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Banks, Bank Reserves and Deposits
- Read: Mishkin and Serletis, Ch. 15 and 16. Ch. 14 Central Banking is covered in Assignment 1.
- Key concerns in this set of notes:
- How is the quantity of deposits (bank money) determined?
- How does the central bank affect the money supply in practice?
- How does the central bank affect the overnight interest rate?
1
Money and Deposits:
- We know that there are two main types of assets serve as money in a modern economy:
(1) currency: coins and bills.
(2) (liquid) deposits at banks or ‘near banks’.
- We also know that most of the money supply is in the form of deposit money.
- Data from Bank of Canada website for July 2019 (M1+):
Currency outside banks $89 billionChequable deposits $942 billion
2
The Payments System: (see Ch. 16. 391-92)
Payments system: method of conducting transactions in the economy.
- Exchanges with currency: sellers receive currency from buyers.
- Exchanges involving deposit money: transfers between deposits
- Settled internally if transfer is between deposits at the same bank.
- Between depositors at different banks?
(1) Automated Clearing Settlement System (small transactions)
- sum up today’s cheques, debits (withdrawals) from Bank A paid to depositors at Bank B ;
- sum up today’s cheques, debits (withdrawals) from Bank B paid to depositors at Bank A;
- balance of the two sets of transactions is transferred between Bank A and Bank B’s accounts at the Bank of Canada.
(2) Large-Value Transfer System (LVTS): - concerned with transactions of $50,000+.
- Electronic, banks monitor their positions in real time.
- Can only make payments if sufficient funds at Bank of Canada, sufficient collateral or lines of credit with other members of the system (15 of them: banks, near banks)
- Transfers between accounts at the Bank of Canada at the end of each banking day.
3
Bank Reserves:
Bank Reserves:Are funds held by banks and near banks to meet their obligations to
depositors.
- Obligations? depositors’ may ask for some or all of their funds.
- What kinds of assets act as reserves?
- currency (coins and bills) at the bank or in its ATMs.
- balances (deposits) at the central bank (Bank of Canada)
i.e. to meet cheque-clearing / electronic clearing obligations.
Reserve ratio (r): reserves held as a proportion of deposits.
i.e. Reserves/Deposits
- Holding bank reserves imposes a cost on the bank:
- could used these funds for loans: interest on loans is foregone.
- So why do banks hold reserves? i.e. why isn’t r=0?
4
Why hold bank reserves?
- Compulsion!
In the past, Canadian banks had to maintain a minimum reserve ratio by law (“required reserves”)
e.g., 1980 Bank Act required $1 of reserves for every $10 of demand deposits (r=0.1 if banks met this requirement exactly)
U.S. still has compulsory reserve requirements for liquid deposits:- larger deposits: r=.10, r=.03 for smaller deposits.
(https://www.federalreserve.gov/monetarypolicy/reservereq.htm)
- Why have required reserves? raise confidence that banks can meet depositors demands for funds.
- Canada eliminated required reserves in 1994.
- Cost-benefit comparison: benefit of holding reserves exceeds cost
- The benefit of holding reserves? (cost: foregone loan interest)
- avoid customer dissatisfaction (cash in bank machines!): deposits are a bank’s raw material!
- avoid having costs of raising funds at short notice to meet depositors demands.
- borrow from Bank of Canada (at Bank Rate or higher).- borrow via markets or other banks- sell securities or reduce outstanding loans.
- these are all costly.
- So: hold reserves if anticipated costs of a shortfall are larger than the cost of holding reserves.
5
- Banks determine "r" taking into account :
- the possible costs of a reserve shortfall vs. cost of holding reserves (foregone interest income)
- “r” reflects the behavior of the bank
- Some variables affecting the size of “r”:
- attractiveness of making loans: - return on loans: opportunity cost of reserves. - perceived creditworthiness of potential borrowers.
- consequences of shortfalls:- borrowing rate for shortfalls- problems if unable to borrow (not an issue in Canada: Bank of
Canada) – a concern in times of crisis?
- likelihood of deposit withdrawals.
( A point about terminologyText, p. 380: makes a distinction between reserves held in normal times -- it calls these ‘desired reserves’ and reserves held in in times of crisis – it calls these ‘excess reserves’. They both reflect bank behavior – I will treat them as the same thing, i.e. my r=rd +e in text)
6
Deposit Expansion Process: a simple case
- See Mishkin and Serletis, Ch. 15
- Say that there is an increase in the quantity of reserves in the banking system of $1000
- Let: r = .10 (outcome of bank behavior)
Stage 1: Say that these new reserve funds are all deposited in Bank A:
Bank A sees both its deposits and reserves rise by $1000:
Change in Bank A’s balance sheet:
Bank A Assets Liabilities
Reserves +1000 Deposits +1000
- Bank A has extra reserves of $900.
- only: r x 1000 = 100 of reserves are needed to back the new deposits.
- Bank A lends out its excess reserves so at the end of Stage 1:
Bank AAssets Liabilities
Reserves +100 Deposits +1000Loans +900
- Loans are spent by the borrowers.
- those paid by the borrowers take the $900 and deposit it in their bank (say Bank B).
7
Stage 2: Bank B has $900 more in deposits and reserves
- New reserves are likely in the form of a transfer between Bank A's account at the Bank of Canada and Bank B's account at the Bank of Canada.
- Bank B needs .1x$900 in reserves to back these deposits: $90
- Bank B will have $810 to lend out so at the end of Stage 2:
Bank B
Assets LiabilitiesReserves +90 Deposits +900Loans +810
- The $810 of loans are spent by the borrowers.
- those paid by the borrowers take the $810 they are paid and deposit it in their bank (Bank C).
Stage 3: Bank C has $810 more in deposits and reserves
- Bank C needs .lx$810 in reserves to back these deposits: $81
- Bank C will have $729 to lend out so at the end of Stage 3:
Bank CAssets LiabilitiesReserves +81 Deposits +810Loans +729
- The process continues indefinitely.
8
What is the final effect of this deposit expansion process?
New Deposits created at each stage:
Stage: New deposits:1 1000 (Bank A)2 1000x(1-r) = 900 (Bank B)3 1000x(1-r)2 = 810 (Bank C)4 1000x(1-r)3 = 729..N 1000x(1-r)N-l
Total new deposits = 1000 + 1000x(1-r) + 1000x(1-r)2 + ...+ 1000x(1-r)N-l
= 1000x [ 1 + (1-r) + (1-r)2 + ...+ (1-r)N-l ]
= 1000 x 1 (true as N approaches infinity 1-(1-r) see Appendix)
= l000 x (1/r)
- with r=0.1 a $1000 increase in reserves will ultimately raise the quantity of deposits by:
1000/.1 = $10,000
9
Deposit multiplier: it is the multiple by which an extra $1 of reserves raises the quantity of deposits.
i.e., the quantity of deposits that can be supported with $1 of reserves.
- in the simple deposit expansion process the multiplier = 1/r
Deposit multiplier = 10 in the example (1/r = 1/.1 = 10).
- If the total quantity of reserves in the banking system was "MB" then the total quantity of deposits (DD) in the system would be:
DD = MB ∙ 1/r
- where “r” is the desired reserve ratio for the banking system.
- this suggests another way of looking at the relationship between reserves and deposits:
MB = r x DD
i.e., DD amount of deposits that "uses up" all available reserves (MB) given that the reserve ratio is ‘r’
- Total stock of reserve assets (MB) is called:
High-Powered Money or the Monetary base
10
Deposit Expansion and Multipliers: More Complicated Cases
- Case above is very simple: possible complications?
- Could allow for different types of deposits each with a different "r"
i.e. high turnover types of deposits may have a higher ‘r’
(a more complex multiplier could be found that depends on desired r for each type of deposit and the publics desired share of funds in each type of deposit);
- Could allow households and businesses to hold some of their money as currency rather than as deposits.
i.e. now: two uses for reserve assets: (1) act as reserves for deposits;(2) act as currency in hands of public.
- look at this case (text does a version of this case).
11
Deposit and Money Multiplier when the Public Holds Currency:
- In the case where reserve assets can be held as currency as well as reserves less deposit money is created for a given value of MB.
Define: c = Currency / Deposits = Currency/DD (a desired ratio)
then when reserve assets are all "used up":
MB = r DD + c DD
and so: DD = MB x 1/(r+c)
where 1/(r+c) is the deposit multiplier when the public holds currency.
e.g. if r=0.1 (as above) and c=0.1 (in line with Cdn. data)
Deposit multiplier =1/(.1+.1) = 5 (vs. 10 in simple case)
- Size of the money supply in this case?
Money supply (M) = Currency + DD = c DD + DD = MB x (c+1)/(r+c)
(c+1)/(r+c) = is the money multiplier
Money multiplier: shows how much an extra $1 of reserves expands the money supply.
(Reminder: the textbook is slightly different since it breaks MB into two types of reserves ‘desired’ and ‘excess’ which have their own reserve ratios rd and e. So where I have ‘r’ they have rd+e )
12
Monetary Base, Reserves and the Money Supply:
- Deposit expansion - deposit multiplier story:
- gives relationships between the monetary base (MB) and the size of the money supply.
- Implication: the Bank of Canada can affect the size of the money supply by altering the supply of reserve assets (MB).
- the effect of the change in MB on money supply will be quite mechanical if the deposit and money multipliers are stable.
- for this to be so: ‘r’ and ‘c’ must be stable.
- these variables involve choices by the banks and the public.
- choices will likely change with time.
- desired r: depends on costs and benefits of holding reserves.
(can be affected by Bank of Canada's policies)
- currency in circulation (rather than as reserves):
- interest rates are an opportunity cost of holding currency.
- size of the illegal/underground economies(large then higher demand for cash)
- bank panics, crises: have raised currency demand rapidly in past.
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- Money Multipliers in times of crisis:
- US in the Great Depression
- bank panics: increased currency demand and higher r: reduced the money multipliers.
- although MB was quite stable money supply fell.
http://www.moneyandbanking.com/commentary/2014/11/10/monetary-policy-a-lesson-learned (Cecchetti and Shoenholtz)
- Financial crisis in the US 2007-09:
- large increases in the monetary base;
- the increase in the money supply is much smaller;
- multipliers fell substantially (see graph)
St. Louis Federal Reserve website:Aug. 2008 Feb. 2009 Feb. 2014
Monetary base $875.2 billion $1624.6 billion $3869.4 billionM1 $1410.0 billion $1560.9 billion $2731.5 billionM2 $7794.5 billion $8343.4 billion $11,113.0 billion
14
What might explain this?
- Banks weren’t lending much of the extra reserves (r rose)
- recession and crisis: borrowers regarded as riskier; perception: few profitable lending opportunities(?).
- deposit expansion wasn’t happening.
- Maybe public is holding more currency (did ‘c’ rise?)
It seems to be the first one (see also text Figures 15-1, 15-2):
- What happens post-crisis. post-recesssion?
- US economy has recovered from the post-crisis recession.
- Will money supply now soar? i.e. will ‘r’ fall to old levels and money multipliers rise back to normal levels?
- if so will there be inflation? recall: Quantity theory of money.
- Can the US central bank soak up the reserves? ‘shrink balance sheet’
- Can it keep ‘r’ permanently higher? e.g. pay interests on reserves.
15
The B ank of Canada and Control of the Monetary Base and Money Supply
- See: Mishkin and Serletis, Ch. 15, pp. 365-72, Ch. 16, 403-12.
Deposit Expansion and Central Bank Control of the Money Supply:
- Key result:
Money Supply = (Monetary Base) x (Money Multiplier)
where: Monetary Base = quantity of reserve assets.
- To change the size of the money supply a central bank can either:
(1) Use policies that change the size of the money multiplier
How?- In the past: changes in legally required reserves could be made.
- Without required reserves: changes in penalties for reserve shortfalls can influence “r”; could subsidize holding reserves.
- In normal times, policies targeting the multiplier are of secondary importance in Canada or the US (even though US has required reserves).
- some countries do target multipliers e.g. China. (e.g. Sept. 2019 https://www.bloomberg.com/news/articles/2019-09-
06/china-cuts-banks-reserve-ratio-to-ramp-up-easing-support)
- US may target it when it's multiplier begin to rise to usual levels.
(2) Change the supply of reserves in the banking system
16
- "reserve management"
17
The Bank of Canada’s Reserve Management Tools
- We will look at three in particular:
(1) Open Market Operations (buying or selling securities);
(2) Deposit shifts (moving Federal government funds between accounts at the private banks and the central bank);
(3) Loans or ‘Advances’ by the central bank to private banks.
- Simple examples below (text provides a slightly different examples).
- Ideas are quite simple and can be generalized to other similar measures.
- Lots of experimentation since 2008 with variations of the usual policies.
(see text pp. 413-419)
18
(1) Open Market Operations (OMOs):
- The B of C can alter the quantity of reserves by buying and selling securities.
- Almost always Treasury Bills (T-Bill): short-term Federal government debt.
Case 1: Bank of Canada reduces it's T-Bill holdings by $100m
- B of C Sells T-bills to the “public”
- Public has $100 million additional treasury bills.
- Public pays by cheque or transfer of $100m to the B of C.
- Public’s deposits at their chartered bank fall by $100m
- Chartered bank’s deposits at B of C are reduced by $100m
General Public Assets Liabilities
T-bills +100m Deposits at banks -100m
Chartered BanksAssets Liabilities
Deposits -100m Deposits -100m at BofC (reserves, settlement balances)
Bank of CanadaAssets Liabilities
T-bills -100m Deposits -100m(banks)
- End result? Bank reserves have fallen by $100 million.- chartered banks have $100 million fewer deposits at the B of C.
- the quantity of deposits in the banking system will contract.
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Case 2: Bank of Canada raises its Treasury bill holdings by $l00 million
- Say the B of C buys $100m in T-Bills from the public.
- B of C pays $100m to the public.
- The public has $100 million fewer treasury bills.
- Public receives $100m claim from the B of C (cheque, transfer).
- this is “deposited” into the banking system: public's deposits rise by $l00m.
- the chartered banks have $100m claim on B of C.
- the B of C credits the chartered bank's accounts with $l00m.(these are reserves or settlement balances)
- Bank reserves have risen by $100 million
- chartered banks have $100 million more deposits at the Bank of Canada.
- the quantity of deposits in the banking system will expand.
(Text example: buys T-Bills from a dealer not the public: but has the same effect)
Open Market Operations (cont’d):
- In Canada OMOs are typically done through:
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“Purchase and Resale Agreements” (PRAs, "repos") or
“Sale and Repurchase Agreements” (SRAs, "reverse repos").
- PRAs and SRAs are self-reversing OMOs.
- Common tools since the mid-1990s.
- T-Bills are the usual asset for OMOs but any purchase or sale by B of C can have the same effect.
- why use T-Bills? Avoid private assets and possible favoritism;
T-Bill market is well-developed and liquid.
- During the 2007-08 Subprime crisis: - willingness to consider securities other than T-Bills.
- US right in recent years: "Quantitative Easing" (QE)- OMOs buying longer-term assets
e.g. QE II 5-yr. government bonds
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(2) Government Deposit Shifts:
- The Government of Canada has bank accounts at the major chartered banks as well as the Bank of Canada (B of C).
- B of C acts as the Federal government’s banker
- Shifting funds between government accounts at chartered banks and the B of C changes the quantity of reserves.
Moving funds to Chartered Banks:
- This is typically done by auction (banks bid to receive the deposit).
- Bank of Canada transfers $l00m from government accounts at the Bank of Canada to government accounts at the chartered banks:
Bank of CanadaAssets Liabilities
Deposits -100m(gov't)Deposits +l00m(banks)
Chartered BanksAssets Liabilities
Deposits +l00m Deposits +l00mat BofC (gov't)
(reserves)
-This action raises the quantity of reserves in the banking system by $l00m
- deposit expansion will occur.
Moving Funds from Chartered Banks to the B of C:
- A transfer of $l00m from government deposits at the chartered banks to government deposits at the B of C would reduce reserves by $l00m.
(reverse signs on changes in example above)
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(3) Lending by Bank of Canada:
- Advances: loans by the Bank of Canada to members of the payments system e.g. banks, dealers .
- B of C stands ready to lend in this way.
- Minimum rate charged: “Bank rate”.
- Typically:
Bank rate = overnight rate + 0.25% (top of the 0.5% operating band for the overnight rate)
- Typically securities act as collateral for advances.
- An increase in B of C loans to chartered banks raises reserves
- loan creates additional chartered bank deposits at the B of C.
- Bank rate is the minimum rate charged on advances.
(via effect on advances the Bank rate could be an important policy tool; US equivalent: Discount Rate)
- Advances can be used as part of the day-to-day functioning of the payments system.
- fill shortfalls a chartered bank may have on a given day.
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Lender of Last Resort: Loans or Advances in Crisis
- Advances can also be used as part of the B of C’s “lender of last resort” role.
- Discretionary “emergency” lending to financial institutions.
- Discretionary? - BofC must judge importance to the financial system;- discretion over rate charged and collateral required.
- Origins as a tool vs. banks runs: a method of providing banks with funds to meet depositor demands.
- “Lender of last resort” role is of most importance during a “crisis”:
- US: Sept. 11, 2001 ; Black Monday 1987.
- Subprime crisis (Financial crisis 2007-09): - Bank-like institutions experiencing the equivalent of a bank
run.
e.g. unable to sell (roll over) their paper as it comes due.
- US central bank (Federal Reserve) effectively extended the “lender of last resort” function to these FIs.
- Similar steps in Canada.
- Goal of "lender of last resort" role: stability of financial system- consequences for reserve management a secondary consideration.
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- B of C uses all three reserve management tools above:
- OMOs: main tool (flexible, under BofCs control).
- Government Deposit transfers for day-to-day reserve management:
- mainly to neutralize changes caused by other factors affecting reserves e.g. government-public transactions, changes in public
demand for currency.
- Advances are always possible at the Bank rate (or higher in discretionary cases).
- Much of the day-to-day reserve management is concerned with “neutralizing” or "sterilizing" the effect of changes in reserves produced by actions other than monetary policy.
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Monetary Policy, the Overnight Rate and Reserve Management
- Reserve management affects the size of the money supply.
- Size of the money supply is typically not the intended target.
(it has been in the past: 1970s, 1980s and ‘Monetarism’)
- Immediate (operational) objective?
- Short-term interest rates: affected by changing reserves and the money supply.
- Ultimate objectives?
- Prices and inflation rates;
- Levels of aggregate output and employment.
26
- The Bank of Canada’s current practice (see also Figure 16-5):
- Overnight rate: “the interest rate at which major financial institutions borrow and lend one-day (or "overnight") funds among themselves; the Bank sets a target level for that rate.”
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Modeling the Effects of Reserve Management on the Overnight Rate
- US: the equivalent of the “overnight rate” is the “Federal Funds Rate”; many of the world’s major central banks operate in a similar way (see text: p.393)
Demand for Reserves by banks:
- Negatively related to the level of the overnight rate (ior).
i.e. could always lend out funds held as reserves at the overnight rate.
- higher the overnight rate: fewer funds held as reserves, more lent out
- Negatively sloped curve in graph with overnight rate on vertical axis and quantity of reserves on horizontal axis.
- Shifts in demand for reserves are caused by changes in anything, other than the overnight rate, that affects the amount of reserves banks want to hold.
- rise in level of required reserves; rise in public’s demand for currency; rise in penalties for having a shortfall in reserves.
- financial crisis: demand for reserves rose in the US.- why? uncertainty about ability to raise funds in other markets; risk and creditworthiness of customers banks might lend to.
Supply of reserves:
28
- Controlled by the central bank via its reserve management tools (see above).
- In diagram: vertical line (simplest case) – see below. Shifted at the discretion of the central bank.
Equilibrium: Supply = Demand
- Level of the overnight rate where Supply = Demand:
- If ior is too low: excess demand for reserves, banks attempt to build up reserves, this bids up ior.
- If ior is too high: excess supply, banks are trying to lend out their extra reserve assets, ior falls.
29
- Reserve management and the overnight rate:
- B of C raises reserves: - Supply shifts right: more reserves are available in the overnight
market. - Overnight rate falls.
- B of C reduces reserves: - Supply shifts left: fewer reserves are available in the overnight
market.- Overnight rate rises.
(reverse the shift in the diagram above)
30
- Shifts in demand for reserves can also affect the overnight rate.
- Demand shifts right: rise in overnight rate.
- Demand shifts left: fall in overnight rate (reverse the shift above)
- If the B of C is trying to maintain a particular target rate it will need to counter the effects of Demand shifts by changing the supply of reserves counter the effects of Demand shifts.
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Complications: Ceilings and Floors on the Overnight Rate
- Central banks often put a ceiling on the overnight rate.
- How? By being willing to lend (supply reserves, make advances) without limit at some ceiling rate.
- Canada: Bank rate (top of the announced 0.5% operating band for the overnight rate: i + 0.25%)
- US : Discount rate
- This makes the supply of reserves horizontal at this rate (iBR).
- So: a sudden, large rise in demand for reserves could shift demand right and force the overnight rate up to the Bank rate.
- Central banks can also put a floor on the overnight rate.
- policy: will pay ifloor on bank reserves in B of C accounts. i.e. B of C will borrow without limit at ifloor
- Overnight rate will not fall below this level: - banks will instead deposit reserve assets at B of C.
i.e. reserve assets available for borrowing fall to 0 below this rate.
- Canada: ifloor = iBR–0.5%
- Diagram? Demand for reserve assets is flat at: ifloor= iBR–0.5%
- So sharp shift left in demand for reserves can drive the overnight rate to this limit.
(US now pays interest on reserves: since 2008 -- will this be used to "soak up reserves" when US recovers?)
32
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- Monetary policy with ceilings and floors:
- Changing the supply of reserve assets shifts the vertical part of the supply curve.
- this changes the overnight rate as before (provided that the rate is not at the ceiling or floor).
- Central bank can also affect the overnight rate by changing the ceiling or floor rates.
- Canadian system: changing ceilings and floors is currently not too important.
- B of C: targets the ‘overnight rate’ via reserve management.
- Bank rate (iBR) and floor rate (iBR–0.5%) are tied directly to the target for the overnight rate.
i.e. they are a 0.5% ban around the target.
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Appendix: Geometric Series and the Math Behind the Deposit Multiplier
-The following expression is the sum of a geometric series:
∑i=0
N−1
ai = 1+ a + a2 + a3 + ... + aN-1
∑i=0
N−1
ai means this is a sum of terms ai from i=1 to N-1)
- Now take the expressions above and subtract ‘a’ times the expression:
∑i=0
N−1
ai = 1+a + a2 + a3 + ... + aN-1 (series)
a ∑i=0
N−1
ai = a+ a2 + a3 +... + aN + aN (series times 'a') ________________________
(1-a)∑
i=0
N−1
ai = 1 - aN (difference: between series and series times 'a' )
Divide through by (1-a) to get:
∑i=0
N−1
ai[1−aN
1−a ]
- In our deposit expansion example on page 9 we are interested in:
∑i=0
N−1
(1−r )i=¿ 1 + (1-r) + (1-r)2 + ...+ (1-r)N-l
- This is just the geometric series expression above with a = (1-r) so:
∑i=0
N−1
(1−r )i¿1r
(the last equality is true since 0<(1-r)<1 and N→∞ so that (1-r)N =0 )
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