Tuesday, March 12, 2013

Banking Example #5: Bank 'Spends' Excess Reserves

Examples of a bank spending money; in one case by crediting a deposit and in another by transferring reserves.

Setup: Two commercial banks, A and B, and two people, x and y. Reserve requirements are 10% of deposits, but there are no capital requirements. Person x banks at A and person y banks at B.


Initial balance sheets :

B, x, y
Assets Liabilities
$0 $0

Bank A
Assets Liabilities
$100 reserves (excess) $0
Negative Equity Equity
----------------------- $100


Balance sheets after person x does $10 worth of work for Bank A and the bank pays him.

Bank A
Assets Liabilities
$100 reserves ($1 required, $99 excess) $10 deposit for x
Negative Equity Equity
----------------------------------------- $90

Person x
Assets Liabilities
$10 deposit at A $0
Negative Equity Equity
----------------------- $10


Balance sheets after person y does $10 worth of work for Bank A and the bank pays her.

Bank A
Assets Liabilities
$90 reserves ($1 required, $89 excess) $10 deposit for x
Negative Equity Equity
---------------------------------------- $80

Bank B
Assets Liabilities
$10 reserves ($1 required, $9 excess) $10 deposit for y
Negative Equity Equity
--------------------------------------- $0

Person x
Assets Liabilities
$10 deposit at A $0
Negative Equity Equity
----------------------- $10

Person y
Assets Liabilities
$10 deposit at B $0
Negative Equity Equity
----------------------- $10


Note that since person x banks at A (the same bank buying his services) no reserves leave the bank to pay him. However, since person y banks at B, in order for Bank A to pay her, reserves are transferred to Bank B to back her newly credited deposit. In both cases, however, Bank A's equity decreases. Also note that only banks (and the Treasury/gov) have Fed deposit accounts, thus there are limited ways in which reserves leave the banking system (Treasury/gov Fed deposit accounts are not considered part of this "system."). Notice, for example, above that there are still $100 of reserves in aggregate (banks A and B) at the end of this scenario. Of this, $2, in total, was changed from "excess" reserve status to "required" reserve status. Joe in Accounting helped me with this example here and here.

Aggregation:

Now in terms of aggregates, let's look how the aggregated commercial banks purchased work from the aggregated non-bank private sector in this case (assuming each of these aggregated sectors consists of nothing but Banks A & B for the former, and Persons x & y for the latter):


Commercial Banking Sector
Assets Liabilities
$100 reserves ($2 required, $98 excess) $20 deposits
Negative Equity Equity
---------------------------------------- $80

Non-Bank Private Sector
Assets Liabilities
$20 deposits $0
Negative Equity Equity
----------------------- $20


So here the aggregated commercial banking sector purchased net $20 of services from the aggregated non-bank private sector (the "public") by crediting their bank deposits. Notice that the reserve level of the aggregate banks did not change. In a sense, reserves were not used for these purchases. This same method of payment for purchases applies to anything the aggregated banks purchase from the aggregated non-banks: the banks credit the non-banks' bank deposits. What they buy/pay-for can be anything*: physical cash (e.g. reserve notes and coins), employee time (salaries & bonuses), electricity, office supplies, donuts, contractor services, shareholder dividends, interest to depositors and bank-bond holders, rents, leases, real-estate, Tsy or other securities, or loans (i.e. the banks make new loans to borrowers).

Likewise (though not shown) the aggregate commercial banks sell-to/get-paid-by the non-bank private sector by debiting their bank deposits. This could be for cash, interest, loan principal, points or other service charges on loans & mortgages, account fees, money wiring charges, late fees, certificates of deposit (CDs), savings deposits, Tsy debt or other investment assets, or bank issued stocks (equity) or bonds.

So in summary when banks buy (sell) anything from (to) non-banks, payments are settled by crediting (debiting) bank deposits. The only exception to this is when the banks make purchases or accept payments with cash, but these cases can be seen conceptually as a two step process: first a credit or debit is made to a conceptual bank deposit, and then this conceptual bank deposit is debited or credited by either selling cash to or by buying cash from this same conceptual bank deposit holder: the net change in balance to the conceptual bank deposit is thus $0.

To summarize then, in aggregate:
  1. Banks buy stuff from non-banks (including new loans) by crediting bank deposits
  2. Banks sell stuff to non-banks (including the principal on loans) by debiting bank deposits

Notes:
*Subject to capital constraints

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  4. Two commercial banks, A and B, and two people, x and y. Reserve requirements are 10% of deposits, but there are no capital requirements. Person x banks at A and person y banks at B. GetSomeDosh

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