Chapter 1: The Basic New Keynesian Modelolivierloisel.com/monetary_economics/Chapter 1.pdf · a single monetary authority, a single scal authority. All of them are in nitely lived

Introduction Households Firms Equilibrium PS’s expectations MP instrument

Monetary Economics

Chapter 1: The Basic New Keynesian Model

Olivier Loisel

ensae

December 2020 − January 2021

O. Loisel, Ensae Monetary Economics Chapter 1 1 / 55


Objective of the chapter

The chapter presents the basic NK model and derives its implicationsregarding the role of expectations in the transmission of MP.

As explained in the General Introduction, the motivation for considering thismodel is threefold:

1 like RBC models, it is a (DS)GE model, so that

it is not subject − or little sensitive − to Lucas’ (1976) critique,it provides a welfare criterion to assess the desirability of policies,

2 unlike RBC models, it provides an active role for MP, due to

the inefficiency of economic fluctuations,the non-neutrality of MP in the short term,

3 it is simple.

This model will be used in Chapters 2, 3, and 6.



From the standard RBC model to the basic NK model

As also explained in the General Introduction, the basic NK modelcorresponds to the standard RBC model in which

there is no endogenous capital accumulation (for simplicity),

there is monopolistic competition in the goods market, so that firmsare price-makers (not price-takers),

there is price stickiness in the goods market, so that

economic fluctuations are inefficient,MP is non-neutral in the short term (due to its effects on real moneybalances and the short-term real interest rate).

In particular, it is a GE model, so that its equilibrium conditions are

the first-order conditions of the private agents’ optimization problems,the constraints of these problems,market-clearing conditions.



Which version of the basic NK model? I

There are different versions of the basic NK model, depending on

1 the nature of shocks,2 the degree of steady-state inefficiency,3 the nature of price stickiness,4 the role of money,5 the nature of labor.

Shocks ≡ stochastic exogenous variables (normalized to have a zero mean).

Steady state ≡ equilibrium in the absence of shocks.



Which version of the basic NK model? II

1 For simplicity, I consider only two shocks:

technology shocks,shocks to the elasticity of substitution between differentiated goods.

↪→ Other shocks could be considered, whose normative implications wouldbe qualitatively similar to those of technology shocks:

consumption-utility shocks,labor-disutility shocks,government-expenditures shocks,distortive-tax shocks.



Which version of the basic NK model? III

2 I assume that there is a fiscal authority that offers an employment subsidy(financed by lump-sum taxes), so as to partially or completely offset themonopolistic-competition distortion.

↪→ This assumption enables me to consider alternative degrees ofsteady-state inefficiency.

3 I consider price stickiness

à la Calvo (1983) (at each date, some randomly chosen firms areallowed to change their prices),not à la Rotemberg (1982) (at each date, each firm faces a resourcecost in changing its price, which is quadratic in the price-change size).

↪→ When the steady-state distortion is small, these two alternative ways ofmodeling price stickiness have qualitatively similar positive and normativeimplications.



Which version of the basic NK model? IV

4 I first consider a cashless model, in which money implicitly serves only as aunit of account.

↪→ I show at the end of the chapter how to introduce money explicitly intothis model.

5 I assume that there is a single kind of labor as in Gaĺı (2015, Chapter 3),not several as in Woodford (2003, Chapter 4).

↪→ These two alternative assumptions have qualitatively similar positive andnormative implications.



Time and agents

Time is discrete, indexed by t, and the horizon is infinite.

There are four kinds of agents:

a large number of households,a large number of firms,a single monetary authority,a single fiscal authority.

All of them are infinitely lived.

All households are identical, so that there is a representative household (RH).

The RH is the only agent to have a utility function, so that the basic NKmodel is a representative-agent model.



Markets

A continuum of monopolistically competitive goods markets:

demand from households,supply from firms.

A perfectly competitive labor market:

demand from firms,supply from households.

A perfectly competitive one-period-bond market:

demand from households,supply from households.



Outline of the chapter

Introduction

Households’ behavior

Firms’ behavior

Equilibrium conditions

Role of the private sector (PS)’s expectations

MP instrument



RH’s intertemporal utility

RH’s intertemporal utility function at date 0 is

U0 ≡ E0{∑+∞t=0 βtU (Ct ,Nt)

}, with Ct ≡

[∫ 10

Ct(i)εt−1

εt di

] εtεt−1

,

where β ∈]0, 1[ is the discount factor, U is continuous and twicedifferentiable, and, for each date t,

Ct is the consumption index,

Ct(i) is the quantity of good i consumed by RH,

εt > 1 is the elasticity of substitution between differentiated goods,

Nt is the number of hours worked by RH,

Uc,t > 0, Ucc,t < 0, Un,t < 0, Unn,t < 0.



RH’s optimization problem in words

RH chooses how much

of each good to consume,labor to supply,bonds to hold,

in order to maximize

her intertemporal utility function,

subject to

her intertemporal budget constraint,

taking as given

the price of each good,the wage,the price of bonds

(given the market structure and the large number of households).



RH’s optimization problem formalized

Max[Ct(i)]i∈[0,1],t∈N ,

(Nt)t∈N , (Bt)t∈N

E0

{∑+∞t=0 βtU (Ct ,Nt)

}

subject to

Ct ≡[∫ 1

0Ct(i)

εt−1εt di

] εtεt−1

and

∫ 10

Pt(i)Ct(i)di +QtBt ≤ Bt−1 +WtNt + Tt for t ∈N,

taking as given

B−1, [Pt(i)]0≤i≤1,t∈N , (Qt)t∈N , (Wt)t∈N , and (Tt)t∈N .



Notations and resolution

For each date t,

Pt(i) is the price of good i ,

Qt is the price of one-period nominal bonds(paying one unit of money at maturity),

Bt is the quantity of one-period nominal bonds held by RH,

Wt is the nominal wage,

Tt is a lump-sum component of income.

RH’s optimization problem can be solved in two steps:

1 for any given consumption index Ct , characterize RH’s choice of thedistribution of consumption across goods [Ct(i)]0≤i≤1,

2 characterize RH’s choice of the consumption index Ct and the numberof hours worked Nt .



Distribution of consumption across goods I

Dual optimization problem:

Max[Ct (i)]0≤i≤1

[∫ 10

Ct(i)εt−1

εt di

] εtεt−1

subject to∫ 10 Pt(i)Ct(i)di = Zt .

Lagrangian:

L =

[∫ 10

Ct(i)εt−1

εt di

] εtεt−1− λ

[∫ 10

Pt(i)Ct(i)di − Zt]

.

First-order conditions (FOCs): Ct(i)−1εt Ct

1εt = λPt(i) for all i ∈ [0, 1].



Distribution of consumption across goods II

Using these FOCs to replace Ct(i) in the definition of Ct gives λ = P−1t

where

Pt ≡[∫ 1

0Pt(i)

1−εtdi

] 11−εt

is the aggregate price index.

Replacing λ by P−1t in the FOCs gives the demand schedule

Ct(i) =

[Pt(i)

Pt

]−εtCt for all i ∈ [0, 1].

The limit case εt −→ +∞ corresponds to perfect competition.



Consumption index and number of hours worked I

Replacing Ct(i)εt−1

εt by Ct(i)Pt(i)C−1εtt P

−1t in the definition of Ct gives∫ 1

0Pt(i)Ct(i)di = PtCt .

Therefore, the second step of RH’s optimization problem can be rewritten as

Max(Ct )t∈N,(Nt )t∈N,(Bt )t∈N

E0

{∑+∞t=0 βtU (Ct ,Nt)

}subject to

PtCt +QtBt ≤ Bt−1 +WtNt + Tt for t ∈N,

taking as given

B−1, (Pt)t∈N , (Qt)t∈N , (Wt)t∈N , and (Tt)t∈N .



Consumption index and number of hours worked II

The FOCs of this problem are, for all t ∈N,

−Un,tUc,t

=WtPt

(labor-consumption trade-off condition),

Qt = βEt

{Uc,t+1Uc,t

PtPt+1

}(Euler equation).

Interpretation: at the optimal plan, it must be the case that

Uc,tdCt + Un,tdNt = 0 for any pair (dCt , dNt)satisfying the budget constraint PtdCt = WtdNt ,

Uc,tdCt + βEt{Uc,t+1dCt+1} = 0 for any pair (dCt , dCt+1) satisfyingthe budget constraint Pt+1dCt+1 = − PtQt dCt .



Consumption index and number of hours worked III

Specific functional-form assumption for the period utility:

U (Ct ,Nt) =C1−σt − 1

1− σ −N1+ϕt

1 + ϕ

where σ > 0 and ϕ > 0.

The previous FOCs then become

WtPt

= C σt Nϕt (labor-consumption trade-off condition),

Qt = βEt

{(Ct+1Ct

)−σ PtPt+1

}(Euler equation).



Consumption index and number of hours worked IV

The labor-consumption trade-off condition can be rewritten in log-linearform as

wt − pt = σct + ϕnt ,

where, for any variable Zt , zt ≡ logZt .

A log-linear approximation of the Euler equation around a steady state witha zero inflation rate and a constant consumption level is

ct = Et {ct+1} −1

σ

(it −Et {πt+1} − i

),

where it ≡ − logQt is the log of the gross yield on one-period nominalbonds (referred to as the short-term nominal interest rate), i ≡ − log β,and πt ≡ pt − pt−1 is the inflation rate.



Production function and price rigidity

There is a continuum of firms indexed by i ∈ [0, 1], each firm producing adifferentiated good.

All firms use the same technology, represented by the production function

Yt(i) = AtNt(i)1−α,

where α ∈]0, 1[ and At is a stochastic exogenous factor.

As in Calvo (1983), at each date, each firm may reset its price only withprobability 1− θ (independent of the time elapsed since the lastadjustment), where θ ∈ [0, 1], so that

at each date, a measure 1− θ of firms reset their prices,at each date, a measure θ of firms keep their prices unchanged,the average duration of a price is (1− θ)−1,θ is a natural index of price stickiness.



Aggregate price level dynamics

At each date t, all firms resetting their prices will choose the same pricenoted P∗t because they face the same problem.

Therefore, Pt =[θ (Pt−1)

1−εt + (1− θ) (P∗t )1−εt

] 11−εt .

Dividing by Pt−1, one gets Π1−εtt = θ + (1− θ)

(P∗tPt−1

)1−εt, where

Πt ≡ PtPt−1 .

Log-linearization around a steady state with Πt = 1 yields

πt = (1− θ)(p∗t − pt−1).



Firms’ optimization problem

A firm re-optimizing at date t will choose the price P∗t that maximizes thecurrent market value of the profits generated while this price remainseffective:

MaxP∗t

∑+∞k=0 θkEt{Qt,t+k

[P∗t Yt+k |t −Ψt+k (Yt+k |t)

]},

where

Qt,t+k ≡ βk(Ct+kCt

)−σPt

Pt+kis the stochastic discount factor for

nominal payoffs between t and t + k ,Yt+k |t is output at t + k for a firm that last reset its price at t,Ψt(.) is the nominal cost function at t,

subject to Yt+k |t =(

P∗tPt+k

)−εt+kCt+k for k ∈N,

taking (Ct+k )k∈N and (Pt+k )k∈N as given.



FOC of this problem

The FOC of this problem (henceforth “firms’ FOC”) is

∑+∞k=0 θkEt{Qt,t+kYt+k |t (εt+k − 1)

(P∗t −Mt+kψt+k |t

)}= 0,

where ψt+k |t ≡ Ψ′t+k (Yt+k |t) denotes the nominal marginal cost at t + kfor a firm that last reset its price at t, and Mt+k ≡ εt+kεt+k−1 .

Under flexible prices, this FOC collapses to P∗t =Mtψt|t , so that Mt isthe “desired” (or frictionless) markup.

Dividing by Pt−1, one gets

∑+∞k=0 θkEt

{Qt,t+kYt+k |t (εt+k − 1)

(P∗tPt−1−Mt+kMCt+k |tΠt−1,t+k

)}= 0,

where Πt−1,t+k ≡ Pt+kPt−1 and MCt+k |t ≡ψt+k |tPt+k

is the real marginal cost at

t + k for a firm whose price was last set at t.



Zero-inflation-rate steady state

At the zero-inflation-rate steady state (ZIRSS),

P∗t and Pt are equal to each other and constant over time,

therefore, all firms produce the same quantity of output,

this quantity is constant over time, as the model features nodeterministic trend,

therefore, P∗t

Pt−1= 1, Πt−1,t+k = 1, Mt+k =M≡ εε−1 , Qt,t+k = βk ,

and we note Yt+k |t = Y and MCt+k |t = MC ,

firms’ FOC then implies MC = 1M .



Log-linearization of firms’ FOC

Log-linearization of firms’ FOC around the ZIRSS yields

p∗t − pt−1 = (1− βθ)∑+∞k=0(βθ)kEt{

µt+k +mct+k |t + (pt+k − pt−1)}

,

where µt+k ≡ logMt+k .

This equation can be rewritten as

p∗t = (1− βθ)∑+∞k=0(βθ)kEt{

µt+k +mct+k |t + pt+k}

.

Hence, firms resetting their prices choose a price that corresponds to aweighted average of their current and expected future desired markups overtheir nominal marginal costs.



Market-clearing conditions

Market clearing in the goods markets requires, for all i and t,

Yt(i) = Ct(i).

Therefore, Yt = Ct , where Yt ≡[∫ 1

0 Yt(i)εt−1

εt di

] εtεt−1

.

Market clearing in the labor market requires, for all t,

Nt =∫ 10

Nt(i)di .



Aggregate production function

Using the market-clearing conditions, the production function, and thedemand schedule, one gets

Nt =∫ 10

[Yt(i)

At

] 11−α

di =

(YtAt

) 11−α ∫ 1

0

[Pt(i)

Pt

] −εt1−α

di ,

and therefore the aggregate production function

yt = (1− α)nt + at − dt ,

where dt ≡ (1− α) log∫ 10

[Pt (i)Pt

] −εt1−α

di is a measure of price (and, hence,

output) dispersion across firms.



Average real marginal cost

In the neighborhood of the ZIRSS, dt is equal to zero up to a first-orderapproximation, so that, at the first order,

yt = (1− α)nt + at

(the proof is postponed to Chapter 2).

Noting mct the average real marginal cost at t, mpnt the averagemarginal product of labor at t, and τ the constant employment subsidy, andusing yt = (1− α)nt + at , one gets

mct = log(1− τ) + (wt − pt)−mpnt= log(1− τ) + (wt − pt)− (at − αnt)− log(1− α)

= log(1− τ) + (wt − pt)−1

1− α (at − αyt)− log(1− α).



Real marginal cost

For any firm-level variable z , let zt+k |t denote the value of z at t + k for afirm that last reset its price at t.

Using the demand schedule and the goods-market clearing condition, onegets, at the first order, the real marginal cost

mct+k |t = log(1− τ) + (wt+k − pt+k )−mpnt+k |t

= log(1− τ) + (wt+k − pt+k )−at+k − αyt+k |t

1− α − log(1− α)

= mct+k +α

1− α (yt+k |t − yt+k )

= mct+k −αεt+k1− α (p

∗t − pt+k ) = mct+k −

αε

1− α (p∗t − pt+k ).

Under constant returns to scale (α = 0), one has mct+k |t = mct+k : the realmarginal cost is independent of the output level and, hence, is commonacross firms.



Rewriting firms’ FOC

Using the previous result, firms’ FOC can be rewritten as p∗t − pt−1

= (1− βθ)∑+∞k=0(βθ)kEt {Θ (µt+k +mct+k ) + (pt+k − pt−1)}= (1− βθ)Θ ∑+∞k=0(βθ)kEt {µt+k +mct+k}+ ∑

+∞k=0

(βθ)kEt {πt+k}= βθEt

{p∗t+1 − pt

}+ (1− βθ)Θ (µt +mct) + πt ,

where Θ ≡ 1−α1−α+αε .

Using the aggregate price level dynamics equation, one then gets

πt = βEt {πt+1}+ χ (µt +mct) ,

where χ ≡ (1−θ)(1−βθ)θ Θ.



Natural level of output

Independently of the nature of price setting, the average real marginal costcan be rewritten, at the first order, as

mct = log(1− τ) + (wt − pt)−mpnt= log(1− τ) + (σyt + ϕnt)− (yt − nt)− log(1− α)

= log(1− τ) +(

σ +ϕ + α

1− α

)yt −

1 + ϕ

1− α at − log(1− α),

using the labor-consumption trade-off condition, the goods-market-clearingcondition, and the (approximate) aggregate production function.

Now, firms’ FOC implies that, under flexible prices, mct = −µt .

Therefore, the natural level of output, defined as the equilibrium level ofoutput under flexible prices and noted ynt , is such that

−µt = log(1− τ) +(

σ +ϕ + α

1− α

)ynt −

1 + ϕ

1− α at − log(1− α).



Output gap and New Keynesian Phillips curve

Therefore, the natural level of output is

ynt =1− α

σ(1− α) + ϕ + α

[log

(1− α1− τ

)+

1 + ϕ

1− α at − µt]

.

The natural level of output does not depend on it , i.e. MP is neutralunder flexible prices.

Subtracting the two equations on the previous slide, one gets mct

+µt =(

σ + ϕ+α1−α

)ỹt , where ỹt ≡ yt − ynt is called the output gap.

Rewriting firms’ FOC, one gets the New Keynesian Phillips curve (NKPC)

πt = βEt {πt+1}+ κỹt ,

where κ ≡ χ(

σ + ϕ+α1−α

).



Interpretation of the NKPC

The NKPC is forward-looking because, when a firm resets its price, itknows that it will not be able to change this price for some (random) time.

Therefore, the current inflation rate depends on

the current situation (term κỹt),the expected future situation (term βEt {πt+1}).

The slope κ of the Phillips curve is decreasing in θ and β: the stickier theprices or the higher the discount factor, the less prices react to the currentsituation.

As prices become flexible (θ −→ 0), the NKPC becomes yt = ynt .



IS equation

Using the goods-market-clearing condition and the definition of the outputgap, one can rewrite the Euler equation as the IS equation

ỹt = Et {ỹt+1} −1

σ(it −Et {πt+1} − rnt ) ,

where

rnt ≡ i + σEt{∆ynt+1}

= i +σ(1− α)

σ(1− α) + ϕ + α

(1 + ϕ

1− α Et{∆at+1} −Et{∆µt+1})

is the natural rate of interest (unique equilibrium value of the ex anteshort-term real interest rate it −Et {πt+1} consistent with the output levelbeing constantly equal to its natural level).



Set of equilibrium conditions

Given (at , µt , it)t∈N, (ỹt , πt)t∈N is determined by

the IS equation ỹt = Et {ỹt+1} − 1σ (it −Et {πt+1} − rnt ),the NKPC πt = βEt {πt+1}+ κỹt ,

for t ∈N, which implies that MP is not neutral (unless θ −→ 0).

Given (at , µt , it , ỹt , πt)t∈N, (yt , ct , nt ,wt − pt)t∈N is determined by

the definition of the output gap ỹt ≡ yt − ynt ,the goods-market-clearing condition ct = yt ,

the aggregate production function yt = (1− α)nt + at ,the labor-consumption trade-off condition wt − pt = σct + ϕnt ,

for t ∈N.



Role of PS’s expectations I

Provided that limk−→+∞

Et {ỹt+k} = 0, iterating the IS equation forward yields

ỹt = −1

σEt

{∑+∞k=0

(rt+k − rnt+k

)},

where rt ≡ it −Et {πt+1} is the ex ante short-term real interest rate.

Using a no-arbitrage condition, one can interpret Et{

∑+∞k=0 rt+k}

as the exante long-term real interest rate.

Therefore, the output gap depends on PS’s expectations of the future pathof the short-term interest rate (through the long-term interest rate).



Role of PS’s expectations II

Provided that limk−→+∞

Et {πt+k} = 0, iterating the NKPC forward yields

πt = κEt{∑+∞k=0 βk ỹt+k

}.

Therefore, the inflation rate also depends on PS’s expectations of the futurepath of the short-term interest rate.

So MP affects the economy not only through changes in the currentshort-term interest rate, but also through changes in PS’s expectations ofthe future path of the short-term interest rate.



Role of PS’s expectations III

As an illustration, assume for simplicity that CB controls directly rt andfollows the rule rt = γrt−1 + ξt , where γ ∈]0, 1[ and ξt is an i.i.d. MPshock occurring at date t.

Then Et{

∑+∞k=0 rt+k}= rt

(1−γ) , ỹt =−rt

σ(1−γ) + f[(

Et{rnt+k})k∈N

]and

πt =−κrt

σ(1−γ)(1−βγ) + g[(

Et{rnt+k})k∈N

], where f and g are linear

functions.

Therefore, the more persistent the short-term interest rate (the closer to 1 isγ), the larger the effect of the MP shock on the long-term interest rate, theoutput gap, and the inflation rate.



In Woodford’s (2003) words I

“Successful monetary policy is not so much a matter of effective control of overnight

interest rates as it is of shaping market expectations of the way in which interest rates,

inflation, and income are likely to evolve over the coming year and later. (...)

[O]ptimizing models imply that private sector behavior should be forward-looking; hence

expectations about future market conditions should be important determinants of

current behavior. It follows that, insofar as it is possible for the central bank to affect

expectations, this should be an important tool of stabilization policy. (...) Not only do

expectations about policy matter, but, at least under current conditions, very little else

matters.



In Woodford’s (2003) words II

[T]he current level of the overnight interest rates as such is of negligible importance for

economic decisionmaking. The effectiveness of changes in central-bank targets for

overnight rates in affecting spending decisions (and hence ultimately pricing and

employment decisions) is wholly dependent upon the impact of such actions upon other

financial-market prices, such as long-term interest rates, equity prices, and exchange

rates. These are plausibly linked, through arbitrage relations, to the short-term interest

rates most directly affected by central-bank actions. But it is the expected future path

of short-terms rates over coming months and even years that should matter for the

determination of these other asset prices, rather than the current level of short-term

rates by itself. Thus the ability of central banks to influence expenditure, and hence

pricing, decisions is critically dependent upon their ability to influence market

expectations regarding the future path of overnight interest rates, and not merely their

current level.”



In Bernanke’s (2004b) words I

“Informal discussions of monetary policy sometimes refer to the Fed as ‘setting interest

rates.’ In fact, the FOMC does not set interest rates in general; rather, the Committee

‘sets’ one specific interest rate, the federal funds rate. The federal funds rate, the

interest rate at which commercial banks borrow and lend to each other on a short-term

basis (usually overnight) is not important in itself. Only a tiny fraction of aggregate

borrowing and lending is done at that rate. From a macroeconomic perspective,

longer-term interest rates–such as home mortgage rates, corporate bond rates, and the

rates on Treasury notes and bonds–are far more significant than the funds rate, because

those rates are the most relevant to the spending and investment decisions made by

households and businesses. These longer-term rates are determined not by the Fed but

by participants in deep and sophisticated global financial markets.



In Bernanke’s (2004b) words II

Although the FOMC cannot directly determine long-term interest rates, it can exert

significant influence over those rates through its control of current and future values of

the federal funds rate. The crucial link between the federal funds rate and longer-term

interest rates is the formation of private-sector expectations about future monetary

policy actions. Loosely speaking, long-term interest rates embody the expectations of

financial-market participants about the likely future path of short-term rates, which in

turn are closely tied to expectations about the federal funds rate. Thus, to influence

long-term interest rates, such as thirty-year mortgage rates or the yields on corporate

bonds, the FOMC must influence private-sector expectations about future values of the

federal funds rate. The Committee can do this by its communication policies, by

establishing certain patterns of behavior, or both.”



In European central bankers’ words

González-Páramo (2007): “expectations play an important role in the transmission of

monetary policy. Consider, for instance, the term structure of interest rates. Central

banks have a direct influence only on short-term interest rates through their monetary

policy instruments − typically an overnight call rate. However, consumption andinvestment decisions, and thus medium-term price developments, are to a large extent

influenced by longer-term interest rates, which in turn depend on private sector

expectations regarding future central bank decisions and future inflation.”

Trichet (2008): “Through their actions, central banks can directly control very

short-term interest rates. However, given that for consumption and investment decisions

the longer-term interest rates are more relevant, the whole yield curve is relevant for the

effectiveness of monetary policy. Medium- and long-term interest rates largely depend

on private expectations regarding future central bank decisions.”



Very short-term predictability

CBs monitor markets’ expectations of their next policy-rate decision.

Sometimes, they communicate about this decision to ensure that markets’expectations are aligned with their intentions.

For instance, the ECB has used the code words “vigilance” and “strongvigilance” in its communication between 2005 and 2011 to signal a likelypolicy-rate hike two months ahead and one month ahead respectively(presumably as a trade-off between commitment and predictability).



Expectations of the next monetary-policy decision

Probability of a change of the ECB Interest Rate (Most likely rate change mentionned: +25bp)

8,80%

90,20%

1,00%

36,60%

63,20%

0,20%

88,70%

11,30%

0,00%0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Increase No change DecreaseExpectations on the Decision of January 11, 2007 (Survey Date: December 2006)Expectations on the Decision of February 8, 2007 (Survey Date: January 2007)Expectations on the Decision of March 8, 2007 (Survey Date: February 2007)

Source: Consensus ForecastLast Survey: February 12 2006



Short- to medium-term predictability

However, as we have just seen, what matters for the economy is much lessthe expectation of next month’s policy rate than the expectation of thewhole future trajectory of the policy rate.

This is why CBs also monitor markets’ expectations of their subsequentpolicy-rate decisions, and sometimes communicate about these decisions toensure that markets’ expectations are aligned with their intentions.



Expectations of up to one-year-ahead policy-rate decisions

Forecasts of 3M-Euribor based on futures contracts

3,3

3,4

3,5

3,6

3,7

3,8

3,9

4

4,1

4,2

18/09

/2006

03/10

/2006

18/10

/2006

02/11

/2006

17/11

/2006

02/12

/2006

17/12

/2006

01/01

/2007

16/01

/2007

31/01

/2007

15/02

/2007

% p

er y

ear

Forward rate, March 2007 Forward rate, June 2007

Forward rate, September 2007 Forward rate, December 2007

Source: BSME.Production: POMONE.Last update: 02/03/2007.

IFO release

Gov. C. meeting

Gov. C. meeting

Gov. C. meeting

Gov. C. meeting

IFO release

IFO release

IFO release

IFO release

Gov. C. meeting

IFO release



In Bernanke’s (2004a) words

“The fact that market expectations of future settings of the federal funds rate are at

least as important as the current value of the funds rate in determining key interest

rates such as bond and mortgage rates suggests a potentially important role for central

bank communication: If effective communication can help financial markets develop

more accurate expectations of the likely future course of the funds rate, policy will be

more effective (...).

It is worth emphasizing that the predictability of monetary policy actions has both

short-run and long-run aspects. A central bank may, through various means, improve

the market’s ability to anticipate its next policy move. Improving short-term

predictability is not unimportant, because it may reduce risk premiums in asset markets

and influence shorter-term yields. But signaling the likely action at the next meeting is

not sufficient for effective policymaking. Because the values of long-term assets are

affected by the whole trajectory of expected short-term rates, it is even more vital that

information relevant to estimating that trajectory be communicated.”



Two possible MP instruments I

CBs have the monopoly of issuing bank notes and bank reserves.

Therefore, they control the monetary base (i.e. the supply of money).

In the basic NK model, there are two alternative MP instruments: thesupply of money and the short-term nominal interest rate.

One of the simplest way to introduce money in this model is to make realmoney balances enter the utility function in a separable way.

In this case, the corresponding FOC leads to the following log-linearizedmoney-demand equation: mdt − pt = σyt−itν , where ν ≡ −

UmmMUmP

> 0.

The money-market-clearing condition then gives mst − pt = σyt−itν .



Two possible MP instruments II

Money then plays a residual role, as it appears only in latter equation.

If the instrument is ms , then CB chooses ms , and the price on the moneymarket (interest rate i) adjusts so that md (i) = ms .

If the instrument is i , then CB chooses i and adjusts ms so thatms = md (i).

In the presence of money-demand shocks (i.e. shocks added to themoney-demand equation) that CB does not observe in real time, i may bepreferable to ms as an instrument.

This is because unlike ms , i isolates the real variables from these shocks.



Two possible MP instruments III

In practice, before the 2008-2009 crisis (i.e. for conventional MP), the MPinstrument was i :

a MP committee chose a value for i without considering theadjustment in ms necessary for i to reach this value,a specialized staff of the CB adjusted ms for i to reach this value.

The basic NK model is consistent with this practice.

However, the MP instrument has not necessarily been i since the 2008-2009crisis, as unconventional MP (quantitative or credit easing) has, on someoccasions and in some places, pushed ms higher than the value consistentwith the market interest rate being close to the policy rate chosen.



ECB policy rates and EONIA

100

By setting the rates on the standing facilities, the Governing Council effectively determines the corridor within which the overnight money market rate can fluctuate. Chart 4.2 shows the development of key ECB interest rates since January 1999 and how the interest rates on the standing facilities have provided a ceiling and a floor for the overnight market interest rate, measured by the euro overnight index average (EONIA).

Chart 4.2 shows that, in normal times, the EONIA has generally remained close to the rate on the MROs, thus demonstrating the importance of these operations as the main monetary policy instrument of the Eurosystem. This behaviour changed in October 2008, when the Eurosystem adopted non-standard measures to counter the

negative effects of the intensification of the financial crisis (see Box 5.1 and Chapter 5). Chart 4.2 also shows that the EONIA exhibits a pattern of occasional spikes. This pattern is related to the Eurosystem’s minimum reserve system, as explained further in Section 4.3.

Finally, Chart 4.2 shows that the differences between the standing facility interest rates and the rate on the MROs were kept unchanged between April 1999 and October 2008 at ±1 percentage point. The width of the corridor was then temporarily narrowed to ±0.5 percentage point, before being widened again to ±0.75 percentage point in May 2009, when the Governing Council decided to set the rate for the MROs at 1.0%.

Corridor of standing facility

interest rates

EONIA, key ECB interest

rates and the minimum

reserve system

Chart 4.2 Key ECB interest rates and the EONIA since 1999

(percentages per annum; daily data)

0

1

2

3

4

5

6

7

0

1

2

3

4

5

6

7

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

marginal lending rate deposit rate EONIA main refinancing/minimum bid rate

Source: ECB.1) Before 28 June 2000 MROs were conducted as fixed rate tenders. Starting with the operation settled on 28 June 2000, and until the operation settled on 15 October 2008, MROs were conducted as variable rate tenders with a pre-announced minimum bid rate. Since the operation settled on 15 October 2008, MROs have been conducted as fixed rate tenders with full allotment. This procedure is scheduled to remain in place at least until the maintenance period ending on 12 July 2011. The minimum bid rate refers to the minimum interest rate at which counterparties may place their bids (see Section 4.4).

Source: ECB (2011).



ECB MRO rate and EONIA

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

01/09/2008 01/12/2008 01/03/2009 01/06/2009 01/09/2009

%

eonia main refinancing operations rate (fixed rate or minimum bid rate)



Targeted and effective Fed Funds rates

0

0,5

1

1,5

2

2,5

3

3,5

09/02/2008 12/19/2008 04/01/2009 06/15/2009 08/29/2009

%

effective targeted


IntroductionObjective of the chapterFrom the standard RBC model to the basic NK modelWhich version of the basic NK model? IWhich version of the basic NK model? IIWhich version of the basic NK model? IIIWhich version of the basic NK model? IVTime and agentsMarketsOutline of the chapter

HouseholdsRH's intertemporal utilityRH's optimization problem in wordsRH's optimization problem formalizedNotations and resolutionDistribution of consumption across goods IDistribution of consumption across goods IIConsumption index and number of hours worked IConsumption index and number of hours worked IIConsumption index and number of hours worked IIIConsumption index and number of hours worked IV

FirmsProduction function and price rigidityAggregate price level dynamicsFirms' optimization problemFOC of this problemZero-inflation-rate steady stateLog-linearization of firms' FOC

EquilibriumMarket-clearing conditionsAggregate production functionAverage real marginal costReal marginal costRewriting firms' FOCNatural level of outputOutput gap and New Keynesian Phillips curveInterpretation of the NKPCIS equationSet of equilibrium conditions

PS's expectationsRole of PS's expectations IRole of PS's expectations IIRole of PS's expectations IIIIn Woodford's (2003) words IIn Woodford's (2003) words IIIn Bernanke's (2004b) words IIn Bernanke's (2004b) words IIIn European central bankers' wordsVery short-term predictabilityExpectations of the next monetary-policy decisionShort- to medium-term predictabilityExpectations of up to one-year-ahead policy-rate decisionsIn Bernanke's (2004a) words

MP instrumentTwo possible MP instruments ITwo possible MP instruments IITwo possible MP instruments IIIECB policy rates and EONIAECB MRO rate and EONIATargeted and effective Fed Funds rates

Documents

Chapter 1: The Basic New Keynesian Modelolivierloisel.com/monetary_economics/Chapter 1.pdf · a single monetary authority, a single scal authority. All of them are in nitely lived