Monetary Policy in a Macro Model - ECON 40364: Monetary...
Transcript of Monetary Policy in a Macro Model - ECON 40364: Monetary...
Monetary Policy in a Macro ModelECON 40364: Monetary Theory & Policy
Eric Sims
University of Notre Dame
Spring 2020
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Readings
I Mishkin Ch. 20
I Mishkin Ch. 21
I Mishkin Ch. 22
I Mishkin Ch. 23, pg. 553-569
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Approach
I Want to study role of monetary policy in the aggregateeconomy
I For that reason, we will not bother to βmicro-foundβ themacro model of the economy (unlike, for example, inintermediate macro)
I We will just posit a bunch of demand and supply relationshipsso as to get a useable demand-supply macro model
I These demand and supply relationships (or something thatlooks like them) can be motivated from micro principles
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Aggregate Demand
I Aggregate demand is the sum of planned expenditure by thefour primary actors in an economy:
1. Households (consumption)2. Firms (investment)3. Government (government purchases)4. Rest of the world (net exports)
I Total (real) aggregate demand is the sum of plannedexpenditure by each of these actors:
Y ad = C + I + G +NX
I In equilibrium, Y ad = Y (expenditure equals income)
I This is somewhat complicated because expenditure categorieson right hand side may depend on Y
I These are flow concepts but will follow book with no explicittime subscripts
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Consumption
I It is assumed that aggregate consumption is governed by aconsumption function:
C = C +mpc Γ (Y β T )
I Y is income and T is taxes, so Y β T is disposable incomeI C is autonomous consumption. βAutonomousβ means the
exogenous component of an endogenous variable. C isconsumption independent of disposable income. Potentialfactors impacting it (which are not modeled explicitly):
I Future incomeI Interest ratesI UncertaintyI Government spending (via Ricardian Equivalence)
I mpc is the marginal propensity to consume and is between 0and 1
I Something like this can be derived from micro principles
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Investment
I Investment refers to expenses by business on new physicalcapital (as well as new residential construction and inventoryaccumulation)
I Investment function:I = I β dr
I r is βtheβ real interest rate, d is a parameter governingsensitivity to the real interest rate, and I is autonomousinvestment (investment independent of the real interest rate).Possible factors:
I Expectations about the futureI Efficiency of producing new capitalI Government regulations and taxes
I Book includes a βcredit spreadβ variable here. We will returnto that later
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Government Spending and Taxes
I We assume that government spending and taxes arecompletely exogenous. Hence:
G = G (1)
T = T (2)
I We do not think explicitly about government debt, futuretaxes, or future spending. Also, taxes are βlump sumβ
I Not modeling Ricardian Equivalence
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Net Exports
I Net exports depend on the exchange rate (how much onecurrency buys of another), as well as on other non-modeledthings
I A high US interest rate results in an appreciation of the dollarother things being equal (foreigners want to buy US assets,pushing up the value of the dollar relative to other currencies)
I An appreciation of the dollar leads to more imports (cheaperfor US citizens to buy foreign goods) and fewer exports (moreexpensive for foreigners to buy US goods) and hence reducesnet exports
I Net export function, where NX is autonomous net exportsand x is a parameter governing sensitivity to real interest rate:
NX = NX β xr
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Putting it all together
I Total planned (or desired) expenditure:
Y ad = C βmpcT + I + G + NX +mpcY β (d + x)r
I For simplicity, let A = C βmpcT + I + G + NX
I Then:Y ad = A+mpcY β (d + x)r
I One equation in three βunknownsβ (Y ad , Y , and r); d , x ,and mpc are parameters, and A is exogenous
I In equilibrium, total output must equal total plannedexpenditure, Y = Y ad , so:
Y =1
1βmpcAβ d + x
1βmpcr
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Keynesian Cross
ππ
ππππππ ππππππ = ππ
ππππππ = οΏ½οΏ½π΄ + ππππππ β ππ β (ππ + π₯π₯) β ππ
οΏ½οΏ½π΄ β (ππ + π₯π₯) β ππ
ππβ
ππβ
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The IS Curve
I The condition:
Y =1
1βmpcAβ d + x
1βmpcr
Is one equation in two endogenous variables, r and Y
I The IS curve is the set of (r ,Y ) pairs where this conditionholds
I It can be derived graphically:I It is downward slopingI It shifts right whenever A increases
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ππ
ππππππ ππππππ = ππ
ππππππ = οΏ½οΏ½π΄ + ππππππ β ππ β (ππ + π₯π₯) β ππ
οΏ½οΏ½π΄ β (ππ + π₯π₯) β ππ0
ππ0 ππ
ππ
ππ0
ππ1
ππ1
οΏ½οΏ½π΄ β (ππ + π₯π₯) β ππ1
ππ2
πΌπΌπΌπΌ
οΏ½οΏ½π΄ β (ππ + π₯π₯) β ππ2
ππ2
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ππ
ππππππ ππππππ = ππ
ππππππ = οΏ½οΏ½π΄ + ππππππ β ππ β (ππ + π₯π₯) β ππ
οΏ½οΏ½π΄0 β (ππ + π₯π₯) β ππ0
ππ0 ππ
ππ
ππ0
ππ1
πΌπΌπΌπΌ
οΏ½οΏ½π΄1 β (ππ + π₯π₯) β ππ0
πΌπΌπΌπΌβ²
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The MP Curve
I To get an aggregate demand curve, which shows a relationshipbetween aggregate output and the inflation rate or theaggregate price level (where Ο = βP
P ), we need to combinethe IS curve with some description of monetary policy
I Traditionally, this is done through something called the LMcurve, which combines the liquidity preference of moneydemand with a money supply rule
I Given central bankβs modern focus on interest rates ratherthan money supply, we instead do so with the monetary policycurve (MP)
I Difference: with the LM curve, AD curve is downward-slopingin a graph with (P,Y ). With MP curve, AD curve isdownward-sloping with (Ο,Y )
I We need not model money at all, though we could figure outhow Fed must adjust M to meet money demand if we wantedβ the economy is βcashlessβ
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The MP curve and the Taylor PrincipleI Recall the Fisher relationship, r = i β Οe . Fed can control i ,
but not necessarily rI Assume adaptive expectations, so that Οe = Ο.I Then assume Fed sets nominal rate according to:
i = r + aΟ
I Similar to the Taylor rule. r is βautonomous monetary policyβ(movements in rates unrelated to inflation). a > 1 β theβTaylor Principleβ
I Can write the real interest rate as:
r = r + Ξ»Ο
I Where Ξ» = (aβ 1). Taylor principle requires Ξ» > 0. Idea:when Ο increases, Fed responds by raising i by sufficientlymuch so as to raise r
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The AD Curve
I Simply combine the IS and MP curves. You get:
Y =1
1βmpcAβ d + x
1βmpc(r + Ξ»Ο)
I Can also re-arrange with Ο on LHS:
Ο = β 1βmpc
(d + x)Ξ»Y +
1
(d + x)Ξ»Aβ 1
Ξ»r
I Provided Ξ» > 0 (Taylor principle satisfied):
1. AD curve is downward-sloping2. AD curve is flatter the bigger is Ξ»3. AD curve shifts out/up when A increases4. AD curve shifts down/in when r increases
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ππ ππ
ππ
ππ
ππ ππ
ππ
ππ
ππ = ππ
ππ = οΏ½οΏ½π + ππππ
οΏ½οΏ½π
πΌπΌπΌπΌ
ππ0
ππ0
ππ0
ππ0
ππ1
ππ1
ππ1
ππ2
ππ2 ππ1 ππ2
π΄π΄π΄π΄
ππ2
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Shifts of the AD Curve
I The AD curve is drawn holding r (which governs the positionof the MP curve) and A (which governs the position of the IScurve) fixed
I An increase in r will result in an increase in the real interestrate for a given inflation rate; from the IS curve, this results ina lower level of output. So the AD curve shifts left
I An increase in A will shift the IS curve right. For a giveninflation rate, the real interest rate is given, which means thatoutput increases. So the AD curve shifts right
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ππ ππ
ππ
ππ
ππ ππ
ππ
ππ
ππ = ππ
ππ = οΏ½οΏ½π + ππππ
οΏ½οΏ½π0
πΌπΌπΌπΌ
ππ0
ππ0
ππ0
ππ0
π΄π΄π΄π΄
οΏ½οΏ½π1
ππ1
ππ1
π΄π΄π΄π΄β²
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ππ ππ
ππ
ππ
ππ ππ
ππ
ππ
ππ = ππ
ππ = οΏ½οΏ½π + ππππ
οΏ½οΏ½π
πΌπΌπΌπΌ
ππ0
ππ0
ππ0
ππ0
π΄π΄π΄π΄
πΌπΌπΌπΌβ²
ππ1
π΄π΄π΄π΄β²
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The Taylor Principle and the Slope of the AD Curve
I The Taylor principle (a > 1 or Ξ» > 0) calls for the Fed toraise the real interest rate when inflation increases
I The higher real interest rate causes output to decline from theIS curve, which makes the AD curve downward-sloping
I What if the Taylor principle isnβt satisfied? i.e. Ξ» < 0?
I Higher inflation results in lower real interest rates, whichstimulates output from the IS curve
I The AD curve is upward-sloping. For reasons we will talkabout later, this is undesirable.
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π π
π
π
π π
π
π
π = π
π = οΏ½οΏ½ + ππ, π < 0
οΏ½οΏ½
πΌπ
π0
π0 π0
π1
π0
π1
π2
π2 π1 π2
π΄π·
π2
π1
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Aggregate Supply
I Relationship between Ο and Y (or P and Y )I Accepted paradigm:
I Aggregate supply (AS) curve is vertical in the βlong runβ orβmedium run.β The level of output where itβs vertical, orβpotential output,β is determined by labor supply, availablecapital, and technology.
I Prices and/or wages are βstickyβ in the short run, so βshortrunβ AS curve is upward-sloping instead of vertical
I Many policy debates among macroeconomists are over theβshapeβ of the AS curve (i.e. how far from vertical is the AScurve in the short run) and how long it takes to transitionfrom short run to medium/long run
I Let Y P denote potential output; take this to be exogenous(equilibrium concept in model without nominal rigidity)
I LRAS (long run aggregate supply) is vertical at this point
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Short Run AS
I The assumed short run AS curve is:
Ο = Οe + Ξ³(Y β Y P) + Ο
I Where:
1. Οe : how much inflation firms/households expected fromβyesterdayβ to βtodayβ (note slightly different than Οe in theFisher relationship, which is expected inflation from βtodayβ toβtomorrowβ . . . this is where time subscripts would be handy)
2. Ξ³: parameter governing how steep AS is (related to underlyingprice and/or wage stickiness)
3. Ο: βinflation shockβ (e.g. increase in oil prices), also calledβcost-push shock.β Zero on average; if it changes, onlychanges for one period (simplifying assumption)
I If Y > Y P , firms/households have pressure to increaseprices/wages, which puts upward pressure on Ο. Ξ³ big: itβseasy to do this. Ξ³ small: prices/wages are very sticky
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ππ = ππππ + πΎπΎ(ππ β ππππ) + ππ
ππππ
ππππ + ππ
ππ
ππ LRAS
πΎπΎ π π π π π π π π π π
πΎπΎ ππππππ
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Short Run AS Curve (SRAS)
I The following are relevant things to remember about the AScurve:
1. If Ξ³β β, no distinction between SRAS and LRAS2. AS curve crosses point Y = Y P at Ο = Οe + Ο. The inflation
shock Ο is zero on average, so weβll often think of this point asbeing where Ο = Οe . In other words, if households and firmsare not surprised by inflation, then Y = Y p regardless of whatΞ³ is
I In a sense, nominal rigidities matter only if agents areβfooledβ (Lucas 1972)
3. The AS curve shifts up if Οe or Ο increase4. The AS curve shifts right if Y P increases
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ππ = ππππ + πΎπΎ(ππ β ππππ) + ππ
ππππ
ππ0ππ + ππ
ππ
ππ LRAS
ππ1ππ + ππ
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ππ = ππππ + πΎπΎ(ππ β ππππ) + ππ
ππππ
ππππ + ππ0
ππ
ππ LRAS
ππππ + ππ1
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ππ = ππππ + πΎπΎ(ππ β ππππ) + ππ
ππ0ππ
ππππ + ππ
ππ
ππ πΏπΏπΏπΏπΏπΏπΏπΏ0
ππ1ππ
πΏπΏπΏπΏπΏπΏπΏπΏ1
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General Equilibrium
I Equilibrium occurs where AD and AS intersect
I For simplicity, assume these intersect initially at the LRASI Exogenous variables cause curves to shift and change the
equilibriumI Demand shocks:
I IS shocks: changes in A (C , I , T , G , NX )I Monetary shocks: changes in r
I Supply shocks:I Potential output shocks: changes in Y P
I Inflation shocks: changes in ΟI Expected inflation shocks: changes in Οe
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π΄π΄π΄π΄
ππ0
ππ0
ππ
ππ πΏπΏπΏπΏπ΄π΄π΄π΄
π΄π΄π·π·
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Demand Shock
π΄π΄π΄π΄
ππ0
ππ0
ππ
ππ πΏπΏπΏπΏπ΄π΄π΄π΄
π΄π΄π΄π΄
ππ1
ππ1
π΄π΄π΄π΄β²
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IS Shock: What Happens to r
ππ ππ
ππ
ππ
ππ ππ
ππ
ππ
ππ = ππ
ππ = οΏ½οΏ½π + ππππ
οΏ½οΏ½π
πΌπΌπΌπΌ
ππ0
ππ0
ππ0
ππ0
π΄π΄π΄π΄
πΌπΌπΌπΌβ²
ππ0β²
π΄π΄π΄π΄β²
π΄π΄πΌπΌ
ππ1
ππ1
ππ1 ππ1
(a)
(a) (a)
(a)
(b)
(b)
(c) (c)
(c) (c)
(a) to (b): direct effect (b) to (c): indirect effect due to higher ππ
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MP Shock: What Happens to r
ππ ππ
ππ
ππ
ππ ππ
ππ
ππ
ππ = ππ
ππ = οΏ½οΏ½π + ππππ
οΏ½οΏ½π0
πΌπΌπΌπΌ
ππ0
ππ0
ππ0
ππ0
π΄π΄π΄π΄
οΏ½οΏ½π1
ππ0β²
ππ0β²
π΄π΄π΄π΄β²
π΄π΄πΌπΌ
ππ1
ππ1 ππ1
ππ1
(a)
(a) (a)
(a)
(b) (b)
(b)
(c)
(c) (c)
(c)
(a) to (b): direct effect (b) to (c): indirect effect due to lower ππ
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Monetary Neutrality: MP Shock When AS is Vertical
ππ ππ
ππ
ππ
ππ ππ
ππ
ππ
ππ = ππ
ππ = οΏ½οΏ½π + ππππ
οΏ½οΏ½π0
πΌπΌπΌπΌ
ππ0
ππ0
ππ0
ππ0
π΄π΄π΄π΄
οΏ½οΏ½π1
ππ0β²
ππ0β²
π΄π΄π΄π΄β²
π΄π΄πΌπΌ
ππ1
ππ1 ππ1
(a)
(a) (a)=(c)
(a)
(b) (b)
(b)
(c)
(c)
(c)
(a) to (b): direct effect (b) to (c): indirect effect due to lower ππ
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Supply Shock: Increase in Οe or Ο
π΄π΄π΄π΄
ππ0
ππ0
ππ
ππ πΏπΏπΏπΏπ΄π΄π΄π΄
π΄π΄π΄π΄
π΄π΄π΄π΄β²
ππ1
ππ1
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Supply Shock: Increase in Y P
π΄π΄π΄π΄
ππ0
ππ0
ππ
ππ πΏπΏπΏπΏπ΄π΄π΄π΄
π΄π΄π΄π΄
π΄π΄π΄π΄β²
πΏπΏπΏπΏπ΄π΄π΄π΄β²
ππ1
ππ1
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Decrease in Y P : Effect on r
ππ ππ
ππ
ππ
ππ ππ
ππ
ππ
ππ = ππ
ππ = οΏ½οΏ½π + ππππ
οΏ½οΏ½π
πΌπΌπΌπΌ
π΄π΄π΄π΄
π΄π΄πΌπΌ
ππ0 ππ0
ππ0
ππ0
π΄π΄πΌπΌβ²
ππ1
ππ1
ππ1 ππ1
(c)
(a) (a)
(a) (b)
(c)
(a)
(c) (c)
(a) to (b): direct effect (b) to (c): indirect effect due to higher ππ
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Algebraically Solving for EquilibriumI AS with AD:
Ο = Οe + Ξ³
(1
1βmpcAβ d + x
1βmpc(r + Ξ»Ο)β Y p
)+ Ο
I Solve for Ο:
Ο =1βmpc
1βmpc + (d + x)λγ(Οe + Ο)+
Ξ³
1βmpc + (d + x)λγA
β (d + x)Ξ³
1βmpc + (d + x)λγr β Ξ³(1βmpc)
1βmpc + (d + x)λγY P
I Once you have this, you can get Y from the AS curve:
Y = Y P +1
Ξ³(Ο β Οe β Ο)
I Then can get r = r + Ξ»Ο and components of output
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Dynamics and the βSelf-Correcting Mechanismβ
I Assume Ο = 0 (its average value)
I From AS, if Y 6= Y P , then Ο 6= Οe
I Y > Y p β Ο > Οe : agents were surprised with moreinflation than they expected
I Stands to reason that, going forward in time, they will thenrevise up expectations
I Οe going up: shifts AS curve up, which makes Y fall with noeffect on Y P
I This process will continue until Y = Y P and inflation stopschange
I And vice-versa in the other direction
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Adjustment from Positive Gap: Qualitative
π΄π΄π΄π΄
ππ0
ππ
ππ πΏπΏπΏπΏπ΄π΄π΄π΄
π΄π΄π΄π΄
ππ0 ππ1 = ππππ
ππππ
ππ1
π΄π΄π΄π΄β²
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Being More SpecificI Put time subscripts on all variables: t is present, t β 1 is one
period in past, t + 1 one period in future, and so onI Assume adaptive expectations, so that Οe in the AS curve is
Οtβ1I Then AS curve is:
Οt = Οtβ1 + Ξ³(Yt β Y P
t
)+ Οt
I AD curve is:
Yt =1
1βmpcAt β
d + x
1βmpc(rt + Ξ»Οt)
I The interesting dynamics are on the supply side. As Οt
changes, the position of the AS curve will change dynamicallyover time. Assume Οt = 0 (unconditional mean)
I Adjustment occurs slowly, only eventually do you get to Y P
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Adjustment from Positive Gap: More Specific
π΄π΄π΄π΄
πππ‘π‘
ππ
ππ πΏπΏπΏπΏπ΄π΄π΄π΄
π΄π΄π΄π΄
πππ‘π‘ ππππ
πππ‘π‘β1
π΄π΄π΄π΄β²
πππ‘π‘+1
πππ‘π‘+1
πππ‘π‘+2
πππ‘π‘+2
π΄π΄π΄π΄β²β²
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Quantitative Dynamics
I Create an Excel file
I Assume the following parameters and exogenous variables:mpc = 0.7, d = 0.3, x = 0.1, r = 1, Ξ» = 1, A = 4.95,Ξ³ = 0.5, Y P = 12.5
I Assume Οtβ1 = 0
I Implies that Οt = 0.8 and Yt = 14.1
I Use Excel to trace out dynamic paths
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Adjustment from Positive Gap: Quantitative
0
0.5
1
1.5
2
2.5
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Inflation
12
12.5
13
13.5
14
14.5
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Output
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Positive IS Shock: Dynamic Adjustment
π΄π΄π΄π΄
ππππ
πππ‘π‘β1
ππ
ππ πΏπΏπΏπΏπ΄π΄π΄π΄
π΄π΄π΄π΄
πππ‘π‘
πππ‘π‘
π΄π΄π΄π΄β²
π΄π΄π΄π΄β²
πππ‘π‘+1
πππ‘π‘+1
π΄π΄π΄π΄β²β²
πππ‘π‘+2
πππ‘π‘+2
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Quantitative Adjustment from Positive IS Shock
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
-5 0 5 10 15 20 25
Inflation
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
13
13.1
13.2
-5 0 5 10 15 20 25
Output
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
-5 0 5 10 15 20 25
r
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Monetary Shock
I An exogenous monetary tightening (increase in r) has effectsin terms of output and inflation similar to an IS shock(exogenous increase in A)
I Difference: monetary shock does not affect rt in medium/longrun
I βNatural rate of interestβ: r consistent with IS curve holdingat Y P . Call it rP (potential or long run real interest rate):
rP = β1βmpc
d + xY P +
1
d + xA
I Does not depend on r
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Adjustment from Positive r Shock
0
0.5
1
1.5
2
2.5
-5 0 5 10 15 20 25
Inflation
11.2
11.4
11.6
11.8
12
12.2
12.4
12.6
-5 0 5 10 15 20 25
Output
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
-5 0 5 10 15 20 25
r
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Application: Volcker Disinflation
0.002.004.006.008.00
10.0012.0014.0016.0018.0020.00
FFR
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
1980
-07-
0119
80-0
9-01
1980
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0119
81-0
1-01
1981
-03-
0119
81-0
5-01
1981
-07-
0119
81-0
9-01
1981
-11-
0119
82-0
1-01
1982
-03-
0119
82-0
5-01
1982
-07-
0119
82-0
9-01
1982
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0119
83-0
1-01
1983
-03-
0119
83-0
5-01
1983
-07-
0119
83-0
9-01
1983
-11-
0119
84-0
1-01
1984
-03-
0119
84-0
5-01
1984
-07-
01
Output
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
1980
-07-
0119
80-0
9-01
1980
-11-
0119
81-0
1-01
1981
-03-
0119
81-0
5-01
1981
-07-
0119
81-0
9-01
1981
-11-
0119
82-0
1-01
1982
-03-
0119
82-0
5-01
1982
-07-
0119
82-0
9-01
1982
-11-
0119
83-0
1-01
1983
-03-
0119
83-0
5-01
1983
-07-
0119
83-0
9-01
1983
-11-
0119
84-0
1-01
1984
-03-
0119
84-0
5-01
1984
-07-
01
Inflation
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Adjustment from Positive Y P Shock
π΄π΄π΄π΄
ππ0ππ
πππ‘π‘β1
ππ
ππ πΏπΏπΏπΏπ΄π΄π΄π΄
π΄π΄π΄π΄
π΄π΄π΄π΄β²
πΏπΏπΏπΏπ΄π΄π΄π΄β²
πππ‘π‘
πππ‘π‘ ππ1ππ
π΄π΄π΄π΄β²β²
πππ‘π‘+1
πππ‘π‘+1
π΄π΄π΄π΄β²β²β²
πππ‘π‘+2
πππ‘π‘+2
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Quantitative Adjustment from Positive Y P Shock
1
1.2
1.4
1.6
1.8
2
2.2
-5 0 5 10 15 20 25
Inflation
12
12.2
12.4
12.6
12.8
13
13.2
13.4
13.6
-5 0 5 10 15 20 25
Output
2
2.2
2.4
2.6
2.8
3
3.2
-5 0 5 10 15 20 25
r
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Adjustment from One Period Ο Shock
π΄π΄π΄π΄
ππππ
πππ‘π‘β1
ππ
ππ πΏπΏπΏπΏπ΄π΄π΄π΄
π΄π΄π΄π΄
π΄π΄π΄π΄β²
πππ‘π‘
πππ‘π‘
πππ‘π‘β1 + 1
π΄π΄π΄π΄β²β²
πππ‘π‘+1
πππ‘π‘+1
π΄π΄π΄π΄β²β²β²
πππ‘π‘+2
πππ‘π‘+2
53 / 66
Quantitative Adjustment from Positive Ο Shock
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
-5 0 5 10 15 20 25
Inflation
11.2
11.4
11.6
11.8
12
12.2
12.4
12.6
-5 0 5 10 15 20 25
Output
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
-5 0 5 10 15 20 25
r
54 / 66
Application: Oil Shocks and Stagflation
0
0.02
0.04
0.06
0.08
0.1
0.12
Output
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
Inflation
55 / 66
Monetary Policy Objectives
I When it comes to the business cycle, monetary policy has adual mandate: it wants to stabilize inflation around some lowand stable rate and achieve βmaximum employmentβ
I In the context of our model, we can think about the first halfof the mandate as keeping Οt close to constant, and thesecond half as keeping Yt close to Y P
t
I Define the output gap as Xt = Yt β Y Pt
I Hence, objectives are to keep Οt close to constant and Xt
close to zero
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Monetary Policy Tools
I The primary tool of monetary policy (in this simple model) isthe parameter Ξ»
I Governs how strongly policy reacts to inflation
I Recall algebraic expression for AD curve:
Ο = β 1βmpc
(d + x)Ξ»Y +
1
(d + x)Ξ»Aβ 1
Ξ»r
I Ξ» influences two things:I Slope of AD curve (bigger Ξ» and AD curve is flatter)I Shift of AD curve conditional on IS shock, A (bigger Ξ» and AD
curve shifts up less; horizontal shift of AD curve unaffected byΞ»)
57 / 66
Ξ» and the Effects of IS Shocks
π΄π΄π΄π΄
ππ0
ππ0
ππ
ππ πΏπΏπΏπΏπ΄π΄π΄π΄
π΄π΄π΄π΄ (ππ π π π π π π π π π π )
π΄π΄π΄π΄ (ππ ππππππ) π΄π΄π΄π΄β²
π΄π΄π΄π΄β²
ππ1
ππ1 ππ1β²
ππ1β²
58 / 66
Ξ» and IS Shocks
I After an increase in A, a bigger Ξ» results in:
1. Smaller increase in Ο2. Smaller increase in Y . Since Y P doesnβt change, this means
that the gap, X , goes up by less
I Bigger Ξ» is a βwin-winβ from perspective of dual mandateconditional on IS shocks
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IS Shock: Ξ» = 1 vs. Ξ» = 10
11.21.41.61.8
22.22.42.62.8
3
-5 0 5 10 15 20 25
Inflation
lambda=1 lambda=10
12.212.312.412.512.612.712.812.9
1313.113.2
-5 0 5 10 15 20 25
Output
lambda=1 lambda=10
22.22.42.62.8
33.23.43.63.8
4
-5 0 5 10 15 20 25
r
lambda=1 lambda=10
60 / 66
Ξ» and the Effects of Y P Shocks
π΄π΄π΄π΄
ππ0ππ
ππ0
ππ
ππ πΏπΏπΏπΏπ΄π΄π΄π΄
π΄π΄π΄π΄ (ππ π π π π π π π π π π )
ππ1ππ
πΏπΏπΏπΏπ΄π΄π΄π΄β²
π΄π΄π΄π΄β²
π΄π΄π΄π΄ (ππ ππππππ)
ππ1β²
ππ1β²
ππ1
ππ1
61 / 66
Ξ» and Potential Output Shocks
I After an increase in Y P , a bigger Ξ» results in:
1. Smaller increase in Ο2. Bigger increase in Y . Since Y P increases, this means that the
gap, X , goes down by less the bigger is Ξ»
I Bigger Ξ» is a βwin-winβ from perspective of dual mandateconditional on potential output shocks shocks
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Y P Shock: Ξ» = 1 vs. Ξ» = 10
0
0.5
1
1.5
2
2.5
-5 0 5 10 15 20 25
Inflation
lambda = 1 lambda=10
12
12.2
12.4
12.6
12.8
13
13.2
13.4
13.6
-5 0 5 10 15 20 25
Output
lambda = 1 lambda=10
2
2.2
2.4
2.6
2.8
3
3.2
-5 0 5 10 15 20 25
r
lambda=1 lambda=10-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0-5 0 5 10 15 20 25
Output Gap
lambda=1 lambda=10
63 / 66
Divine Coincidence
I Divine Coincidence: there is no tradeoff between objectives ofmonetary policy
I Responding strongly to inflation both stabilizes inflation andthe output gap
I So named by Blanchard and Gali (2007)
I Forms the basis of the call for βinflation targeting,β eitherimplicity or explicitly done by several leading central banks
I Divine coincidence does not hold conditional on inflationshocks (Ο)
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Ξ» and the Effects of Ο Shocks
π΄π΄π΄π΄
ππ0
ππ0
ππ
ππ πΏπΏπΏπΏπ΄π΄π΄π΄
π΄π΄π΄π΄ (ππ π π π π π π π π π π )
π΄π΄π΄π΄β²
ππ1
ππ1
ππ0 + 1
π΄π΄π΄π΄ (ππ ππππππ)
ππ1β²
ππ1β²
65 / 66
Ο Shock: Ξ» = 1 vs. Ξ» = 10
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
-5 0 5 10 15 20 25
Inflation
lambda=1 lambda=10
9.5
10
10.5
11
11.5
12
12.5
13
-5 0 5 10 15 20 25
Output
lambda=1 lambda=10
2.72.82.9
33.13.23.33.43.53.63.7
-5 0 5 10 15 20 25
r
lambda=1 lambda=10
66 / 66