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.

13

- 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.

19

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:

20

“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

21

(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)

22

(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.

23

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.

24

- 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.

25

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.”

27

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.

31

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

33

- 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.

34

35

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 )

36