Download Gains from Commitment in Monetary Policy: Implications of the Cost

Gains from Commitment in Monetary Policy: Implications of the
Cost Channel
Ufuk Devrim Demirely
University of Colorado at Boulder
Abstract
Many empirical studies …nd robust evidence that marginal cost of production directly depends on the nominal rate of interest. This relationship induces a cost channel for monetary
policy transmission. Although the empirical literature provides ample evidence for a cost channel, studies that evaluate the welfare gains from monetary policy commitment have so far entirely
ignored its presence. This study shows that, overlooking the cost channel, one signi…cantly underestimates the welfare gains from monetary policy commitment. I …nd that there is a robust
positive relationship between the size of the cost channel and welfare gains from monetary policy
commitment. Using a version of the new Keynesian model calibrated to the U.S. economy, I
…nd that failure to take into account the presence of a cost channel leads to an understatement
of the gains from monetary policy commitment by an amount equivalent to a 0.48 percentage
points permanent cut in quarterly in‡ation.
Keywords: Cost Channel; Optimal Monetary Policy; Commitment; Discretion
JEL classi…cation: E44, E52
I would like to thank an anonymous reviewer and Theodore Palivos for valuable comments and suggestions.
University of Colorado at Boulder, Department of Economics, 256 UCB, Boulder, CO, 80309, USA, tel: (303)
492 2585, email:[email protected].
y
1
1
Introduction
In dynamic economic systems, private agents’ current choices depend upon their expectations of
future government actions. In their seminal contribution, Kydland and Prescott (1977) discuss
how this property often generates a policy environment in which commitment on the part of the
policy maker to an optimal plan delivers superior welfare outcomes relative to discretionary policy.
The new Keynesian model of Clarida et al. (1999), which has become a benchmark framework for
macroeconomic policy analysis, is a glaring example for a policy setup in which the commitment
capacity of the policy maker matters for welfare outcomes. Consequently, studies that quantitatively evaluate the welfare gains from commitment in monetary policy frequently adopt the new
Keynesian setup (see e.g., Demirel 2012, Adam and Billi, 2007, Schaumburg and Tambalotti, 2007,
Dennis and Soderstrom, 2006). In the standard new Keynesian model, monetary policy a¤ects the
economy only through a conventional demand-side channel, i.e. by in‡uencing households’saving
and investment decisions. A number of empirical studies (including Tillmann, 2008, Ravenna and
Walsh, 2006, and Barth and Ramey, 2001), however, …nd robust evidence that …rms’ marginal
cost directly depends on the nominal interest rate, which points to a supply-side mechanism for
monetary policy transmission referred to as the cost channel. In this paper, I show that studies
that disregard this supply-side transmission channel signi…cantly underestimate the value of monetary policy commitment. I …nd that, in the presence of a cost channel, welfare gains from full
commitment in monetary policy can be much greater relative to an economy in which monetary
policy is transmitted only through a demand-side mechanism.
To facilitate comparison with the related literature, I adopt a version of the new Keynesian
model that accommodates a cost channel. As in Ravenna and Walsh (2006) and Cooley and Nam
(1998), I incorporate a cost channel into the model by introducing a working capital constraint,
which requires …rms to pay for a certain fraction (denoted ) of their operational costs in advance
using borrowed funds. This speci…cation links …rms’marginal cost directly to the nominal rate of
interest and induces a cost channel for monetary policy transmission. In this setup, the parameter
measures the intensity of the cost channel. In the case
that involve
= 0 a cost channel is absent and cases
> 0 capture varying intensity levels. For alternative values of
; I evaluate the
optimal monetary policy and compute welfare under full discretion and full commitment. I show
that the welfare gains from monetary policy commitment increase monotonically in the parameter
. Thus, when a cost channel is present (i.e. when
> 0), monetary policy commitment yields
greater welfare gains.
The intuition behind this result is rather straightforward. As is well known, in the face of
cost-push disturbances, the policy maker in the new Keynesian model faces a trade-o¤ between
stabilizing in‡ation and stabilizing the output gap. Full policy commitment yields higher welfare
because it enables the policy maker to e¤ectively control private agents’future expectations, which
leads to a more favorable in‡ation/output-gap trade-o¤ in the face of cost-push shocks. But, as
discussed in Demirel (2009) and Ravenna and Walsh (2006), in the presence of a cost channel, a
2
trade-o¤ between stabilizing in‡ation and stabilizing the output-gap emerges in the face of virtually
all types of shocks. Since, in this environment any shock can act as a cost-push disturbance, the
ability to manipulate future expectations makes a bigger di¤erence in volatility outcomes relative
to the case in which, due to absence of a cost channel, only a subset of shocks can pose a trade-o¤
between stabilizing in‡ation and stabilizing the output-gap. Consequently, the value of monetary
policy commitment increases signi…cantly if a cost channel is present.
Quantitative …ndings suggest that an analysis based on a version of the new Keynesian model
that entirely overlooks the presence of a cost channel underestimates the value of monetary policy
commitment by an amount equivalent to a 0:48 percentage points permanent cut in quarterly
in‡ation under a commonly adopted parametrization of the new Keynesian model. Although this
…gure can be sensitive to the choice of parameter values, it remains signi…cant under reasonable
parametrizations. Furthermore, the positive relationship between the size of the cost channel (as
measured by the parameter ) and the gains from monetary policy commitment is found to be
robust under a range of parametrizations of the new Keynesian model as well as under alternative
model speci…cations.
The rest of the paper is organized as follows: Section 2 outlines the model and derives the
objective function and the constraints of the policy maker. Section 3 casts the optimal policy
problem and discusses the solution procedures under full commitment and discretion. Section 4
presents the welfare computations and discusses the implications of the cost channel. Section 5
provides a robustness analysis and Section 6 concludes.
2
Model
The model economy is inhabited by a large number of identical households, a continuum of monopolistically competitive …rms, and a benevolent government. Each household maximizes
Us = Es
1
X
t s
L1+
t
1+
log Ct
t=s
where
and ;
!
(1)
2 (0; 1); variables Ct and Lt respectively denote composite consumption and work e¤ort
> 0. Households consume a continuum of di¤erentiated products (indexed by i 2 [0; 1])
each produced by a monopolistic competitor. The variable Ct corresponds to the Dixit-Stiglitz
hR
i t =( t 1)
(
1)= t
aggregator of di¤erentiated products de…ned as Ct = i C(i)t t
di
where C(i)t denotes the consumption of variety i: The random variable
between di¤erentiated products and follows the process ln
"
;t
N (0;
2 );
> 1; and
t
t
denotes the elasticity of substitution
= (1
) ln +
ln
t 1 + " ;t
where
2 [0; 1). This speci…cation implies that the the individual demand
for variety i and aggregate consumer price index are respectively given by C(i)t = (P (i)t =Pt )
R
1=(1 t )
and Pt = i P (i)1t t di
where P (i)t denotes the price level for the ith product.
t
Ct
Households enter each period with nominal balances Mt . They provide labor services to pro3
ducers in a competitive labor market and receive wage income at the start of the period. Given
their total nominal wealth, they make consumption, saving, and work decisions at the start of
each period. Households face a cash-in-advance constraint that requires consumption expenditures
to be made using nominal balances. They also have access to a bond market where they trade
one-period government bonds (denoted Bt ). The bond market opens at the start of each period
and bonds mature at the end of the period they are purchased. Consequently, nominal balances of
the household evolve according to the rule
Mt+1
Mt + Wt Lt
Pt Ct
Bt
Tt + Rt Bt +
(2)
t
where Wt denotes the nominal wage rate, Rt is the gross nominal interest rate,
t
=
R
(i)t di and
i
Tt respectively denote …rm pro…ts and taxes paid. The cash-in-advance constraint requires
Pt Ct
Mt + Wt Lt
Bt :
(3)
Households maximize (1) subject to (2), (3), and individual demand functions. In an equilibrium
with a positive net nominal interest rate, the following familiar …rst-order conditions must be
satis…ed:
1
= Et
Ct
1
Rt
t+1
Lt Ct =
Wt
Pt
(5)
Pt Ct = Mt + Wt Lt
where
t+1
(4)
Ct+1
Bt :
(6)
= Pt+1 =Pt denotes the gross in‡ation rate. Firms use a CRS technology Y (i)t = At L(i)t
to produce di¤erentiated products, where Y (i)t and L(i)t respectively denote the amount of variety
i produced and employment by …rm i: The productivity parameter At follows the process ln At =
A ln At 1
+ "A;t where "A;t
N (0;
2)
A
and
A
2 [0; 1).
As discussed earlier, …rms face a working capital constraint that requires them to borrow the
amount Wt L(i)t , where
denotes the fraction of the costs that must be covered using externally
raised funds. Following Rotemberg (1982), it is also assumed that …rms face quadratic price adjustment costs de…ned in real terms by ( =2)[(P (i)t =P (i)t
1)
1]2 . Each monopolistic competitor
sets the price level for its di¤erentiated product to maximize a discounted sum of pro…ts given by
maxEs
P (i)t
where
s;t
1
X
s;t
t=s
=
Ct
Cs
1
1
(
(1 + z)P (i)t
1
Wt At (1 + (Rt
1) ) Y (i)t
Pt
2
P (i)t
P (i)t 1
2
1
)
denotes the stochastic discount factor and the term Wt At 1 (1 + (Rt
1) )
corresponds to the nominal marginal cost of production. Observe that the nominal interest rate
4
Rt a¤ects the marginal cost unless
= 0: As in Demirel (2012), in a symmetric equilibrium, …rm
maximization yields the …rst-order condition
where e t =
et
t(
Wt
[1 + (Rt
Pt At
t Yt
t
(
1) ]
1)
t
(1 + z)
= Et
t;t+1
t
e t+1
(7)
1). The constant z > 0 is an ad valorem production subsidy. It is assumed
that the government sets the subsidy rate once-and-for-all to eliminate the steady-state distortion
that arises from monopolistic competition and the presence of a cost channel, i.e. 1 + z = [ =(
1)][(1 + (R
3
1) )]:
Gains from Commitment and the Cost Channel
Having laid out the model, I next characterize the optimal monetary policy under full discretion
and full commitment and compute welfare under both speci…cations. These welfare outcomes are
then compared to assess the implications of a cost channel on the gains from monetary policy
commitment.
3.1
The Welfare Criterion and Policy Constraints
Following Demirel (2012) and Benigno and Woodford (2006), I adopt a linear-quadratic approximation approach to the computation of the optimal monetary policy. This method involves formulating a second-order approximation to households’life-time expected utility (which de…nes the policy
maker’s welfare criterion) and …rst-order approximations to the model’s structural equations (which
describe the policy maker’s constraints). Following Demirel (2012), a second-order approximation
to (1) can be obtained as
Wt = AEs
1
X
t s
2Y
t=s
1+
2
2
t
ybt2 + O k" ; "A k3 + t:i:p:
(8)
where k" ; "A k denotes an upper-bound on the magnitude of the shocks, O k" ; "A k3 represents
the terms of third and higher order, t:i:p: stands for "terms independent of policy" and A = Y 1+ .
The in‡ation variable is de…ned as
yt
t
= log(
t=
) and the output gap variable ybt = log(Yt =Yn;t ) =
yn;t corresponds to the log-deviation of actual output from the natural level (Yn;t ); i.e., the
level that obtains in the absence of price adjustment costs.1
The constraints the policy maker faces in the outlined economy are found by log-linearizing the
1
Under perfect price ‡exibility (i.e., in the case = 0 and in the absence of monopolistic competition which involves
! 1 ), prices are set to equalize the marginal cost of production Wt =At to the marginal revenue Pt in each period:
1
Therefore we have, Wt =(Pt At ) = Ln;t Cn;t =At = 1: Given Yn;t = At Ln;t = Cn;t , we can …nd Yn;t = (1= ) 1+ At ,
which implies log(Yn;t =Y ) = yn;t = at ; where at = log(At =A). The constants A = 1 and Y respectively denote the
non-stochastic steady-state levels of At and Yt :
t
5
…rst-order conditions (4)-(6) and (7). As discussed in Demirel (2012), this yields
Et
Et
where rt = log(Rt =R),
t+1
t+1
+ Et ybt+1 = ybt + rt
=
(1 + )b
yt
t
= Y = , vt = (
vt + O k" ; "A k2
ert
(9)
bt + O k" ; "A k2
1) log(At =A), bt = [Y =( (
A
R
R+1
e=
(10)
1))] log( t = ), and
:
The constants Y , R, and A = 1 respectively denote the non-stochastic steady-state levels of Yt ,
Rt , and At . Using the steady-state versions of (4)-(6) and the market clearing conditions, Y and
1
1
R can be found as Y = (1= ) 1+ ; R =
:
Equation (9) describes an IS relationship and (10) is a forward-looking Phillips curve. Note
that in the presence of a cost channel (when > 0), we have e > 0 and the log-deviation of the
interest rate from its steady-state value (rt ) appears in the Phillips curve equation (10). Also note
that e is increasing in ; which implies that in‡ation becomes more responsive to a given change
in the interest rate as the size of the cost channel increases.
Given the quadratic welfare criterion (8) and the linear policy constraints (9) and (10), we are
now in a position to evaluate the policy problem and compute welfare under the optimal policy.
3.2
Optimal Policy Under Full Commitment and Full Discretion
In the presence of a commitment device, the policy maker is able to follow a particular plan, which
makes it possible to successfully manipulate private agents’ future expectations. The optimal
monetary policy problem under full commitment, therefore, involves choosing At
s
= f t ; ybt ; rt g1
t=s
to maximize (8), subject to (9) and (10). This problem can be solved using a Lagrangian of the
form
max Es
At
s
1
X
t=s
t s
n
Wt +
+
1;t
h
(1 + ) ybt
t
yt
2;t [b
+ rt
vt
=
2;s 1
= 0:
subject to
1;s 1
ert
t+1
bt
ybt+1 ]
t+1
i
(11)
(12)
where s denotes the initial period and Wt is as described in (8). Note that, under full commitment,
the choice set of the policy maker includes the entire sequence of variables f t ; ybt ; rt g1
t=s :
The presence of future expectations in the constraints (9) and (10) renders the policy problem
described by (11) non-recursive, i.e., the optimal decision rule in this case cannot be described as
6
a time-invariant function of the exogenous state variables bt and vt . Non-recursive structures are
frequently encountered in optimal policy problems in the presence of forward-looking elements in
policy constraints. Kydland and Prescott (1980) use a method to recursively reformulate a dynamic
optimal taxation problem by extending the state space to include certain co-state variables. More
recently, Marcet and Marimon (2009) develop a general theory to apply this approach to a large
class of non-recursive problems. Employing the same methodology, the above problem can be
rede…ned recursively by introducing the co-state variables
max Es
At
s
1
X
t s
t=s
fWt +
1;t
+
h
subject to
=
1;t
1;t 1
and
ert
(1 + ) ybt
t
2;t
1;t
ybt + rt
and
vt ]
=
2;t
2;t
2;t
as follows:
i
bt +
1
(
t
(13)
1;t t
+ ybt ) g
2;t 1 :
Marcet and Marimon (2009) show that there is a duality theorem linking (13) to (11) and that the
solutions to these two problems are identical provided that the initial condition (12) is satis…ed.
Problem (13) does not involve any future expectations in the Lagrangian and is recursive. Given
this recursive structure, it is now possible to characterize the solution to (13) using a saddle-point
functional equation of the form
V (vt ; bt ;
1;t ;
2;t )
=
+
f
min
max
yt ; t ;rt g
1;t ; 2;t gfb
yt
2;t [b
+ rt
vt ]
n
Wt +
1
2;t
1;t
(
t
subject to
=
1;t
where the value function V (vt ; bt ;
1;t ;
1;t 1
2;t )
and
2;t
h
t
(1 + ) ybt
ert
+ ybt ) + Et V (vt+1 ; bt+1 ;
=
i
bt +
1;t+1 ;
1;t t
(14)
2;t+1 )
2;t 1 ;
(15)
describes the maximum life-time utility the optimal pol-
icy can deliver under commitment. Solving (14) subject to (15) we obtain the optimal commitment
policy.
The co-state variables
1;t
and
2;t
describe the value to the planner of committing to the
optimal contingency plan devised in the initial period s: The endogenous evolution of these costate variables guides the optimal commitment policy by keeping track of past promises the policy
maker makes under full commitment. Upon a revision of the ongoing contingency plan, the policy
maker treats past expectations of the private sector as given. As discussed in Demirel (2012) and
Marcet and Marimon (2009), this results in setting the values of the co-state variables
1;t
and
2;t
to zero at the time of revision. Since discretionary policy involves revising ongoing policy plans in
each period, the policy maker sets
1;t
=
2;t
= 0 in all periods. Consequently, the state of the
economy under discretion is entirely described by the exogenous variables bt and vt . As
2;t
1;t
and
are no longer part of the state vector, they can be dropped from the value function of the policy
7
maker and the discretionary equilibrium can be characterized by solving
V (vt ; bt ) =
f
min
max
yt ; t ;rt g
1;t ; 2;t gfb
+
yt
2;t [b
n
Wt +
+ rt
vt
1;t
h
ert
(1 + ) ybt
t
bt
f2;t (bt ; vt )] + Et V (vt+1 ; bt+1 )
i
f1;t (bt ; vt )
where functions f1;t (bt ; vt ) and f2;t (bt ; vt ) respectively correspond to the expectations
and Et (
bt+1 ).
t+1 + y
Note that
1;t
=
2;t
E(
(16)
t+1 )
= 0 in all periods also implies that time t expectations
of future in‡ation and output gap depend only on the exogenous state variables bt and vt . Since the
discretionary policy maker is unable to manipulate future expectations, f1;t (bt ; vt ) and f2;t (bt ; vt )
are treated as exogenous in (16). In equilibrium, however, these expectations are formed consistently
with the optimal discretionary policy.
In what follows, the optimal policy under commitment and discretion are computed by solving
(14) and (16) respectively, using linear-quadratic dynamic programming tools. These solutions are
then used to compute welfare under both speci…cations.
4
Welfare Analysis
To assess how the presence of a cost channel e¤ects the value of monetary policy commitment, I
next compute the welfare gains resulting from a switch in monetary policy from a fully discretionary
stance to full commitment under alternative values for the parameter . Recall that
is the fraction
of operational costs that is required to be paid in-advance, thus, provides us with a continuous
measure for the size of the cost channel. As mentioned earlier, the case
absence of a cost channel and the cases that involve
= 0 corresponds to the
> 0 capture varying intensity levels. To
the remaining parameters of the model, I assign some of the most commonly adopted values in the
literature. These values are picked to have the model’s steady-state properties match the long-run
characteristics of the U.S. data. The adopted parameter values and target statistics are presented
in Table 1.
To place the results in economic context, as in Dennis and Soderstrom (2006), welfare gains are
expressed in terms of compensating in‡ation variations. Speci…cally, for each considered value of ;
I compute the permanent decrease in quarterly in‡ation that is needed to compensate the household
for a switch from full commitment to full discretion in monetary policy. The quadratic measure (8)
suggests that an x percentage points permanent decrease in quarterly in‡ation increases welfare
by the amount [ Y
=2(1
)] (x=100)2 : Let Wcom and Wdisc respectively denote the welfare
levels under full commitment and full discretion. Then, the reduction in quarterly in‡ation that is
required to increase life-time welfare by the amount
n
x= [ Y
=2(1
)]
W = Wcom
1
W
o1=2
Wdisc can be found as
100:
Figure 1 displays the welfare gains (calculated as in 17) under alternative values of
8
(17)
ranging
from from 0 to 2.2 Note that this range includes values that are greater than one. This is motivated
by the empirical …ndings of Ravenna and Walsh (2006) and Chowdhury et al. (2006). Employing
the GMM methodology and using two alternative sets of instruments, Ravenna and Walsh (2006)
estimate the coe¢ cient that measures the impact of the nominal interest rate on …rms’ marginal
cost (which corresponds to
R
R+1
in equation 10) to be around 1:27 and 1:91 in the United States.
Chowdhury et al. (2006) estimate this coe¢ cient to be around 1:3 in the United Stated and in
United Kingdom and 1:5 in Italy. Taken together, these two sets of …ndings suggest that the
parameter
might be greater than one. Chowdhury et al. (2006) also discuss how …nancial market
imperfections might cause this coe¢ cient to be greater than one by driving a wedge between the
policy-controlled interest rates and the lending rates faced by the …rms.
It is observed that the value of monetary policy commitment increases monotonically in : In
the case
= 1; a switch from a fully discretionary policy to full commitment is equivalent to a
1:13 percentage points permanent cut in quarterly in‡ation. The compensating in‡ation variation
that corresponds to the same policy switch, however, is only 0:65 percentage point in the case
= 0: Therefore, ignoring the presence of a cost channel, one underestimates the value of monetary
commitment by an amount equivalent to a 0:48 percentage points permanent cut in the quarterly
in‡ation rate.
To gain intuition for these results, it will be useful to recall a key implication of the cost channel
in the new Keynesian model. As suggested by (7), in the face of a mark-up (cost-push) shock, the
policy maker is unable to stabilize in‡ation and the output gap simultaneously. This is because the
interest rate response needed to relieve the in‡ationary pressure exerted by the shock further exacerbates the contraction in output. In the absence of a cost channel, the policy maker encounters this
trade-o¤ only in the face of cost-push disturbances. If a cost channel is present (i.e., in the case the
nominal interest rate directly a¤ects …rms’marginal cost), however, this trade-o¤ emerges in the
face of all types of shocks.3 Recall that the increase in welfare under commitment stems from the
fact that, under full commitment, the monetary authority can successfully control future in‡ation
expectations, which results in an improved trade-o¤ between stabilizing in‡ation and stabilizing
the output-gap. However, the ability to manipulate private expectations matters only if the policy
maker is subject to shocks that generate a trade-o¤ between stabilizing in‡ation and stabilizing
the output-gap. Since, in the presence of a cost channel, all shocks pose an in‡ation/output-gap
trade-o¤ and the intensity of this trade-o¤ increases with the fraction ; we observe a positive relationship between the welfare gains from commitment and : Accordingly, the value of commitment
in monetary policy increases in the size of the cost channel.
2
For each considered value of ; welfare is computed by simulating 1000 data sequences (each 1000 quarters long)
and averaging the discounted sum of utilities across all simulations.
3
It can easily be seen from (9) and (10) that, in the face of a productivity shock, the nominal rate response needed
to stabilize in‡ation will create output-gap deviations provided that the nominal rate appears in the Phillips curve
equation (10). Observe that this is no longer the case if = 0. As discussed in Clarida et al. (1999), in this case the
policy maker can perfectly stabilize in‡ation and the output-gap simultaneously.
9
5
Robustness Analysis
5.1
Alternative Parametrizations
This section evaluates the sensitivity of our …ndings under alternative parametrizations of the new
Keynesian model. Figure 1 also illustrates the relationship between the gains from commitment
and the fraction
under alternative parameter values. Considered cases include increased price
‡exibility ( = 17), enhanced competition across …rms (
(
= 25), and a steeper Phillips curve
= 2). It is observed that, the patterns that characterize the benchmark calibration exercise
are robust under the considered range of parametrizations. In all considered cases, gains from
commitment monotonically increase in .
The results presented thus far have been derived under a particular combination of the autoregressive parameters
v
and
. To assess the implications of shock persistence, Figure 2 shows
the gains under alternative values of
v
and
: Observe that, regardless of the degree of shock
persistence, welfare gains from commitment is increasing monotonically in the parameter : Furthermore, under a …xed value for ; gains increase (nonlinearly) in the persistence of shocks. As
shocks become more persistent, the trade-o¤ the policy maker faces between stabilizing in‡ation
and stabilizing the output gap intensi…es, thus, the welfare impact of commitment becomes larger.
These results are in line with the …ndings of the previous literature (see e.g., Clarida et al. 1999).
5.2
Alternative Models
In this section, I evaluate the robustness of the main results under alternative model speci…cations.
To this end, I consider a family of models in which pricesetting is characterized as in Calvo (1983)
and Yun (1996) with di¤erent degrees of in‡ation indexation. In these models, a measure (1
) of
randomly selected …rms reset their prices at the start of each period while the remaining …rms change
prices automatically following an indexation rule that adjusts the ongoing price level according
to in‡ation. Let the parameter
denote the degree of in‡ation indexation. Upon receiving a
pricesetting signal, a …rm determines a new price P (i)s to maximize the expectation of a discounted
sum of pro…ts given by
Es
1
X
t=s
where
s;t
=
Ct
Cs
t s
s;t
(1 + z)P (i)s
Pt
Ps
1
1
Wt At 1 (1 + (Rt
1) ) Y (i)t
(18)
1
1
denotes the stochastic discount factor.
Recall that, in the presence of a cost channel, all shocks act as cost-push disturbances. If a
cost channel is absent, however, only shocks to the elasticity of substitution between di¤erentiated
products ("
;t )
exert cost-push pressures. To evaluate whether the main results would still obtain in
the absence of these inherently cost-push disturbances, I also assume that
t
=
for all t. Given this
assumption and the fact that in a symmetric equilibrium we have P (i)s = P s for all i, the overall
10
price level can be found to follow the rule Pt = f [Pt
1 (Pt 1 =Pt 2 )
]1
+ (1
)(P s )1
g1=(1
):
As discussed in Demirel (2012) and Woodford (2003, Chapter 3), this pricesetting structure
alters both the objective function and the constraints of the policy maker. The quadratic welfare
criterion becomes
Wt = AEs
1
X
t s
(
1+
2
2
t 1)
t
t=s
where
=
=[2(1
)(1
ybt2 + O k" ; "A k3 + t:i:p:
(19)
)]: As in (8), expression (19) is obtained by formulating a second-order
approximation to the expected life-time utility of the household around a steady-state. Furthermore, the Phillips curve equation becomes
Et (
where
= (1
t+1
t)
=(
)= and e =
)(1
t 1)
t
h
(1 + )b
yt
i
R
R+1
ert + O k" ; "A k2
(20)
: Equation (20) is obtained by linearizing the
…rst-order conditions of (18) around a steady-state.4 Observe that when
and (20) become very similar to those of (8) and (10). Thus the case
= 0, the forms of (19)
= 0 can be thought of as a
version of our previous model in which inherently cost-push disturbances (i.e., the shocks that can
exert cost-push pressures in the absence of a cost channel) are excluded.
Figure 3 shows the welfare gains from a shift form discretion to commitment under alternative
values of the parameters
in‡ation acceleration (
t
and
t 1 ).
: Gains are expressed in terms of compensating variations in
We observe that, regardless of the degree of in‡ation indexation,
welfare gains increase monotonically in the parameter : This is because, as the size of the cost
channel increases, cost-push e¤ects of productivity shocks become magni…ed. This exacerbates
the trade-o¤ between stabilizing in‡ation and the output gap even in the absence of inherently
cost-push shocks. Consequently, being able to control future in‡ation expectations through full
commitment has a larger moderating impact on the trade-o¤ between in‡ation and output gap
stabilization and results in more signi…cant welfare gains. Also observe that, for a …xed value of ;
gains increase in the degree of in‡ation indexation in the considered range of : As in‡ation inertia
increases under higher degrees of indexation, the excessive response of in‡ation to a productivity
shock that obtains under discretion tends to persist longer. This renders discretionary policy more
welfare-reducing. Consequently, commitment delivers more sizable welfare gains as the degree of
indexation increases.
6
Conclusion
This paper has evaluated the value of monetary policy commitment in the new Keynesian model
extended to accommodate a cost channel for monetary policy transmission. It is found that, in an
4
A detailed derivation of (19) and (20) is available from the author upon request.
11
economy where interest rate movements directly a¤ect the marginal cost of production, a switch
from full discretion to full commitment in monetary policy yields greater welfare gains relative to
an environment where interest rate movements a¤ect the economy only through a conventional
demand side mechanism. This result is found to be robust under a range of parametrizations of
the new Keynesian model as well as under some alternative pricesetting structures. In the light of
the evidence provided by previous empirical studies that support the existence of a cost channel,
these …ndings suggest that monetary policy commitment matters more than previously predicted
using the standard version of the new Keynesian model.
12
Tables and Figures
Parameter
Value
Target Statistic
0:9913
2% Annual real rate
1
Unit labor supply elasticity
7:66
Adam and Billi (2007)
17:5
Adam and Billi (2008)
25
Devote 20% of available time for work
0:75
Prices adjust on average once a year
)
(0:8; 0)
Demirel (2012)
b)
(0:152%; 0:180%)
Demirel (2012)
1
=R
( v;
(
v;
Table 1: Benchmark Parameter Values
7
Benchmark
φ =2
σ =25
θ=17
Welfare Gains from Commitment
6
5
4
3
2
1
0
0.25
0.50
0.75
1
1.25
1.50
1.75
2
τ
Figure 1: Gains from monetary policy commitment (expressed in terms
of compensating in‡ation variations) as a function of
13
7
(ρ ,ρ )=(0,0)
ν
6
σ
(ρ ,ρ )=(0.2,0.2)
ν σ
Welfare Gains form Commitment
(ρ ,ρ )=(0.4,0.4)
ν σ
5
(ρ ,ρ )=(0.5,0.5)
ν σ
(ρ ,ρ )=(0.6,0.6)
ν
σ
4
3
2
1
0
0.25
0.50
0.75
1
1.25
1.50
1.75
2
τ
Figure 2: Gains from monetary policy commitment (expressed in terms
of compensating in‡ation variations) as a function of
levels of shock persistence
14
under di¤erent
4
χ=0
χ=0.3
χ=0.6
Welfare Gains from Commitment
3.5
3
2.5
2
1.5
1
0.5
0
0.25
0.50
0.75
1
1.25
1.50
1.75
τ
Figure 3: Gains from monetary policy commitment (expressed in terms
of compensating variations in in‡ation acceleration) as a function of
under di¤erent levels of in‡ation indexation
15
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