Araújo, Eurilton

English

Research Papers in Economics

Supply-side effects of monetary 
policy and the central bank’s 
objective function
Eurilton Araújo
Insper Working Paper
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citação completa do documentoSupply-side e⁄ects of monetary policy and
the central bank￿ s objective function
Eurilton Araœjo￿
Ibmec Sªo Paulo
Abstract
This paper considers a new Keynesian model with the cost channel
and evaluates the supply-side e⁄ects of monetary policy on macroeco-
nomic volatility and welfare, taking into account the endogenous na-
ture of the objective function of monetary authorities. When the cost
channel matters, supply-side e⁄ects of monetary policy depend on the
degree of interest rate pass-through and the degree of price rigidity.
Numerical results show that the welfare consequences of an increase
in the degree of interest rate pass-through are independent of how the
central bank speci￿es its loss function. By contrast, the welfare conse-
quences of an increase in price rigidity depend critically on the nature
of the loss function considered. Macroeconomic volatility as a func-
tion of the pass-through is almost independent of the central bank￿ s
loss function. In contrast, this volatility as a function of the degree of
price rigidity depends more on the nature of the loss function.
Keywords: monetary policy, interest income taxation, discretion
JEL Classi￿cation: E43, E52, E58
￿Address: Ibmec Sao Paulo. Rua Quata, 300. Zip Code: 04546-042. Sao Paulo, Brazil.
Phone: 55-11-4504-2422. Email: euriltona@isp.edu.br.1 Introduction
Monetary policy analysis emphasizes the e⁄ects of interest rate changes on
aggregate demand. Nevertheless, ￿rms￿costs of external ￿nance are also
sensitive to monetary policy outcomes. The model presented in Ravenna &
Walsh (2006) changes the basic new Keynesian framework by introducing
supply-side e⁄ects of monetary policy through the lending costs of ￿rms.
In this model, a trade-o⁄ between stabilizing in￿ ation and the output gap
emerges endogenously.
In Ravenna & Walsh (2006), ￿rms borrow at the policy rate controlled by
the central bank. Therefore, the interest rate pass-through is always equal
to one. Following Chowdhury et al. (2006), I consider the e⁄ects of ￿nancial
market imperfections on ￿rms￿lending costs, which imply varying degrees of
pass-through from the policy risk-free interest rate to the bank lending rate.
Thus, the e⁄ects of changes in the policy rate can be ampli￿ed or dampened.
When the cost channel matters, supply-side e⁄ects of monetary policy
depend on the degree of interest rate pass-through and the degree of price
rigidity.
In this paper, I derive the optimal monetary policy under discretion and
evaluate quantitatively the macroeconomic e⁄ects of di⁄erent degrees of in-
1terest rate pass-through and price rigidity. I consider both exogenous and
endogenous loss functions. Following Walsh (2005), I take into account that
the relative weights attached to competing objectives in the policy maker￿ s
loss function depend on structural parameters, and therefore are not exoge-
nous.
Numerical simulations show that the welfare consequences of an increase
in the degree of interest rate pass-through are independent of how the central
bank speci￿es its loss function. By contrast, the welfare consequences of an
increase in price rigidity depend critically on the nature of the loss function
considered. Macroeconomic volatility as a function of the pass-through is
almost independent of the central bank￿ s loss function. On the other hand,
the volatilities of macroeconomic variables as a function of the degree of price
rigidity seem to be more sensitive to the way the loss function is speci￿ed.
The rest of the paper is organized as follows. In section 2, I describe
brie￿ y the model. In section 3, I derive the optimal monetary policy under
discretion. Results are presented in section 4. I o⁄er my conclusions in
section 5.
22 The Model
2.1 Households
Households with a time-separable utility and a discount factor ￿, where 0 <
￿ < 1 , maximize their expected lifetime utility given a sequence of budget
constraints. The period utility is given by:
U(Ct;Nt) =
C
1￿￿
t
1 ￿ ￿
￿ ￿
N
1+￿
t
1 + ￿
where Ct and Nt are consumption and employment, respectively.
The parameter ￿ denotes the inverse of the intertemporal elasticity of
substitution and ￿ is the inverse of the elasticity of substitution between
work and leisure.
At each date, the budget constraint is:
Mt+1 ￿ Mt = WtNt ￿ Dt + ItDt + ￿t ￿ PtCt ￿ PtTt
where Dt is the household￿ s deposit at ￿nancial intermediaries, Mt is
nominal money balances, Wt is the nominal wage, It is the gross nominal
interest rate, ￿t is nominal pro￿ts received from ￿rms, and Tt is a real lump-
3sum tax. The government satis￿es its intertemporal budget constraint, not
explicitly considered, by adjusting Tt.
Aggregate demand is derived from the representative household￿ s Euler
equation. After imposing market clearing conditions, the log-linear form of
the Euler equation is:
xt = Et(xt+1) ￿
1
￿
[it ￿ Et(￿t+1)] + gt (1)
The variables xt; it and ￿t are the output gap, the nominal risk-free
interest rate and in￿ ation, respectively. In￿ ation and the nominal interest
rate are expressed in log-deviations from their steady states.
A shock gt is added to the aggregate demand equation. This disturbance
follows an autoregressive process:
gt = ￿ggt￿1 + "
g
t (2)
where 0 < ￿g < 1 is the autoregressive coe¢ cient and "
g
t is white noise,
with variance ￿2
g.
42.2 Financial Intermediaries
The ￿nancial intermediaries receive deposits from households and supply
loans to ￿rms at the gross nominal interest rate Il
t. At the end of each period,
deposits and interests are repaid to households. Following Chowdhury et
al.(2006), I consider ￿nancial market imperfections, which are captured by
means of a function ￿(It) that depends on the risk-free interest rate. The
function ￿(It) is de￿ned in the interval (0;1) and can be interpreted as a
measure of the likelihood of defaults on loans.
The pro￿ts are: Il
t[1 ￿ ￿(It)]Zt ￿ ItDt ￿ vZt, where Zt is the supply of
loans and v, a positive parameter, measures managing costs per unit of loans.
The ￿nancial intermediaries maximize pro￿ts subject to the balance sheet
constraint Zt = Dt. The ￿rst order condition in log-linear form implies:
i
l
t = (1 +  )it
where il
t is the bank lending rate and it is the policy risk-free interest rate.
The e⁄ects of changes in it on il
t, captured by  , can be ampli￿ed or
dampened according to the relative importance of ￿nancial market imper-
fections and managing costs. Thus, the model generates varying degrees of
5pass-through from the policy risk-free interest rate to the bank lending rate.
2.3 Firms
Firms in a monopolistic competitive environment produce di⁄erentiated goods
with a linear technology using only labor. The Calvo mechanism describes
price decisions, where ! is the fraction of ￿rms not adjusting their price in a
given period. This parameter measures the degree of price rigidity.
Following Ravenna & Walsh (2006) and Chowdhury et al.(2006), ￿rms
have do pay for their wage bills before the goods market opens. Therefore,
they have to borrow from ￿nancial intermediaries at the gross nominal inter-
est rate Il
t. In log-linear form, real marginal costs are mct = il
t + st, where
il
t and st are the bank lending rate and real unit labor costs in log-deviations
from their steady states.
In the neighborhood of a zero-in￿ ation steady state, the new Keynesian
Phillips curve characterizes in￿ ation dynamics according to the following
expression:
￿t = ￿Et(￿t+1) + k(￿ + ￿)xt + k(1 +  )it + ut (3)
6where k =
(1￿￿!)(1￿!)
! .
A cost-push shock ut is added to the new Keynesian Phillips curve. This
shock follows an autoregressive structure:
ut = ￿uut￿1 + "
u
t (4)
0 < ￿u < 1 is the autoregressive coe¢ cient and "u
t is white noise, with
variance ￿2
u.
3 Optimal Monetary Policy under Discretion
The policy problem is to choose time paths for ￿t, xt and it that minimize
the central bank￿ s loss function, which translates the behavior of macroeco-
nomic aggregates into a welfare measure to evaluate di⁄erent policy choices.
Clarida et al. (1999) and Giannoni & Woodford (2003a, 2003b) discuss more
extensively the design of optimal monetary policies in new Keynesian models.
The policymaker seeks to minimize the objective function
L =
1
2
UcY E
"
1 X
t=0
￿
t(￿￿￿
2
t + ￿xx
2
t)
#
(5)
subject to the constraints imposed by the structural equations (1) to (4).
7The positive weights placed on the stabilization of in￿ ation and the output
gap are ￿￿ and ￿x. The variables Uc and Y are steady state values for the
marginal utility of consumption and output. The product UcY is a scale
parameter which is normalized to one.
Woodford (2003) and Ravenna & Walsh (2006) show that expression (5)
can be interpreted as a second-order approximation to the lifetime utility
function of a representative household. In this case, the endogenous weights
￿￿ and ￿x are given by the following expressions:
￿￿ =
￿
k
(6)
￿x = (￿ + ￿) (7)
The parameter ￿ is the demand elasticity faced by individual ￿rms.
I assume that monetary policy is set under discretion. In practice, mon-
etary authorities do not make any kind of binding commitments concerning
the course of future policy actions. In this context, the central bank can-
not manipulate private expectations, which are taken as given. The optimal
policy is obtained by solving the following sequence of static optimization
8problems:
Min
￿t;xt;it
1
2
[￿￿￿
2
t + ￿xx
2
t] + Ft
subject to
xt = ￿
1
￿
it + ft (8)
and
￿t = k(￿ + ￿)xt + k(1 +  )it + ht (9)
where ft = Et(xt+1) + 1
￿Et(￿t+1) + gt and ht = ￿Et(￿t+1) + ut
The solution of the optimization problem implies:
xt = ￿
k(￿ ￿ ￿ )
￿
￿t (10)
where ￿ = ￿x
￿￿. If the central bank￿ s objective function is endogenous,
then ￿ =
k(￿+￿)
￿ .
The following ￿rst order stochastic di⁄erence equation, obtained from
equations (1),(3), and (10), describes in￿ ation dynamics.
9￿t =
￿2
1 ￿ ￿1
Et(￿t+1) +
k￿(1 +  )
1 ￿ ￿1
gt + ut
where ￿1 = ￿
k2(￿￿￿ )2
￿ and ￿2 = ￿ + (1 +  )k(1 ￿
k￿(￿￿￿ )
￿ ).
To ￿nd an analytical solution, according to the method of undetermined
coe¢ cients, I posit the following decision rule for in￿ ation:
￿t = a1 gt + a2ut (11)
I solve for the unknown coe¢ cients a1and a2 as a function of the structural
parameters. The results are:
a1 =
k￿(1 +  )
1 ￿ ￿1 ￿ ￿g￿2
a2 =
1
1 ￿ ￿1 ￿ ￿u￿2
I ￿nd the paths for xt and it from equations (10) and (1).
104 Results
The parameters are calibrated following Ravenna & Walsh (2006). I set
￿ = 0:99, ￿ = 1:5, ! = 0:75, ￿ = 1, ￿ = 1:2, and   = 0:3. The exogenous
loss function is de￿ned by ￿￿ = 1 and ￿x = 0:25. When the central bank￿ s
objective is to maximize the utility function of the representative household,
￿￿ and ￿x are set according to (6) and (7). The shocks are calibrated ac-
cording to Giannoni & Woodford (2002b). The autoregressive coe¢ cients
are ￿u = ￿g = 0:35. Finally, the variances are ￿2
g = 0:35 and ￿2
u = 0:17.
The parameter   is allowed to vary in the interval [￿1;1]. The lower
bound corresponds to the situation in which the cost channel is absent. The
degree of price rigidity ! is allowed to vary in the interval [0:55;0:85].
Figures 1 and 2 show the e⁄ects of di⁄erent degrees of interest rate pass-
through with exogenous and endogenous loss functions. There is a clear
pattern in the behavior of volatilities as a function of the degree of interest
rate pass-through. The volatility of in￿ ation and the central bank￿ s loss
increase with the degree of pass-through. The volatilities of the output gap
and the interest rate as a function of   do not follow any monotonic pattern,
but their behavior seem to be independent of the way the positive weights
placed on the stabilization of in￿ ation and the output gap are speci￿ed.
11Though the volatilities of macroeconomic variables have di⁄erent magnitudes
according to the loss function in which the optimal policy is based on, these
di⁄erences are small. In addition, the welfare e⁄ects of an increasing degree
of pass-through do not depend on the speci￿cation of the central bank￿ s loss
function. The welfare performance, based on both loss functions, deteriorates
as a function of  .
Figures 3 and 4 show the e⁄ects of di⁄erent degrees of price rigidity with
exogenous and endogenous loss functions. The output gap is less volatile if
the optimal policy is based on the endogenous loss function. The behavior of
the volatility of in￿ ation as a function of ! is very di⁄erent when the policy
is based on di⁄erent speci￿cations for the loss function. If the central bank
designs its policy based on the endogenous loss function, in￿ ation decreases
as ! increases. On the other hand, we do not observe this monotonic behavior
in the equilibrium associated with the exogenous loss function. The output
gap and the interest rate as a function of ! behave in the same way under
both loss functions. The welfare performance, based on both loss functions,
are very di⁄erent. If the central bank￿ s loss function is exogenous, the welfare
measure increases with the degree of price rigidity. In contrast, the welfare
performance, measured by the endogenous loss function, deteriorates as !
12increases. In sum, when the cost channel matters, the welfare consequences
of an increase in price rigidity depend critically on the nature of the loss
function.
The discrepancy between the welfare performances as a function of ! can
be explained by the fact that this parameter a⁄ects the evaluation of the loss
function in two ways. First, the degree of price rigidity has an impact on
the volatilities of in￿ ation and the output gap because ￿ =
k(￿+￿)
￿ . Second,
the weight ￿￿ is an increasing function of !. In fact, the relative weight ￿,
which is constant if the loss function is exogenous, decreases as a function of
! if the loss function is endogenous. Therefore, more weight is attached to
in￿ ation relatively to the output gap as ! increases.
5 Conclusion
This paper considers a new Keynesian model with the cost channel and eval-
uates the supply-side e⁄ects of monetary policy on macroeconomic volatility
and welfare, taking into account the endogenous nature of the objective func-
tion of monetary authorities. Numerical results suggest that the impact of
endogenous objectives on the evaluation of monetary policies is quantitatively
13important, and can change the conclusions about how a structural change in
the economy a⁄ects macroeconomic volatility and welfare measures.
This paper draws two main conclusions. First, macroeconomic volatility
as a function of the pass-through is almost independent of the central bank￿ s
loss function. In contrast, this volatility as a function of the degree of price
rigidity depends more on the nature of the loss function. Second, though
the welfare consequences of an increase in the degree of interest rate pass-
through are independent of how the central bank speci￿es its loss function,
the welfare implications of an increase in price rigidity depend critically on
the nature of the loss function.
14References
Clarida, R., J. Gali and M. Gertler (1999) "The Science of Monetary Policy:
A New Keynesian Perspective" Journal of Economic Literature 37, 1661-
1706.
Chowdhury, I., M. Ho⁄mann, and A. Schabert (2006) "In￿ ation Dynamics
and the Cost Channel of Monetary Transmission" European Economic Re-
view 50, 995-1016
Giannoni, M., and M. Woodford (2003a) "Optimal Interest-Rules I: General
Theory" NBER working paper 9419
Giannoni, M. and M. Woodford (2003b) "Optimal Interest-Rules II: Appli-
cations", NBER working paper 9420
Ravenna, F., and C. Walsh (2006) "Optimal Monetary Policy with the Cost
Channel" Journal of Monetary Economics 53,199-216
Walsh, C. " Endogenous objectives and the evaluation of targeting rules for
monetary policy" Journal of Monetary Economics 52, 889-911
Woodford, M. ( 2003) Interest and Prices: Foundations of a Theory of Mon-
etary Policy, Princeton University Press: Princeton
15Figure 1: Pass-Through E⁄ects with Exogenous Loss
-1 -0.5 0 0.5 1
0
0.1
0.2
0.3
0.4
v
o
l
a
t
i
l
i
t
y
phi
Output Gap
-1 -0.5 0 0.5 1
0.2
0.4
0.6
0.8
1
v
o
l
a
t
i
l
i
t
y
phi
Inflation
-1 -0.5 0 0.5 1
0.9
1
1.1
1.2
1.3
v
o
l
a
t
i
l
i
t
y
phi
Interest Rate
-1 -0.5 0 0.5 1
0.4
0.5
0.6
0.7
L
o
s
s
phi
Loss Function
16Figure 2: Pass-Through E⁄ects with Endogenous Loss
-1 -0.5 0 0.5 1
0
0.1
0.2
0.3
0.4
v
o
l
a
t
i
l
i
t
y
phi
Output Gap
-1 -0.5 0 0.5 1
0.2
0.4
0.6
0.8
1
v
o
l
a
t
i
l
i
t
y
phi
Inflation
-1 -0.5 0 0.5 1
0.8
1
1.2
1.4
1.6
v
o
l
a
t
i
l
i
t
y
phi
Interest Rate
-1 -0.5 0 0.5 1
4
6
8
10
L
o
s
s
phi
Loss Function
17Figure 3: Price Rigidity E⁄ects with Exogenous Loss
0.6 0.7 0.8
0
0.1
0.2
0.3
0.4
v
o
l
a
t
i
l
i
t
y
omega
Output Gap
0.6 0.7 0.8
0.45
0.5
0.55
0.6
0.65
v
o
l
a
t
i
l
i
t
y
omega
Inflation
0.6 0.7 0.8
1
1.5
2
2.5
3
v
o
l
a
t
i
l
i
t
y
omega
Interest Rate
0.6 0.7 0.8
0.45
0.5
0.55
0.6
0.65
L
o
s
s
omega
Loss Function
18Figure 4: Price Rigidity E⁄ects with Endogenous Loss
0.6 0.7 0.8
0.02
0.04
0.06
0.08
v
o
l
a
t
i
l
i
t
y
omega
Output Gap
0.6 0.7 0.8
0
0.5
1
1.5
v
o
l
a
t
i
l
i
t
y
omega
Inflation
0.6 0.7 0.8
1
1.5
2
2.5
v
o
l
a
t
i
l
i
t
y
omega
Interest Rate
0.6 0.7 0.8
0
10
20
30
L
o
s
s
omega
Loss Function
19

Supply-side effects of monetary policy and the central bank’s objective function

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Supply-side effects of monetary policy and the central bank’s objective function

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