Download 9 Money

Money
Spring 2013
1
What is money?
• 3 functions of money:
– Store of value
– Unit of account
– Medium of exchange
• Whether something is “money” is not always so clear:
– Physical bills and coins
– Balances on checking accounts
– Balances on savings accounts
– Other financial investments (stocks, bonds, etc.)
– Gold
– Foreign currency
– Cigarettes
• Objects used as “money” need to be
– Easy to carry
– Hard to counterfeit
– Easily divisible (Sargent and Velde: “The Big Broblem of Small Change”)
• Historically:
– Commodity money (e.g. gold)
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ECON 52, Spring 2013
2 THE BANKING SYSTEM AND MONEY SUPPLY
– Paper money “backed” by gold or silver
– “Fiat” money
• Fiat money as
– A social convention
– Encouraged by the legal system ( “legal tender”)
• Different measures of the quantity of money in the economy or “money supply”
Monetary base
M0
M1
M2
Physical Currency
Central Bank Reserves
Physical Currency
Physical Currency
Demand deposits
Physical Currency
Demand deposits
Savings deposits
Some mutual funds (“money market”)
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The banking system and money supply
An Example
1. Ann has $1 in physical currency
2. Ann deposits $1 in a Bank
3. The Bank lends Bob $1 and gives him the loan in physical currency
• What has happened? (See slides)
• What is M0 at each stage?
• What is M1 at each stage?
• Distinction between money and wealth
Reserve requirements
• Legally, if a bank receives $1 in deposits it cannot make a loan of $1
• Reserve requirements: for each dollar of deposits the bank must keep ρ in reserves (deposits
in the central bank)
• ρ varies by country and by type of deposit. Range: ρ = 0 to ρ = 0.3 approx. Historically
even higher
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ECON 52, Spring 2013
2 THE BANKING SYSTEM AND MONEY SUPPLY
• Two purposes of reserve requirements:
– Make (almost) sure that the bank can always meet withdrawals
– Give the central bank control over the money multiplier (see below)
• Bank earns interest on loans but (traditionally) not on reserves
• Banks usually want to have as little reserves as they can, so they just have ρd
• Therefore bank balance sheet is typically:
Assets
Liabilities
Reserves: ρd
Loans and bonds: (1 − ρ) d
Deposits: d
• Recently:
– Interest rates are very low, so opportunity cost of having reserves is very low
– In US, Central Bank has started paying interest on reserves.
How central banks adjust the money supply
• Buy bonds from banks. Pay with reserves. The central bank is “creating reserves”. Also
known as “printing money” even though it does not involve printing money. Suppose the
central bank creates ∆ reserves to buy bonds.
• See slides
• Overall, the increase in the money supply is:
Monetary base
M1
∆
∆
ρ
• The Central Bank controls the monetary base directly and M1 and other measures of the
money supply indirectly.
• The “money multiplier” is
m=
1
ρ
• Multiplier measures how much M1 increases per unit of increase in the monetary base.
• What if borrowers don’t just keep the money in deposits?
– Transactions with each other but always paying in deposits: calculation is not affected
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ECON 52, Spring 2013
3 NOMINAL AND REAL INTEREST RATES
– Take out physical cash: need to adjust calculation
• What if banks keep excess reserves? Then the money multiplier becomes smaller
• See graph of excess reserves and monetary aggregates.
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Nominal and Real interest rates
• Notation:
– pt : price level in period t
– it+1 : nominal interest rate between t and t + 1
– πt+1 : rate of inflation between period t and period t + 1, i.e.
pt+1
pt
≡ 1 + πt+1
• Suppose you make a loan of 1 dollar at a nominal interest rate of it+1
• You give up:
1
pt
goods at t that you could have consumed if you didn’t make the loan
• You get 1 + it+1 dollars at t + 1
• You can buy
1+it+1
pt+1
goods at t + 1
• Overall, for each good you get
1 + rt+1 ≡
1+it+1
pt+1
1
pt
= (1 + it+1 )
=
pt
pt+1
1 + it+1
1 + πt+1
• Therefore the real interest rate is
rt+1 =
1 + it+1
−1
1 + πt+1
≈ it+1 − πt+1
• Sometimes know as the Fisher equation (for Irving Fisher)
• Note that until t + 1 you don’t really know what the real interest rate is, because there might
be uncertainty about pt+1 .
• Expectations of pt+1 (or equivalently, expectation of πt+1 are extremely important)
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ECON 52, Spring 2013
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4 MONEY DEMAND
Money demand
• Why do people hold money?
• Opportunity cost: money doesn’t pay interest, other assets do
• Benefit of holding money: “double coincidence of wants” problem
A simple model of money demand (Baumol-Tobin)
• There are two kinds of assets
– money (M1)
– interest-paying assets (stocks, bonds, etc.)
• Money is necessary to make transactions (you cannot use interest-bearing assets for these)
• Households consume c in a period (a month or a quarter, maybe). This is a real (as opposed
to nominal) amount.
• The price level is p
• Therefore households spend pc in nominal terms
• pc is not spent all at once: households spend a little bit each day within the period
• Therefore the household doesn’t need to have pc in money all at once
• Household can “go to the bank” as many times as it wants during the period
• Each time it goes to the bank, it transfers enough assets into “money” to pay for expenses
until it goes to the bank again.
– We call this “withdrawing” money, but it can mean a transfer from savings to checking
as well as taking out physical cash.
• There is a cost F of “going to the bank”.
– Bank fees
– Mental cost of dealing with the issue.
• F is a real cost, so if the price level is p, the nominal cost is pF
• If the household goes to the bank once, it has to withdraw pc at the beginning of the period.
Then it draws down the balance, so on average it holds M = pc
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ECON 52, Spring 2013
4 MONEY DEMAND
• If the household goes to the bank N times, it withdraws
pc
M = 2N
.
pc
N
each time. On average it holds
• Draw graph.
• The household tries to minimize the costs associated with managing money:
– Cost of going to the bank. Minimized by few visits to the bank, high money holdings.
– Foregone interest from holding money rather than other assets. Minimized by many
visits to the bank, low money holdings.
• Mathematically:
min pF N + i
N
pc
2N
• i is the interest rate:
– Nominal or real?
– Why?
• FOC:
pF −
ipc −2
N =0
2
r
N=
ic
2F
and therefore
pc
2N
pc
= q
ic
2 2F
r
cF
=p
2i
M=
• Alternatively
M
=
p
r
cF
2i
• The quantity
M
p
is known as “real money balances”. It is an answer to the question: “how many goods would
the household be able to buy with the amount of money it holds?”
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ECON 52, Spring 2013
5 EQUILIBRIUM IN THE MONEY MARKET
• Interpretation of the role of c, F and i
Generalization
• Inspired by the Baumol-Tobin model, we can write a more general money-demand function
as:
M
= mD (Y, i)
p
• Having Y or c doesn’t matter very much: different ways of measuring number of transactions
• i matters because it is the opportunity cost of holding money
• Don’t fixate of the exact function that arises from the Baumol-Tobin model but on the main
economic forces it illustrates
• Plot the money-demand function. What happens if
– GDP increases
– The cost of going to the bank increases
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Equilibrium in the money market
• Central bank decides the supply of money
– directly controls the monetary base
– understands that the banking system will generate a multiplier
• Households choose how much money to hold, according to their money demand
• In equilibrium, supply must equal demand:
M = mD (Y, i) · p
• In this equation,
– M is exogenous. Controlled by the central bank
– Y , i and p endogenous
• Suppose the central bank adjusts the money supply. How does the economy adjust?
– Increasing prices?
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ECON 52, Spring 2013
6 THE “CLASSICAL” VIEW
– Increasing GDP?
– Lower nominal interest rates? If so, do real interest rates also fall? Recall that real
interest rates are rt+1 = it+1 − πt+1 ?
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The “Classical” view
• Complete separation of the real economy from the monetary economy (the “classical dichotomy”)
• The real variables (in particular, Yt and rt+1 ) depend only on real parameters and shocks
(technology, preferences, etc.), as in the Neoclassical/RBC model
• What happens in our money market equilibrium if there is an unexpected permanent increase
in M ?
Mt = mD (Yt , it+1 ) · pt
• Y is not affected (depends on real preferences and technology)
• rt+1 is not affected (depends on real preferences and technology)
• Conjecture: pt+1 and pt rise by exactly the same amount
– If conjecture is true πt+1 is not affected
[Careful about the timing: one thing is inflation between t and t + 1 and another is
inflation between t − 1 and t]
– Therefore if conjecture is true
it+1 = rt+1 + πt+1
is not affected
– Therefore if conjecture is true, pt increases one-for-one with Mt
– Which confirms the conjecture
• Conclusion: prices rise immediately in the same proportion as M
• Conclusion: one necessary ingredient for the classical view to hold is that prices must be
flexible.
• One main distinction between neoclassical/RBC models vs. Keynesian/New Keynesian models: are prices flexible?
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ECON 52, Spring 2013
6 THE “CLASSICAL” VIEW
Inflation and money growth
• Suppose the money supply grows at a constant rate γ:
Mt+1 = (1 + γ) Mt
• How will prices behave?
• Conjecture: suppose the real economy is in a steady state. Then
pt+1 = (1 + γ) pt
• Let’s verify our conjecture.
• If the conjecture is true, inflation will be
πt+1 =
pt+1
−1
pt
=γ
• Nominal interest rates will be
it+1 = rss + γ
• Money market equilibrium implies
Mt = mD (Yss , rss + γ) pt
Mt
= mD (Yss , rss + γ) (constant)
pt
which verifies our conjecture
• Conclusion: inflation is exactly proportional to the rate of growth of the money supply
• Graphs with evidence
– Cross country
– US over time
• Exercise, what happens if at time t the rate of growth of the money supply increases from γ
to γ 0 > γ?
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ECON 52, Spring 2013
6 THE “CLASSICAL” VIEW
“Velocity” and the Quantity Theory of money
• “Velocity of money”: how many times a unit of money is used per unit of time
• Example:
– The money supply is $2
– At the beginning of the period, Ann and Bob each hold $1
– Ann produces an apple and sells it to Bob for $1. Bob produces a banana and sells it
to Ann for $1
– Ann produces asparagus and sells it to Bob for $1. Bob produces a blueberry and sells
it to Ann for $1
– Ann produces an apricot and sells it to Bob for $1. Bob produces a blackberry and sells
it to Ann for $1
• In the example:
– Nominal GDP is 6
– The money supply is 2
– Each dollar changes hands 3 times per period
• In general, we say that
M ·V ≡P ·Y
• M is the money supply
• P is the price level
• Y is real GDP, so P · Y is nominal GDP
• V is the velocity of money
• This equation is an identity, not a theory. It holds by definition
• The quantity theory is the assumption that Y and V are exogenous, or at least do not depend
on M
• Implication: M determines P
• Does the quantity theory hold in the classical model? Recall:
1. Money market equilibrium
Mt = mD (Yt , it+1 ) · pt
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ECON 52, Spring 2013
7 SEIGNORAGE
2. Yt and rt+t determined by real factors
• Velocity will be
Pt · Y t
Mt
Yt
= D
m (Yt , it+1 )
Vt =
• Suppose the rate of money growth is high. Then
– Inflation will be high (π = γ)
– Nominal interest rates will be high (i = r + π)
– Money demand will be low (mD (Y, i) is decreasing in i - people go a lot to the bank to
avoid the opportunity cost of holding money)
– Velocity will be high
• Conclusion: in our model, velocity
– Does not depend on the level of M
– Depends on the rate of growth of M
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Seignorage
• Historically, seignorage was a fee that the government charged in order to transform raw gold
into gold coins
• Now the term is used to describe the revenue the government obtains due to the ability to
issue money
– People are willing to give up goods in exchange for pieces of paper
– The government has the ability to produce these pieces of paper
• Government budget constraint (in nominal terms)
Bt+1 = pt [Gt − τt ] + (1 + it ) Bt − [Mt+1 − Mt ]
where
– Bt+1 is nominal public debt
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ECON 52, Spring 2013
7 SEIGNORAGE
– Gt is real government spending
– τt is real government revenue
– it is the nominal interest rate
– Mt is the money supply
• You can also write this as
Mt+1 + Bt+1 = pt [Gt − τt ] + (1 + it ) Bt + Mt
• Interpretation: money is like debt that doesn’t pay interest
• No magic: printing money doesn’t create resources
• Seignorage is like a tax - a tax on what exactly?
• Historical use of this tax
• Inflation as a fiscal phenomenon
• Limits to how much revenue can be raised
– To collect a lot, you need high growth rate of money supply
– BUT high γ implies high i and that implies low mD
• “Friedman rule”
– there is no cost to producing money, so there shouldn’t be an opportunity cost of holding
money
– policy goal: try to keep the nominal interest equal to 0
– (implicitly: don’t use this tax!)
– Since
i=r+π
this requires
π = −r
so this requires constant deflation!
• Very low nominal interest rates can also be a symptom of the economy not doing well - we’ll
come to the “liquidity trap”
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