Money SupplyECON 40364: Monetary Theory & Policy

Eric Sims

University of Notre Dame

Fall 2020

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Readings

I Friedman Ch. 1, Ch. 2 (sections “Mystery of Money” and“The Supply of Money”)

I Mishkin Ch. 3

I Mishkin Ch. 14

I GLS Ch. 31

I Rendahl and Freund

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What is Money?

I Money is something that is accepted as payment for goods orservices or in the repayment of debts

I Friedman: “Money is whatever is generally accepted inexchange for goods and services – accepted not as an objectto be consumed but as an object that represents a temporaryabode of purchasing power to be used for buying still othergoods and services.”

I Something has value as a medium of exchange because peoplethink other people will accept that thing in exchange forgoods and services

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Stock vs. Flow

I Properly understood, money is a stock concept – somethingyou accumulate and can carry across time (balance sheet).Not a flow concept (income statement)

I An asset is a claim on current and/or future resource/financialflows that you own; a liability is a claim against you oncurrent and/or future resource/financial flows

I For the holder of money, it is an asset. For the issuer, it is aliability

I Money can be publicly or privately created. Most money isprivately created

I It is backed by something – something tangible (e.g. preciousmetals) or intangible (e.g. full faith and credit)

I What is (and isn’t) money is increasingly less clear

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Functions of Money

I Three functions of money:

1. Medium of exchange2. Unit of account3. Store of value

I Any asset can serve as a store of value (e.g. house, land,stocks, bonds), but most assets do not perform the first tworoles of money

I Unit of account is important (particularly in a diverseeconomy), though anything could serve as a unit of account

I Medium of exchange role is the most important role ofmoney:

I Eliminates need for barter, reduces transactions costsassociated with exchange, and allows for greater specialization

I Even when currencies have failed (e.g. Wiemar Republic),people resort to alternative monies (e.g. cigarettes) beforeengaging directly in barter

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Liquidity

I As a store of value, money tends to be crummy relative toother assets like stocks and houses, which offer some expectedreturn over time

I Why then do people hold money? Because they value liquidity

I One popular definition of liquidity: ease with which an assetcan be converted into a medium of exchange (i.e. money)

I Money is the most liquid asset because it is the medium ofexchange

I If you held all your wealth in housing, and you wanted to buya car, you would have to sell (liquidate) the house, which maynot be easy to do, may take a while, and may involve sellingat a discount if you must do it quickly

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Liquidity (continued)

I Need to take a somewhat nuanced interpretation of “ease withwhich asset can be converted into a medium of exchange”

I We will use term “cash” to refer to physical currency ordemand deposits which can be used in exchange

I Shares of stock are nearly perfectly liquid in that I can easilyconvert them to cash quickly . . .

I . . . but maybe not at the price I expectI Example: I have $1000, and I don’t need to spend it today. I

might need to spend it tomorrow (or the day after)I I could store cash (either in currency under my mattress or in a

checking account), or I could buy Apple stock (AAPL)I If I store $1000 in cash, I will have $1000 in cash when I need itI If I buy $1000 in Apple, I can get cash when I need it, but I’m

uncertain as to how much cash (i.e. price could go up or down)

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Liquidity (continued)

I In addition to market liquidity, by which we mean the actualease of selling an asset without affecting its market price, onemight also measure an asset’s liquidity by how much thatasset’s price fluctuates

I The (nominal) value of money doesn’t fluctuate – one dollarin cash today gives you one dollar with certainty tomorrow.Money is a special asset because it “trades at par” (par =face value)

I Not true for other assets like stocks, real estateI So-called near monies are assets that are very nearly as liquid

as cash with either small transactions cost of liquidating themor small price uncertainty:

I Money market fundsI Non-transactions deposits (savings accounts, time deposits)I Government bonds with short time to maturity

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The Island of Stone Money

I In Ch. 1, Friedman discusses the monetary system of theisland of Uap

I Their currency was fei – large stone wheels

I People freely accepted these fei in exchange for goods andservices, even without actually taking physical possession ofthem

I Seems crazy, but you and I do this all the timeI e.g. I write you a check, my bank transfers funds from my

account to your bank accountI We never take physical possession of anything (though we

have the right to)

I In some deep sense, monetary systems rest on a fictionI True particularly for fiat moneyI But true even for commodity-based money

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Evolution of Money and PaymentsI Commodity-based money: money made up of precious metals

or other commoditiesI Difficult to carry around, potentially difficult to divide, price

may fluctuate if precious metal or commodity has consumptionvalue independent of medium of exchange role (i.e. not reallyperfectly liquid)

I Currency: pieces of paper or coins that are accepted asmedium of exchange. May be “backed” by some commodity(e.g. government guarantees conversion of paper into gold)

I Problems: easily stolen, difficult to track, and difficult totransport

I Checks: instructions for holder of your money (a bank) totransfer money to another person or institution. Eliminatesneed to carry currency around

I Problems: processing of checks and transfer is potentiallycostly, people may not accept checks if they doubt soundnessof your financial institution

I Electronic payment and e-money: like checks, but transferhappens instantaneously with a complete record (e.g. debitcard) 10 / 45

Fiat MoneyI Prior to 1971, every major currency had been linked directly

or indirectly to a commodityI No more

I Fiat money is currency, checks, and/or electronic entries thatare not backed by any commodity or precious metal

I In other words, fiat money is not “convertible”

I It is only backed by the “full faith and credit”

I Fiat money has no “fundamental” value – it is only valuablebecause people accept it in exchange. For this reason,sometimes people say fiat money is a “bubble”

I Advantages: easily divisible, can be fully electronic, value doesnot fluctuate due to demand and supply of a commodity, easyfor government to change quantity

I Potential problems: maybe too easy for government tomanipulate quantity. Precarious in the sense of being a bubble– only has value because people believe it does

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Measures of the Money Supply

I Most basic definition of the money supply is “currency incirculation,” C . Also called “M0”

I Obviously currency isn’t the only thing that can be used inexchange – checks can as well

I M1: currency in circulation plus demand deposits (money heldin checking accounts), plus travelers checks, plus “other”checkable deposits (interest-bearing checking accounts).Again, think of this as “cash”

I M2: M1 + savings deposits and money market depositaccounts, small time deposits (e.g. CDs), and money marketaccounts (i.e. M1 plus “near monies”)

I Descending order of liquidity – M2 includes less liquid assetsthan M1

I M3 (discontinued) includes M2 plus “large” time deposits,institutional money market funds, and short term repurchaseagreements

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Money Supply

I We often think of the central bank (e.g. the Federal Reserve)as setting the money supply

I This is not quite accurate, though in normal times it is not abad approximation

I Why? Money supply includes privately-created assetsI Can’t even perfectly control M0: central bank can print more

currency, but cannot ensure it stays in circulation – i.e. itcould be deposited in a bank

I Reserves: currency not in circulation (“vault cash”) plus bankdeposits at the central bank

I Central bank also cannot prevent banks from creatingdeposits, which we think of as constituting money in terms ofM1

I The money supply is jointly set by three actors:1. Central bank2. Commercial banks3. Depositors

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T-AccountsI In thinking about the money creation process, it is useful to

use T-Accounts, which are tabular depictions of aninstitution’s balance sheet

I A balance sheet shows the assets and liabilities of aninstitution

I Asset: a piece of property, note, or electronic entry that isvaluable and entitles the holder to some payout (e.g. stock,bond, cash)

I Liability: a liability is an obligation that requires the holder topay at some point in the future as a result of some pasttransaction

I For example, if I make you a loan, the loan is an asset to me(it’s a piece of paper that says you have to pay me back), buta liability for you

I Equity (or sometimes “net worth”) is the difference betweenthe values of assets and liabilities. If you liquidated all assetsand paid off all liabilities, how much money would you be leftwith 15 / 45

Example T-Account for a Homeowner

Assets Liabilities + Equity

Value of Home $100,000 Mortgage $80,000Checking account $10,000 Student loans $50,000Stocks $50,000 Credit card debt $10,000

Equity $20,000

I Equity is just the difference between total value of assets andtotal value of liabilities for an agent (household, firm, etc.)

I In an aggregate sense, household equity is equal to the totalvalue of non-financial assets, what we call capital

I Financial assets (stocks, bonds, deposits) are just contractualclaims – one person’s asset is another’s liability, and hencethese are not net assets (capital) in an aggregate sense

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Balance Sheet for the Fed

Assets Liabilities

Securities Currency in circulationLoans Reserves

I Monetary liabilities are not really liabilities in the formal sense– these are IOUs to be paid off with other IOUs

I Monetary liabilities of the Fed: monetary base (currency plusreserves)

I It can freely create these liabilities, and hence controls themonetary base

I Reserves: deposits banks hold at the Fed plus currency inbank vaults

I Securities: holdings of US government bonds and privatesector stocks and bonds

I Loans: loans made to financial institutionsI Don’t worry about equity – Fed is “owned” by Treasury and

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Balance Sheet for the Banking System as a Whole

Assets Liabilities

Loans Demand depositsSecurities Savings depositsReserves Borrowings

Equity

I Loans are assets for banks because they are IOUs that promisethe bank back its money

I Deposits are liabilities: banks have to pay out cash on demand

I Reserves: vault cash and deposits at central bank

I Borrowings: loans bank has taken out from Fed or otherinstitution

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The Monetary Base

I The monetary base is the sum of currency in circulation plusreserves:

MB = C + R

I The Fed can affect the base through open market operationsand loans to financial institutions

I The split between currency and reserves is determined by thepublic’s desire to hold cash versus deposits – central bankcannot perfectly control split between C and R, but cancontrol MB

I An open market operation involves the purchase (or sale) ofsecurities (typically short term government securities likeTreasury Bills)

I Open market operations create (or eliminate) monetaryliabilities and alter the asset composition of the bankingsystem

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Open Market PurchaseI Suppose that the Fed decides to purchase $100 of securities

from the banking systemI To do this, the Fed simply creates reserves – it credits the

banking system with reserves in exchange for the securitiesI For the Fed:

Assets Liabilities

Securities +$100 Reserves +$100

I For the banking system as a whole:

Assets Liabilities

Securities -$100Reserves +$100

I An open market purchase increases reserves (and hence themonetary base), while a sale does the opposite

I In a sense, what is special about a central bank is that it canexpand or contract the size of its balance sheet arbitrarily

I Private sector cannot do this on its own20 / 45

Loans to Financial Institutions

I Commercial banks can borrow directly from the Fed throughthe discount window or other lending facilities

I Suppose the Fed loans the banking system $100. Fed balancesheet:

Assets Liabilities

Loans +$100 Reserves +$100

I Banking system balance sheet:

Assets Liabilities

Reserves +$100 Borrowings +$100

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Currency Withdrawal

I The Fed cannot directly control reserves

I Suppose that depositors want to withdraw $100

I Banking system has to meet this withdrawal demand bydrawing down reserves

Assets Liabilities

Reserves -$100 Deposits -$100

I Withdrawals reduce reserves, but increase currency incirculation, leaving monetary base unaffected

I Hence, Fed can control MB, but not C or R directly

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Borrowed vs. Non-Borrowed Reserves

I Even though the Fed can completely control open marketoperations, there is some uncertainty about loans to financialinstitutions

I It is therefore convenient to split the monetary base into twocomponents: the non-borrowed monetary base and borrowedreserves:

MB = MBn + BR

I Where MBn is the non-borrowed monetary base and BR isborrowed reserves (e.g. discount loans)

I Because the Fed has complete control of MBn through openmarket operations, it can always adjust MBn givenfluctuations in BR to hit a target MB

I We therefore think of the Fed as directly controlling themonetary base

I But what about the money supply?

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From Monetary Base to Money Supply

I The Fed can directly control the monetary base

I But what about the money supply?

I For these purposes, think of the money supply as currency incirculation plus demand deposits (so M1)

I There exists a relationship between the monetary base and themoney supply, but it is not directly controlled by the Fed

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Multiple Deposit Creation

I In a “fractional reserve” banking system, banks do not holdthe total value of deposits in reserves

I The Fed stipulates by law a minimum fraction of totaloutstanding deposits that commercial banks must hold

I Call this the required reserve ratio, or rr

I Suppose, for simplicity, that banks do not hold any “excessreserves” (reserves in excess of what is required by the Fed)

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A Hypothetical Bank Balance Sheet

I Suppose a bank, call it Bank A, has the following balancesheet:

Assets Liabilities

Loans $1000 Deposits $1000Securities $100Reserves $100

I Assume that rr = 0.1. So deposits are a multiple of reserves.Bank equity in this example is $200. The bank makes money(return on equity) by earning returns on its loans andsecurities. Reserves (i.e. cash in vault) earn nothing (at leasttraditionally, before payment of interest on reserves in lastdecade) and hence do not create equity in a dynamic sense.

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Open Market Operation

I Suppose that the Fed purchases $100 of securities from thebank. Balance sheet goes from:

Assets Liabilities

Loans $1000 Deposits $1000Securities $100Reserves $100

to:

Assets Liabilities

Loans $1000 Deposits $1000Securities $0 (-$100)Reserves $200 (+$100)

I The direct effect of the open market operation is to alter thecomposition of assets at a bank

I The central bank has expanded the size of its balance sheet bycreating reserves

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Excess ReservesI Now the bank is holding 20 percent of its deposits as reserves.

This is more than rr = 0.1I Reserves don’t make money. Loans or securities doI Suppose bank makes a loan for $100 (equal to the value of

the excess reserves)I When it does this, it just creates a deposit for the person

getting a loan. The bank creates a liability (deposit) at sametime it creates an asset (loan) (without affecting equity). Cando this because of fractional reserve requirement

I New balance sheet:

Assets Liabilities

Loans $1100 (+$100) Deposits $1100 (+$100)Securities $0Reserves $200

I A bank can expand the size of its balance (by creatingliabilities) whenever it has excess reserves

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Ex Nihilo

I Does Bank A create money “out of thin air”?

I No

I In this example, what allows it to create deposits is that itholds (excess) reserves

I Even if there were not an explicit reserve requirement, otherparties wouldn’t accept checks from Bank A if it wasn’tknown that Bank A had reserves (or more generally solidbacking assets)

I So the bank creates money, but it isn’t out of thin air (Freundand Rendahl)

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Bank B

I Suppose that Bank B has an initial balance sheet that looksjust like Bank A’s, but Bank B didn’t sell securities to the Fed

I Initial balance sheet:

Assets Liabilities

Loans $1000 Deposits $1000Securities $100Reserves $100

I The person getting the loan from Bank A isn’t getting a loanto keep deposits with bank A. He/she is getting the loan tobuy something

I Suppose that person uses the $100 deposit and buyssomething, and the seller then deposits the $100 in Bank B

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New Balance Sheets for Banks A and B

I Bank A:

Assets Liabilities

Loans $1100 Deposits $1000 (-$100)Securities $0Reserves $100 (-$100)

I Bank B:

Assets Liabilities

Loans $1000 Deposits $1100 (+$100)Securities $100Reserves $200 (+$100)

I Bank A is back to its reserve requirement

I Now bank B is holding reserves equal to 0.1818 of deposits, inexcess of rr = 0.1

I Bank B will not want to sit on these excess reserves

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Bank B Makes Loans

I Suppose that Bank B makes a loan for $90, equal to its excessreserves:

Assets Liabilities

Loans $1090 (+$90) Deposits $1190 (+$90)Securities $100Reserves $200

I The deposits created for Bank B will only temporarily bethere. The borrower will deposit them in another bank, call itBank C, and Bank B’s balance sheet will revert to:

Assets Liabilities

Loans $1090 Deposits $1100 (-$90)Securities $100Reserves $110 (-$90)

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Bank C

I Initial balance sheet looks like all the others:

Assets Liabilities

Loans $1000 Deposits $1000Securities $100Reserves $100

I After getting the deposit, its balance sheet will be:

Assets Liabilities

Loans $1000 Deposits $1090 (+$90)Securities $100Reserves $190 (+$90)

I But now Bank C is sitting on $81 in excess reserves. It willwant to loan it out

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Bank C Makes Loans

I Suppose that Bank C makes a loan for $81, equal to its excessreserves:

Assets Liabilities

Loans $1081 (+$81) Deposits $1171 (+$81)Securities $100Reserves $190

I The deposits created for Bank C will only temporarily bethere. The borrower will deposit them in another bank, call itBank D, and Bank C’s balance sheet will revert to:

Assets Liabilities

Loans $1081 Deposits $1090 (-$81)Securities $100Reserves $109 (-$81)

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Multiple Deposit Creation

I The open market operation increases (excess) reserves forBank A

I Bank A then makes a loan, which generates $100 additionaldeposits for Bank B

I Bank B then makes a loan, which generates $90 additionaldeposits for Bank C

I Bank C then makes a loan, which generates $81 additionaldeposits for Bank D

I And so on!

I Total change in deposits for a $1 open market purchase:

∆D = 1 + (1 − rr) + (1 − rr)2 + (1 − rr)3 + . . .

I This simplifies to an expression called the “simple depositmultiplier”:

∆D =1

rr

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Deposit Creation and the Money Supply

I Recall that we are thinking of the money supply as M1:currency in circulation plus deposits

I An open market purchase of $100 increases deposits by1rr × $100 with no effect on currency in circulation

I Hence, the change in the money supply is 1rr times the change

in reserves, or more generally times the change in themonetary base:

∆M =1

rr∆MB

I We could call the money multiplier the simple depositmultiplier:

mm =1

rr

I Then we have a relationship between the monetary base andthe money supply:

M = mm×MB

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The Simple Model is too Simple

I The simple model assumes the following:

1. Banks hold no excess reserves: they either make loans or buysecurities to just satisfy the reserve requirement

2. Lenders who get loans deposit the entirety of the loan in abank – there is no currency holding

I Holding excess reserves or currency outside of a bank will“slow down” multiple deposit creation and lower the moneymultiplier

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A More General Model

I Let c = CD be the desired currency to deposit ratio and

e = ERD be the excess reserve ratio held by banks. rr = RR

D isthe required reserve ratio, which the central bank can set.Total reserves, R = ER + RR

I Recall MB = C + R and M = C +D

I Can derive an expression:

M = mm×MB

I Where:

mm =1 + c

rr + e + c

I If c = e = 0, this reduces to simple multiplier

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0

0.5

1

1.5

2

2.5

3

3.5

M1 multiplier

M1 multiplier

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0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

c

e

rr

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Monetary Aggregates During COVID-19

2020-02 2020-03 2020-04 2020-05 2020-06 2020-07 2020-083,800

4,000

4,200

4,400

4,600

4,800

5,000

5,200

5,400

5,600

3,400,000

3,600,000

3,800,000

4,000,000

4,200,000

4,400,000

4,600,000

4,800,000

5,000,000

5,200,000

BillionsofDollars

MillionsofD

ollarsM1MoneyStock(left)MonetaryBase;Total(right)

Source:BoardofGovernorsoftheFederalReserveSystem(US) fred.stlouisfed.org

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Money Multiplier During COVID-19

0.9

0.95

1

1.05

1.1

1.15

1.2

2020-01-08 2020-02-08 2020-03-08 2020-04-08 2020-05-08 2020-06-08 2020-07-08

M1 Money Multiplier

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What Can a Central Bank Control?

I The Fed can control the monetary base, MB, and the requiredreserve ratio, rr

I It cannot influence currency holdings, c, or excess reserves, e

I In “normal” times c and e are pretty stable, so the Fed cancontrol M pretty well

I In extreme circumstances, not so:I In Great Depression, currency holdings shot up (bank runs)

and the money multiplier fell. The Fed did not adjust the basemuch, so the money supply fell

I In Great Recession, excess reserves went up. The Fedmassively raised the monetary base, but because of the declinein the money multiplier, this had only limited effect on themoney supply

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