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New Keynesian Economics
Prof. Eric Sims
University of Notre Dame
Fall 2013
Sims (ND) New Keynesian Economics Fall 2013 1 / 26
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 2013 2 / 26
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 2013 3 / 26
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 ,t
Pt,X
)Pt : aggregate price, weighted-average of individual prices
f1 < 0: demand decreasing in relative price
Sims (ND) New Keynesian Economics Fall 2013 4 / 26
Price Stickiness
Suppose firms have to set their individual prices “in advance” basedon what they expect the aggregate price to be, Pe
t . 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 who
cannot 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 > Pe
t
Sims (ND) New Keynesian Economics Fall 2013 5 / 26
Phillips Curve
Pt = Pet + γ(Yt − Y f
t )
Y ft : hypothetical amount of output that would produced in RBC
model 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 Pt
γ→ 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 2013 6 / 26
“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 f
t
Would also be case in “short run” if γ→ ∞
Sims (ND) New Keynesian Economics Fall 2013 8 / 26
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 At
and 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 2013 9 / 26
Household Side
Identical to what we already had:
Nt = Ns(wt , rt)
Ct = C (Yt − Gt ,Yt+1 − Gt+1, rt)
Mt = PtMd (rt + πe
t+1,Yt)
Sims (ND) New Keynesian Economics Fall 2013 10 / 26
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 2013 11 / 26
LM Curve
Upward-sloping graph in (rt ,Yt) space
Idea: when Yt goes up, money demand rises. Holding Mt and Pt
fixed, 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 2013 12 / 26
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 2013 13 / 26
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 2013 14 / 26
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 f
t )
Mt = PtMd (rt + πe
t+1,Yt)
rt = it − πet+1
Only difference: replace old labor demand curve with Phillips Curve
Sims (ND) New Keynesian Economics Fall 2013 15 / 26
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 2013 16 / 26
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 2013 17 / 26
Labor Market Equilibrium
Nd(Yt0)
wt
Nt
Ns(rt0)
wt0
Nt0
Sims (ND) New Keynesian Economics Fall 2013 18 / 26
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 f
t , 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 2013 19 / 26
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 2013 20 / 26
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= Pe
t in the medium run. “Fool me once . .. fool me twice”
Idea: Pet adjusts to surprise changes in price level, so that PC shifts in
such 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 2013 21 / 26
Applications
Limits of monetary expansion:
Central bank cannot keep Yt > Y ft for long without leading to inflation
If 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 Pe
t 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 2013 22 / 26
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 can
do
With sticky prices and fixed Mt , no guarantee that Yt = Y ft
Optimal policy: set Mt to bring about Yt = Y ft
Necessitates 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 2013 23 / 26
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 2013 24 / 26
Effects of ZLB
Makes LM curve horizontal at rt = −πet+1. Pt has no effect on LM
⇒ AD curve vertical
Normal dynamics can be vicious: the ZLB can be a “trap”
If Yt < Y ft , then Pt < Pe
tNormal dynamics: Pe
t would fall, pushing PC outBut with vertical AD, this has no effect on Yt : you get stuckCould be pernicious if we endogenized πe
t+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 2013 25 / 26
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 2013 26 / 26