Q: FED and interests.

  1. vanesch

    vanesch 6,236
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    I have a nagging question which comes probably from a misunderstanding, and I guess that the answer will point me to what exactly I do not understand. It's about monetary theory and macro economy. Here it goes.

    If I understand well, the "money base" (MB) is all issued by the FED (the Central Bank). Using the fractional reserve banking system, commercial banks can issue a larger amount of M1 money (deposits, loans...).

    The FED can act upon the money base by Open Market Operations, that is, by buying up federal bonds. In doing so, it issues MB-money (it "prints" money) and takes over federal bonds. It can reduce the money base (MB) by re-selling bonds, and taking up MB-money (destroying money, "burning bills").

    In principle, "after all is said and done" the FED could sell all bonds again, recuperate all money, and reduce the money base to 0. (it will never do so, but one can understand that the 'balance' is right here)

    However, the FED also has a discount window, where it issues loans to banks, and it charges a discount rate.

    And this is where I have difficulties. Imagine that there is no money (that the FED took back all money by selling all federal bonds back again) in the money base, EXCEPT for a single bank that has taken a loan of $ 100,- at the discount window, and let us say that the discount rate is 10%

    After 1 year, the bank wants to pay back. How does this bank do so ? There IS only $ 100,- in the money base, and now this poor bank is supposed to give back $ 110, - ??
  2. jcsd
  3. Hypothetically speaking if there were no legal us tender in the world then the bank won't be able to meet it's legal obligations (because they physically can't, this is the kind of random hypothetical question i might expect in an idiosyncratic contracts exam).

    Economically speaking a economy that doesn't have money at all (not just usd but any money) isn't all that interesting for us because (apart from the fact that the only economies that don't have money were the ones before money was invented i.e. a long long time ago) there is no role for monetary policy.

    On a practical level this hypothetical could never exist. Even in the impossible event that there is no legal us tender in the world, presumably people in the us (or any other jurisdiction that currently use usd) would just resort to using alternative currencies e.g. japanese yen or canadian dollar etc. The opposite to an economy with money is an economy where exchange is based on barter. No one barters anymore because literally it costs to much to engage in economic activity otherwise.
  4. vanesch

    vanesch 6,236
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    I understand of course that this is an artificial example ; it is just to illustrate something strange in its most simplified aspect, and it is the point I thought I misunderstood:

    The fact that the FED asks interest on a loan of base money, means that each loan results in an absolute reduction of base money. An entity that engages in a loan of base money of the FED must hence be sure that it will end up obtaining MORE base money than it borrowed. This is base money, and not "value". Base money cannot (in contrast to value) be *produced* in the economy (its only source is the FED), so in one way or another, borrowing base money from the FED must result in operations extracting base money from somewhere else in order to pay back the loan.

    This is strange, no ?
  5. What are you asking?

    Obviously the bank would be unable to repay the loan without additional funds. In practice, the money supply could never be reduced to 0 through open market operations. If that were the objective, though, I imagine the Fed would just stop issuing discount loans.
  6. Ok I see what you mean. The answer is the money multiplier. Essentially the idea is that for any given amount of money a bank obtains from the central bank, the bank can then lend it back to any other person/organisation. That person/organisation with funds just borrowed (can either exchange it with someone else or keep in the bank, even if they exchange it to another person or organisation they would also have same options and therefore all money eventually end up in a bank for one reason or another) would deposit that amount in the bank (or some other bank) who can then lend those fund out again. Theoretically the banks could lend out 100% of those funds and therefore the money supply could expand infinitely. However in real life banks usually keep a percentage of each deposit as reserves (against demand on deposits). Therefore each time they lend out the funds the original money lent out is reduced and eventually approaches a limiting value. Thus the physical amount of money is much less than the actual money supply. I can't remember the figures but I think most of the money supply is in form of deposits (in banks). Going back to your example, because of the money multiplier, each time the FED sell bonds, they decrease the money supply disproportionately to the physical amount they take back and vice versa (that is, because of the money multiplier the money supply does not equal money base and in fact money supply is always greater than money assuming money is greater than 0) and this is why monetary policy can be a powerful lever in the economy.


    @talk2glenn. You're right I should've been referring to the money supply which i've i just changed (in my defence it's been a while since I've discussed these matters; my macro is a bit rusty). When I say money = money base.

    @vanesch: Also I want to add that money doesn't equal wealth. Goods + services = wealth (in a narrow sense) and goods and services are created by labour + capital (in a simple model of an economy). Money is used as a proxy for goods + services. Even if all the money is taken out of the economy it doesn't mean people can't pay the interest. All it means is they have to find a different medium of exchange to do so. In your example because central bank has taken all USD out of the economy unless the central banks accepts alternative forms of payment (other than USD) the bank can't pay it back which isn't the same as they aren't capable of doing so.

    I guess it's because the hypothetical is quite restrictive and specific we've found it hard to know what your real question is. I hope this answer helps anyway.
    Last edited: Oct 22, 2010
  7. You are confused. The money base is M0 (the amount of physical currency in the economy) plus Central Bank excess reserves, and the two figures are fairly close.

    M1 includes demand deposits and things like traveler's checks.

    This is accurate, though. Open market operations remove M0 from the economy. Due to the multiplier effect, this has a larger impact on M1 and M2.

    Nothing about this is reasonable.

    Unlike open market operations, markets transactions do not remove M0. By definition, there is enough capital in the system to repay outstanding loans. This is accounting 101.

    It's alarmist crap peddled to the lowest common denominator.

    The amount on deposit plus the amount held in reserves always equals the amount of loans.
  8. vanesch

    vanesch 6,236
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    Yes. No. Well, actually, it is because someone told me such a story that I got thinking about it. The story itself which you quote is apparently "well-known" (especially in anti-kapitalist circles), but by itself it is wrong, if all the lending is done by commercial banks. I think this is the answer skill was pointing at.

    The reason is that with commercial banks, the money (also the interest) "keeps in circulation": the people who get the benefit of the bank (the wages of the personnel for instance) keep this interest in circulation and offset the "sink".
    In the example, the $ 200 000,- interest on the 1 million loan is borrowed at bank B, but it goes into the hands of the employees of bank A as wages (say), and they will spend it in the economy, from which bank B will eventually get paid back.
    So the only thing you need to do when you borrow a million $, is to make sure that you will be able to *create value* for $ 200 000,- by the time you need to pay it back + interests. This creation of value will "suck in" enough money (say, from the bank employees, because you sell them pizzas) again to "close the circle". So the story as such is wrong, for commercial banks and commercial loans.

    However, and this is how I came upon this problem for me, it DOES seem right if you think of loans by the FED, because the interest you pay to the FED is not circling around anymore, it is effectively destroyed.

    Now, indeed, as long as the government issues bonds, the FED can create money by buying them. So it seems that you need a budget deficit in order for this interest not to be diminishing base money.

    Mmmm, so in fact, if that's true (if the FED will buy bonds by exactly the same amount as you pay interests to the FED) the money base will remain intact, and you can see these interests in fact as a kind of taxes you pay to the government.

    Yes, this might be the solution to my difficulty:
    - you pay interests to the FED, and hence "destroy" base money
    - the FED buys bonds for exactly the same amount and "creates" base money
    - the government can have a deficit (issuing bonds) for exactly the same amount

    you could have paid directly your interests as taxes to the government.

    Does that sound about right ?
  9. loseyourname

    loseyourname 3,632
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    Money isn't only created by the Fed. As you mentioned, with the fractional reserve system, there is a money multiplier so that money borrowed from the Fed (and you're borrowing whether you sell bonds or borrow from the discount window) can be re-loaned and those loans will earn higher interest than the discount rate (they have to, or the bank wouldn't make it's money back and then what you're imagining could theoretically happen). Every dollar the Fed injects become $1.10, or whatever, but the point is there ends up being more money than just what the Fed directly prints.

    Even if the Fed took all M1 out of circulation (which it can't because the total amount of bonds it owns to sell is only like $700 billion, far less than the amount of M1 in circulation), M2 and M3 assets can still be converted into M1.
  10. This is not correct.

    MS = (1/RR)*M0, where RR is the Reserve Requirement, M0 is the amount of cash in the system.

    If M0 = 0, then by definition the MS also equals 0. The Federal Reserve cannot remove all the cash from the system without reducing M1, M2, and M3 to 0 as well. The Fed also has sufficient bonds to do this, again because by definition the number of outstanding bonds owned by the fed is always equal to the amount of M0 (currency) in circulation (assets equal liabilities).

    You can understand this through a simple thought experiment.

    A bank does not have sufficient cash on hand to repay its obligations to the Fed. To meet those obligations, it must liquidate (or undo) its outstanding loans. The borrows must in turn liquidate their loans, and so on through the system.
  11. I think you're over thinking this. 'Creating' or 'destroying' money (through monetary policy) doesn't create or destroy wealth per se (there is a cost of producing money but it's small due to economies of scale and the efficiency gains of using money outweigh the alternative of bartering). As you've pointed out under very special circumstances banks might not have enough legal tender to pay back the FED. But that's more of idiosyncratic legal issue rather than an economic one. It doesn't the change the real value of goods and services in the economy.

    You can't create intrinsic wealth or value through the mere process of creating and using fiat money and conversely you don't really destroy intrinsic wealth or value by withdrawing use of fiat money. All you really need to get out from fiat money is that one of it's uses is as a nominal proxy for real goods and services because it's more efficient to use than a bartering system (there are huge efficiency gains from using the fiat system).

    It's interesting that the story you've referred to is a famous one (as you say in anti-kapitalist circles anyway). Personally I haven't heard those arguments before until this forum. If I give my forthright opinion on the matter laid out in the article that was linked or any other form of the same argument I find it logically fallacious because it fails to distinguish between real and nominal values. Real values are what matters.

    *I use efficiency, real, and nominal in the economic sense.

    EDIT: For emphasis, I will use the example of fed conducting monetary policy by injecting funds into the economy. The fact that they are 'printing' billions and billions of dollars doesn't mean real wealth has just been created out of thin air. All it means is the amount of money (i.e. nominal value) in the economy has increased but (all else being constant) the amount of real goods and services is the same. That is, nominal values have changed but the real values haven't.
    Last edited: Oct 27, 2010
  12. vanesch

    vanesch 6,236
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    I wasn't talking about value o wealth at all, you know. Purely monetary considerations. "conservation laws" in the money flow is what I'm talking about.

    I know but that's absolutely not what I was talking about. My example was of course abstract and idiosyncratic, but just to isolate a single issue. A gedanken experiment that helps me go to the exact point I was looking at, namely something like "the law of conservation of money under the hypothesis of a loan from the FED". So I do away with everything that doesn't play a role in THIS particular issue in my gedanken experiment.

    I know, but again, I wasn't, in any way, making any reference to real value or wealth.

    True, but you also have to look at the conservation laws in the money fluxes themselves, independently of what they represent as economic value.

    I wanted to find out whether there was a "leak" in these flows with FED loans. Turns out there IS actually a leak, UNLESS the government issues bonds at the same rate as the interest that is paid back on the FED loans AND the FED buys these bonds (in other words, injects exactly the same amount of base money as it took out). The point is that the one who "gets to spend it" is the government.

    So I *think* the issue I had is solved by this:
    there is conservation of base money when there are FED loans when:
    - the FED takes (and hence destroys) the money corresponding to the interest rate on the loans
    - the state issues bonds equal to this amount (hence can balance a deficit of exactly this amount)
    - the FED buys those bonds and issues an equal amount of base money

    As total amount of base money is conserved in the combination of these 3 operations, there are no inflationary pressures due to this operation, and the state is to spend an amount of money equal to the interests paid to the FED without compensating this with taxes, and without creating debt.

    So it is AS IF you paid your interests on your FED loans DIRECTLY as a tax to the state.

    I wanted to hear some comments on that - I have the impression it is correct.
  13. vanesch I'm still not sure what you mean so I just want to clear a couple of things up with my interpretation of your post and hopefully you can help clarify a few things I don't quite understand.

    Ok this is what I think your example means:

    - Suppose there is no legal tender in the economy. The FED lends out $100 (principal) to person A on the promise that it will be paid back with interest of say 10% (i.e. $10) in a year's time (that is A has to pay Fed back at year end of $110). So at start of year 0 the money base equals $100. At end of year 0 the money base is -$10.
    - At start of year 1, the government issues $10 bond. The Fed immediately buys that $10 bond (ie injects $10 into money base). Net result from this transaction is money base is 0.
    - Assuming Fed was charging govt. the same interest, at end of year 1 government has to pay back $11 even though the money base is 0. So end of year 1 the money base is -$11.
    - This process can be repeated infinitely.

    From this example you conclude that:


    From these statements I don't understand why:
    - 'the one who "gets to spend it" is the government';
    - 'there are no inflationary pressures due to this operation' (I understand why there might not be inflation since there is no money in the economy or negative money but I don't understand why inflation is relevant in this economy);
    - 'the state is to spend an amount of money equal to the interests paid to the FED without compensating this with taxes, and without creating debt. So it is AS IF you paid your interests on your FED loans DIRECTLY as a tax to the state.'

    I think you may have a set of perfectly reasonable arguments but I'm not sure I understand what they are yet and I want to clarify the things I don't get.
  14. vanesch

    vanesch 6,236
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    Right. Remember, I'm just trying a gedankenexperiment to try to understand the flow of base money. I'm not thinking of any realistic economy problem here.



    Ah. Interesting. I didn't know the FED was charging Gvmt any interest, and I didn't know that the Gov. had to "pay back" bonds that the FED owned. I thought they went "into the bit bucket". This complicates the issue somewhat, then.
    Let us, for the moment, assume that bonds bought by the FED are "put in the safe forever" and never come out anymore, nor should the gov. pay any interest to the FED for the bonds in their safe.


    Government spending is equal to T + dD + dM0
    T = taxes
    dD = debt increase
    dM0 = money base increase by the open market operations of the FED.

    If T and dD = 0 in our example, the government can still spend dM0, equal to $10,- here.

    Yes, this is true. Consider my example as "delta's" on top of an existing, fixed amount of money.
    What I meant was, this operation doesn't bring any money IN or OUT of circulation after all. As much is destroyed as there has been created.

    So do I, I want to understand the money flow from a physicist's PoV :-) Conservation laws and the like...
  15. Yep. Open market operations means buying and selling financial securities which including government bonds eg. treasury bonds.

    vanesch I think you're confusing some concepts here. Government spending (G) = T + dD. There is no dM0 in G. G represents a quantity of real goods and services which can be denominated in fiat money (i.e. M0) or some other form of medium of exchange. Adding dM0 would be double accounting. This is what I meant in my earlier post in making the distinction between real and nominal values. Increasing M0 doesn't increase G (with a caveat; if govt. obtains more amount of money they can use it immediately to acquire more goods and services (i.e. arbitrage) but over the long run prices of goods (i.e. nominal values) will change to reflect the real value of goods; you can change nominal value of goods but not the real value of goods by increasing M0).

    The convention in economics is to denote flows like G, investment (I), consumption (C) etc. in real terms but denominated in nominal values (See here national income identity).
    Last edited: Nov 5, 2010
  16. vanesch

    vanesch 6,236
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    Yes, I know that. But as long as the FED holds the bonds of the government, I thought it was as if they didn't exist. In other words, the government issuing bonds, which are then bought up by the FED, is in fact nothing else but the Government printing fresh (M0) money out of thin air (but does it via the FED).

    I thought it was only whenever the FED decided to sell bonds again to the public by taking in (M0) money, that the government was to pay these bonds ; in other words, the FED selling bonds to the public comes down to the state taking in taxes and burning the money (back into thin air).

    As long as the gov. bonds are in the FED's safe, it is as if they never existed, and as if the government had printed money.

    I thought that that was the fundamental principle of the open market operations: printing money and destroying money in the money base - only they do it via an intermediate piece of paper called a government bond.

    Ok, we are touching the heart of the problem here. I thought that open market operations were (indirectly) the government printing fresh money or destroying old money (in which case you can understand this term must enter into the balance for G and is no double counting).

    I thought it went like this (hypothetical thought experiment):

    The government has earned, say $ 100 billion in taxes.

    The government issues $ 50 billion in bonds.

    The government has now 150 billion to spend.

    (this is your equation: G = 150 b = T + dD = 100 b + 50 b)

    However, the FED buys up 40 billion of these newly issued bonds.

    This means that there are only 10 billion bonds in private circulation (so this is the ACTUAL debt increase dD of the gov), and has issued 40 billion of new dollars (d M0).

    So the original 50 b is decomposed in 10 b actual debt increase (dD) and 40 b money base increase (dM0).

    This is the *monetary* flow. Not the flow of actual value, where there is no such thing as issuing "base value" out of thin air, I agree there. But I'm interested in the flow of money here, not of value.
  17. The Federal Reserve is an independent organization; it is not a part of the "government", as you mean it.

    Treasury bonds held by the Fed still earn interest (payable by the Treasury to the bond holder) and have a maturity date, and indeed for practical intents and purposes the Treasury cannot differentiate between bonds held by the Fed and bonds held by the market. The only exception of note is central bank profits - if the Fed is revenue positive at the end of the year, the earnings are transferred to the Treasury.

    When the central bank buys bonds on the open market, it is typically (but not necessarily) buying them from private bond holders, and not from the Treasury directly. Vise versa, when the Treasury issues bonds, it is typically selling them to private investors, and not to the Fed directly. This independence is critical to the apparent stability of the currency; if the Board bought Treasury's directly, it would radically devalue the dollar (the implication being the Treasury cannot find willing buyers on the open market).

    The government has no control over the money supply; the Reserve Board has that power as an independent authority. The Treasury only has legal power to destroy damaged currency, to be replaced with new, a supply-neutral activity.
  18. vanesch

    vanesch 6,236
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    I know, but let's call "government" then both together, with independent decision makers. Let's call it "the state" although I know that officially, the FED is a private institution, it is unique, and has a public mission (namely issuing national fiat money).

    I didn't know that.

    Ok, so this is again a left hand right hand trick, right :-) So FAPP (for all practical purposes) we can consider that the Government gives interest to the FED which it gets back at the end of the year.

    I know, but again this is a closed loop: the Gov. issues bonds to private investors (which give currency to the Gov. in exchange for a newly printed sheet of paper - the bond).
    These private investors sell their bond to the FED which prints new money to buy it.
    The Gov. pays interest to the FED with "old" money, and the FED gives it back to the Gov. at the end of the year (this is something I didn't know, but I think it remains a zero-operation).

    If you call the union of Treasury, FED and Gov. "the State", then the net operation of issuing bonds which are bought up eventually by the FED is the FED printing new money and injecting it, through government expenses, into the money circuit.
    In other words, the State prints fresh money to pay state expenses with.
    (the different institutions simply serve as a kind of safety lock so that not a single person can do crazy things and harm too much the confidence of people in national fiat money).

    I have to say I'm not explicitly interested in the US system ; I think the US system is a model for several other fiat money systems, so I want to understand how it works.

    After that, I would like to understand how the European system works, because it must be a unique system as there is not a single state associated with a Central Bank.


    Yes, I understand that these are institutions with independent decision power, but I consider them all as being part of "The State".
  19. What the government gets back isn't the interest its paying on the bonds, but the revenues the Fed generates through its open market operations; government coupon payments are just one piece of this revenue. Remember, in addition to to Treasurys, the Fed is buying and selling all kinds of securities, and earning fees and interest on its independent loans. The Fed also has expenses; it has to finance itself, and often loses money on its exchanges.

    What the government gets back is just the banks profits.

    This is not necesarily the case. The Treasury sells government bonds when its expenses exceed its revenues. The Reserve Board buys government bonds when it wants to increase liquidity in the system. These activities are separate and independently motivated.

    One does not follow the other, and there is only a tacit connection - the Fed deals in Treasury bonds out of convenience, not of necesity. It could just as easily trade in foreign debt, private debt, or commodities. In some countries, the central banks deliberately diversify their holdings; their Central Bank might trade more in US government debt or dollars than in local currency and/or local government debt.

    Think of it this way; treasury bonds are a vehicle which the Fed uses to get from point A to point B on the open market operations highway. Traveling the highway only requires that you have a vehicle; the type isn't really important. They all have their advantages and their disadvantages. Countries that want to maintain fixed exchange rates tend to prefer commodities or foreign currencies. Countries that have floating exchange rates tend to prefer local currency and debt denominated in that currency.

    Even the Federal Reserve doesn't deal exclusively in US Treasury debt. At the height of the financial crisis, it bought private mortgage-backed securities. It regularly trades in foreign and private debt, and maintains a sizable stock of gold reserves beneath New York city (famously stolen in Die Hard 3), and recently began trading in a number of more exotic debt instruments. Check it out here:


    Treasurys account for only about a quarter of the Board's current assets.

    I think I addressed this above, but let me try to be more explicit; I meandered alot. The Fed wants to inject new money into the system. Treasury certificates are often a convenient and available means to do this, and because of their influence on the broader loan market, trading in them has the added benefit of pushing interest rates in a desired direction.

    However, the Board's desire to adjust the money supply is not dependent on or directly linked to government bonds. If they weren't available, or for whatever reason the Fed didn't want to trade in them at the moment, it - like any investor - has an array of available options, including gold, corporate bonds, or foreign debt.

    There is no intrinsic link between the government issuing new debt and the Reserve Board buying and selling that debt.

    The ECB is modeled off of the Fed, and once you understand the process, you can apply it anywhere. Forgetting the institutional nuances between bank systems, the underlying rules are the same. It's all driven by the so-called "impossible triad": a country cannot simultaneously manipulate the interest rate, exchange rate, and inflation rate. It can buy points in one, but it has to sell points in the other. Central Banks are set up to manage these trade offs in an organized fashion.

    This is usually restated as a country being unable to have all 3 of the following:

    1. Fixed exchange rate
    2. Free flow of currency
    3. Independent monetary policy

    The United States has 2 and 3. China has 1 and 3. Hong Kong has 1 and 2. Europe, like the US, has 2 and 3. Make sense?
  20. vanesch

    vanesch 6,236
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    I know, but all else equal, if the government pays one single extra dollar of interest to the FED, the FED earns one extra dollar in benefits, so a delta on the interests of government to the FED flows back to the treasury. In other words, the government shouldn't care about the interest rate it has to pay to the FED. It will flow back in any case.

    I know, but the motivations behind the decisions of these different parts of the State don't really matter if one wants to understand the pure money flow.

    Remember, the initial problem I wanted to understand was:

    If a bank gets a loan with the FED of $100,- and has to pay back this loan at the end of the year with 10% interest (say, I know my numbers aren't realistic), then it has to pay back $110,- . This means that $ 10,- base money is withdrawn from the system, and that the FED has made $10,- extra benefit (all else equal).

    Now, if the FED's policy is to keep the amount of base money constant, then it sees that during the loan, $100, - extra base money was injected, and now $110,- base money has been withdrawn. It should hence, in the interest of its policy, inject $10,- into the circuit, by buying federal bonds.
    Now, the gov. issues $10,- worth of bonds (this is unrelated to this, if you want to, we can think of the gov. issuing much more and just looking at the difference), and the FED buys them up, in its monetary policy to inject $10,- in the circuit.

    The total operation is now:
    - the FED earned $10,- as interests on the bank loan,
    - the FED used $10,- to buy up the bonds.

    The private bank has given $10,- of its benefits to the FED as interest on the loan.

    The FED has now $10,- worth of bonds in its safe, and the government has issued a $10,- bond and got $10,- for it, which it can now spend as government spending, say, to buy doughnuts for the President.

    The final balance is:

    - The amount of base money is constant.
    - The private bank paid for the doughnuts of the President
    - There's now a $10,- bond lying in the FED's safe.

    Anyway, thanks for your efforts in trying to help me gain insight in this matter...
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