Central Banking and the Money Supply
Marshall Urias
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Roadmap
We saw that with banks, inside money (demand deposits) replacedoutside money (fiat currency) so that financial intermediationmobilized all the savings of the economy for investment in capital.
Central bank has two additional tools
reserve requirementsbank loans
First step toward explaining coexistence of fiat money and deposits
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Legal restrictions on financial intermediation
What if people prefer inside money to fiat money?
Prices would have to be expressed in a different unit of account, andthe government would be unable to raise any revenue from seigniorage
Central bank can use reserve requirement to have both inside andoutside money valued in equilibrium
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Reserve requirements
Reserves are held in the form of vault cash or deposits within FederalReserve banks
No required reserves on the first $14.5 million of deposits, 3% onreservable deposits less than $103.6 million, and 10% on depositsexceeding $103.6 million
Reserve requirements on Canadian chartered banks were phased outin 1994
Reserve requirements in China are now 14.5% for large banks and12.5% for small banks
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Environment
Continue environment of people with three-period lives and illiquidcapital
Capital pays return X > (n/z)2 two periods after its creation
Let Mt = zMt−1 with z ≥ 1
Initial middle-aged begin with stock of money
The net worth of a bank is what is owed to shareholders
Assume net worth is zero (liabilities completely take the form ofdeposits)
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The bank’s balance sheet
Assets Liabilities
Reserves γH Deposits HInterest-bearing assets (1− γ)H Net worth 0Total assets H Total liabilities H
Table: Balance sheet. Deposits H are subject to reserve requirement γ, so thatthe bank must hold at least γH. Given that capital offers a higher return, thebank just satisfies the reserve requirements, purchasing (1− γ)H ofinterest-bearing assets.
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Prices
The price level pt : the value of a good in terms of fiat money
Let ht be the goods deposited in banks by an individual
Supply and demand for fiat money (individuals do not hold currency)
νtMt = γNtht
Hence, the price level satisfies
pt =Mt
γNtht
Consider zero reserve requrement policy in Canda: γ = 0
Implies pt =∞ (no demand for fiat money)
There must be other sources of demand for fiat money (currency,bank demand other than through reserve requirement)
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Seigniorage
Let St denote seigniorage revenue at date t
St = νt(Mt −Mt−1)
= νtMt
(1− 1
z
)= γNtht
(1− 1
z
)Seigniorage rises with an increase in the reserve requirement γ, anincrease in the real stock of bank deposits Ntht , and an increase inthe rate of fiat money creation z
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Capital and output
Output is the sum of
labor endowmentcapital invested directly ktcapital invested directly in intermediaries: (1− γ)ht
Output Yt satisfies
Yt = Nty + Nt−2Xkt−2 + Nt−2X (1− γ)ht−2
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Effect on output of reducing reserve requirements
An increase in γ reduces output by reducing bank intermediation
How large is this effect?
At the end of 2008, total net private capital stock in the UnitedStates was $34, 261 billion
Required reserves by U.S. commerical banks was $53 billion
Replacing all reserves with new capital stock would raise capital stockby under 0.16%
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Deposits
So far, we assumed deposits Ntht were fixed in examining effects onprices, seigniorage, and output
Willigness to make deposits depends on rate of return (depends onsubstitution and income effects) held by banks
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Gross real rate of return on deposits
One-period return on capital is x = X 1/2
Competitive banking induces banks to offer depositors the rate ofreturn they earn on assets
Rate of return is weighted average of return on money and capital:
r = γ(nz
)+ (1− γ)x
= x − γ[x −
(nz
)]
Increase in reserve requirement lowers rate of return on deposits
Increase in z lowers rate of return on deposits
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Welfare
What are the effects of reserve requirements on individual welfare?
From νt = (γNtht)/Mt , an increase in reserve requirements raisesvalue of money and benefits the initial middle-aged (money holders)
Increase in γ lowers r and hence reduces c2 even if seignioragerevenue is returned to future generations
Welfare on future generations is lower because of lower return
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Central bank definitions of money
In general, in economies with outside and inside money, there aredistinctions about the various ‘moneyness’ associated with differenttypes
Central banks define monetary aggregates
Definition of money varies across countries because deposit contractsand other assets differ
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Famous quotes on moneyness
’I have always found it useful to explain to the student that ithas been rather a misfortune that we describe money by a noun,and that it would be more helpful for the explanation of monetaryphenomenon if ‘money’ were an adjective describing a propertywhich different things could possess to varying degrees’
(Friedrich Hayek, Denationalization of Money: the Argument Refined)
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Famous quotes on moneyness
...it may be worth emphasizing what has been already statedabove, namely, that ‘liquidity’ and ‘carrying-costs’ are both a mat-ter of degree; that that it is only in having the former high rela-tively to the latter that the pecularity of ‘money’ consists...Thereis, clearly, no absolute standard of ‘liquidity’ but merely a scale ofliquidity–a varying premium of which account has to be taken
(John Maynard Keynes, The General Theory of Employment, Interest, andMoney-Chapter 17, 1936)
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Famous quotes on moneyness
In brief, the general approach consists of regarding each asset as ajoint product having different degrees of ‘moneyness,’ and definingthe quantity of money as the weighted sum of the aggregated valueof all assets...
(Friedman and Schwartz, A Monetary History of the United States, 1970)
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The total money supply in the model
Define M1t as the total nominal stock deposits at period t
Deposits are the only form of money in this economy
Stock of fiat money in a reserve-requirement economy is referred toas the monetary base
M1t =Mt
γ
1/γ is called the money multiplier
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Relationship between M1 and other variables
pt =Mt
γNtht=
M1tNtht
Quantity theory holds if Ntht does not depend on rate of return
If demand for deposits, Ntht is affected by the rate of return ondeposits, then the change in the price level depends on the tool usedto change M1
Typology
One-time increase in monetary base does not affect rPermanent increase in monetary base reduces rLower γ increase M1t and raises r
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Central bank lending
Banks must demonstrate that they meet the level of reserves requiredfor deposits
If they fall short, they are faced with one of three options
sell interest-bearing assets for fiat moneyborrow from other banks (federal funds market)borrow from central bank (discount window)
Point of central bank lending is to permit banks to meet reserverequirements without precipitously selling off interest-bearing assets
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Limited central bank lending
Let δ be the fraction of a bank’s reserves financed by loans from acentral bank
Let ΓBt represent the total nominal amount of borrowed reserves
Mt is the stock of fiat money not borrowed from reserves
δ =ΓBt
ΓBt + Mt
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Bank balance sheet with central bank loans
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Equilibrium price
Demand for fiat money comes from borrowed reserves δγNtht andnon-borrowed reserves νtMt
Supply and demand for money
δγNtht + νtMt = γNtht
so that
νtMt = γ(1− δ)Ntht
νt =γ(1− δ)Ntht
Mt
pt =Mt
γ(1− δ)Ntht
Central bank lending raises price level
Effectively lowers reserve requirement from γ to γ(1− δ)
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Intermediated investment and total money stock
Bank holdings of interest-bearing assets
(1− γ)Ntht + δγNtht = [1− γ(1− δ)]Ntht
Required reserves equal sum of borrowed and non-borrowed reserves
γM1t = δγM1t + Mt
or
M1t =Mt
γ(1− δ)
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Rate of return paid by banks on deposits
r = γ(nz
)+ [1− γ(1− δ)]x − ψδγ
where ψ is interest rate charged by central bank
if ψ = x , then
r = γ(nz
)+ (1− γ)x
If the central bank charges no nominal interest rate on loans(ψ = n/z), then
r = [1− γ(1− δ)]x + γ(1− δ)(nz
)
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Unlimited central bank lending
Suppose central bank just sets the interest it will charge, ψ, andpermits banks to borrow as much as they desire
A fixed return to capital x leads to indeterminacy
if ψ > x , then no bank borrows
if ψ < x , then the bank borrows unlimited amounts
if ψ = x , then any borrowed reserves is possible, and the price level isindeterminate
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Breaking the indeterminacy
A diminishing marginal product of capital restores determinacy
Assume return f (k), where f (0) = 0, f ′(0) =∞, and f ′′(k) < 0
Banks borrow until f ′(k) = ψ
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Limits of central bank lending
Expanding lending raises the price level, which hurts current holdersof fiat money
Real effect on capital of lowering the rate charged by the central bankis bounded above by γNtht
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Central bank lending in the United States and Canada
From 1980-1995, the Bank of Canada followed a floating penalty rate:the bank rate was equal to the 91-day Treasury bill rate plus onequarter of 1%
The United States sets a rate and changes it infrequently(administered rate)
Since 1995, the Bank of Canada has also followed an administeredrate
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Central bank lending rates
Figure: Source: the Bank rate is from various issues of the Bank of CanadaReview. The discount rate is from the Federal Reserve Bulletin. Both series aremonthly.
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Excess reserves since the 2007 financial crisis
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Summary
Reserve requirements give rise to a money multiplier whereby thetotal money supply is a multiple of the monetary base
Reserve requirements increase the demand for fiat money (andseigniorage) but reduce intermediation (and output)
Higher reserve requirements make future generations worse off bylowering the rate of return that banks can pay on deposits
Central bank lending is equivalent to a decrease in the reserverequirement
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