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First of all, fed funds rate is the rate banks borrow reserves' from each other. Interest rate on loans is the rate the bank charges to public for its loan. From one line of logic, we think of the rate bank charges to public should clearly be greater than the interest rate itself bear to borrow since banks are making a margin. And empirical data clearly support it.

However, another line of logic does not quite support it. We know the banks borrow reserve money in fed funds market, which is clearly better than the money it lends to the public in the following sense: one unit of fed funds can support 10 units of additional deposit if the reserve-deposit ratio is 10%. So the banks with this addtional 1 unit of reserve, can theoretically make 10 more units of loans and therefore creating 10 more units of deposit. So reserve is better money. Hence, theoreticaly, the fed funds rate should at leastbe higher than the rate banks make loans to the public, if not 10 folds.

My question being whether there is a logical fallacy in my understanding and if not, what kind of reality deviated it from theory.

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I know saying banks creating money is going to raise rage from a wide range of people, even economists. But anyway, this is the truth. – Kun Nov 21 '15 at 17:40
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One thing that you need to change in this question is that you seem to have a fundamental misunderstanding of how the money multiplier works. It is not that a bank receives 1 and can loan out 10. It is actually that a when a bank gets 1 they can only loan out 0.90 (with a reserve requirement of 10%). This fundamental misunderstanding is what lead you to believe that there would be an incentive for banks to drive the federal funds rate above the nominal rate on interest. I would recommend you watch the following video: youtube.com/watch?v=lMpmwcSMQTw – DornerA Nov 23 '15 at 17:51
    
I recommend you reading this essay published by the Bank of England. bankofengland.co.uk/publications/Documents/quarterlybulletin/… – Kun Nov 24 '15 at 14:26
    
@DornerA Kun's understanding is actually correct. The exact nitty gritty transaction details are inconsequential to the basic concept at large which is that more reserves do allow for the creation for more bank deposits because of the money multiplier. Banks do not directly influence the Fed to inject more reserves into their coffers, but their indirect actions do. – user2662680 Dec 2 '15 at 0:10
    
@user2662680 you are not arguing the same point as he is. You said that more reserves lead to banks (PLURAL) creating more deposits. His misunderstanding comes when he says that a bank (SINGULAR) that gets 1 dollar can instantly loan out 10. The money multiplier works because the money travels through many (in theory infinitely many) banks. – DornerA Dec 2 '15 at 0:25
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I think you are missing the credit risk attached to any loan. You, as an individual borrower, are far more likely not to reimburse your loan than a bank. Thus the loan is far less risky.

Central bank money could only be qualified as "better" (even that does not mean much) because it is issued by the Central bank, deposits are issued by commercial bank, so you bear the risk that your bank fail, but it happens that in most country individual deposits are insured by some state agency. So I cannot really see why central bank money would be better than deposits.

Nowadays, the amount of reserves that a bank must hold does not actually play a big role in the economy (as opposed to what most of economic textbooks and economic professors are teaching in undergrad schools). The most important part is the interest rate that is paid on those reserve, which is fixed by the central bank and which act as an opportunity cost for the bank when it decides to lend to an individual rather than holding reserves.

However I see your point, but the fact is that this way of thinking is misleading. Banks create (in theory) as many loans as they want, because there are no physical constraints, if you want, that prevent them to do so. The only constraint is a regulatory constraint that states that in order to remain solvent (in order to be able to repay the depositors) banks should invest x% of the assets in reserves. Those reserves would be held on a central bank account in central bank money, and the return on those reserves will be the fed fund rate decided by the central bank (the same way a commercial bank decide how much interest it will pay on your savings account). So it is true that one more unit of reserves gives the right to issue more than one unit of loans but this does not mean that one money is better or worse than another. It's is just a matter of regulation.

It may be hard to get, but the point is really that central bank money is safer so cheaper than deposits, no matter what regulatory constraints apply to banks.

You may want to read this paper which may be a bit complicated but you should get the intuition. This two docs may be simpler (with nice pictures) : doc 1, doc 2.

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I take your point about the cedit risk. But fractional reserve means with 1 unit of reserve, the banks can generate 10 units more loans hypotetically, right? Even accounted for credit risk and possible transfer of the deposit issues to other banks, which will cost reserve, the reserve money's interst rate should be higher. In other words, reserve money is better than deposit because 1 unit of reserve can support 10 units of deposit (loans). And hence 1 unit of reserve earns 10 times the interest a 1 unit deposit could earn. Do you see my point? – Kun Nov 21 '15 at 20:34
    
First, fractional banking generating 10 units of loans for 1 units of reserves would work only when a) money supply is not fixed by the central bank and b) the bank in question is the only bank in the economy.. – ChinG Nov 21 '15 at 21:00
    
@ChinG What do you mean by money supply is not fixed by the central bank? In this argument, let us assum central bank fix monetary base. Moreover, the bank in question is certainly not the only bank, otherwise there is no borrowing in fed funds market. – Kun Nov 21 '15 at 21:25
    
@Kun I just edited my answer, does that sound clearer? – Louis. B Nov 21 '15 at 22:37
    
@Louis. B I think the paper you suggested answers just what I am wondering. I will take some time reading it and hopefully I will learn something! Thank you very much. – Kun Nov 21 '15 at 22:45

Loans in the federal funds market are also nicknamed 'overnight loans.' This means they cannot use that money to make loans because the money gets returned as soon as the bank's reserves are cleared by the Fed.

If the lending bank was willing to use the money for an asset such as a loan, they would simply loan it to a consumer at the higher rate. There is no way that a bank would loan to another bank for any long period of time because, as you pointed out, they can get a higher rate of return by loaning it elsewhere. Typically, the banks that are lending in the federal funds market are banks who have decided to hold excess reserves for one reason or another. If the bank was looking to loan the money for a period of time, they would have already done so outside of the federal funds market.

Also, if the federal funds rate was higher than the nominal interest rate, banks would not go to the federal funds market to get a loan (because they can get one for cheaper in the public market), which would make the existence of a federal funds market pointless.

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I agree with the first two paragraphs. I disagree your claim in the third paragraph. Banks need reserve to satisfy the deposit reserve ratio, so they either need to decrease deposit or increase reserve. If the requirement is 0.1, i.e. reserve/deposit>0.1. Borrowing 1 unit from the Fed funds market increase the numerator and borrowing from the public means a decrease in their demand depsoit (because by borrowing we mean deposit becomes loans on bank's liability account) decrease the denominator. Simple algebra means borrowing one unit reserve from fed funds and one unit from public is different – Kun Nov 22 '15 at 18:54
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You are misunderstanding what I said. I am not saying that the bank would be borrowing from the public (against their deposits). I am saying that the bank would borrow from another bank at the nominal rate (because it's lower). It is the exact same transfer as borrowing in the federal funds market. – DornerA Nov 22 '15 at 18:59
    
Well, directly borrowing from other banks is the definition of fed funds market (if you mean transfers of reserve) . Fed funds market is not operated by the Fed, only the discount window is. – Kun Nov 22 '15 at 20:01
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Ok, if that is your hangup think of it this way. Suppose banks can only borrow in the federal funds market. Also, suppose the federal funds rate is higher than the nominal rate of interest. Banks would simply forgo lending past their reserve requirement because their rate of return would be lower than the rate they need to pay to borrow the money, so no trading would occur in the federal funds market. Therefore, the federal funds market would serve no purpose. – DornerA Nov 22 '15 at 20:05
    
Okay. So you still did not get my point. I am saying 1 unit of fed funds support 10 unit of borrowing. So even if fed funds is say 2 percent, you would still be lending 1 percent if there is perfect demand and no risk . This is beacuse with 1 unit reserve, you are now lending 10 unit, which earns you ten times 1 percent, which is 10 percent. – Kun Nov 22 '15 at 20:44

The core premise of your question is correct. Banks receive a tremendous advantage from Fed actions and any discerning economist should be concerned over the amount of corporate welfare doled out banks....especially as they will take that money and engage in maturity mismatching which is an incredibly volatile, dangerous and inflationary practice that transfers wealth from the public to the private banking sector.

There are many such ways banks receive corporate welfare. This includes Fed dividends (for not loaning out 100% of our deposits!). It also includes interest on "excess reserves" (again our deposits). Troubled banks are given below market interest rates with discount window loans. But the bigger problem with the discount window is that it creates a certainty that the Fed will backstop bad behavior. Then there is the open market. The Fed overpays for REPO's from special banks (primary dealers). There is also a good reason to suggest the REPO market is being churned as well to encourage excess trading volume. But the big problem with the open market is it provides artificial liquidity guarantees to the banking system at large. If banks know that the Fed will ensure that the money market will hum along at a very low rate, then they are more apt to engage in maturity mismatching which creates inflation and volatility. The entire system is corrupt beyond belief and most economists are totally oblivious to this reality.

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Hi. This answer seems to mostly be opinion (and or rhetoric). Your answer would be greatly improved if you are able to back these statements up with any facts or possibly a model. – cc7768 Dec 2 '15 at 1:12
    
The question is not a math one. It's one of policy. You can not understand central banking without understanding the political philisophy behind its actions. It is an illusion to keep separate economics from politics and any attempt to do so will result in confusion. – user2662680 Dec 2 '15 at 1:29
    
I didn't ask specifically for mathematical facts (it happens that I find models and numbers to be convincing but I understand people find different types of arguments to be useful). As is, your answer is a series of unbacked assertions. It would greatly benefit from a reference to any type of research (economic or political science based -- a newspaper article might even be better than nothing). Although I believe you and I disagree about this topic, a well informed answer I disagree with can still be a high quality answer. – cc7768 Dec 2 '15 at 1:40
    
A mathematical framework is worthless without proper conceptual context. eg I can mathematically calculate how fast a ball will drop using physics, but if I don't have the right variables/context (like wind resistance), my formula is worthless. This is a conceptual/political paradigm so political answers are apt. As for a references, this is a circular demand. A statement can not not be validated by another. To imply otherwise is to advocate dogma and mob logic. If you have specific questions, I would be happy to answer them. – user2662680 Dec 2 '15 at 2:50
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What @cc7768 is saying is that if you are going to make assertions, back them up. Don't respond by saying maths without the right assumptions is worthless, back up your own claims with evidence. – Jamzy Dec 2 '15 at 23:25

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