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If the Federal Reserve acts as a lender of last resort and steps in to prevent bank runs, then how do banks still fail?

Do they only step in if the bank is solvent but in emergency need of funds?

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First, it is actually not Fed that prevents bank runs. Bank runs in the US are prevented by Federal Deposit Insurance Corporation (FDIC) which insures deposits that people have at the bank up to \$250000. This is what prevents the bank runs as runs are created when people worry bank will fail and they will loose their deposits. This is because bank never has enough money to let all people withdraw them at the same time as loans are made long term while deposits can be withdrew at a depositors whim and consequently if people worry bank will fail they will all 'run' to their bank in order to make sure they get their money before bank fails and stops paying out deposits.

Second, generally and broadly speaking the literature agrees that there is some rationale for saving banks under two conditions (Hanson, Kashyap & Stein 2011; Osinski Seal & Hoogduin, 2013):

  1. They are systemically important (their collapse would lead to collapse of other institutions).
  2. They are only illiquid not insolvent.

The point 1 is considered to be more important than the second so even illiquid institutions might be considered to be worth saving if they are too systemically important.

Now Fed or other government bodies can't be always $100\%$ sure about how systemically important bank is or whether it is illiquid or only insolvent, but central banks around the world typically create and track some measures of systemic importance of various banking institutions. For example, Fed has whole dedicated unit/department just for researching systemic risk. In addition they will also try to estimate whether bank is insolvent or just illiquid. Lastly, since no research can give you $100\%$ correct answer at the speed Fed usually has to act there is also some discretion involved in the decision process. So partially it also depends on what decision makers at Fed think should be done in each specific case.

However, if some banks are judged to be insolvent and not systemically important they are routinely allowed fail. In fact as the data from FDIC show the total number of commercial banks that have to register for deposit insurance (basically any 'ordinary' bank) fell by almost 200 just between year 2018-2019.

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  • $\begingroup$ Ah that makes a lot of sense. I'm curious though, I see in many sources that the lender of last resort is to prevent bank runs. Is this the historical reason why they were created--a role now obsolete because of FDIC? Or is there some value in which a solvent, illiquid bank can push more pressure (if not a run) onto other banks as well? $\endgroup$ Dec 24 '20 at 18:21
  • $\begingroup$ @curiousgeorge historically Thornton and Bagehot argued that one of the reasons why there should be lender of last resort is also to prevent bank runs but those guys lived in past before anyone else thought of deposit insurance (if I remember correctly those gentleman lived in 19 century). In present day most economists consider the deposit insurance sufficient to prevent bank runs but central bank still has a role of lender of last resort but for the above mentioned reasons (the bank run was never sole argument for this function even historically). $\endgroup$
    – 1muflon1
    Dec 24 '20 at 19:44
  • $\begingroup$ I see thanks and lastly just to clarify when you say "saving banks" does that mean lending to them the amount they need at the discount rate? $\endgroup$ Dec 25 '20 at 1:27
  • $\begingroup$ @curiousgeorge it is not necessarily at a discount rate (although it might be). The issue is that if a company looks like it is going to fail nobody is willing to lend the company because debts are dischargeable in bankruptcy. Fed can simply lend the bank at ‘normal rate’ when nobody else would (I use ‘normal’ in quotation marks because there might be some people willing to lend even falling bank at very high rates on the off-chance it survives). Or sometimes Fed will ask for equity (stocks in return). It is very case specific and depends on what caused the failure in the first place $\endgroup$
    – 1muflon1
    Dec 25 '20 at 1:34
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This is a four page paper describing the loan loss reserve as "the money set aside to offset future losses on outstanding loans":

https://www.richmondfed.org/~/media/richmondfedorg/publications/research/economic_brief/2012/pdf/eb_12-03.pdf

However there is no "money" set aside to absorb bad debt charges in the income statement. Instead an expense for bad loan write-off will reduce the loan loss reserve, then reduce equity claims, and then reduce the claims of unsecured or uninsured creditors as the magnitude of the expense charge increases due to defaulted or non-performing loans in the asset portfolio.

As a matter of public policy the Lender of Last Resort operations should not extend to banks that do not have enough equity to absorb expected charges for losses in the asset portfolio. These failing banks are identified by safety and soundness metrics supervised by bank regulators and the failing banks are forced into the bank resolution process managed by the FDIC.

Bank deposit insurance schemes are similar to a loan loss reserve in the aggregate bank sector. Deposit insurance fees and provisions for loan losses are expenses in the income statement which both reduce retained earnings and thus reduce the growth rate of equity in a bank or banking sector compared to an accounting scheme which does not apply these expense customs. So one could just add the deposit insurance fund or loan loss reserve back to the loan assets and add it back to the equity claims and the books will balance. We see that banks are investing in a loan portfolio and the first loss on bad loans is charged to equity.

This 19 page paper describes how banks fail in a context where the credit standard (pledged collateral) does not cover the entire value of defaulted loans in a bank or banking system.

http://heterodoxnews.com/htnf/htn71/10466211.pdf

Banks advance loans in the absence of precise knowledge in relation to the outcome of borrowers’ projects. Consequently, uncertainty in relation to loan repayment emerges. Thus, banks introduce the ‘credit standard’ as insurance against loans, so that should borrowers’ projects fail, borrowers have an alternative means of honouring their debt obligations. It is argued in this paper that in the competitive atmosphere under which this sector operates, it is not possible to secure the entire loan portfolio by introducing the credit standard, and in recent years this difficulty has been further exacerbated by financial liberalisation, which may have caused bank failures.

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