new keynesian economics - university of notre dameesims1/int_macro_nk_slides_2014.pdf · 2014. 12....
TRANSCRIPT
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New Keynesian Economics
Prof. Eric Sims
University of Notre Dame
Fall 2014
Sims (ND) New Keynesian Economics Fall 2014 1 / 27
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New Keynesian Economics
New Keynesian (NK) model: leading alternative to RBC model
Basic gist: some kind of friction prevents efficient equilibrium fromobtaining in short run
This means there is some welfare-justification for activist economicpolicy
Sims (ND) New Keynesian Economics Fall 2014 2 / 27
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Price Stickiness
NK model has RBC “backbone”
Only difference is that nominal prices are assumed to be “sticky”
Justification: menu costs, optimization frictions, etc.
Could also do this with wage stickiness
Sims (ND) New Keynesian Economics Fall 2014 3 / 27
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Detour: Firm Heterogeneity and Price-Setting
Assume that there are a large number of monopolistically competitivefirms, indexed by i , producing different “kinds” of fruit
These different kinds of fruit are aggregated into an aggregatemeasure of fruit available for consumption or investment
The demand for each kind of fruit, i , depends on the relative price ofthe good, plus stuff:
Yi ,t = f
(Pi ,tPt
,X
)Pt : aggregate price, weighted-average of individual prices
f1 < 0: demand decreasing in relative price
Sims (ND) New Keynesian Economics Fall 2014 4 / 27
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Price Stickiness
Suppose firms have to set their individual prices “in advance” basedon what they expect the aggregate price to be, Pet . Take this to beexogenous
Suppose that some fraction of firms are unable to adjust theirindividual price to aggregate prices that are different than what wasexpected
Menu costsInformational processing costs
If Pt turns out to be higher than expected, Pt > Pet , the firms whocannot update will have relative prices that are “too low” ⇒ they willhave more demand
“Rules of game”: firms produce output to meet demand always
Some firms producing more ⇒ aggregate output, Yt , rises whenPt > Pet
Sims (ND) New Keynesian Economics Fall 2014 5 / 27
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Phillips Curve
Pt = Pet + γ(Yt − Y ft )
Y ft : hypothetical amount of output that would produced in RBCmodel with flexible prices (“potential,” “flexible-price,” or “naturalrate”)
γ: parameter governing extent of price stickiness
γ→ ∞: prices perfectly flexible, so Yt = Y ft regardless of Ptγ→ 0: prices perfectly sticky, Pt = Pet since all firms have price stuck
Sometimes also called “AS” for “Aggregate Supply”
Sims (ND) New Keynesian Economics Fall 2014 6 / 27
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Phillips Curve
PC
Yt
Pt
Pte
Ytf
Sims (ND) New Keynesian Economics Fall 2014 7 / 27
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“Long Run” Phillips Curve
Over sufficiently long periods, all firms should be able to adjust theirprices
So in long run, should have no relationship between Pt and Yt : LRPCvertical at Y ft
Would also be case in “short run” if γ→ ∞
Sims (ND) New Keynesian Economics Fall 2014 8 / 27
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Labor Demand
“Rules of game”: firms produce enough output to meet demand giventheir relative price
The only variable input is Nt : Kt and At are exogenous
Production function: Yt = AtF (Kt ,Nt)
Given price, firms choose labor to produce sufficient output, given Atand Kt
No longer wage = marginal product labor demand
Labor demand vertical, determined by Yt , At , and Kt
Investment demand the same as before: It = I (rt ,At+1, q,Kt)
Sims (ND) New Keynesian Economics Fall 2014 9 / 27
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Household Side
Identical to what we already had:
Nt = Ns(wt , rt)
Ct = C (Yt − Gt ,Yt+1 − Gt+1, rt)Mt = PtM
d (rt + πet+1,Yt)
Sims (ND) New Keynesian Economics Fall 2014 10 / 27
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Short run equilibrium
Following equations must all hold:
Nt = Ns(wt , rt)
Ct = C (Yt − Gt ,Yt+1 − Gt+1, rt)It = I (rt ,At+1, q,Kt)
Yt = AtF (Kt ,Nt)
Yt = Ct + It + Gt
Pt = Pet + γ(Yt − Y ft )
Mt = PtMd (rt + π
et+1,Yt)
rt = it − πet+1
Only difference: replace old labor demand curve with Phillips Curve,treat Pet and Y
ft as exogenous
Same endogenous variables: Yt , Ct , It , Nt , wt , rt , it , Pt .
Sims (ND) New Keynesian Economics Fall 2014 11 / 27
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New Graphical Setup
To characterize the “demand” side of the economy, we use a newgraphical setup called the “IS-LM-AD” curves
IS curve: set of (rt ,Yt) pairs where Yt = Ct + It + Gt , given optimalCt and It
Exactly the same as Y d curve
LM curve: set of (rt ,Yt) pairs where money demand = moneysupply, taking Mt and Pt as given
AD curve: set of (Pt ,Yt) pairs where we’re on both IS and LM curves
Could define and derive all these graphs in RBC model: none of thisrelies on price stickiness assumption
Sims (ND) New Keynesian Economics Fall 2014 12 / 27
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LM Curve
Upward-sloping graph in (rt ,Yt) space
Idea: when Yt goes up, money demand rises. Holding Mt and Ptfixed, rt would have to rise to “offset” this so that money marketcould remain in equilibrium
Will shift out to right if: (i) Mt increases or (ii) Pt decreases
Simple rule: LM curve shifts out if MtPt goes up
Sims (ND) New Keynesian Economics Fall 2014 13 / 27
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IS Curve
Derivation identical to Y d curve
Downward-sloping in (rt ,Yt) space
Shifts right if: (i) At+1 goes up, (ii) q goes up, (iii) Gt goes up (shiftsright one-for-one with Gt), (iv) Gt+1 goes down, (v) Kt goes down, or(vi) uncertainty goes down
Sims (ND) New Keynesian Economics Fall 2014 14 / 27
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AD curve
Start with a Pt
As Pt rises, LM curve shifts in. Point Yt where IS and LM intersect islower
Reverse if Pt falls
AD curve slopes down in (Pt ,Yt) space
AD curve shifts if either (i) LM shifts (change in Mt) or (ii) IS shifts(change in At+1, q, Gt , Gt+1, Kt , or uncertainty)
Sims (ND) New Keynesian Economics Fall 2014 15 / 27
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Equilibrium: graphically
Start in IS-LM diagram. Determine position of AD
Combine with PC to get Yt and Pt . Re-adjust LM if necessary
Try to figure out components of output, Ct and It
Lastly, given Yt and rt , determine the position of the vertical labordemand curve and labor supply to determine Nt and wt
Sims (ND) New Keynesian Economics Fall 2014 16 / 27
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IS-LM-AD-PC Equilibrium
LM
IS
PC
AD
LRPC
rt
Yt
Yt
Pt
Yt0=Yt
f
Pt0=Pt
e
rt0
Sims (ND) New Keynesian Economics Fall 2014 17 / 27
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Labor Market Equilibrium
Nd(Yt0)
wt
Nt
Ns(rt0)
wt0
Nt0
Sims (ND) New Keynesian Economics Fall 2014 18 / 27
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Exogenous Shocks
Split into three categories:
Monetary shock: shifts AD
Supply shock: shifts PC
IS/Demand Shock: shifts IS and hence ADImportant simplifying assumption: assume that shocks which shift IShave no effect on Y ft , and hence no effect on the position of PC
Would get this if Y s were vertical (no sensitivity of labor supply tointerest rate)Allows us to separate “demand” from “supply” cleanly
Sims (ND) New Keynesian Economics Fall 2014 19 / 27
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Cookbook Approach
Take the following steps to figure out effects of change in anexogenous variable
1 Start in IS-LM diagram. See if either curve shifts to derive any shift inAD
2 See if PC shifts (e.g. if Y ft or Pet change)
3 Combine AD and PC shifts to determine new equilibrium Pt and Yt4 Go “back” to IS-LM diagram, using new Pt to shift LM curve in such a
way that quantities line up5 Given Yt and rt , go to labor market diagram to determine wt and Nt
Do labor market “last” in contrast to RBC model
Sims (ND) New Keynesian Economics Fall 2014 20 / 27
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Effects of Shocks
Variable: ↑ Mt ↑ At (Supply) IS Shock (positive)Yt + + +Pt + - +rt - - +Ct + + ?It + + ?Nt + ? +wt + ? ?
Price stickiness makes output effects of supply shocks smaller andoutput effects of demand shocks larger relative to RBC
Nominal rigidity: bigger possible role for “demand”
Sims (ND) New Keynesian Economics Fall 2014 21 / 27
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Dynamics
Think about a period, t, as being divided into two parts: the “shortrun” (morning) and the “medium run” (afternoon)
Pet fixed in short run
But Pet can adjust to Pt 6= Pet in the medium run. “Fool me once . .. fool me twice”
Idea: Pet adjusts to surprise changes in price level, so that PC shifts insuch a way that Yt = Y ft in “medium run”
Means money is neutral in medium run: prices effectively flexible afterenough time
Sims (ND) New Keynesian Economics Fall 2014 22 / 27
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Applications
Limits of monetary expansion:
Central bank cannot keep Yt > Y ft for long without leading to inflationIf they try to do this forever, expectations will adjust, and monetaryexpansion wouldn’t have an effect
Costly disinflation:
To bring Pt down, central bank can reduce Mt , but this implies outputloss in short runCan be “costless” if central bank can commit to reduction in Mt infuture and people believe it, so Pet also falls: inward shift of AD alongwith outward shift of PCImportant for central bank to have independence for them to have thiscredibility
Sims (ND) New Keynesian Economics Fall 2014 23 / 27
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Optimal Monetary Policy
Not realistic to think of Mt as purely exogenous
How ought central bank to set Mt to maximize welfare?
From RBC, we know that Yt = Y ft is “efficient”: best economy cando
With sticky prices and fixed Mt , no guarantee that Yt = Y ftOptimal policy: set Mt to bring about Yt = Y ftNecessitates moving Mt in same direction as Yt in response to“supply” shocks and in the opposite direction of Yt in response to“demand” shocks
Sims (ND) New Keynesian Economics Fall 2014 24 / 27
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Zero lower bound
ZLB: nominal interest rates cannot go below zero
Especially relevant right now
What are implications for our model?
Sims (ND) New Keynesian Economics Fall 2014 25 / 27
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Effects of ZLB
Makes LM curve horizontal at rt = −πet+1. Pt has no effect on LM⇒ AD curve verticalNormal dynamics can be vicious: the ZLB can be a “trap”
If Yt < Y ft , then Pt < Pet
Normal dynamics: Pet would fall, pushing PC outBut with vertical AD, this has no effect on Yt : you get stuckCould be pernicious if we endogenized πet+1: expecting deflation wouldshift AD curve inward (by raising real rates), exacerbating the output“gap”: deflationary “spiral”
ZLB: exacerbates effects of price stickiness for supply and demandshocks
Sims (ND) New Keynesian Economics Fall 2014 26 / 27
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Escaping the ZLB
Way out of ZLB for central bank: engineer inflation expectations
Another reason why credibility is important
↑ πet+1: implies reduction in real interest rate, outward shift of AD,and increases in Pt
A lot of “non-standard” monetary policies in last years basically boildown to this
Sims (ND) New Keynesian Economics Fall 2014 27 / 27