In the General Theory Keynes First Trashed and then Restated the Fisher Equation

I am sorry to have gone on a rather extended hiatus from posting, but I have been struggling to come up with a new draft of a working paper (“The Fisher Effect under Deflationary Expectations“) I wrote with the encouragement of Scott Sumner in 2010 and posted on SSRN in 2011 not too long before I started blogging. Aside from a generous mention of the paper by Scott on his blog, Paul Krugman picked up on it and wrote about it on his blog as well. Because the empirical work was too cursory, I have been trying to update the results and upgrade the techniques. In working on a new draft of my paper, I also hit upon a simple proof of a point that I believe I discovered several years ago: that in the General Theory Keynes criticized Fisher’s distinction between the real and nominal rates of interest even though he used exactly analogous reasoning in his famous theorem on covered interest parity in the forward exchange market and in his discussion of liquidity preference in chapter 17 of the General Theory. So I included a section making that point in the new draft of my paper, which I am reproducing here. Eventually, I hope to write a paper exploring more deeply Keynes’s apparently contradictory thinking on the Fisher equation. Herewith is an excerpt from my paper.

One of the puzzles of Keynes’s General Theory is his criticism of the Fisher equation.

This is the truth which lies behind Professor Irving Fisher’ss theory of what he originally called “Appreciation and Interest” – the  distinction between the money rate of interest and the real rate of interest where the latter is equal to the former after correction for changes in the value of money. 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 equalized, 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 money lent. . . .

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. The prices of existing assets will always adjust themselves to changes in expectation concerning the prospective value of money. The significance of such changes in expectation lies in their effect on the readiness to produce new assets through their reaction on the marginal efficiency of capital. 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. (pp. 142-43)

As if the problem of understanding that criticism were not enough, the problem is further compounded by the fact that one of Keynes’s most important pre-General Theory contributions, his theorem about covered interest parity in his Tract on Monetary Reform seems like a straightforward application of the Fisher equation. According to his covered-interest-parity theorem, in equilibrium, the difference between interest rates quoted in terms of two different currencies will be just enough to equalize borrowing costs in either currency given the anticipated change in the exchange rate between the two currencies over reflected in the market for forward exchange as far into the future as the duration of the loan.

The most fundamental cause is to be found in the interest rates obtainable on “short” money – that is to say, on money lent or deposited for short periods of time in the money markets of the two centres under comparison. If by lending dollars in New York for one month the lender could earn interest at the rate of 5-1/2 per cent per annum, whereas by lending sterling in London for one month he could only earn interest at the rate of 4 per cent, then the preference observed above for holding funds in New York rather than in London is wholly explained. That is to say, forward quotations for the purchase of the currency of the dearer money market tend to be cheaper than the spot quotations by a percentage per month equal to the excess of the interest which can be earned in a month in the dearer market over what can be earned in the cheaper. (p. 125)

And as if that self-contradiction not enough, Keynes’s own exposition of the idea of liquidity preference in chapter 17 of the General Theory extends the basic idea of the Fisher equation that expected rates of return from holding different assets must be accounted for in a way that equalizes the expected return from holding any asset. At least formally, it can be shown that the own-interest-rate analysis in chapter 17 of the General Theory explaining how the liquidity premium affects the relative yields of money and alternative assets can be translated into a form that is equivalent to the Fisher equation.

In explaining the factors affecting the expected yields from alternative assets now being held into the future, Keynes lists three classes of return from holding assets: (1) the expected physical real yield (q) (i.e., the ex ante real rate of interest or Fisher’s real rate) from holding an asset, including either or both a flow of physical services or real output or real appreciation; (2) the expected service flow from holding an easily marketable assets generates liquidity services or a liquidity premium (l); and (3) wastage in the asset or a carrying cost (c). Keynes specifies the following equilibrium condition for asset holding: if assets are held into the future, the expected overall return from holding every asset including all service flows, carrying costs, and expected appreciation or depreciation, must be equalized.

[T]he total return expected from the ownership of an asset over a period is equal to its yield minus its carrying cost plus its liquidity premium, i.e., to q c + l. That is to say, q c + l is the own rate of interest of any commodity, where q, c, and l are measured in terms of itself as the standard. (Keynes 1936, p. 226)

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 = lc.

But in equilibrium, the nominal rate of interest must equal the liquidity premium, because if the liquidity premium (at the margin) generated by money exceeds the nominal interest rate, holders of debt instruments returning the nominal rate will convert those instruments into cash, thereby deriving liquidity services in excess of the foregone interest from the debt instruments. 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. Thus, substituting the nominal interest rate for the liquidity premium, and expected inflation for the carrying cost of money, we can rewrite the Keynes equilibrium condition for money to be held in equilibrium as q = r = ipe. But this equation is identical to the Fisher equation: i = r + pe.

Keynes’s version of the Fisher equation makes it obvious that the disequilibrium dynamics that are associated with changes in expected inflation can be triggered not only by decreased inflation expectations but by an increase in the liquidity premium generated by money, and especially if expected inflation falls and the liquidity premium rises simultaneously, as was likely the case during the 2008 financial crisis.

I will not offer a detailed explanation here of the basis on which Keynes criticized the Fisher equation in the General Theory despite having applied the same idea in the Tract on Monetary Reform and restating the same underlying idea some 80 pages later in the General Theory itself. But the basic point is simply this: the seeming contradiction can be rationalized by distinguishing between the Fisher equation as a proposition about a static equilibrium relationship and the Fisher equation as a proposition about the actual adjustment process occasioned by a parametric expectational change. While Keynes clearly did accept the Fisher equation in an equilibrium setting, he did not believe the real interest rate to be uniquely determined by real forces and so he didn’t accept its the invariance of the real interest rate with respect to changes in expected inflation in the Fisher equation. Nevertheless it is stunning that Keynes could have committed such a blatant, if only superficial, self-contradiction without remarking upon it.

Advertisements

18 Responses to “In the General Theory Keynes First Trashed and then Restated the Fisher Equation”


  1. 1 JKH September 6, 2017 at 4:16 am

    I look at the GT occasionally, and find chapter 17 to be most challenging, although I can’t recall much of its detail at this moment.

    A cursory comment for now: covered interest parity is “provable” as a “theory” by observation of actual covered interest arbitrage markets. Markets exist in interest rates for different terms, and in spot and forward exchange rates. So the parity is borne out in fact (at least roughly if not perfectly) by arbitrage in these observable markets. I think it’s a stretch to say this is a straightforward application of the Fisher equation. There is no similar market mechanism that arbitrages across different discrete markets the internal composition of the nominal interest rate into its real and expected inflation components, at least insofar as these components could be subject to “correction” such as might happen continuously through discrete market efficiencies under such arbitrage operations.

  2. 2 Nick Rowe September 6, 2017 at 4:33 am

    It certainly is hard to understand what Keynes is saying there. But at that point in the GT, isn’t Keynes still assuming that money wages are held constant? So M/W (the stock of money in wage units) is held constant (it cannot jump down) when expected inflation jumps up (for some exogenous reason). And if M/W cannot jump, then the Fisher effect cannot work like it normally does.

    In the standard ISLM model, this is like showing the effect of an exogenous increase in expected inflation, holding M/P constant. We get a rise in nominal i, but also a fall in real r. And the amount by which r falls depends on the relative slopes of IS and LM. And if we “forget” about the effect of increased Y on increasing money demand (and Keynes does tend to “forget” that effect at times in his analysis), the LM is horizontal, and the only effect of an increase in expected inflation is to reduce real r as we move down along the IS curve.

    Which is my *guess* at what Keynes is thinking in that passage. But I think this fits with what you are saying about the difference between equilibrium relations and the adjustment process, with Keynes talking about the latter.

  3. 3 JP Koning September 6, 2017 at 10:56 am

    If money is updated so that it pays interest, that means money’s q increases and the overall return on money (q + l – c) rises relative to competing assets. To restore equilibrium, what happens? Do the liquidity services l provided by money have to decline, or does c, or expected inflation, rise?

  4. 4 Nick Rowe September 7, 2017 at 2:45 am

    JP: the liquidity services provided by money have to decline, at the margin. This happens because the real quantity of money increases. (Holding the future nominal growth rate of money constant, so the rationally expected inflation rate stays constant.)

  5. 5 David Glasner September 7, 2017 at 9:21 am

    JKH, Chapter 17 is actually my favorite chapter in the GT, so go figure. By a straightforward application of the Fisher equation, I mean that the reasoning that leads to the covered interest parity theorem is exactly the same as the reasoning that Fisher used to derive the Fisher equation. In fact, if you read Fisher’s original 1896 exposition in Appreciation and Interest, the argument is presented in terms of expected changes in the relative values of two different currencies. So the original Fisherian paradigm was exactly analysis to Keynes’s covered interest parity analysis. You are right that in covered interest parity there is an arbitrage mechanism that maintains the equalities more closely that when it just depends on individual expectations, but the reasoning is identical.

    Nick, Interesting point about, the fixed wage assumption. I had not thought of that before. On it’s face, it seem a bit implausible to me that that is what Keynes had in mind, but that would be an interesting line of reasoning to follow. I will have to think about it more and see where it leads.

    JP, If money yields competitive interest, people will increase their holdings of money, presumably by shifting out of alternative higher-yielding financial instruments, thereby reducing l correspondingly.

    Nick, If the future nominal growth rate of money is held constant, the rational expectation will be for the value of money to fall. To keep rationally expected inflation constant, the quantity of money will have to increase to match the increased quantity of money people want to hold once the foregone interest associated with holding money is reduced.

  6. 6 JP Koning September 8, 2017 at 6:31 am

    David: “…thereby reducing l correspondingly.”

    I understand that this is one way to balance the equation. But what is the intuition behind this?

  7. 7 David Glasner September 8, 2017 at 7:39 am

    JP, Not trying to be pedantic, but what does “this” mean? Why liquidity premium falls as holdings of cash increase, or, why holdings of cash increase?

  8. 8 JP Koning September 8, 2017 at 10:00 am

    By “this,” I meant why the liquidity premium falls as holdings of cash increase. What is the intuition behind that?

  9. 9 David Glasner September 8, 2017 at 10:12 am

    JP, Each additional unit of currency in your wallet provides less liquidity services than the previous one. If I have one dollar, I will be able to go into a store and make a purchase of up to one dollar if I pass by the store window and see some item unexpectedly on sale, rather than have to go to my bank first and withdraw one dollar. There aren’t many things I can buy for just one dollar, so having 2 dollars instead of 1 dollar would enhance my ability to make unplanned purchases. Each additional dollar expands my ability to make unplanned purchases. Eventually I will have so many dollars in my wallet, that an additional dollar won’t enable me to make any additional purchases that I couldn’t have already made.

  10. 10 JP Koning September 8, 2017 at 9:36 pm

    Ok, I understand how from an individual’s perspective each additional unit of money in my wallet provides me with less liquidity services, or L, as my holdings of money increase.

    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.)

  11. 11 JKH September 9, 2017 at 2:55 pm

    From GT chapter 11:

    “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.

  12. 12 JKH September 10, 2017 at 9:12 am

    Evidence of consistency across chapters 11 and 17:

    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.

  13. 13 JKH September 11, 2017 at 4:15 pm

    Final comment (I think/hope)

    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.

  14. 14 David Glasner September 11, 2017 at 6:22 pm

    JKH, Thanks for your detailed comments. I just haven’t been able to concentrate on your attempts to explain your position to me. I hope to be able to read them carefully and respond some time soon.

  15. 15 JKH September 11, 2017 at 8:21 pm

    David,

    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.

  16. 16 JKH September 17, 2017 at 6:24 am

    David,

    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. 


  1. 1 Should-Read: David Glasner: In the General Theory Keynes First Trashed and then Restated the Fisher Equation - Daily Economic Buzz Trackback on September 6, 2017 at 11:02 am

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s




About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

Enter your email address to follow this blog and receive notifications of new posts by email.

Join 1,538 other followers

Follow Uneasy Money on WordPress.com

%d bloggers like this: