The New Keynesian Model: Dynamicsesims1/new_keynesian_dynamics_sp2018.pdfDynamics I The New...
Transcript of The New Keynesian Model: Dynamicsesims1/new_keynesian_dynamics_sp2018.pdfDynamics I The New...
The New Keynesian Model: DynamicsECON 30020: Intermediate Macroeconomics
Prof. Eric Sims
University of Notre Dame
Spring 2018
1 / 21
Dynamics
I The New Keynesian model is a special case of the neoclassicalmodel β we simply swap labor demand with an AS curve,most general form of which is:
Pt = PΜt + Ξ³(Yt β Y ft )
I Call Y ft the βflexible priceβ level of output β the level of
output which would emerge in the neoclassical model
I If firm could freely adjust price, it would do so such that it ison its labor demand curve, which would entail Yt = Y f
t
I Refer to Yt β Y ft as the output gap β the gap between actual
output and what it would be in the absence of price stickiness
I To see this graphically, draw in a hypothetical AS curve forthe neoclassical model β call this AS f
3 / 21
A Negative Output Gap
π€π€π‘π‘ πππ‘π‘
πππ‘π‘ πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
π΄π΄π΄π΄
πΌπΌπ΄π΄
ππ0,π‘π‘
ππ0,π‘π‘ ππ0,π‘π‘
πππ π (π€π€π‘π‘ ,πππ‘π‘)
πΏπΏπΏπΏ(πΏπΏπ‘π‘ ,ππ0,π‘π‘)
π΄π΄π‘π‘πΉπΉ(πΎπΎπ‘π‘ ,πππ‘π‘)
πππ‘π‘ = πππ‘π‘
πππ‘π‘
π΄π΄π΄π΄
πποΏ½0,π‘π‘ π€π€0,π‘π‘
ππ0,π‘π‘ππ ππ0,π‘π‘
ππ
ππππ(π€π€π‘π‘ ,π΄π΄π‘π‘ ,πΎπΎπ‘π‘)
π΄π΄π΄π΄ππ
π€π€0,π‘π‘ππ
Sticky price model
Hypothetical flexible price model
ππ0,π‘π‘ππ
0 subscript: equilibrium value
f superscript: hypothetical flexible price equilibrium
πΏπΏπΏπΏ(πΏπΏπ‘π‘ ,ππ0,π‘π‘ππ )
ππ0,π‘π‘ππ
ππ0,π‘π‘
4 / 21
Transition from Short Run to Medium RunI With a negative output gap, the firm is producing less than it
would likeI The reason the gap exists is because a friction (e.g. menu
cost) prevents it from lowering price all the way necessary toclose the gap
I Given equilibrium real wage, firm would like to hire morelabor. But only way to put more labor to use is to have moredemand for output, which would require a drop in Pt .
I Once it is given the opportunity to do so, the firm will changePΜt in such a way that the AS curve intersects the AD curveat Y f
tI Hence, as we transition from short run (price sticky) to
medium run (price flexible), the exogenous component of theprice level, PΜt , will adjust so as to shift the AS curve andβclose the gapβ
I We will not use different time subscripts or anything to thinkabout this transition, so this is admittedly a bit loosey-goosey
5 / 21
Closing a Negative Output Gap
π€π€π‘π‘ πππ‘π‘
πππ‘π‘ πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
π΄π΄π΄π΄
πΌπΌπ΄π΄
ππ0,π‘π‘
ππ0,π‘π‘ ππ0,π‘π‘
πππ π (π€π€π‘π‘ ,πππ‘π‘)
πΏπΏπΏπΏ(πΏπΏπ‘π‘ ,ππ0,π‘π‘)
π΄π΄π‘π‘πΉπΉ(πΎπΎπ‘π‘ ,πππ‘π‘)
πππ‘π‘ = πππ‘π‘
πππ‘π‘
π΄π΄π΄π΄
πποΏ½0,π‘π‘ π€π€0,π‘π‘
ππ1,π‘π‘
= ππ0,π‘π‘ππ
ππ1,π‘π‘
= ππ0,π‘π‘ππ
ππππ(π€π€π‘π‘ ,π΄π΄π‘π‘ ,πΎπΎπ‘π‘)
π΄π΄π΄π΄ππ
π€π€1,π‘π‘ = π€π€0,π‘π‘ππ
Sticky price model
Hypothetical flexible price model
Sticky price model, post price adjustment
πποΏ½1,π‘π‘ = ππ0,π‘π‘ππ
0 subscript: equilibrium value
f superscript: hypothetical flexible price equilibrium
1 subscript: equilibrium value after price adjustment
πΏπΏπΏπΏοΏ½πΏπΏπ‘π‘ ,ππ0,π‘π‘ππ οΏ½
= πΏπΏπΏπΏ(πΏπΏπ‘π‘,ππ1,π‘π‘)
ππ1,π‘π‘ = ππ0,π‘π‘ππ
ππ0,π‘π‘
π΄π΄π΄π΄β²
6 / 21
Dynamic Response to Shocks
I We shall assume that the economy initially sits in theneoclassical, no output gap equilibrium
I Then something exogenous changes and causes either the ADor AS to shift
I This will in general result in a non-zero output gap in theshort run
I This will put pressure on PΜt to adjust to shift the AS curve toclose the gap
7 / 21
Monetary Shock, β Mt
π€π€π‘π‘ πππ‘π‘
πππ‘π‘ πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
π΄π΄π΄π΄
πΌπΌπ΄π΄
ππ0,π‘π‘ = ππ2,π‘π‘
ππ0,π‘π‘= ππ2,π‘π‘
ππ0,π‘π‘= ππ2,π‘π‘
πππ π (π€π€π‘π‘ ,πππ‘π‘)
πΏπΏπΏπΏοΏ½πΏπΏ0,π‘π‘,ππ0,π‘π‘οΏ½= πΏπΏπΏπΏ(πΏπΏ1,π‘π‘,ππ2,π‘π‘)
π΄π΄π‘π‘πΉπΉ(πΎπΎπ‘π‘ ,πππ‘π‘)
πππ‘π‘ = πππ‘π‘
πππ‘π‘
π΄π΄π΄π΄
ππ0,π‘π‘ = πποΏ½0,π‘π‘ π€π€0,π‘π‘= π€π€2,π‘π‘
ππππ(π€π€π‘π‘ ,π΄π΄π‘π‘ ,πΎπΎπ‘π‘)
π΄π΄π΄π΄ππ
πΏπΏπΏπΏ(πΏπΏ1,π‘π‘,ππ0,π‘π‘)
π΄π΄π΄π΄β²
π€π€1,π‘π‘
ππ1,π‘π‘ ππ1,π‘π‘
ππ1,π‘π‘
ππ1,π‘π‘
πΏπΏπΏπΏ(πΏπΏ1,π‘π‘,ππ1,π‘π‘)
Original
Post-Shock
Post-shock, indirect effect of πππ‘π‘ on LM curve
0 subscript: original
1 subscript: post-shock
2 subscript: post-shock, post price adjustment
Original, hypothetical flexible price
Post-shock, flexible price
ππ2,π‘π‘ = πποΏ½2,π‘π‘
Post-shock, post-price adjustment
π΄π΄π΄π΄β²
8 / 21
Monetary Neutrality, Short Run vs. Medium Run
I Money is non-neutral in the short run β AD shifts when Mt
changes which causes Yt (and rt and other real variables) tochange
I But this puts pressure on PΜt
I As economy transitions to medium run, PΜt adjusts in such away as to close the output gap, and the neoclassicalequilibrium emerges β money is neutral and the classicaldichotomy holds
9 / 21
Supply Shock, β At
π€π€π‘π‘ πππ‘π‘
πππ‘π‘ πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
π΄π΄π΄π΄
πΌπΌπ΄π΄
ππ0,π‘π‘
ππ0,π‘π‘
= ππ0,π‘π‘ππ
ππ0,π‘π‘
πππ π (π€π€π‘π‘ ,πππ‘π‘)
πΏπΏπΏπΏ(πΏπΏπ‘π‘ ,ππ0,π‘π‘)
π΄π΄0,π‘π‘πΉπΉ(πΎπΎπ‘π‘ ,πππ‘π‘)
πππ‘π‘ = πππ‘π‘
πππ‘π‘
π΄π΄π΄π΄
ππ0,π‘π‘ = πποΏ½0,π‘π‘ π€π€0,π‘π‘
ππππ(π€π€π‘π‘,π΄π΄0,π‘π‘ ,πΎπΎπ‘π‘)
π΄π΄π΄π΄ππ
ππππ(π€π€π‘π‘,π΄π΄1,π‘π‘ ,πΎπΎπ‘π‘)
π΄π΄1,π‘π‘πΉπΉ(πΎπΎπ‘π‘ ,πππ‘π‘)
π΄π΄π΄π΄β²
π΄π΄π΄π΄ππβ²
π€π€1,π‘π‘
ππ1,π‘π‘ ππ2,π‘π‘
= ππ1,π‘π‘ππ
ππ1,π‘π‘
ππ1,π‘π‘
ππ1,π‘π‘
πΏπΏπΏπΏ(πΏπΏπ‘π‘ ,ππ1,π‘π‘)
Original
Post-Shock
Post-shock, indirect effect of πππ‘π‘ on LM curve
Post-shock, post-price adjustment
Original, hypothetical flexible price
Post-shock, flexible price
0 subscript: original
1 subscript: post-shock
2 subscript: post-shock, post price adjustment
ππ2,π‘π‘ = πποΏ½2,π‘π‘
πΏπΏπΏπΏ(πΏπΏπ‘π‘ ,ππ2,π‘π‘)
ππ2,π‘π‘
π΄π΄π΄π΄β²β²
ππ2,π‘π‘
π€π€2,π‘π‘
10 / 21
Supply Shock Dynamics
I Output under-reacts to At in the short run (the more so theflatter is the AS curve, i.e. the smaller is Ξ³)
I The price level falls, but not enough to implement theneoclassical equilibrium
I At new short run equilibrium, firm would like to produce more.Must lower price in order to do this. So downward pressure onPΜt
I AS shifts as economy transitions through time to restoreneoclassical equilibrium
11 / 21
IS Shock, e.g. β At+1
π€π€π‘π‘ πππ‘π‘
πππ‘π‘ πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
πππ‘π‘
π΄π΄π΄π΄
πΌπΌπ΄π΄
ππ0,π‘π‘
ππ0,π‘π‘= ππ2,π‘π‘
ππ0,π‘π‘= ππ2,π‘π‘
πππ π (π€π€π‘π‘ ,πππ‘π‘)
πΏπΏπΏπΏ(πΏπΏπ‘π‘ ,ππ0,π‘π‘)
π΄π΄π‘π‘πΉπΉ(πΎπΎπ‘π‘ ,πππ‘π‘)
πππ‘π‘ = πππ‘π‘
πππ‘π‘
π΄π΄π΄π΄
ππ0,π‘π‘ = πποΏ½0,π‘π‘ π€π€0,π‘π‘= π€π€2,π‘π‘
ππππ(π€π€π‘π‘ ,π΄π΄π‘π‘ ,πΎπΎπ‘π‘)
π΄π΄π΄π΄ππ
π΄π΄π΄π΄β²
πΌπΌπ΄π΄β²
πΏπΏπΏπΏ(πΏπΏπ‘π‘ ,ππ1,π‘π‘)
ππ1,π‘π‘
π€π€1,π‘π‘
ππ1,π‘π‘ ππ1,π‘π‘
ππ1,π‘π‘
Original
Post-Shock
Post-shock, indirect effect of πππ‘π‘ on LM curve
0 subscript: original
1 subscript: post-shock
2 subscript: post-shock, post price adjustment
Original, hypothetical flexible price
Post-shock, flexible price
π΄π΄π΄π΄β²
ππ2,π‘π‘ = πποΏ½2,π‘π‘
Post-shock, post-price adjustment
πΏπΏπΏπΏ(πΏπΏπ‘π‘ ,ππ2,π‘π‘)
ππ2,π‘π‘
12 / 21
IS Shock Dynamics
I After a positive IS shock, Yt and Pt both rise
I But at new equilibrium, firm is producing more output than itwould find optimal (i.e. labor input exceeds quantity of laborfirm would demand at equilibrium real wage)
I Firm wants to reduce labor, which requires increasing Pt toreduce demand
I This results in PΜt rising, AS shifting in, and neoclassicalequilibrium being restored
13 / 21
Phillips Curve
I Our discussion about dynamics above suggests there ought toexist some kind of relationship between the output gap andthe change in prices (i.e. inflation).
I Subtract previous periodβs price level from both sides of ASrelationship:
Pt β Ptβ1 = PΜt β Ptβ1 + Ξ³(Yt β Y ft )
I Normalize previous periodβs price level to Ptβ1 = 1, whichmeans we can re-interpret changes as percentage changes.
Call Οet = PΜtβPtβ1
Ptβ1the inflation rate expected to obtain
between t β 1 and t. Firm sets PΜt where if it guesses inflationcorrectly it will produce Yt = Y f
t . Then:
Οt = Οet + Ξ³(Yt β Y f
t )
I An equation like this is called a Phillips Curve after Phillips(1958)
14 / 21
Empirical Relationship Between Inflation and the OutputGap
-2
0
2
4
6
8
10
12
14
-.08 -.06 -.04 -.02 .00 .02 .04 .06
Output Gap
Inflation
Inflation - Output Gap Scatter Plot1960 - 2016
I Pretty weak β more of a βblobβ than a clear positiverelationship
15 / 21
Subsample Differences
0
2
4
6
8
10
12
14
-.08 -.06 -.04 -.02 .00 .02 .04 .06
Output Gap
Infla
tio
n
Inflation - Output Gap Scatter Plot1960 - 1984
-1
0
1
2
3
4
5
-.08 -.06 -.04 -.02 .00 .02 .04
Output Gap
Infla
tio
n
Inflation - Output Gap Scatter Plot1984 - 2016
I βWrongβ sign in early sample; looks much closer to theory inlater sample
16 / 21
What Gives?
I Does the fact that the sign of the correlation looks βwrongβinvalidate the theory?
I Not necessarily β correlation between gap and inflation shouldonly be positive holding Οe
t (equivalently PΜt) fixed
I What do inflation expectations look like in data?
I Large and volatile in early sample; much more stable in latersample
17 / 21
Expected Inflation
1
2
3
4
5
6
7
8
9
10
60 65 70 75 80 85 90 95 00 05 10 15
Mean Expected Inflation
18 / 21
Can Monetary Policy Permanently Engineer HigherOutput?
I No
I Can temporarily raise output by increasing Mt , but in mediumrun this puts upward pressure on prices and the effect goesaway
I Continually trying to raise output will only result in moreinflation
I Further, it may cause the firm to anticipate the change in Mt ,which could cause the AS curve to shift simultaneously withthe AD shift, resulting in no effect of monetary expansion onoutput
I It is really only unanticipated monetary expansion that canstimulate output, and even then only for a while
19 / 21
Fully Anticipated Increase in Mt , so that PΜt also rises
π΄π΄π΄π΄
ππ0,π‘π‘ = ππ1,π‘π‘
πΏπΏπΏπΏοΏ½πΏπΏ0,π‘π‘,ππ0,π‘π‘οΏ½ =
πΏπΏπΏπΏοΏ½πΏπΏ1,π‘π‘,ππ1,π‘π‘οΏ½
π΄π΄π΄π΄
π€π€0,π‘π‘ = π€π€1,π‘π‘
πΏπΏπΏπΏ(πΏπΏ1,π‘π‘,ππ0,π‘π‘)
π΄π΄π΄π΄β²
π΄π΄π΄π΄β²
πποΏ½1,π‘π‘
0 subscript: initial equilibrium
1 subscript: post-shock equilibrium where πΏπΏπ‘π‘ increases but this is anticipated and reflected in πποΏ½π‘π‘
π€π€π‘π‘ πππ‘π‘
Original
πππ‘π‘ πππ‘π‘
πππ‘π‘
Post-shock
πππ‘π‘
πππ‘π‘
Indirect of price on position of LM
πππ‘π‘
πππ‘π‘
πΌπΌπ΄π΄
ππ0,π‘π‘= ππ1,π‘π‘
ππ0,π‘π‘= ππ1,π‘π‘
πππ π (π€π€π‘π‘ ,πππ‘π‘)
π΄π΄π‘π‘πΉπΉ(πΎπΎπ‘π‘,πππ‘π‘)
πππ‘π‘ = πππ‘π‘
πππ‘π‘
πποΏ½0,π‘π‘
20 / 21
Costless Disinflation
I Can central bank lower prices (disinflation) without incurringan output loss?
I Conventional wisdom for 1980-1982 recession was that it wascaused by Fed trying to get inflation under control (negativemonetary shock)
I Suppose that the Fed announces in advance that it is going toreduce Mt . If people believe this, prices may adjust down inanticipation, causing AS curve to shift down at same time theAD shifts in
I In principle, this allows for a reduction in Pt with no change inYt β i.e. costless disinflation
I Underscores importance of central bank credibility andcommunication: for this to work, people must believe thecentral bank, and the central bank must clearly communicateits objectives
21 / 21