new keynesian economics - university of notre dame

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


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


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


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


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”


Phillips Curve

PC

Yt

Pt

Pte

Ytf


“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→ ∞


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)


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)


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


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


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


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)


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


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


IS-LM-AD-PC Equilibrium

LM

IS

PC

AD

LRPC

rt

Yt

Yt

Pt

Yt0=Yt

f

Pt0=Pt

e

rt0


Labor Market Equilibrium

Nd(Yt0)

wt

Nt

Ns(rt0)

wt0

Nt0


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


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”


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


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


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


Zero lower bound

ZLB: nominal interest rates cannot go below zero

Especially relevant right now

What are implications for our model?


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


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


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