’ message was that such a Fisher decomposition of *the* interest rate (i.e. the relevant interest rate standard) is artificial.

]]>In his example in Chapter 17, Keynes is comparing own interest rates for houses, wheat, and money.

Consider the comparison just between houses and money.

He assumes a house rate of interest on houses (the house own rate) as consisting of a pure yield factor of q1. He assumes for simplification that both the carrying cost and the liquidity premium are 0.

He assumes a money rate of interest on money (the money own rate) as consisting of a liquidity premium of l3. He assumes for simplification that both the yield and the carrying cost are 0.

He then assume a money rate of inflation on houses of a1.

So the money rate of interest on houses becomes a1 + q1.

This is consistent with a Fisher decomposition approach where the real rate is q1 and the expected inflation rate is a1.

But in chapter 11, he rejects the idea that this Fisher composition applies to the money rate of interest on money, which in chapter 17 terms is the money own rate, l3.

This is quite consistent with the fact that this l3 rate for the money rate of interest on money does not include an ‘a’ factor for money comparable to the case of houses or other capital assets. The money own rate l3 requires no additional ‘a’ factor for the appreciation of money in terms of money, since money is already the standard for the l3 expression. There is no such thing as the appreciation of money in terms of itself – not in the same way that there is for the appreciation of houses in terms of money. L3 is the own rate for money.

Thus, he is saying that the Fisher decomposition does not apply to the money rate of interest on money. But he is not saying that the Fisher decomposition does not apply to the money rate of interest on houses or anything else.

Notwithstanding the (+ a) composition of money rates of interest on commodities such as houses in chapter 17, his entire framework is consistent with the rejection of a Fisher decomposition for the money rate of interest on money, where the latter is the interest rate standard for the MEC. And the rest of chapter 17 shows why that must be the interest rate that becomes the standard. He compares the rate of decline of the returns for various kinds of capital assets as production increases. He contends for example that the q1 for houses will decline to a greater degree than the l3 for money, due to the respective characteristics of q1 and l3. By this sort of analysis, he similarly concludes that all MECs will eventually decline to the level of l3, at which point production will stop. And he concludes that the relevant rate of interest and the one that will set the standard is the money rate of interest on money.

The expected rate of inflation included in a Fisher decomposition acts directly on the MEC/own interest rates for all commodities, meaning all commodities other than money.

The inflation adjusted rate for houses is q1 + a1 (the rate of interest on houses in money terms)

And so on for all non-money commodities

In that context, q1 can be interpreted as a real rate.

But there is no such money adjustment for the money rate of interest on money, because l3 is already an “own rate” in its expression.

And this is where Keynes’ framework runs into conflict with Fisher. The Fisher decomposition can work for MECs and interest rates for all non-money commodities. But it doesn’t work in Keynes’ framework where he has developed an analysis that concludes that it is the “own rate” for money that must be the standard against which the MEC for all other capital assets are compared. That all seems consistent to me – i.e. the rejection of the Fisher decomposition for the money rate of interest on money, but an implicit acceptance of it in all other cases.

Again, unlike houses or wheat, there is no ‘a’ appreciation factor applicable in the case of the money rate of interest on money. In this very strict sense, the money rate of interest on money l3 is also an inflation adjusted rate, which means it is comparable at the level of the own rates or the real rates for other commodities. And going back to chapter 11, it is possible this has something to do with the admittedly odd reference in that context to a real rate for money.

Keynes’ depiction by example of the money own rate as l3 – but without an ‘a’ adjustment similar to the cases of adjusting the own rates for houses and wheat – is in fact consistent with his chapter 11 rejection of the Fisher decomposition for the money rate of interest. When expressing interest rates in money terms, there is no active adjustment to l3 in the same way as there is for q1 and c2. The ‘a’ factor for the money rate of interest on money is zero – which is why there is no Fisher decomposition for the money rate of interest on money in Keynes’ framework. So I think his entire framework, including the relationship between chapters 11 and 17, looks to be consistently constructed, in my view.

]]>“The stimulating effect of the expectation of higher prices is due, not to its raising the rate of interest (that would be a paradoxical way of stimulating output — in so far as the rate of interest rises, the stimulating effect is to that extent offset), but to its raising the marginal efficiency of a given stock of capital. If the rate of interest were to rise pari passu with the marginal efficiency of capital, there would be no stimulating effect from the expectation of rising prices. For the stimulus to output depends on the marginal efficiency of a given stock of capital rising relatively to the rate of interest.”

I’m not familiar with the original Fisher on this subject, but JMK seems to be interpreting the Fisher effect as one in which an increase in expected inflation is supposed to increase the nominal interest rate by the same amount (assuming the real rate unchanged). Whether or not that’s an accurate interpretation (and God knows given the recent confusion around neo-Fisherism), I think it’s natural for him to point out as he does in the context of his own MEC framework that an increase in expected inflation directly increases the MEC schedule due to the higher expected revenue (assuming the interest rate unchanged). And he does in fact point out that a hypothetical concomitant increase in the interest rate would have an offsetting effect on the benefit otherwise of such an MEC increase.

You say:

“Thus, every asset that is held, including money, must generate a return including the liquidity premium l, after subtracting of the carrying cost c. Thus, a standard real asset with zero carrying cost will be expected to generate a return equal to q (= r). For money to be held, at the margin, it must also generate a return equal to q net of its carrying cost, c. In other words, q = l – c.”

I suspect you don’t mean q = l – c

I will be interested to know if that in fact is what you intended

In Keynes’s Chapter 17 framework:

Total return = q + l – c

where

q = physical yield

l = liquidity premium

c = physical carrying cost

Total return is q + l – c, for anything – including money

In order to focus on these components, he simplifies by assuming in an example the following total returns:

Houses q

Wheat -c

Money l

In that simplified example, houses perhaps being an example of a “standard real asset”, it is true that the total return for houses is q

But the return for money is not q = l – c

q is not equal to l – c in any case

q is the physical yield component for any return

You say:

“Similarly, the carrying cost of holding money is the expected depreciation in the value of money incurred by holding money, which corresponds to expected inflation.”

Money in Keynes’ framework has no physical yield (q) and negligible or no physical carrying cost (c) – which is not much of a stretch from reality in the case of fiat money at least

Again, it doesn’t seem to be part of his Chapter 17 framework.

He says:

“and of money that its yield is nil and its carrying cost negligible, but its liquidity-premium substantial”

Carrying cost is a physical cost in his framework.

He specifically says “most assets, except money, suffer some wastage …”

So c for money is negligible or 0.

c is physical, not monetary

Keynes seems to deflect his consideration of Fisher’s model by pointing to his own MEC framework, where inflation has a direct impact on the MEC rather than on the interest rate. I think you’re transforming Keynes’ framework in a way that introduces some contradictions in the meaning of the components of the equations – and I think it’s relevant that q and c are intended to be physical components in all cases and that for example in the case of money, the relevant c might have something to do with the costs of banknote replacement or gold coin debasement or something along those lines – not inflation. That said, this really goes to your intention, which seems to be to integrate the physical real with the monetary in a way that Keynes did not intend in chapter 17. The argument in chapter 17 is about why money is resistant to the kinds of physical q and c drags that affect other potential commodity choices for the relevant interest rate. That makes money the natural choice for the most important interest rate. Your interpretation seems to me to be inconsistent with Keynes’ framework, rather than being a correction to it. Perhaps I need to consider this more, but at this stage it’s not quite coming together for me.

]]>And if the economy-wide supply of money increases, then the aggregate measure of L has to decrease too.

But my question only assumed that money starts to pay interest, I didn’t assume that the total supply of money increases. If the total supply of money stays constant and money starts to pay interest, doesn’t this mean that expected inflation has to take on the brunt of adjusting?

(I realize my line of questioning doesn’t have much to do with the thrust of your post, but I always find your discussions about Keynes q – c + l so interesting that I’m tempted to wander around a bit.)

]]>