is-lm equilibrium - lhendricks.orglhendricks.org/econ520/islm/islm_equil_sl.pdf · is "lm! lm...
TRANSCRIPT
Objectives
In this section you will learn how to
1. put IS and LM together and derive the equilibrium;2. determine the effects of shocks and policies on equilibrium
output and interest rate
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Model Summary
I Endogenous objects: Y, iI Exogenous objects: I,c0,G,T
I also M, which we take as controlled by CB for now
I Equations:I IS: Y = C(Y−T) + I(Y, i) + GI LM: M/P = YL(i)
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IS-LM GraphLM
IS
A
Output (Income), YY
Inte
rest
rat
e, i
i
Equilibriu
m in
Finan
cial M
arke
ts Equilibrium in Goods Market
What happens in each market in each quadrant?
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Taxes and Investment
I A common argument:I higher taxes reduce disposable income and savingI saving = investmentI investment must fall
I Another common argument:I higher taxes reduce the government deficitI more money available for investment
I Which argument is right?
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Policy Mix
I By combining monetary and fiscal policy, the government can,in principle, move Y and i independently.
I Monetary expansion: Y ↑, i ↓I Fiscal expansion: Y ↑, i ↑I Combination: Y ↑, i unchangedI In a typical recession, monetary and fiscal policies expand
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Example: 2001 RecessionP
erce
nt
1999
2.0
1.5
1.0
0.5
0.0
!0.5 1 2 3 4 1 2 3 4 1 2 3 4 1 2 33 4
2000 2001 2002
Growth rate of output
The shock: bursting ofthe tech bubble =⇒ I ↓
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Policy ResponsesP
erce
nt
7
6
5
4
3
2
1
19993 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3
2000 2001 2002
Federal funds rate
Per
cent
21.5
21.0
20.5
20.0
19.5
19.0
18.5
18.0
17.5
17.0
Revenues
Spending
19993 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3
2000 2001 2002
Government spending / revenue
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Analysis of the 2001 Recession
IS
Output, YYY!
Inte
rest
rat
e, i
IS "
LM!
LMDrop ininvestmentdemand
Monetaryexpansion
IS !
A!
A
Y "
A"Fiscalexpansion
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Liquidity Traps
I Why do monetary policies have such a hard time pulling Japanout of recession?
I Real interest rates near zeroI Suggests flat LM curveI “Liquidity trap”
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US Federal Funds Rate
myf.red/g/czDx
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
fred.stlouisfed.orgSource:BoardofGovernorsoftheFederalReserveSystem(US)
EffectiveFederalFundsRate
Percent
Soure: Fred
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Japan’s Central Bank Rate
Source: Trading Economics
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Liquidity Trap
M/P
i
MsMd
Y ↓ I The LM curve is derivedby varying Y and tracingout i,M/P points thatclear the money market.
I For low Y the interest ratehits 0 and the LM curvebecomes flat.
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A Few Major Caveats
The IS-LM model makes the government look too powerful.
I By raising G it can achieve any level of Y.I When is this a reasonable shortcut?
It looks like saving lowers output.
I What is missing?
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Why Do We Still Have Recessions?
In the model, the government can stabilize output too easily.
Real world complications:
1. Big and variable lags until policies become effective2. Lags in diagnosis and implementation of policies3. Expansionary fiscal policies create debt4. Expansionary monetary policies create inflation
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An important point to remember
The IS-LM model makes strong assumptions: fixed prices, elasticsupply, government can borrow without cost.When applying the model, you need to consider how theseassumptions modify the results.(Or build a more comprehensive model)
Adding Banks
In the IS/LM model, the Fed looks very powerful.
I it controls i and thus investment.
In reality, the behavior of banks can undo monetary policy actions.
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The role of banks
Banks take in deposits and turn them into loans.A fraction of the deposits is held as CB reserves.Reserves provide bank liquidity.The Fed requires banks to hold about 10% of their deposits inreserves.
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Adding Banks
Why do banks matter for monetary policy?
Suppose the Fed increases the supply of money.
I this is vague for now (how the Fed actually do this?)
Typically, this increases the amount of loans banks make, whichdrives down i.In some situations, banks absorb the additional money withoutcreating additional loans.
I they increase their CB reservesI then monetary policy has no power to lower interest rates
I example: 2008 financial crisis
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The Money Multiplier
Money = currency + checkable deposits (+ perhaps other stuff)
I M = CU + D
The Fed does not directly control M.It controls high powered money H
I supplied as currency CU or reserves central bank R.
How do we get from H to M?
I the answer is: via bank lending
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Bank lending
In principle, banks could make loans of unlimited size.In practice, the reserve requirement limits bank lending
The Fed requires that banks hold fraction θ of their deposits in aFed account.Only the remainder can be lent out.
R≥ θD (1)
Typically, θ ≈ 0.1.Of course, banks may hold larger reserves: θ ≥ θ
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Money Demand With BanksHouseholds:
Md = $Y×L(i) (2)
Split into deposits D and currency CU.Assume: fraction c goes into currency
CUd = cMd (3)
Dd = (1− c)Md (4)
Banks: choose reserve ratio θ ≥ θ :
Rd = θD (5)= θ(1− c)$YL(i) (6)
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Money Market Clearing
H = CUd + Rd (7)= [c + θ(1− c)]$Y×L(i) (8)
With a fixed reserve ratio θ :
I higher H =⇒ lower i
With variable θ :
I bank actions can change the “effective” money supply and ieven with constant H
I example: 2008. Banks raise θ to gain liquidity.
This is an important limitation of monetary policy.
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Money Market Clearing
H
A
Hd ! CUd " Rd
Central Bank Money, H
Demand for CentralBank Money
Supply of CentralBank Money
Inte
rest
rat
e, i
i
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Money Market Clearing With Banks
Demand for money
Demand for checkable deposits
Demand for reserves by banks
Demand for Central Bank
Money
Supply of Central Bank
MoneyDemand for
currency
!
Demand for moneyMd ! $Y L(i)
Demand for checkable deposits
Dd ! (1"c) Md
Demand for reserves by banksRd ! (1"c) Md
Demand for Central Bank
MoneyHd ! CUd # Rd !
[c # (1"c)] Md !
[c # (1"c)] $Y L(i )
Supply of Central Bank
Money
H
Demand for currency
CUd ! c Md !
$
$
$
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The Money Multiplier
1c + θ(1− c)
H = $Y L(i) (9)
A $1 increase in CB money supply increases money available tohouseholds by 1
c+θ(1−c) > 1
The lower the reserve ratio θ , the larger the multiplier
Intuition: each dollar of H can be lent out many times
I round 1: lend (1−θ) and put θ in reservesI round 2: (1−θ) returns as new deposits and is lent out againI round 3: ...
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The Fed Funds Rate
Long ago, changing the reserve requirement θ was an importanttool of monetary policy
I this is no longer the case
Today, the main monetary policy tools is the Federal Funds Rate
I Banks lend reserves to each other over night at the Fed FundsRate
I The Fed controls the FFR tightly by choosing available reserves
The mechanism:
I H ↓=⇒ R ↓=⇒ i ↑I again, the complication is that banks may reduce θ which
dampens the effect on i
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Reading
Blanchard and Johnson (2013), ch. 5 and 9.2On how the Fed works:
I Johnson, Manuel (2002). “Federal Reserve System.” TheLibrary of Economics and Liberty: a very brief overview of howthe Fed operates.
I Monetary Policy Basics: a brief summary of fed operations.I Labonte and Makinen (2017): A more detailed description
(including unconventional monetary policy).
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