Banking Intermediation, FRB & Bank Runs

Having described the tools available to the ECB (and these can be generalized to other CBs), I would like to briefly consider the functioning of the banking sector. In this post I will consider the very basic concepts of banking intermediation,  such as fractional reserve banking (FRB) and the logic of bank runs. This post belongs to a long postponed series summarizing the very few and limited financial insights I have stumbled upon over the years. Here, I begin by considering first, Banking intermediation, then Fractional Reserve Banking (FRB) and conclude with an overview of the ensuing consequences, with a focus on Bank Runs.

Banking intermediation

Before considering issues such as the money market, I will discuss the banking sector in an unregulated, unsupervised environment, where CBs do not exist. Although it means I will momentarily exclude some crucial aspects of modern money markets, it has several advantages. For one, people do not borrow from the central bank. They borrow from commercial banks, who themselves borrow from one another, from other financial institutions and, of course, from the Central Bank. Therefore, in order to understand money markets it is necessary to understand how financial intermediation happens between financial institutions, and between them and companies and individuals. It is through this inquiry that it is possible to understand how unrepresentative the previously presented model is of the deeply imperfect nature of this market.

Fractional Reserve Banking

If you have the time and are interested, Fractional Reserve Banking is well explained in this 1964 report to the Subcommittee on Domestic Finance of the Committee on Banking and Currency of the US House of Representatives. It is also well explained in this 1932 report of the Committee on Finance and Industry of the British House of Commons. It’s not a particularly new business model, so these exposes are not outdated. Nevertheless, the main point is that money can be multiplied in the banking sector through leverage and lending.

A common and simple example of how it works can be laid out as such (the following is taken from this wikipedia article, as are the table and the chart):

“The relending model begins when an initial $100 deposit of central bank money is made into Bank A. Bank A takes 20 percent of it, or $20, and sets it aside as reserves, and then loans out the remaining 80 percent, or $80. At this point, the money supply actually totals $180, not $100, because the bank has loaned out $80 of the central bank money, kept $20 of central bank money in reserve (not part of the money supply), and substituted a newly created $100 IOU claim for the depositor that acts equivalently to and can be implicitly redeemed for central bank money (the depositor can transfer it to another account, write a check on it, demand his cash back, etc.). These claims by depositors on banks are termeddemand deposits or commercial bank money and are simply recorded in a bank’s accounts as a liability (specifically, an IOU to the depositor). From a depositor’s perspective, commercial bank money is equivalent to central bank money – it is impossible to tell the two forms of money apart unless a bank run occurs (at which time everyone wants central bank money). At this point in the relending model, Bank A now only has $20 of central bank money on its books. The loan recipient is holding $80 in central bank money, but he soon spends the $80. The receiver of that $80 then deposits it into Bank B. Bank B is now in the same situation as Bank A started with, except it has a deposit of $80 of central bank money instead of $100. Similar to Bank A, Bank B sets aside 20 percent of that $80, or $16, as reserves and lends out the remaining $64, increasing money supply by $64. As the process continues, more commercial bank money is created. In the real world, the money a bank lends may end up in the same bank so that it then has more money to lend out. Although no new money was physically created in addition to the initial $100 deposit, new commercial bank money is created through loans.”

There are Several criticisms of FRB, some of which have been highlighted by mainstream economists. Milton Friedman did so in A Program for Monetary Stability , reviewed here by Ritter for the American Economic Review. Inving Fischer (of the Fischer equation) also criticised it in 100% money.The main concern is that Fractional reserve lending implies that money is created ex nihilo. Because money is created out of thin air criticisms generally point to the fact that debt demands more debt in order to be paid off, that FRB exacerbates the business cycle and that it leads to inflation. These days however, only the Austrian School seems to maintain its fervent opposition of this form of banking. Critics from this school of thought, such as Soto or Caplan, Zarlenga and Ron Paul.

I will not engage in a full fledge debate of this issue by advancing a consistent argument about how the benefits of FRB outweight its costs. I do not disagree with the diagnosis.  Finance is an extremely imperfect market with plenty of pitfalls. My disagreement lies with the treatment. Whereas the Austrian school would do away with FRB altogether, I must boringly stand with the establishment and prefer regulation over prohibition. That being said, regulation (and for that sake participation) still requires an understanding of this market. Below I describe some of its most striking features.

Implications – Lending, Reserves, Liquidity, Solvency and Bank Runs

The most contemporary, simplified and stylized description of the functioning of Fractional Reserve Banking was provided by Diamond 1997. In my understanding, the article does two interesting things. First it explains how banking intermediation is paretto efficient, in that it provides more liquidity than would be available otherwise, which in turn should allow for higher consumption and higher intertemporal utility. Secondly, it describes the process and logic leading to bank runs. Because I am interested in understanding how the financial sector ( of which banking is a part) works, I shall focus on the second point. In my description of the model for bankruptcy conditions I admittedly add some things and exclude others. If this leads to confusion I apologise.

Diamond models a financial world with 3 periods, 2 types of depositors and a range of unknown investments.

In the first period, period 0, investors chose between two investments. The first one is a liquid asset, which yields returns “R” after one period. The second is a less liquid asset which yields returns “X” after two periods. For the sake of argument, “R<X” and the investors divide all of their wealth between the two assets, so that a fraction “α” of it is invested in the liquid asset and a fraction “1-α” is invested in the illiquid asset. For the time being we will not make assumptions about the size of “α”.

If everything works as expected, at the end of period 1 (the second period) investors would take their returns from the liquid asset and reinvest it in 1 period liquid assets one more time. This would imply the following structure of assets/investments and expected returns at each period:

However, the model goes on to postulate that there are two individuals in this modeled world. Type 1 individuals suffer a liquidity shock in period 1 (the second period), which requires them to liquidate all of their assets in period 1 in order to satisfy the liquidity shock. This means that in period 1, a fraction “p” of the total population of investors, corresponding to those who belong to type 1. To satisfy the costs of the liquidity shock, type 1 individuals must liquidate all of their assets in period 1. Because the asset yielding R after two periods is illiquid, it cannot be sold in the first period for its full value. As a result, in order to satisfy their liquidity needs in period 1, type 1 individuals will have top sell the illiquid asset at a discount, “P”. This means that while type 2 investors continue to enjoy a structure of investments and returns as before, type 1 investors now face the following structure:

So far so good. Presuming that the shock in period 1, “Z”, is indeed a liquidity shock, then

However, if the shock is too high, then it is possible that it will be a (in)solvency shock:

So far the model says nothing about banking. What would a bank do in this model?

Banks as liquidity providing intermediaries

Consider that a bank exists such that in exchange for deposits, it provides liquidity, and intermediates between “would-be investors” and “investments”. In this case “investors become depositors and the bank becomes the investor. The big difference is that in this case the bank is available to supply full liquidity to type 1 investors in period 1, so that if they decide to withdraw all of their funds in that period, the bank promises to provide them with a return R on all of their deposits, despite only actually getting a return of R on “α” of its investments, which still correspond to the fraction invested in liquid assets. As a result, the bank has total assets to the value of

And total expected liabilities of  “pR”. Therefore, the Bank Run Condition, that the total liquidated value of the bank’s assets be below the expected liability payment is:

It is important to understand that the equation is a condition, not a causal relationship. Therefore, and because it is an inequality it is possible for variables to vary on either side of the inequality without causing a change to the other side.  In this case, a run on the bank is more likely as,

  • p, the probability of a solvency shock, increases,
  • P, the discount price of the illiquid asset decreases
  • R, the returns on the liquid asset decrease.

Complementarily, with a shock to expected retuns of the liquid asset,

In this case, a run on the bank is more likely under similar circumstances as before, and as

  • q, the probability of a shock to the liquid asset, increases
  • S, the size of the shock to the liquid asset increases

Other issues: Differences in investment, type 2 participation and risk misperception

It is possible to account for some more levels of complexity in this model. First, I consider what happens when the fractions of liquidity preferences differ between the bank and the depositors. In this case, say that while depositors continue to expect the bank to face a solvency condition of

The bank actually faces a solvency condition of

In this case, for the bank to remain solvent, there’s an it’s investment plan must be such that its actual assets are at least as high as its perceived assets condition:

Therefore, if , then the discounted value of the illiquid assets must be at least as high as the value of the liquid assets.

Next I consider the condition under which Type 2 individuals participate in the bank run. Assuming that these individuals can observe the effects of the liquidity shock in period 1, they will consider the structure of the bank’s assets and liabilities in period 2.

Period 2 Bank Assets:  

Period 2 Bank Liabilities: 

If condition for type 2 individuals to participate in a bank run, that the bank’s assets in period 2 be less than it expected liabilities, can be shown to be

Which is a less stringent condition than for type 1 individuals, because pR<R.

Finally, it is interesting to consider the case where depositors have a misperception of the likelihood of their own liquidity shock, so that they presume it to happen with likelihood p, but it actually happens with probability p’. Assuming that  then,

Type 1 Depositors expected solvency condition:  

Bank’s expected solvency condition:  

This can be shown to yield the following bank run condition

Therefore, the risk of a bank run will increase with the mismatch between actual and perceived liquidity shock probabilities (if p-p’ is positive and large) and if the bank decides to invest a lot in less liquid assets (if β is very much higher than α).


Diamond established that due to imperfect information about future shocks which impede perfect foresight, banks are able and likely to face bankruptcy when they operate within the model of Fractional Reserve Lending. However, imperfections also arise from asymmetries of information between lenders and borrowers.

The next post will consider this issue at length.

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2 Responses to Banking Intermediation, FRB & Bank Runs

  1. Pingback: The Daily Climb « georgesblogforum

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