monetary policy in a macro model - econ 40364: monetary...
TRANSCRIPT
Monetary Policy in a Macro ModelECON 40364: Monetary Theory & Policy
Eric Sims
University of Notre Dame
Spring 2020
1 / 66
Readings
I Mishkin Ch. 20
I Mishkin Ch. 21
I Mishkin Ch. 22
I Mishkin Ch. 23, pg. 553-569
2 / 66
Approach
I Want to study role of monetary policy in the aggregateeconomy
I For that reason, we will not bother to âmicro-foundâ 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
3 / 66
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
4 / 66
Consumption
I It is assumed that aggregate consumption is governed by aconsumption function:
C = C +mpc à (Y â T )
I Y is income and T is taxes, so Y â T is disposable incomeI C is autonomous consumption. âAutonomousâ 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
5 / 66
Investment
I Investment refers to expenses by business on new physicalcapital (as well as new residential construction and inventoryaccumulation)
I Investment function:I = I â dr
I r is âtheâ 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 âcredit spreadâ variable here. We will returnto that later
6 / 66
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 âlump sumâ
I Not modeling Ricardian Equivalence
7 / 66
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 â xr
8 / 66
Putting it all together
I Total planned (or desired) expenditure:
Y ad = C âmpcT + I + G + NX +mpcY â (d + x)r
I For simplicity, let A = C âmpcT + I + G + NX
I Then:Y ad = A+mpcY â (d + x)r
I One equation in three âunknownsâ (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
1âmpcAâ d + x
1âmpcr
9 / 66
Keynesian Cross
ðð
ðððððð ðððððð = ðð
ðððððð = ᅵᅵðŽ + ðððððð â ðð â (ðð + ð¥ð¥) â ðð
ᅵᅵðŽ â (ðð + ð¥ð¥) â ðð
ððâ
ððâ
10 / 66
The IS Curve
I The condition:
Y =1
1âmpcAâ d + x
1âmpcr
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
11 / 66
ðð
ðððððð ðððððð = ðð
ðððððð = ᅵᅵðŽ + ðððððð â ðð â (ðð + ð¥ð¥) â ðð
ᅵᅵðŽ â (ðð + ð¥ð¥) â ðð0
ðð0 ðð
ðð
ðð0
ðð1
ðð1
ᅵᅵðŽ â (ðð + ð¥ð¥) â ðð1
ðð2
ðŒðŒðŒðŒ
ᅵᅵðŽ â (ðð + ð¥ð¥) â ðð2
ðð2
12 / 66
ðð
ðððððð ðððððð = ðð
ðððððð = ᅵᅵðŽ + ðððððð â ðð â (ðð + ð¥ð¥) â ðð
ᅵᅵðŽ0 â (ðð + ð¥ð¥) â ðð0
ðð0 ðð
ðð
ðð0
ðð1
ðŒðŒðŒðŒ
ᅵᅵðŽ1 â (ðð + ð¥ð¥) â ðð0
ðŒðŒðŒðŒâ²
13 / 66
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 Ï = âP
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 bankâs 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 (Ï,Y )
I We need not model money at all, though we could figure outhow Fed must adjust M to meet money demand if we wantedâ the economy is âcashlessâ
14 / 66
The MP curve and the Taylor PrincipleI Recall the Fisher relationship, r = i â Ïe . Fed can control i ,
but not necessarily rI Assume adaptive expectations, so that Ïe = Ï.I Then assume Fed sets nominal rate according to:
i = r + aÏ
I Similar to the Taylor rule. r is âautonomous monetary policyâ(movements in rates unrelated to inflation). a > 1 â theâTaylor Principleâ
I Can write the real interest rate as:
r = r + λÏ
I Where λ = (aâ 1). Taylor principle requires λ > 0. Idea:when Ï increases, Fed responds by raising i by sufficientlymuch so as to raise r
15 / 66
The AD Curve
I Simply combine the IS and MP curves. You get:
Y =1
1âmpcAâ d + x
1âmpc(r + λÏ)
I Can also re-arrange with Ï on LHS:
Ï = â 1âmpc
(d + x)λY +
1
(d + x)λAâ 1
λr
I Provided λ > 0 (Taylor principle satisfied):
1. AD curve is downward-sloping2. AD curve is flatter the bigger is λ3. AD curve shifts out/up when A increases4. AD curve shifts down/in when r increases
16 / 66
ðð ðð
ðð
ðð
ðð ðð
ðð
ðð
ðð = ðð
ðð = ᅵᅵð + ðððð
ᅵᅵð
ðŒðŒðŒðŒ
ðð0
ðð0
ðð0
ðð0
ðð1
ðð1
ðð1
ðð2
ðð2 ðð1 ðð2
ðŽðŽðŽðŽ
ðð2
17 / 66
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
18 / 66
ðð ðð
ðð
ðð
ðð ðð
ðð
ðð
ðð = ðð
ðð = ᅵᅵð + ðððð
ᅵᅵð0
ðŒðŒðŒðŒ
ðð0
ðð0
ðð0
ðð0
ðŽðŽðŽðŽ
ᅵᅵð1
ðð1
ðð1
ðŽðŽðŽðŽâ²
19 / 66
ðð ðð
ðð
ðð
ðð ðð
ðð
ðð
ðð = ðð
ðð = ᅵᅵð + ðððð
ᅵᅵð
ðŒðŒðŒðŒ
ðð0
ðð0
ðð0
ðð0
ðŽðŽðŽðŽ
ðŒðŒðŒðŒâ²
ðð1
ðŽðŽðŽðŽâ²
20 / 66
The Taylor Principle and the Slope of the AD Curve
I The Taylor principle (a > 1 or λ > 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 isnât satisfied? i.e. λ < 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.
21 / 66
ð ð
ð
ð
ð ð
ð
ð
ð = ð
ð = ᅵᅵ + ðð, ð < 0
ᅵᅵ
ðŒð
ð0
ð0 ð0
ð1
ð0
ð1
ð2
ð2 ð1 ð2
ðŽð·
ð2
ð1
22 / 66
Aggregate Supply
I Relationship between Ï and Y (or P and Y )I Accepted paradigm:
I Aggregate supply (AS) curve is vertical in the âlong runâ orâmedium run.â The level of output where itâs vertical, orâpotential output,â is determined by labor supply, availablecapital, and technology.
I Prices and/or wages are âstickyâ in the short run, so âshortrunâ AS curve is upward-sloping instead of vertical
I Many policy debates among macroeconomists are over theâshapeâ 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
23 / 66
Short Run AS
I The assumed short run AS curve is:
Ï = Ïe + γ(Y â Y P) + Ï
I Where:
1. Ïe : how much inflation firms/households expected fromâyesterdayâ to âtodayâ (note slightly different than Ïe in theFisher relationship, which is expected inflation from âtodayâ toâtomorrowâ . . . this is where time subscripts would be handy)
2. γ: parameter governing how steep AS is (related to underlyingprice and/or wage stickiness)
3. Ï: âinflation shockâ (e.g. increase in oil prices), also calledâcost-push shock.â 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 Ï. γ big: itâseasy to do this. γ small: prices/wages are very sticky
24 / 66
ðð = ðððð + ðŸðŸ(ðð â ðððð) + ðð
ðððð
ðððð + ðð
ðð
ðð LRAS
ðŸðŸ ð ð ð ð ð ð ð ð ð ð
ðŸðŸ ðððððð
25 / 66
Short Run AS Curve (SRAS)
I The following are relevant things to remember about the AScurve:
1. If γâ â, no distinction between SRAS and LRAS2. AS curve crosses point Y = Y P at Ï = Ïe + Ï. The inflation
shock Ï is zero on average, so weâll often think of this point asbeing where Ï = Ïe . In other words, if households and firmsare not surprised by inflation, then Y = Y p regardless of whatγ is
I In a sense, nominal rigidities matter only if agents areâfooledâ (Lucas 1972)
3. The AS curve shifts up if Ïe or Ï increase4. The AS curve shifts right if Y P increases
26 / 66
ðð = ðððð + ðŸðŸ(ðð â ðððð) + ðð
ðððð
ðð0ðð + ðð
ðð
ðð LRAS
ðð1ðð + ðð
27 / 66
ðð = ðððð + ðŸðŸ(ðð â ðððð) + ðð
ðððð
ðððð + ðð0
ðð
ðð LRAS
ðððð + ðð1
28 / 66
ðð = ðððð + ðŸðŸ(ðð â ðððð) + ðð
ðð0ðð
ðððð + ðð
ðð
ðð ð¿ð¿ð¿ð¿ð¿ð¿ð¿ð¿0
ðð1ðð
ð¿ð¿ð¿ð¿ð¿ð¿ð¿ð¿1
29 / 66
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 ÏI Expected inflation shocks: changes in Ïe
30 / 66
ðŽðŽðŽðŽ
ðð0
ðð0
ðð
ðð ð¿ð¿ð¿ð¿ðŽðŽðŽðŽ
ðŽðŽð·ð·
31 / 66
Demand Shock
ðŽðŽðŽðŽ
ðð0
ðð0
ðð
ðð ð¿ð¿ð¿ð¿ðŽðŽðŽðŽ
ðŽðŽðŽðŽ
ðð1
ðð1
ðŽðŽðŽðŽâ²
32 / 66
IS Shock: What Happens to r
ðð ðð
ðð
ðð
ðð ðð
ðð
ðð
ðð = ðð
ðð = ᅵᅵð + ðððð
ᅵᅵð
ðŒðŒðŒðŒ
ðð0
ðð0
ðð0
ðð0
ðŽðŽðŽðŽ
ðŒðŒðŒðŒâ²
ðð0â²
ðŽðŽðŽðŽâ²
ðŽðŽðŒðŒ
ðð1
ðð1
ðð1 ðð1
(a)
(a) (a)
(a)
(b)
(b)
(c) (c)
(c) (c)
(a) to (b): direct effect (b) to (c): indirect effect due to higher ðð
33 / 66
MP Shock: What Happens to r
ðð ðð
ðð
ðð
ðð ðð
ðð
ðð
ðð = ðð
ðð = ᅵᅵð + ðððð
ᅵᅵð0
ðŒðŒðŒðŒ
ðð0
ðð0
ðð0
ðð0
ðŽðŽðŽðŽ
ᅵᅵð1
ðð0â²
ðð0â²
ðŽðŽðŽðŽâ²
ðŽðŽðŒðŒ
ðð1
ðð1 ðð1
ðð1
(a)
(a) (a)
(a)
(b) (b)
(b)
(c)
(c) (c)
(c)
(a) to (b): direct effect (b) to (c): indirect effect due to lower ðð
34 / 66
Monetary Neutrality: MP Shock When AS is Vertical
ðð ðð
ðð
ðð
ðð ðð
ðð
ðð
ðð = ðð
ðð = ᅵᅵð + ðððð
ᅵᅵð0
ðŒðŒðŒðŒ
ðð0
ðð0
ðð0
ðð0
ðŽðŽðŽðŽ
ᅵᅵð1
ðð0â²
ðð0â²
ðŽðŽðŽðŽâ²
ðŽðŽðŒðŒ
ðð1
ðð1 ðð1
(a)
(a) (a)=(c)
(a)
(b) (b)
(b)
(c)
(c)
(c)
(a) to (b): direct effect (b) to (c): indirect effect due to lower ðð
35 / 66
Supply Shock: Increase in Ïe or Ï
ðŽðŽðŽðŽ
ðð0
ðð0
ðð
ðð ð¿ð¿ð¿ð¿ðŽðŽðŽðŽ
ðŽðŽðŽðŽ
ðŽðŽðŽðŽâ²
ðð1
ðð1
36 / 66
Supply Shock: Increase in Y P
ðŽðŽðŽðŽ
ðð0
ðð0
ðð
ðð ð¿ð¿ð¿ð¿ðŽðŽðŽðŽ
ðŽðŽðŽðŽ
ðŽðŽðŽðŽâ²
ð¿ð¿ð¿ð¿ðŽðŽðŽðŽâ²
ðð1
ðð1
37 / 66
Decrease in Y P : Effect on r
ðð ðð
ðð
ðð
ðð ðð
ðð
ðð
ðð = ðð
ðð = ᅵᅵð + ðððð
ᅵᅵð
ðŒðŒðŒðŒ
ðŽðŽðŽðŽ
ðŽðŽðŒðŒ
ðð0 ðð0
ðð0
ðð0
ðŽðŽðŒðŒâ²
ðð1
ðð1
ðð1 ðð1
(c)
(a) (a)
(a) (b)
(c)
(a)
(c) (c)
(a) to (b): direct effect (b) to (c): indirect effect due to higher ðð
38 / 66
Algebraically Solving for EquilibriumI AS with AD:
Ï = Ïe + γ
(1
1âmpcAâ d + x
1âmpc(r + λÏ)â Y p
)+ Ï
I Solve for Ï:
Ï =1âmpc
1âmpc + (d + x)λγ(Ïe + Ï)+
γ
1âmpc + (d + x)λγA
â (d + x)γ
1âmpc + (d + x)λγr â γ(1âmpc)
1âmpc + (d + x)λγY P
I Once you have this, you can get Y from the AS curve:
Y = Y P +1
γ(Ï â Ïe â Ï)
I Then can get r = r + Î»Ï and components of output
39 / 66
Dynamics and the âSelf-Correcting Mechanismâ
I Assume Ï = 0 (its average value)
I From AS, if Y 6= Y P , then Ï 6= Ïe
I Y > Y p â Ï > Ïe : agents were surprised with moreinflation than they expected
I Stands to reason that, going forward in time, they will thenrevise up expectations
I Ïe 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
40 / 66
Adjustment from Positive Gap: Qualitative
ðŽðŽðŽðŽ
ðð0
ðð
ðð ð¿ð¿ð¿ð¿ðŽðŽðŽðŽ
ðŽðŽðŽðŽ
ðð0 ðð1 = ðððð
ðððð
ðð1
ðŽðŽðŽðŽâ²
41 / 66
Being More SpecificI Put time subscripts on all variables: t is present, t â 1 is one
period in past, t + 1 one period in future, and so onI Assume adaptive expectations, so that Ïe in the AS curve is
Ïtâ1I Then AS curve is:
Ït = Ïtâ1 + γ(Yt â Y P
t
)+ Ït
I AD curve is:
Yt =1
1âmpcAt â
d + x
1âmpc(rt + λÏt)
I The interesting dynamics are on the supply side. As Ït
changes, the position of the AS curve will change dynamicallyover time. Assume Ït = 0 (unconditional mean)
I Adjustment occurs slowly, only eventually do you get to Y P
42 / 66
Adjustment from Positive Gap: More Specific
ðŽðŽðŽðŽ
ððð¡ð¡
ðð
ðð ð¿ð¿ð¿ð¿ðŽðŽðŽðŽ
ðŽðŽðŽðŽ
ððð¡ð¡ ðððð
ððð¡ð¡â1
ðŽðŽðŽðŽâ²
ððð¡ð¡+1
ððð¡ð¡+1
ððð¡ð¡+2
ððð¡ð¡+2
ðŽðŽðŽðŽâ²â²
43 / 66
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, λ = 1, A = 4.95,γ = 0.5, Y P = 12.5
I Assume Ïtâ1 = 0
I Implies that Ït = 0.8 and Yt = 14.1
I Use Excel to trace out dynamic paths
44 / 66
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
45 / 66
Positive IS Shock: Dynamic Adjustment
ðŽðŽðŽðŽ
ðððð
ððð¡ð¡â1
ðð
ðð ð¿ð¿ð¿ð¿ðŽðŽðŽðŽ
ðŽðŽðŽðŽ
ððð¡ð¡
ððð¡ð¡
ðŽðŽðŽðŽâ²
ðŽðŽðŽðŽâ²
ððð¡ð¡+1
ððð¡ð¡+1
ðŽðŽðŽðŽâ²â²
ððð¡ð¡+2
ððð¡ð¡+2
46 / 66
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
47 / 66
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 âNatural rate of interestâ: r consistent with IS curve holdingat Y P . Call it rP (potential or long run real interest rate):
rP = â1âmpc
d + xY P +
1
d + xA
I Does not depend on r
48 / 66
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
49 / 66
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
-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
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
50 / 66
Adjustment from Positive Y P Shock
ðŽðŽðŽðŽ
ðð0ðð
ððð¡ð¡â1
ðð
ðð ð¿ð¿ð¿ð¿ðŽðŽðŽðŽ
ðŽðŽðŽðŽ
ðŽðŽðŽðŽâ²
ð¿ð¿ð¿ð¿ðŽðŽðŽðŽâ²
ððð¡ð¡
ððð¡ð¡ ðð1ðð
ðŽðŽðŽðŽâ²â²
ððð¡ð¡+1
ððð¡ð¡+1
ðŽðŽðŽðŽâ²â²â²
ððð¡ð¡+2
ððð¡ð¡+2
51 / 66
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
52 / 66
Adjustment from One Period Ï Shock
ðŽðŽðŽðŽ
ðððð
ððð¡ð¡â1
ðð
ðð ð¿ð¿ð¿ð¿ðŽðŽðŽðŽ
ðŽðŽðŽðŽ
ðŽðŽðŽðŽâ²
ððð¡ð¡
ððð¡ð¡
ððð¡ð¡â1 + 1
ðŽðŽðŽðŽâ²â²
ððð¡ð¡+1
ððð¡ð¡+1
ðŽðŽðŽðŽâ²â²â²
ððð¡ð¡+2
ððð¡ð¡+2
53 / 66
Quantitative Adjustment from Positive Ï 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 âmaximum employmentâ
I In the context of our model, we can think about the first halfof the mandate as keeping Ït close to constant, and thesecond half as keeping Yt close to Y P
t
I Define the output gap as Xt = Yt â Y Pt
I Hence, objectives are to keep Ït close to constant and Xt
close to zero
56 / 66
Monetary Policy Tools
I The primary tool of monetary policy (in this simple model) isthe parameter λ
I Governs how strongly policy reacts to inflation
I Recall algebraic expression for AD curve:
Ï = â 1âmpc
(d + x)λY +
1
(d + x)λAâ 1
λr
I λ influences two things:I Slope of AD curve (bigger λ and AD curve is flatter)I Shift of AD curve conditional on IS shock, A (bigger λ and AD
curve shifts up less; horizontal shift of AD curve unaffected byλ)
57 / 66
λ and the Effects of IS Shocks
ðŽðŽðŽðŽ
ðð0
ðð0
ðð
ðð ð¿ð¿ð¿ð¿ðŽðŽðŽðŽ
ðŽðŽðŽðŽ (ðð ð ð ð ð ð ð ð ð ð ð )
ðŽðŽðŽðŽ (ðð ðððððð) ðŽðŽðŽðŽâ²
ðŽðŽðŽðŽâ²
ðð1
ðð1 ðð1â²
ðð1â²
58 / 66
λ and IS Shocks
I After an increase in A, a bigger λ results in:
1. Smaller increase in Ï2. Smaller increase in Y . Since Y P doesnât change, this means
that the gap, X , goes up by less
I Bigger λ is a âwin-winâ from perspective of dual mandateconditional on IS shocks
59 / 66
IS Shock: λ = 1 vs. λ = 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
λ and the Effects of Y P Shocks
ðŽðŽðŽðŽ
ðð0ðð
ðð0
ðð
ðð ð¿ð¿ð¿ð¿ðŽðŽðŽðŽ
ðŽðŽðŽðŽ (ðð ð ð ð ð ð ð ð ð ð ð )
ðð1ðð
ð¿ð¿ð¿ð¿ðŽðŽðŽðŽâ²
ðŽðŽðŽðŽâ²
ðŽðŽðŽðŽ (ðð ðððððð)
ðð1â²
ðð1â²
ðð1
ðð1
61 / 66
λ and Potential Output Shocks
I After an increase in Y P , a bigger λ results in:
1. Smaller increase in Ï2. Bigger increase in Y . Since Y P increases, this means that the
gap, X , goes down by less the bigger is λ
I Bigger λ is a âwin-winâ from perspective of dual mandateconditional on potential output shocks shocks
62 / 66
Y P Shock: λ = 1 vs. λ = 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 âinflation targeting,â eitherimplicity or explicitly done by several leading central banks
I Divine coincidence does not hold conditional on inflationshocks (Ï)
64 / 66
λ and the Effects of Ï Shocks
ðŽðŽðŽðŽ
ðð0
ðð0
ðð
ðð ð¿ð¿ð¿ð¿ðŽðŽðŽðŽ
ðŽðŽðŽðŽ (ðð ð ð ð ð ð ð ð ð ð ð )
ðŽðŽðŽðŽâ²
ðð1
ðð1
ðð0 + 1
ðŽðŽðŽðŽ (ðð ðððððð)
ðð1â²
ðð1â²
65 / 66
Ï Shock: λ = 1 vs. λ = 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