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THREE ESSAYS ON BUSINESS CYCLE AND MONETARY POLICY

B \

Yongjae C hoi

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

2006

ABSTRACT

THREE ESSAYS ON BUSINESS CYCLE AND MONETARY POLICY

BV

v.

Yongjae Choi

It is well known that monetary policy can have different consequences across
sectors. However, the recent discussion about optimal monetary policy has often
ignored the sectoral impacts of monetary policy actions since aggregate inflation and
output are thought to be main policy concerns. The first chapter demonstrates that
if people care only about their own sector or industry. monetary policy makers should
pay attention to the stabilization of sectoral inflations and output gaps rather than
aggregated variables. T 0 address the issue. we construct a dynamic stochastic general
equilibrium model with sticky prices and two sectors: durable and nondurable goods.
Simulation results show that while following optimal policy rules to target aggregated
variables results in poor outcomes under discretion, optimal policy rules designed to
target disaggregated variables. such as strict output gap targeting and durable goods
sector targeting, yield results close to the optimal preconnnitment equilibrium.

The second chapter investigates the role of durability of goods to generate the
substantial effect of money on output and inflation. Following the strand of New-
Keynesian research, price stickiness is introduced into a two sector model so that a
monetary Shock has a non- negligible real effect. We show that durability can change
output and inflation dynamics in important ways. This effect happens through two
channels: consumer’s intratemporal consumption decision over two goods: durable
and nondurable, and firm’s backward-looking price setting decision due to durability
of goods. Simulation results show that even though durability can account for the
inertia in inflation and persistence in output together, it. can help to more convincingly
explain inertia in inflation.

The third chapter estimates N ew—Ix'eynesian structural model and evaluates alter-

native monetary policy regimes. Estimated two sector model and alternative policy

regimes are used to calculate the optimal monetary policy frontier. The structural
model that consists of two sectors: durable and nondurable, is estimated by the Full
Information Maximum Likelihood (FIML). Given the structure of the economy and
discretionary monetary policy regimes, we find that changes in monetary policy re-
sponses to aggregate or disaggregate inflation and output gap can imply substantial
differences in long-run inflation and output variances. More importantly, this chapter
shows that in terms of monetary policy frontier, monetary policy could have been
more effective if the central bank had focused on sectoral stabilization as opposed to

traditional stabilization.

To My Parents

iv

ACKNOWLEDGEMENTS

I would like to thank first. of all my advisor, Rowena Pecchenino for her suggestions
and encouragements. I am slao in debt with my other committee members, Raoul
Minetti, Luis Araujo, and Long Chen for helpful comments and suggestions.

Throughout all the hours of Ph.D program, my parents encouraged me with love
and belief. This dissertation is just the fruits of their love and commitment. I also

would like to thank Kyongl‘iwa Jeong for her invaluable advice and friendship.

Contents

LIST OF TABLES
LIST OF FIGURES

1 Optimal Monetary Policy in Two Sector Model

1.1 Introduction ................................
1.2 The Model .................................
1.2.1 Households ............................
1.2.2 Firms ...............................
1.3 Optimal Monetary Policy .‘ .v i ......................
1.3.1 Policy Objective Function ....................
1.3.2 Configuration of the model ....................
1.3.3 Calibration and Results .....................
1.4 Optimal Policy Design ..........................

1.5 The Role of Durability and Relative Price Stickiness .

1.6 Conclusion .................................

2 Two Sector Business Cycle:

Durable and Nondurable Goods

2.1 Introduction ................................

2.2 The Model .................................
2.2.1 Households ............................
2.2.2 Firms ...............................

2.3 IVIulti-Periods Case ............................

vi

viii

ix

10
13
15
16
17
29
32
35

37
37
39

2.3.1 Three Periods Case . . .

ooooooooooooooooooooo

2.3.2 Aggregate Demand and Supply Equation ............
2.3.3 N-Period Case ...........................
2.4 Simulation .................................
2.4.1 Stylized Facts ...........................
2.4.2 Monetary Policy .........................
2.4.3 Main Results ...........................
2.4.4 Sensitivity Analysis ........................
2.5 Conclusion .................................

3 Econometric Policy Evaluation in Two Sector Model

3.1 Introduction ................................
3.2 The Structural Model ...........................
3.3 Data and Preliminary Estimation ....................
3.4 Discretionary Policy and Loss Function .................
3.5 Estimation and Optimal Policy Frontier ................

3.5.1 Parameter Estimates .......................

3.5.2 Optimal Policy Frontier

3.5.3 Sensitivity Analysis . . .

3.6 Conclusion ............

A Appendix

Bibliography

vii

46
47
48
50
50

57
62

64
64
66
68
72
74
74
76
79
82

84

87

List of Tables

1.1
1.2
1.3
1.4
1.5
1.6
1.7

3.1
3.2
3.3
3.4

Baseline Parameters ........................... 19
Outcomes in the Case of a Cost Shock ................. 24
Outcomes in the Case of Aggregate Demand Shocks .......... 26
Outcomes in the Case of Alternative Objective Function ....... 28
Outcomes of Alternative Delegations Schemes and Optimal Taylor Rule 31

The Welfare Loss (104) of the Change of Durability (6) ........ 33

The Welfare Loss (104) of the Change of Relative Price Stickiness

(an, ad) .................................. 34
Estimation Results of the Intertemporal IS Equation ......... 69
Estimation Results of the Phillips Curve ................ 71
Estimation Results of the Reaction Function .............. 72
Results of FIML Estimation ....................... 75

viii

List of Figures

1.1
1.2
1.3
1.4

2.1
2.2
2.3
2.4
2.5

3.1
3.2
3.3
3.4

The Real GDP, the Inflation Rate and the Federal Funds Rate . . . . 3
The Impulse Responses of Sectoral Output Gaps ............ 20
The Impulse Responses of Inflations ................... 23
The Impulse Responses of Relative Prices ................ 24
The Impulse Responses of Output Gaps and Inflations ........ 55
The Impulse Responses of Output Gaps with New Monetary Policy Rule 58

The Impulse Responses of Inflations with New Monetary Policy Rule 59

The Impulse Responses to Change of Depreciation Rate (6) ...... 60
The Impulse Responses to Change of Relative Price Stickiness (a) . . 61
Optimal Policy Frontier ......................... 77
Optimal Policy Frontier(DCT) ...................... 79
Sensitivity Analysis of Policy Frontier .................. 80
Sensitivity Analysis of Policy Frontier .................. 81

ix

Chapter 1

Optimal Monetary Policy in Two
Sector Model

1 . 1 Introduction

It is well known that monetary policy can have different consequences across
sectors. Housing, consumer durables, and agriculture are often cited as examples of
sectors that are sensitive to the change of monetary policy.1

However, in academic literature as well as practice, the diflerent impacts of mon-
etary policy on sectors are sometimes ignored under the assumption that society
and the central bank have an interest only in aggregated variables such as inflation
and output? The following episode illustrates the case that a part of the economy

can be influenced severely by the monetary policy which was implemented based on

aggregated variables in late 70’s and early 80’s.

“Construction workers protesting soaring interest rates on mortgages and
construction loans jammed downtown streets here at noontime yesterday
with hundreds of pieces of construction equipment. Pickup trucks, cement
mixers, backhoes and flatbed trucks carrying bulldozers were part of the
protest procession. ------ Jack Scelza, president of the Home Builders

 

lFor surveys of literature on the sectoral impacts of monetary policy actions, see Mann (1969)
and Bordo (1980).

2In recent years, New Keynesian models have been increasingly popular for optimal monetary
policy analysis. These models have focused on the central bank’s objective to target aggregated vari-
ables. See, for example, Clarida, Call and Gertler (1999), Goodfriend and King (1997), McCallum
and Nelson (1999), Svensson (1997. 1999, 2002), and \Noodford (1999. 2003).

Association of Hartford County, CT, said that housing construction had
dropped from 23,500 units a year before the 1974 recession to 14,000 units
annually through 1979.”(New York T imes, Apr 10, 1980)

This episode tells us that even though overall stabilization policy could be suc-
cessful, sectoral impacts may be considerable, so that monetary policy makers should
consider sectoral responses and stabilization. It also shows us that agents may care
about their own sector’s stabilization rather than the aggregated one.

Therefore, one important issue to be addressed is whether it is an appropriate
policy goal for the central bank to seek to stabilize only aggregated variables, if
people care about the stabilization of their own sector or industry. The purpose of this
paper is to answer this question. Specifically, this paper examines the characteristics
of desirable monetary policy within a two sector model with durable and nondurable
goods sectors.

The reason for considering this issue in the context of durable and nondurable
goods sectors is that these two sectors seem to show considerably different responses
to monetary policy actions. Figure 1.1 plots the (log) real GDP (RGDP), its com-
ponents: durable and nondurable goods, the rate of GDP deflater inflation (INF)
and the Federal Funds rate (F F R).3 The graph shows that ex post real interest rate
is associated with excess volatility of durable goods’ output during early 70’s and
80’s. In other words, this historical data shows that two sectors respond differently
to monetary policy action, which is implemented by the change of the Federal Funds
rate, and durable goods sector could be influenced more severely. This stylized fact
also has been confirmed by related studies (Mankiw (1985), Baxter (1996), Weder
(1998))

We also investigate whether the main principles obtained in one good models, such
as the “stabilization bias” under pure discretion, still hold in the two goods model.
This paper will show that basic principles still hold regardless of the nature of shocks,
i.e., whether it is a cost shock or sector specific.

In addition, when a central bank’s objective is to minimize deviations of the

 

3The data runs from 19542Q3 to 2004zQ4 and all GDP series are detrended by HP filter.

20

 

   
    
     

 

 

 

 

 

 

 

 

 

—— INF —————— FFR
15 s
:11 i".
10 4 xi“ "' I i f".
"i ‘|' ". {“\
5 -‘ 1
o [ITT‘TIIITII'1'IITTIEIIITIIII'Vl'Ir‘I'TTrlI'I'ITTEI
55 60 65 70 75 80 85 90 95 00
0.15
0.10 a
0.05 -—
/\ t, I
0.00 _."~,".y,._i, ‘,"— x “.7; / 4’ Ll
I, I ‘ \JI’ " V
I
-0.05 _
-0.10 -
—— DURABLE ------- NONDURABLE ————— HGDP
-0.15 [I'VEIIIEUIUEIUlt't'l‘iTT'l'T'lI‘IIUIII'IIrWIEIT'I'

 

 

55 60 65 70 75 80 85 90 95

Figure 1.1: The Real GDP, the Inflation Rate and the Federal Funds Rate

disaggregated variables from their targets, rather than that of aggregated variables,
this paper will argue that, under some circumstances, a central bank should not seek
to target the aggregate output gap and inflation, but disaggregated variables.

This result leads to the question of what kind of monetary policy rule performs
well in the two goods model considered. Simulation results illustrate that it could be
optimal to target disaggregated variables.4 Specifically, we consider the strict output
gap targeting in which the central bank targets only sectoral output gaps, and durable
goods sector targeting in which the central bank targets durable goods’ output gap
and inflation only. Finally, we examine the implications of optimal monetary policy
when durability and relative price stickiness change.

To address above issues, we construct a dynamic stochastic general equilibrium
model with two sectors; durable and nondurable. The model used in this paper is the
simplified version of Erceg and Levin (2001). W hile they assume that price as well
as nominal wage are sticky, we just assume that only price is sticky. Furthermore
they incorporate Taylor(1979) style’s staggered price and nominal wage setting into
their model while we introduce Calvo (1983) style’s staggered price setting into the
model. They concluded that targeting a weighted average of aggregate wage and price
inflation rate is close to the optimal policy outcome. But in this paper we will argue
that under discretionary policy, the central bank can obtain benefit from targeting
disaggregate inflations and output gaps.

The remainder of the paper is organized as follows. In section 1.2 we present the
basic two sector model, where aggregate demand and supply relations are derived.
Section 1.3 presents the method and basic results of simulation. Section 1.4 con-
siders the optimal policy rules, where social welfare loss is minimized. Section 1.5
presents the implications of optimal monetary policy when durability and relative

price stickiness change. Section 1.6 concludes.

 

4As to similar approaches, see, for example. Aoki (2001) and Erceg and Levin (2001).

1 .2 The Model

1.2. 1 Households

There is a continuum of infinitely—lived individuals, whose total is normalized to
unity, and are two different types of goods: nondurable and durable goods. Consumers
obtain utility from both nondurable and durable goods. We denote a typical durable
good as d and a typical nondurable good as n. The representative household is
assumed to have preferences over nondurable goods consumption (Cmt), the service
flow from the durable good stock (St), real money balances (gin), and leisure (It). A

specific functional form for expected utility is assumed

 

 

00 1—1/

1 I A! I

t ,1 I— .- t ,

Et 2 l3 1_ 001’1,tCt a + 1_ Vt’zi (—Pt) + avatlifi] , (1-1)
t=0 '

where Ct is the household’s consumption of a composite consumption good, Alt are
the household’s nominal money balances, Pt is the aggregate price index, It is the
household’s leisure, x3 is the subjective utility discount factor, 21; is the elasticity
of intertemporal substitution of the consumption bundle, 1/ is the elasticity of real
money demand, % is the elasticity of marginal disutility of labor supply, and 09’s are
disturbances.

We normalize total available time for work effort (at) and leisure (It) to one. Then
labor supply of the households is given by nt 2 1 — It. The composite consumption
good Ct is defined as

C, a 07

n,t

83—7, 0 < 7<1, (1.2)

where Cn,t denotes the purchase of nondurable goods and St is the service flow of

durable stock. The stock of durable consumption goods evolves as follows
St+1=(1— (5)5} + Cd.t- 0 < 6 S 1, SO = given, (1.3)

where Cdt is the purchase of durable goods in period t, and (5 represents the rate of

depreciation. There is a positive initial endowment of the durable stock SO. Equation

(1.3) implies that durable goods begin to yield a service flow in the period after the
durable good is purchased. Alternatively, we can assume that installation of the
durable goods requires one period for stocks.5 CM and Cd.t are assumed as Dixit-

Stiglitz aggregates of differentiated products as follows

0
0n _ H“
1 612—1 ”—1 1 2%} d—l
Cn,t: ‘/Ocn,t(3) n (12 7 Cult: /Ocd.t(5) d dz , (14)

where Q, for j = n, d is the elasticity of substitution between any different varieties of
the differentiated goods. It is also the price elasticity of demand for any single variety
of the differentiated goods. It follows from the above specification of preferences that
the minimum cost of obtaining a unit of the sectoral composite goods (Cmt and Cd,t)

is given by the sectoral price index

I
1 1-9,- 1‘9) .
Pjt E /0 ])j_t(:) J for j = n,d, (1.5)
where pj,t(z) is the price of good .2 in period t and sector 3'. Given the relative size
9 of the nondurable goods sector, the aggregate price index or the general price level
Pt is defined as

1—
Pt = Prf.th,t 9, O < 9 <1, (1.6)

The optimal allocation of demand across the various differentiated goods by con-

sumers satisfies

 

.0 (*l 45
cj’t(z) = ( 11ft ) Cj,t forj 2: n,d, (1.7)
.79

for each good 2 in sector j . The household’s nominal budget constraint in period t is

 

5This setting of durable goods is in parallel with the literature on investment decision. In contrast,
Obstfeld and Rogoff (1996), Startz (1989), and Barsky. House and Kimball (2004) assume that
durable goods provide service flow in the same period they are purchased.

as follows

Pn,tCn,t+Pd,t (St+1 — (I — d)St)+rWt-l-Bt=I'tht+ilft_1+Et+Rt_1Bt_1+TRt,

(1.8)
where PM and Pd,t denote the price index of nondurable goods and durable goods
respectively, hit is nominal money holding for next period, Bt is nominal bond hold-
ing for next period, Wt is nominal wage, St is profit, Rt—l is nominal interest rate
and is assumed to be the central bank’s interest rate instrument, and TRt is gov-
ernment transfer. we assume that complete financial markets exist in the economy.
Households are, therefore, able to insure themselves against all types of uncertainty
in the model. It follows from this assumption that all households will consume same
amounts of the composite consumption goods. Finally, we assume that all distur-

bances follow stationary AR(1) processes
a)“ = Pj'i'f’jJ—l + fig. 0 S pj < 1, tirjfig 2 given for j = 1, 2,3, (1.9)

where innovations {’s have zero means and standard deviations oj for j = 1, 2, 3.

In every period t, each household maximizes its expected lifetime utility, with
respect to its choice of nondurable consumption (Crag), durable stock (St), real money
balances (AI/1%), bonds (Bt), and its labor supply (at), subject to its budget constraint
which is denominated by the general price level (Pt). The first order conditions for

each choice variable are given by

 

_ P.
71,01,403,th H77) C7 13,1 7 = A, ""t (1.10)

1-0
5(1’7)Et‘r’1 t+1 (Cu t+ISt+1)—a Cu. t+1St+1

 

Pd,t Pd t+1
/\t— Et [3(1 —5)/\i 1 ’ , U“)
P + Pt+1

 

. _ , P

Pt .
,thEtAt+1'1—j_ 2 At, (1.13)
t+1
023’t'nt‘ = At?t, (1.14)

where At is “Lagrangian multiplier”, the marginal utility of nominal income in period
t, 2;; is relative price of sector j denominated by the aggregate price index Pt, mt
is real money balances 6%) and Et is the expectations operator conditional upon
all information up to period t. Equation (1.10) states the efficiency condition of
nondurable goods consumption. Equation (1.11) is the efliciency condition of durable
goods services. This intertemporal Euler equation emphasizes that the purchase of
a durable good is partly an investment. The equations (1.12), (1.13) and (1.14)
show the optimal conditions for money demand, bonds and labor supply respectively.

Combining the three Euler equations (1.10), (1.11), and ( 1.13) into one eliminating

Cn,t+1

 

E Lt. (1.15)

 

 

 

,/ _’l’
E livl’2,tSt+1 Pt Pn.t+l _Pd,t (1-5) t[,/, BAH-1]
,/ 7t

t , _ _ _
Mac"; Pt+1 Pn.t Pt Rt Pt+1

The variable Lt is defined as the period t rental price, or user cost, of the durable
good. Equation (1.15) states that the marginal rate of substitution of nondurables
consumption for the service of durables equals the user cost of durables in terms of
nondurables consumption.

The above equations represent a quite complicated system of stochastic nonlinear
difference equations. Therefore, we will loglinearize the above equations around the
steady state with zero sectoral inflations and the efficient level, 109097;) for j=n,d, of
output gaps. By using a log-linear approximation and steady state conditions with
flexible prices, we can derive intertemporal IS equations in both sectors from the

above first order conditions. First, the intertemporal IS equation in the nondurable

sector is derived from a log—linear approximation of Euler equations, (1.10) and ( 1.13),

and from nondurable goods market clearing condition, Yn,t = Cn,t as follows

A A A

(—07 + 1- 1)Yn.t - (-07+ 7 -1)(1- 5)Yn,t—1 + 5(1- 0)(1- ant—1

= (Rt—fin,t+1)—(1—5)(Rt—1—7in,t)—(00’ - 7 +1)Et [Yn,t+1-(1— AWN]

+5(1- 0)(1- ’7')Yd,t - (1 - mil/711+ (1 - p1)(1- 5)’¢’1,t—1v (1-16)

or alternatively

 

 

 

. 1 .
Aymt = _07 + "7' _ lEtaiRt — 7rn,t+1) + EtAYn’t+l
5(1-0)(1-*r) [ . (1-P1) ,
Y — Y J — A , 1.17
+ _0,,, + , _1 d..t d,t—1 -07 + 7 _1 Wu ( )

where X t represents the percent deviation of variable X from its steady state value
under flexible prices. The A denotes quasi-difference Xt — (1 — 6)Xt_1. The sectoral

Pn,t

inflation of nondurable goods sector, any, is defined as The coefficient

n,t—
$717717 < 0 is related to the rate of intertemporal substitution determining to what
extent changes in the real interest rate in terms of nondurable goods, Rt — Et7Tn,t+1a
affect spending growth of consumption.

Likewise, using the law of motion of durable stock (1.3), the first order condition

for durable stock (1.11) and durable goods’ market clearing condition, Yd,t = Cd,t1

we can derive an intertemporal IS equation in the durable goods sector as follows

1
1430—5)

 

Watt = Et AYn,t+1— A(Pt—7Td,t+1)—AP1~,t+1 , (118)

where 15731 is defined as the percent deviation of relative price index (figfi) from its
steady state value. The above two equations, (1.17) and (1.18), represent the ag-
gregate spending relationship, corresponding to a traditional IS equation. Equation
(1.17) represents quasi-difference aggregate demand in the nondurable sector depend-

ing on its own expected future and current output, lagged and ex ante real interest

rate. durable goods’ current and lagged output, and taste shock. Equation (1.18) is

the aggregate demand of durable goods sector. The aggregate demand for durable
goods depends on the future and current period’s relative price, its own real interest
rate (Rt — Etrrd’t +1), and nondurable goods’ output. The reason is that, by defini-
tion, the current purchases of durable goods are determined by the difference between
future and current period’s durable stock (see eq. (1.3)). In general, the standard
results are confirmed in the sense that each sector’s aggregate output depends neg-
atively on real interest rate (Rt — jat) for j=n,d, and positively on the one period
ahead expected future output in the nondurable goods sector. As a special case, note
that if we assume that all goods are totally depreciated in one period, i.e., 6 = 1, the

two equations collapse to the traditional two sector intertemporal IS equations.

1.2.2 Firms

We assun'ie differentiated goods and monopolistic competition in both final goods
markets. The firms use only one variable input: labor. This implies that durable
goods are used only in consumption. Labor is assumed to be homogeneous in both
sectors and there is no restriction for mobility across sectors. The production tech-

nologies are the same in both sectors and operate under a linear technology as follows

flitizl = 1(14j,tnt for j = 71,01. (1.19)

where 2 represents an individual good producer and Iii/'4,t represents technology shock.

The technology shock is assumed to follow a stationary AR(1) process

194$ = P4'1()4,t—1 + £21, 0 S 04 < 1» 204,0 = given: (120)

where the innovation {3 has a zero mean and standard deviation (754.

However, as Blanchard and Kiyotaki (1987) indicate, imperfect competition alone
does not generate monetary nonneuturality. For a model to lead to real effects of
money, we need to assume the sticky price adjustment. As an essential part of the

model, pricing decisions are assumed to be sticky. Specifically, we follow the Calvo-

10

style staggered price setting rule in assuming that in each period a fraction 1 — aj for
j: n, d of producers in each sector is offered the opportunity to choose a new price,
independent of the length of time since the price was set and of what the particular
good’s current price may be, while the remaining producers have to maintain whatever
price they charged before. The representative firm’s profit maximization problem is

as follows

 

 

_g —0
00 p. (z) W {P- (Z)
Marc E, as) A,, ,,. P.-,,(z) 3’, k— , Y't k 1
Q J ’ + J’ P j,t+k 3’ + it’4,t+k\ P j,t+k 3’ +

(1.21)
where (aj-B)k/\t,t+k represents a stochastic discount factor. A, is marginal utility of
income as we defined in the previous section. The left hand side of the bracket repre—
sents the revenue that satisfies the demand condition. Since both goods markets are
operated under monopolistic cognpetition, an individual firm producing the product 2
faces the demand, (git—:3) _ JYJ-J +1; for j = n, (1.6 The right hand side represents

the nominal cost. The first order condition to maximize profit can be written as

 

00 , p;,<z) “9
Et 2(a)” Atat+k(Pi ) Yj,t+k .

j,t+k

 

 

 

 

k=0
*
p- (Z) 6' W P - 1
j.t+k j—l t+k j,t+k P4,t+k ’
10”? (z)

7

According to the above condition, each firm sets its real price, #5517, equal to a
.7

9 .
markup #(E y—é—l) over its real marginal cost. This is the standard result in a model
J
of monopolistic competition and sticky price adjustment. Because the adjusting firms
were selected randomly from among all firms in period t-I, the average sectoral price

index (Pj,t) in period t satisfies

1—9 *1—0-

Pit-6 = “Jpn—f + (1 “ Gill)” J f0” = "’d' (1’23)

 

6This demand equation is derived from the optimal allocation of demand across the various
differentiated goods (eq. (1.6)) and goods market clearing condition, Y1, = C1,, for j z n. d.

11

Since we consider a symmetric equilibrium, the fraction 1 — aj of suppliers that set
a new price for their goods in period t has the same optimal price Pit. The other
fraction aj has the same price charged in period t-1, that is, Pj,t—1-

The above two equations, (1.22) and (1.23), can be used to obtain New-Keynesian
Phillips curve. Let us define sectoral output gap 33j,t as 17]}, — 193-7; for jzn, d. The
variable Y}; is defined as the “natural” rate of output (i.e., an output deviation from
steady state that would prevail in the absence of any price rigidities). Likewise, P113, is
defined as relative price under no price rigidities. By using a log-linear approximation
and the definition of each sector’s average price index, we can derive the aggregate

supply equation or New-Keynesian Phillips curve for each sector as follows

7rn,t = ‘171 (Pm —Y1il,t) + ‘1’2Et (Yn,t+1 _erl,t+1) + (1)3 (Yd,t —Yrii,t)

+‘174Et (Pr,t+1 “Pff't+1) + (1’5 (PM —Pfft) +13Etiin.t+1 (1-24)

A A

”(Lt = ‘1’1 (Yet — Yciit) + ‘1’2 (an — Yrilt) + ‘1’3Et (Yn.t+1 — anit+1)

+‘1’4(Pr,t — P5331) + ‘1’5Et(Pr.t+1 — 152,“) + (3Et77d,t+1, (125)

where (D’s and \Il’s are functions of structural parameters.7

The above two equations describe dynamics of sectoral inflations in both
sectors. W’hile sectoral inflations depend on their own current output gaps and future
inflations like traditional New-Keynesian Phillips curve, they also are determined by
current and future expected relative price gap and future expected nondurable goods’
output gap as well. Note that from (1.15) we can see that the future expected relative
price affects the user cost of durable goods negatively. This change of user cost causes
a perturbation of future marginal rate of substitution between two goods.8 Finally,

when suppliers have to choose a new price in period t, above factors become other

 

7For detailed derivation, see Appendix A.

8Note that in our model, we regard the durable goods as a kind of investment good or financial
asset. rather than just consumption goods, and assume that the installation of the durable goods
requires one period after they are purchased. Therefore, the purchase decision of the durable goods
depends on expected future marginal rate of substitution rather than the current one.

12

determinants with expected future real marginal cost.

These equations are different from the conventional N ew-Keynesian Phillips curve
in two ways. First, when price stickiness is not the same across sectors, relative price
fluctuations become another transmission mechanism, which does not exist in the
one good model. In the face of an unexpected monetary shock and change of relative
prices, households and firms will adjust their behavior. In fact, the pressure of relative
prices reduces the inflationary effect in that sector because of substitution between
two goods. Second, durability might generate non negligible endogenous dynamics
for sectoral inflations. Since durability introduces time non-separability in the utility

function into the model, we can see substantial persistence of variables in the model.

1.3 Optimal Monetary Policy

In this section, we study the optimal response of the endogenous variables,
7Tj,t233j,te and Pry, for j = n,d, to various disturbances. In other words, the pur-
pose of this section is simply to characterize the optimal path of the endogenous
variables that achieves the lowest possible value of the central bank’s loss function,
which is discussed below. Specifically, after defining the appropriate monetary policy
objective, given the structural equations derived in the previous section, we obtain
the optimal precommitment and discretionary equilibrium. Then we compare wel-
fare loss defined by a policy objective loss function, and investigate implications of
each policy regime for stabilization. In the next section, we will discuss the optimal
monetary policy design problem.

To do this we begin with fundamental structural equations, that is, intertemporal
IS equations and New-Keynesian Phillips curves. For convenience, we rewrite these

equations as follows

 

 

. 1 ..
Axn’t Z —0")/ + 7 _ 1A(Rt _. 71fn’et'+_1)m+— EtAIn,t+1
5(1— 0)(1- 1')
+ ”0,, + ’r __1 (Ida Id,t 1) Um, ( )

13

1

1—15(1—6)A(R‘—"d,t+1)_APr,t+l +“d,tv (1-27)

didl = Et Ain7t+1—

where $j.t is output gap for sector j, defined as output relative to the equilibrium

level of output under flexible prices (E 17",, — Y”

n t), A denotes the quasi-difference,

for example, Ar, :2 art — (1 -— 6);rt_1. The disturbance in nondurable goods sector
“mt is defined as EtAf/n’h - A1973, —— fiehAwu + gt.9 Note that we include
an additional shock g, to the equation to capture anything else that might affect
aggregate demand of nondurable goods. For example, that could arise from exoge—
nous government spending. Likewise, the disturbance in durable goods sector ud,t
is defined as EtAi/n’t+1 — EtPQt +1 + 9,. We assume both demand shocks follow

stationary AR(1) processes
it}, = p,u‘j'llj,t-1 +551? 0 S pm]: < 1, uj,0 =2 given, for j = n,d, (1.28)

where {g is an innovation in sector j with a zero mean and standard deviation 021,3“

The below two equations represent sectoral New-Keynesian Phillips curves

“ " ‘ ‘ ‘ ‘ d
7Tn,t = 1’1 (Km “-13:20 + ‘1’2Et (Yn,t+1 “19?,”1) + (1’3 (Yd,t _Yn,t)

+¢4Et (Pr,t+1—P;ft+1) + ‘1’5 (Pat—Pym) +i9’Et7Tn,t+1+€n.t (129)

A A

m, = 111, (17,, — Ydfft) + 1112 (rm, — 11:7,) + 01313, (13,,“ — 17,17, +1)

was, — 15:3,) + ‘1’5Et(Pr,t+1 — Pitt+11+ flEth¢+1 + 6d,, (1.30)

where (D’s and ‘11’s are functions of parameters. The exogenous shock 8]", for jzn, d

is a cost shock. It is assumed that both cost shocks follow stationary AR(1) processes

Pj,t = Pe,ij,t—1+€g,ti 0 S Pe,j < 1, (DJ-.0 2 given. forj = -n.,d._ (1.31)

 

9In the literature, this demand shock is often called the “natural” rate of real interest rate:
the real interest rate which would result in if all prices were flexible. See, for example, Amato et
al..(2001) and VVoodford (1999, 2003).

14

where {it is an innovation in sector j with a mean zero and standard deviation 0e,j-
This makes it possible for the model to capture the variation in inflation independent
of output gap. But note that this addition of the cost shock is different from the
functional form we derived from previous section.

There are two approaches that deal with the cost shock in literature. One is
derived from the distortion assumed within given a model. For example, it could come
from time-varying taxes (Steinsson 2002, Fuhrer 2001) or from markups (Woodford
2003). The other is that it is merely added to the model to represent anything else that
might affect the output gap (McCallum and Nelson 2004, Jensen 2002, and Clarida
et al., 1999). According to Clarida et al., (1999), the cost shock is interpreted as
reflecting deviations from the relationship between the output gap and real marginal
cost. In this paper, we follow the latter approach, so that the cost shock is added to

the structural model.

1.3.1 Policy Objective Function

Given the specification of the economic environment, we have to assume what the
appropriate objectives of the central bank are. Since Barro and Gordon (1983), it is
common to assume that a central bank is concerned with minimizing a quadratic loss
function that depends on output (or output gap) and inflation.10 However, since we
consider two different sectors, it is assumed that the central bank’s objective function
has sectoral output gaps and inflations as arguments. This approach is consistent
with that of Blinder and Mankiw (1984), Waller (1992), Duca and VanHoose (1990),

even though they did not consider inflation as an argument.11 As a baseline case,

 

10Rotemberg and Woodford (1997) and Woodford (2003) showed that such a loss function is
consistent with individual optimality in terms of consumer’s preferences under certain circumstances.
However, according to Clarida, Gali, and Gertler (1999), the approach could be problematic under
some situations. Thus in this paper, we follow the traditional approach used since Barro (1976).

11We will examine the policy implication in next section, as the central bank’s objective function
depends on aggregated variables.

15

the central bank’s objective function is assumed to be of the form:

00
1 .
Min 5(1—13)E, 2 : [3%, , (1.32)
120
_ 2 2 , 2 _ 2
Lt - 7Tn,t+i + 7rd,t+i + I'ln‘f'n,t+i + I’ld‘rd,t+i’ (1'33)

where the parameter #j is the relative weight on output deviations in sector j, 3 is
the subjective discount factor, which is the same as one used in structural equations.
This objective function assumes that target inflations and output gaps in both sectors

are ZBI‘O.

1.3.2 Configuration of the model

As a benchmark case, consider where policy can be conducted as if the monetary
authority at t = 0 preconunits to a policy plan for all remaining periods. The analysis
of optimal responses to shocks under commitment is simply a stochastic constrained
optimization problem. To derive the solution, first we can write the structural equa-

tions (1.26) to (1.31) as a state-space form as follows

X X
1,t =A 1,t +BR,+ Ct+1 ,

EtX2,t X2,t 0
where X13, and X23, are predetermined and forward-looking variables respectively,
B, is the policy instrument, and C is innovation of shocks. Define Zt E [X 1,1 Xi”,
as the column vector of predetermined (X 19,) and forward-looking (th) variables,

with

I
X1,t = inns» “dab emu 6,1,1» Rt—l» $n,t—1i Pr,t—1l

I
X2t = [In’t. Td‘t. “Tut. ”(l9t, Pr’t] .
Then the system can be written compactly as
EtZt+1=AZt+BRt+€t, (1.34)

16

where A, B and g are defined with proper dimension. The policy instrument Rt, that

is, the nominal interest rate is set to minimize an objective function expressed as
1 oo
(1 — 015E, Z Mica. (1.35)
t=0

where Q depends on the specification of the single period loss function under the
policy regime. Then we can form the Lagrangian from equations (1.32), (1.33), and

(1.34) as follows

00
L0 = E0 2 at [2,QZ, + p4,, (AZ, + BR, + g, — Z,+1)], (1.36)

t=0
where X10 is given and Pt+1 are Lagrangian multipliers. This constrained opti-
mization problem is solved in Backus and Driffill (1986), Currie and Levine (1993),
and deerlind (1999). In this study, we solve the problem by following Soderlind’s

approach.

1.3.3 Calibration and Results

The purpose of this subsection is to specify values for the model’s parameters,
find the rational expectation solutions described above, and report the volatility of en-
dogenous variables and losses under alternative policy regimes (Precommitment and
Pure Discretion). The model is interpreted in annual terms. As Jensen (2002) indi-
cates, the choice of baseline parameters is not an easy task, as the literature contains
strongly conflicting views on many of these. Therefore in this study “compromise
values” are used.

Concerning the parameters that determine real interest sensitivity of aggregate
demands, i.e., 1/0 and 1/7, estimates on quarterly data range from very high values
(Rotemberg and Woodford 1998, report a value above 6) to very low ones (Barsky,
House, and Kimball 2004, report a value of 0.2). As a compromised value, we set a

and 7 to 1.5 and 0.8 respectively, and the annual depreciation rate (6) to 10%. The

17

subjective discount factor ([3) is 0.96.12 The disutility parameter of labor supply 05
is set to 2.47 following Rotemberg and Woodford (1998). The share parameter Q of
goods is 0.8 which means nondurable goods takes account for 80 percent out of total
output.

With respect to the aggregate supply equations ( 1.29) and (1.30), the price markup
parameter, 0 -, is assumed to be same across sectors and is set to 7.88 (03351- : 1.15),
which means that an average markup in the goods market is 15%.13 One of the
most controversial parameterizations is concerned with the degree of price stickiness
(in our parameterizations, an and ad). For example, Gali and Gertler (2000), and
Rotemberg and Woodford (1997), report that the price stickiness amounts from three
to eight quarters, while Bils and Klenow’s (2004) micro data study shows that the
median duration of prices is 4.3 months. In addition, Kashyap (1995) found the
frequency of price adjustment is about 14.7 months. Since his data obtained from
retail catalogs consists mostly of apparel, we use it as the proxy for the price stickiness
of the nondurable goods sector. Then, under that assumption, the price stickiness
in the nondurable goods sector (on) would be 0.29.14 Blinder (1994) found that
the time between adjustment of prices is about one year. Since he considers mostly
intermediate goods (i.e., steel, cement, chemicals etc.), we use it as the proxy of the
price stickiness in the durable goods sector. Then the degree of the price stickiness
in the durable goods sector (ad) would be 0.37.

The literature contains some implicit estimates of society’s weight 011 output gap
fluctuation relative to inflation fluctuations in its loss function. Rotemberg and Wood-
ford (1998) report a low value around 0.05, whereas Jensen (2002) and Walsh (2001)
set the weight as 0.25. Following Jensen and Walsh, we set the weight parameter

an to 0.25, and “d to 0.05 to consider the share of sectoral output. But later we

 

12Most literature chooses the discount factor so that the real interest rate ranges from 6.5% to 2%
per year. In our case, the real interest rate would be 4% per year.

13The empirical study of Domowitz, Hubbard and Petersen (1988) show that there is little in-
terindustry variation in the estimated mark-up rate between durable and nondurable goods. Also as
a starting point, some literature assumes that two sectors have the same mark-up rate (For example,
see Bils, Klenow and Kryvtsov (2003) and Barsky, House and Kimball (2003)).

14Since we assume that the probability that a firm adjusts its price follows Poisson distribution,
the probability of no price adjustment is 0.29.

18

Table 1.1: Baseline Parameters
an 2 0.29, ad = 0.37, a = 1.5,7 = 0811,, = 0.25,;id = 0.05,

6 = 7.88, g = 0.8, qb = 247,6 = 0.1,,3 = 0.96

01-1-71 = 01111 Z 08-"- : and = 0'02

 

will investigate the implication of alternative policy regimes when the weights are
different across the two sectors. Finally, to highlight the effect of alternative policies
to shocks, all coefficients of AR(1) process (p’s) are assumed to be zero. For the
standard deviation of the stochastic disturbances of the model, we set an, j and 0e, j
to 0.02 (i.e., 2 percent per a year) respectively. The baseline parameter configuration

is summarized in Table 1.1.

Optimal Responses to Cost Shocks

Figure 1.2 shows the optimal responses of output gaps under alternative poli-
cies: precommitment and pure discretion, as a one standard deviation of cost shock
hits both sectors simultaneously. A significant difference is that the response of ag-
gregated output gaps under precommitment has more persistent effects than that
of pure discretion, even if the cost shock has no persistence. Under optimal pure
discretion, there is no inertia; the output gaps return to their steady-state values in
the period after the shock occurs.15 This effect is known as “history dependent” or
“inertial behavior” in the New-Keynesian literature (see, Clarida, Gali and Gertler
(1999), McCallum and Nelson (2004), Woodford (1998, 1999) and Walsh (2003)).

The main reason is due to the forward-looking expectations in the aggregate supply
equations. If the economy is hit by a temporary cost shock, a contractionary monetary
policy is required to reduce the significant fluctuation of inflation (see eq.(1.29) and
(1.30)). Under such a circumstance, the trade-off between inflation and the output
gap becomes more favorable if the recession, that is, reduction of output, is expected
to persist. More importantly, this result depends on whether the central bank can

credibly commit to a rule rather than discretion.

 

r n . . . . . . . . . . . .

l"Intmtively, under discretion, Since a central bank optimizes its objective period-by-period given
the constraints and takes private sector expectations as given. it is optimal to return to steady-state
values as soon as possible after the shock hits the economy.

19

0-01

0.005

~0.005

-0-01

-0-015

—0-02

-0.025

-0.03

-0. 035

0-01

-0-01

-0.02

~0.03

-0-05

-0-06
0

Commitment. impulse response to a one s.d- of cost shock

 

 

L — Outputgapn
- _. — - Outputgapd

‘ ‘
5 _

--------------------------- ‘0 ---- Aggregate

 

 

 

 

 

p
p

 

 

Discretion impulse response to a one s.d. of cost shock

15

 

 

— Outputgapn
pa , —— - Outputgapd

j; P - ’ - - - Aggregate

 

 

 

I
'5 s

I
'h.

 

-
p-

 

 

Figure 1.2: The Impulse Responses of Sectoral Output Gaps

20

15

The second significant characteristic of the optimal policy is that the optimal
precommitment policy allows for more persistence and larger initial impact of the
durable goods sector than the nondurable goods sector. One explanation for this
result would be the different response to the monetary policy instrument, that is.
nominal interest rate.

In the face of an unexpected cost shock, the central bank increases the nominal
interest rate to offset the increasing inflation at the cost of the output gap. The
problem, however, is that aggregate demands for two goods depend on the “real”
interest rate, not the nominal interest rate. Furthermore, the responses to the real
interest rate are different in the two sectors. While the nondurable goods sector’s
real interest sensitivity of demand is determined by the elasticity of intertemporal
substitution (0) and preference parameter (7), it depends on the durability 6 and
the subjective discount factor ([3) in the durable goods sector (see the intertemporal
IS equations (1.26) and (1.27)). Note that a very small depreciation rate and large
subjective discount rate can increase the real interest sensitivity of aggregate demand
to infinity.

Therefore, given the change in the nominal interest rate, the responses of aggregate
demand of the two sectors are necessarily different. More specifically, the output gap
fluctuation in the durable goods sector is greater than that of nondurable goods sector
to the change in the nominal interest rate. Under these circumstances, the implication
of optimal precommitment is for the central bank to respond less aggressively to
the real interest sensitive sector, in the sense that the central bank allows small
volatility of sectoral output gap compared to pure discretion. However, this policy is
implemented at the cost of higher volatility of nondurable goods output gap, as we
will see later.

Figure 1.3 represents the responses of sectoral and aggregate inflations to one
standard deviation of a cost shock under alternative monetary policies. Basic charac-
teristics of optimal monetary policy are almost the same as the case of the response
of output gaps.

First, optimal precrmimitment policy is characterized by persistent responses to

21

a cost shock such as in the one good model. In particular, by keeping sectoral and
aggregate inflations below their target inflations, which are zero in our case, for several
periods after a cost shock, the central bank is able to reduce expectations of future
inflation. Thus the trade-off between inflation and output gaps stabilization faced
by the central bank is improved. Under pure discretion, all inflations return to their
steady-state values after the occurrence of a positive cost shock. The implications
are the same as in the the case of output gaps. Second, under precommitment,
the durable sector’s inflation undershoots its zero target inflation substantially and
converges to the steady-state value after a long period of time. These responses of
inflations determine the dynamics of the relative price over alternative policy regimes
in Figure 1.4.

Figure 1.4 shows the responses of the relative price under two policy regimes.
As a result of the policy allowing a smaller increase in the durable goods sector’s
inflation than the nondurable sector’s, the durable goods’ relative price in terms of
the nondurable goods’ price falls initially and then goes to its steady-state value under
precommitment. This movement of relative price is implied by that of two sectoral
inflations in Figure 3. In first period after a cost shock, durable goods’ inflation is
low and then remains below the nondurable goods’ inflation for a long time.

Under discretionary policy, the dynamics of relative price converge to its steady
state value quickly compared to under precommitment. The reason is due to the fact
that two sectoral inflations are adjusted to the long-run equilibrium as soon as the
effect of a cost shock disappears. But we can see that the relative price deviates from
its long-run equilibrium for a while. The reason is as follows: since the relative price
pm.” can be expressed as 7rd,t+1 — 7r",t+1 + PM? it depends on its lagged relative
price as well as sectoral inflations. Thus the relative price is affected by its initial
impact so that it shows a sluggish adjustment even though sectoral inflations have

little persistence.

22

Commitment; impulse response to a one s.d. of cost shock

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0-015 1 f
— Inflation"
— - lnflationd
0-01 ,— ---- Aggregate
0-005 - -
° - "“‘f’_"."_"-"_"j'_"_"_”."_’_’_“_‘_':‘_‘_':'_:“:-_“:=
-0.005 - —
-0-01 ‘ 1
o 5 10 15
x 10‘3 Discretion: impulse response to a one s d. of cost shock
20 . 1
Inflation"
-— - lnflationd
15 _ - - - - Aggregate
10 - -
5 - ..
0 '- —__:_T,:—T --—~-
_5 1 1
o 5 10 15

Figure 1.3: The Impulse Responses of Inflations

 

Relative Price: impulse response to a one s.d. of cost shock

 

 

 

 

 

 

 

 

 

 

 

 

0.025 1
— Commitment
---- Discretion
0-02 —
0.015 -
0.01 -
0-005 -
o -
-0005 —
-0.01 . .
0 5 10 15
Figure 1.4: The Impulse Responses of Relative Prices
Table 1.2: Outcomes in the Case of a Cost Shock
Shock PolicylLoss(104) am,” 0:1: £1 I 0W,” 07rd 01; 07;
Symmetric Com. 4.066 1.29 3.76 1.30 1.12 0.94 1.04
Shock Dis. 5.147 0.90 5.58 1.33 1.28 1.02 1.21
Asymmetric Com. 2.072 0.74 3.66 0.27 1.09 0.52 0.34
Shock (ed) Dis. 3.394 0.39 5.52 0.52 1.25 0.87 0.52

 

 

 

 

 

 

 

 

 

Welfare Comparison

Until now we have discussed the dynamics of endogenous variables and charac-
teristics of alternative policy regimes. In this subsection, we calculate welfare defined
by the social loss function, which is also the central bank’s policy objective function,
and standard deviations of endogenous variables in the face of various shocks. Finally
we discuss the implications and characteristics of optimal monetary policies.

For different circumstances, Table 1.2 shows society’s loss (104) and standard
deviations of variables in terms of percentage: output gap (0330'), inflation (07“)
for sector j, and aggregates (am and an) under alternative policies: precommitment

(Com.) and pure discretion (Disc).16 In the first column, shocks represent the case

 

'2
7r.j

and 03.3‘ are the asymptotic variances of inflation and the output gap, and [13- is the relative weight on

the output gap for sector j. In this model, the solution takes the form, X t = A! X ¢_1 + U; where U; is
a vector innovation with mean zero and no serial correlation. Then the variance-covariance matrix of

16The asymptotic value of the loss function is obtained as 0,2”, +0?” +0" 0%,, + 0.103? d, where a

24

of a symmetric cost shock in the two sectors, and of an asymmetric cost shock hits
only the durable goods sector (ed,t) respectively.

First, results show that optimal precommitment policy is always better than pure
discretionary policy regardless of a cost shock that hits the economy in either both
sectors or durable goods sector. In particular, the table shows that the welfare loss
under discretionary policy amounts to 27-64 percent greater than that of precommit-
ment.17

Since we assumed that the central bank minimizes the loss function around the
efficient level of output gaps under flexible prices, there is no “average inflation bias”
problem raised by Kydland and Prescott (1997) and Barro and Gordon (1983). With
no average inflation bias in this model, however, the result shows that discretionary
policy causes lager welfare loss relative to precommitment policy. 18

In terms of standard deviations of sectoral output gaps, optimal precommitment
allows for lower volatility in the durable goods sector than does the pure discretion
at the cost of high standard deviation in the nondurable goods sector. Under pure
discretion, the benefit from improved relative stabilization in the nondurable goods
sector can not counteract the loss from excess fluctuation in the durable goods sector,

despite the fact that the durable goods sector accounts for only 20 percent of the

total.

 

X1.t( 211) is obtained from vec(Z,1) = [I — (M <8 M )]—l vec(£v) where 2.. is the variance-covariance
matrix of v and vec(Z) is the Kronecker product of a matrix Z. The unconditional variances of
inflations and output gaps can be calculated by C2116" for a properly defined matrix C.

1.,In our case, the welfare loss is interpreted as the annual term. When we evaluate it as a quarterly
term, the welfare loss amounts to 7-16 percent. This amount of relative welfare loss seems to be
reasonable compared to other literature. For similar results, see McCallum and Nelson (2004),
Séderstrom (2004), Steinsson (2003), and Walsh (2003).

18This bias is known as “stabilization bias” in the New-Keynesian monetary policy literature,
which Clarida, Gali and Gertler (1999) indicated. In the precommitment policy, the absence of this
bias comes from credible commitment of the cental bank and the forward-looking expectations of
private agents about future inflation in the aggregate supply equations. When the central bank can
credibly commit to its rule, private agents believe that future inflation will fall because the central
bank continues to contract the economy. This expectation of future inflation contributes to fall the
current inflation. So precommitment policy results in improving the social welfare.

25

 

 

 

 

Table 1.3: Outcomes in the Case of Aggregate Demand Shocks
Shock I Policy LLoss(104) [0513,71 l ”and 01r,n Land I 037d 01;
Symmetric Com. 1.942 1.32 2.46 0.96 0.53 0.82 0.69
Shock Disc. 2.126 1.04 2.47 1.24 0.03 0.24 0.69
Asymmetric Com. 0.020 0.13 0.25 0.10 0.05 0.08 0.07
Shock (ud) Disc 0.021 0.10 0.25 0.12 0.00 0.02 0.07

 

 

 

 

 

 

 

 

 

Optimal Responses to an Aggregate Demand Shock

According to the conventional wisdom about optimal monetary policy in the
context of New-Keynesian model, an aggregate demand shock is not regarded as an
important factor that perturbs the economy. The reason is that the output gap
and inflation move in the same direction as an aggregate demand shock occurs. This
implies that it is possible to stabilize the output gap and inflation completely by using
a policy instrument, the nominal interest rate. In other words, for any aggregate
demand shock, the central bank can offset any variations of the output gap and
inflation with the nominal interest rate.

For this policy to be successful, one presumption is that the real interest rate,
which is defined as the difference between the nominal interest rate and expected
future inflation, can track the variation of the demand shock. In the two sector model
considered in this paper, the problem, however, is that for one nominal interest rate,
there exists two real interest rates: the real rate of return in terms of durable and
nondurable goods. Furthermore, even real interest sensitivity of demand is different
across sectors with positive depreciation rate (6) and subjective discounter factor (0).
Therefore, if the two sectors respond to the nominal interest differently, it might be
impossible to stabilize both sectors simultaneously.

It would be interesting to analyze the optimal monetary policy when aggregate
demand shocks matter. Table 1.3 shows society’s loss and standard deviations of
endogenous variables when a one standard deviation of an aggregate demand shock
hits both sectors (symmetric shock), and only the durable goods sector (asymmetric
shock “d,t)-

First, as in the previous case of a cost shock, the optimal percommitment policy

26

is superior to pure discretion in terms of the welfare loss. However, in contrast to
the case of a cost shock, the improvement of welfare loss is less significant as the
central bank moves from pure discretion to precommitment. For example, in terms
of the loss of pure discretion, the welfare loss under precommitment falls to around 5
to 9 percent of discretion for all cases, while in the case of a cost shock, the welfare
improvement under precommitment ranges from 20 to 39 percent. This fact implies
that when a cost shock is a main concern in a particular time, the central bank can

increase relative gain through precommitment.

Optimal Responses to Alternative Objective Function

When we deal with a disaggregated model, one interesting question is what the
proper goal for stabilization is: to target aggregated variables or disaggregated ones.
Thus the issue is whether it is efficient for the society to delegate another objective
different from true social loss function to the central bank, which cannot commit
to a policy rule credibly. To examine the performance of two objectives: to target
aggregated variables or not, first let us assume that the society cares only about
the sectoral output gaps and inflations but can appoint a central banker whose policy
objective is to minimize the deviation of aggregated variables from their efficient level.
So while the true loss function as a criterion to measure welfare becomes equations
(1.32) and (1.33), the central bank implements policy objectives (1.37) and (1.38).
Second, the weight parameter (Aa) should be chosen optimally to compare the losses.
This has been performed numerically by grid search where the parameter AG is varied
between 0.01 and 1 with the grid of 0.01. .

In this subsection, we examine optimal policy implications when society delegate
the central bank to target aggregated variables. In this case, it is assumed that the

central bank minimizes the following loss function
1 0° -
Min, —(1 — ,8)Et Z slut] . (1.37)
2 .
2:0

27

Table 1.4: Outcomes in the Case of Alternative Objective Function

 

 

 

 

Shock Policy Loss( 10“) 03; ,n 0x, d 07f," a,“ d 01 0”
Cost Com. 4.800 1.28 4.23 1.18 1.45 1.09 0.93
Shock Disc. 24.934 1.65 19.34 0.78 2.22 5.48 0.23
Demand Com. 4.052 1.03 4.64 0.48 1.57 0.25 0.13
Shock Disc. 6.645 0.46 8.71 0.47 1.61 1.10 0.04

 

 

 

 

 

 

 

 

 

where Aa is relative weight on the aggregate output gap and initially assumed to be
0.25. Table 1.4 compares the welfare loss and standard deviations of variables to a
cost shock and a demand shock when the cental bank’s objective is to minimize aggre-
gated variables. The results confirm the fact that precommitment is better than pure
discretion and also relative gain of precommitment is large when a cost shock hits the
economy. While the cost shock case reports that the welfare loss under discretionary
policy is about 100 percent greater than that of precommitment in quarterly terms,
the demand shock case shows welfare loss under discretion increases to 16 percent
compared to precommitment.

The comparison of Table 1.2 with Table 1.4 shows that under both policy regimes,
to target disaggregated variables achieves more eflicient outcomes than to target ag-
gregated variables. In particular, under pure discretion, the gain of moving from
the regime that targets aggregated variables to the regime that targets disaggregated
variables is substantial. This implies that it would be unnecessary to stabilize only
aggregated variables when we consider a two sector model and the society cares about
disaggregated variables. A critical assumption for this result is that true social welfare
loss function depends on disaggregated output gaps and inflations. But this does not
mean that any improvement of the welfare loss through targeting aggregated variables
is impossible under “optimal” discretion. In what follows, we will examine various
discretionary policy regimes in which the central bank seeks to minimize the devia-
tions of aggregated variables from their targets and investigate which policy regime

is the best under discretion.

28

1.4 Optimal Policy Design

Up to this point we have discussed the characteristics of optimal monetary poli-
cies and responses of endogenous variables under alternative policy regimes. One
important message of the previous section is that the two sector model has the same
characteristics of optimal monetary policies as the one good model; “inertial behav-
ior” and “stabilization bias” under discretionary policy. Thus precommitment policy
results in a better outcome than discretionary policy regime, as compared in terms
of the welfare loss in the policy objective function.19

There are two ways in which the central bank makes optimal responses to shocks
close to the optimal precommitment equilibrium dynamics of variables: the design
of an optimal policy rule and delegation of a central bank that minimizes society’s
welfare loss under discretion. One famous example of a policy rule is the Taylor rule
(Taylor 1993). According to the Taylor rule, the operating target Rt is set as a linear
function of current inflation and output gap. He showed that the rule could be quite
well matched to the behavior of federal funds rate in the United State in the 1980’s.

On the other hand, as shown by Woodford (1999). if commitments are not possible,
assigning the central bank with a mechanism that makes discretionary policy more
inertial may lead to better social outcomes.20 In addition, other discretionary policy
regimes, for example, nominal income growth targeting (Jensen 2002), the change of
output gap targeting (Walsh 2003b), price level targeting (Vestin 2001), and aggregate
money targeting (S6derstr6m 2004), show that the central bank under discretion
would achieve better outcomes than pure discretion with true welfare loss function.
The reason for these results comes from “inertial behavior” that is characterized by
the optimal precommitment policy in the previous section. Since above discretionary
policy regimes can generate the “inertial behavior” for their own reasons, those are

superior than pure discretion.

 

19Note that the previous precommitment policy regime is not time consistmt in the sense of
Kydland and Prescott (1977). However, we use the regime as a benclnnark case in order to highlight
the performance of alternative policy regimes.

20As an example, he showed that it would be better for a central bank that is expected to act
under discretion to pursue an alternative objective. an interest rate smoothing objective.

29

The purpose of this section is to evaluate the performance of each discretionary
policy regime as well as the simple Taylor rule in the context of our two sector model.
For comparison, the precommitment policy which minimizes the disaggregated output
gaps and inflations is used as a. benchmark case. Second, policy objective functions
should be specified for each discretionary policy.

One of most popular targeting regimes is inflation targeting (IT), which is ad-
vocated by Ball (1999) and Svensson (1997, 1999). In our discussion, the inflation

targeting regime is defined as one to minimize the period loss function
IT _ *, 2 2

where art is aggregate output gap, 7rt is aggregate inflation, and X" is chosen opti-
mally.21 Walsh (2003b) shows that the central bank targeting the “change” in the
output gap, rather than the level, introduces policy inertia and calls it the speed limit

policy (OCT). Thus, the central bank is given the period loss function
T 2 2
LPG = A09(A.z:,+,-) + am, (1.40)

where A represents the “change” of output gap and A09 is chosen by grid search
optimally. Finally, we consider optimal simple Taylor rule (OTR).22 The optimal

simple Taylor rule is assumed to be the form
Rt = Aot1$t+i + Aot27rt+iv (1-41)

where ”\0t1 and /\0t2 are chosen by grid search optimally. Above policies have a
common factor in that those target aggregate output gap and inflation. Now we need
to examine the performance of policies to target disaggregated variables. Specifically,

we consider strict output gap targeting which minimize only sectoral output gaps

 

21Svensson (1997, 1999) defines strict inflation targeting as the case when X‘ = 0 and only inflation
enters the loss function. But flexible inflation targeting as the case when X‘ > 0 and the output gap
enters the loss function. In our simulation, we consider only flerz'ble inflation targeting.

22However, note that simple Taylor rule might not be a global optimal rule because it considers
the use of the instrument within restricted parameterizations and variables.

30

 

 

 

 

 

Table 1.5: Outcomes of Alternative Delegations Schemes and Optimal Taylor Rule

Policy Loss(104) 03;,” 03nd 071-377, 07rd 03; 07; Optimal Weight

COM 4.066 1.29 3.76 1.30 1.12 0.94 1.04 -

OTR 12.255 1.41 11.67 1.50 1.64 2.96 1.29 A0“ = 0.5, ’\0t2 = 1.4
IT 24.934 1.65 19.34 0.78 2.22 5.48 0.23 x\* = 0.01

OGT 26.728 1.70 20.01 0.75 2.33 5.67 0.19 A09 = 0.01

SGT 6.135 1.22 0.47 1.64 2.52 0.59 1.50 it; = 0.6, it; = 0.01

DGT 7.500 1.71 8.71 1.67 0.42 2.93 1.35 Adg = 0.01

 

 

 

 

 

 

 

 

 

(SGT). Thus, the central bank is given the period loss function

LigaT = ”Eighth +fl‘d‘rc21,t+i‘ (1'42)
where weights on output gaps (It; and #2) are chosen optimally. Finally, we consider
the policy to only target the durable goods sector (DGT), Then the policy objective
is given by

DGT _ 2 2
Lt — Adgfd,t+i + 7Td,t+i' (143)

where weights on output gaps (Adg) is chosen optimally.

The first row of Table 1.5 shows outcomes of the optimal precommitment in the
benchmark case, which targets sectoral variables and is included for comparison. The
other five lows include the case of optimal Taylor rule (OTR), inflation targeting
(IT), change in output gap targeting (OGT), strict output gap targeting (SGT) and
durable goods sector targeting (DGT), with all preference parameters (A’s and u’s)
chosen optimally. The table shows the value of social loss and standard deviations of
sectoral and aggregate output gaps and inflations for each policy regime.

First, we note that precommitment shows the best outcome in terms of society’s
welfare loss. The improvement of the welfare loss ranges from 13 to 140 percent rel-
ative to the other optimal discretionary policies, as we interpret the loss in quarterly
terms. Second, optimal Taylor rule produces more efficient outcome than other policy
regimes that minimize the deviation of aggregate output gap and inflation, while the

change in output gap targeting regime results in a poor outcome?3 On the other

 

”In the similar model we consider in this paper, Erceg and Levin (2002) obtain a very poor

31

hand, the strict output gap targeting and the durable goods sector targeting regimes,
which are optimal policies to target disaggregated variables, show more eflicient out-
comes than any other policy rcgimes that minimize the deviation of aggregate output
gap and inflation.

If we look at the standard deviations of variables under various optimal policies,
we can infer why optimal policies under the one good model are no longer optimal in
the two goods model. For example, while optimal inflation targeting with the weight
0.01 in output gap succeeds to stabilize aggregate inflation relative to precommitment
policy, it fails to stabilize the sectoral output gaps, especially the output gap in the
durable goods sector. One the other hand, policies to target disaggregated variables
succeed to stabilize the fluctuation of durable goods sector even if its share is small.24
That is why the latter results in a more efficient outcome in terms of social welfare
loss.

In summary, this simulation result shows that it may not be optimal to stabilize the
aggregate output gap and inflation through various policy regimes when the society’s
true loss depends on disaggregated variables, and suggests that under discretion,

optimal policies in the one good model may not hold in multi-sector model.

1.5 The Role of Durability and Relative Price Stick-
iness

In this section, we examine the role of durability and price stickiness for optimal
monetary policy in the two sector model. We saw that durability (6) is one of the most
important parameters since it causes non-negligible real interest sensitivity differences
in both sectors. Thus it would be interesting to discuss what the implications of

optimal monetary policy are, as durability changes.

 

outcome for the inflation targeting regime. But this difference in the result is due to the specification
of their policy objective function in which they consider only strict inflation targeting in the sense
of Svensson (1997, 1999). Furthermore their price adjustment scheme and nominal wage contract.
are built on Taylor-style staggered price setting.

24In our simulation, we assumed that the output of durable goods accounts for 20 percent out of
total output.

32

Table 1.6: The Welfare Less (104) of the Change of Durability (5)

 

 

 

 

 

Policy 6 = 0.1 6 = 0.4 6 = 0.7 5 = 0.99
Precommitment 4.066 4.136 4.356 3.579
IT 24.934 12.561 9.294 9.913

OT 12.255 5.695 6.297 6.774

OGT 26.728 13.427 9.528 9.987
SOT 6.135 6.654 7.156 7.998

DGT 7.500 6.755 10.385 14.399

 

 

 

 

Table 1.6 shows welfare losses under alternatives policies, as durability changes.
First, we note that overall, as durability decreases, that is, the depreciation rate
(6) increases, the efficiency of policies improves except for the policies that target
disaggregated variables. One possible explanation might be that the fluctuation due
to the durability of goods is reduced as they lose their intrinsic aspect, i.e., durability.
In particular, optimal Taylor rule achieves the second best outcome when durability
is very small.

On the other hand, while the strict output gap and durable goods sector targeting
regimes do not perform well compered to the policies that care about aggregate
variables when durability of goods is low, both policies, especially durable goods
sector targeting regime, are strongly recommended in the case of high durability.
This fact implies that when the durability of goods leads to the high real interest
rate sensitivity difference across two sectors, it is optimal for the central bank to use
policies to target disaggregated output gaps or the sector sensitive to real interest
rate if precommitment is not feasible. Put another way, in the case that durability
introduces sectoral asymmetry into the economy, the policy rules that care about
disaggregated variables become more efficient.

Until now we have used a baseline value of the degree of price stickiness. So we
did not consider the role of the relative price index which is defined as the price index
of composite durable goods relative to composite nondurable goods’ one. In recent
work, some researchers have focused on the implication of sectoral differences of price

adjustment for optimal monetary policy and business cycles.25 In this subsection,

 

25See, for example, Aoki (2001), Ohanian and Stockman (1994), Barsky, House, and Kimball
(2004).

33

Table 1.7: The Welfare Loss (104) of the Change of Relative Price Stickiness (an, ad)

 

 

 

 

 

 

Policy (on = 0, ad = 0.36 an = 0, ad = 0.56 I an = 0, ad = 0.86
Precommitment 2.722 4.787 7.859
IT 9.472 25.180 19.676

OT 14.289 46.345 70.824

OGT 9.451 46.955 23.787
SOT 7.951 7.945 7.939
DGT 5.481 8.091 7.937

 

 

 

 

we consider the implication of sectoral differences of price adjustment for optimal
monetary policy. To highlight the result, we assume that prices of the nondurable
goods sector are completely flexible, which means that the coefficient of price adjust-
ment an is zero. Then we consider the case that the stickiness of price adjustment
of durable goods sector changes from a flexible case, i.e., “(120-362 relatively to an
almost constant case, i.e., ad=0.86.

Table 1.7 shows values of welfare losses under alternative policy regimes when the
degree of price adjustment is different across two sectors. First, the level of loss under
precommitment increases when the relative price stickiness increases. One possible
explanation is that increase in the relative price stickiness introduces an additional
loss into the economy. Second, in contrast with the result of the previous section, the
optimal Taylor rule performs very poorly while inflation targeting results in lowest
welfare loss out of policy regimes that minimize the aggregate variables. This result
suggests that conventional policy rules which seek to stabilize aggregated variables
are not robust.

When the relative price stickiness is high, the simulation result shows that poli-
cies to target disaggregated variables lead to lowest welfare losses. Especially, the
policy to target durable goods sector which has more sticky price appears to achieve
the lowest welfare loss. Targeting durable goods sector inflation with sectoral output
gap can be considered as flexible inflation targeting with an objective to minimize
sectoral variables rather than aggregate ones, in the sense of Svensson (1997, 1999).
When the policy is interpreted like this, the finding is consistent with Aoki (2002)

and Benigno (2004). According to Aoki, the optimal monetary policy is to target

34

sticky price inflation in the model with a flexible-price sector and a sticky-price sec-
tor. In our model, it is possible for the central bank to obtain optimal outcomes
through stabilizing only the durable goods sector, which has high price stickiness, if
the precommitment policy is not available.

In summary, simulation results show that when fundamental structure of the
economy is characterized by multiple-sectors and high relative price stickiness across
sectors, it could be an optimal monetary policy for the central bank to stabilize
either disaggregated variables or one sector with higher relative price stickiness if

precommitment is not available.26

1.6 Conclusion

This paper argues that since monetary policy actions can have different effects
across sectors, sectoral stabilization is an important issue to address. It also explores
the implications and alternative monetary policy rules if people care only about their
own sector or industry. Our main conclusions can be summarized as follows.

First, simulation results show that traditional principles obtained from one good
models still hold in the two sector model considered. Optimal precommitment policy
in a New Keynesian one good model features inertial behavior or history dependence.
This characteristic contributes to the improvement of the trade-off between inflation
and output gap variability through expectations about future inflation.

Second, it might be suboptimal for the central bank to target aggregated variables
in our model. A critical assumption for this result is that the true social welfare loss
function depends on disaggregated output gaps and inflations. We have considered
two typical policy regimes under discretion, i.e., inflation targeting and “change” in
aggregate output gap targeting and optimal Taylor rule. Simulation results shows
that all above policy regimes result in poor outcomes compared to the policy regimes

that care about disaggregated variables.

 

26Even though we did not include the outcome of targeting only nondurable goods sector in the
text, it shows very poor outcome.

35

Third, in regard to optimal monetary policy design in the model considered, the
strict output gap targeting regime, which targets only the disaggregated output gaps,
is a second-best policy rule. In addition, sectoral inflation targeting -in our case,
durable goods sector targeting- also performs well. All these results suggest that the
stabilization of sectoral output gaps is as important as inflation when each sector
responds to the monetary policy instrument differently. .

Fourth, the analysis of durability changes shows that the more durable the good
is, the more policy should care about sectoral variables. The intuition is as follows:
a more durable good means higher real interest rate sensitivity of aggregate demand,
so that the fluctuation of output gaps across sectors will show more different patterns
of dynamics as a shock hits the economy. As long as society is concerned with the
stabilization of sectoral variables, the policy rule to target sectoral variables becomes
more efficient. Finally, the analysis of a change in relative stickiness suggests that if
precommitment is not possible, it could be optimal to stabilize the sector with the

higher relative price stickiness (in our case, durable goods sector).

36

Chapter 2

Two Sector Business Cycle:

Durable and Nondurable Goods

2. 1 Introduction

One of the main concerns in macroeconomics is the effects of monetary distur-
bances on the real economy, in particular the role of money in economic fluctuations.
Monetary shocks can have substantial real effects in ” Keyensian” models because this
sort of model generally incorporates nominal and/ or real rigidities. However, Chari
et al.(1996) argue that the New-Keynesian macroeconomic model developed under
sticky price assumption does not generate sufficient price rigidity beyond the exoge-
nously imposed period of nominal price or wage stickiness and hence have difficulty
in generating a persistent response of output and inflation to monetary shocks. There
have been various attempts to solve the ”persistence problem”. For example, Kiley
(1997) shows that incorporating real rigidities can increase persistence in the model.
Christiano et al. (2001) argue that staggered wage contracts and variable capital
utilization can account for the inertia in inflation and persistence in output. Dotsey
et al. (1999) argue that three features of the ’supply side’ of the economy: produced
inputs, variable capacity utilization, and labor supply variability through changes in
employment can help together to dramatically reduce the elasticity of marginal cost

with respect to output. Therefore, persistence can be generated.

37

On the other hand, consumer durables are thought to play a central role in the
generation and propagation of business cycles. Mankiw( 1985), Baxter(1996), Erecg
and Levin (2002), Weder (1998) investigate whether consumer durables are important
for the generation and propagation of business cycles. Mankiw argued that under—
standing fluctuations in consumer purchases of durables is vital for understanding
economic fluctuations. Baxter constructs a two—sector model that succeeds in gener-
ating business cycles to investigate whether consumer durables are important for the
generation and propagation of business cycles. Weder studies the role of durable goods
and sunspots in the generation and propagation of economic fluctuations. Barsky et
al. investigate the relationship between durable goods and price stickiness and then
Show that the behavior of the model depends on whether durable goods have sticky
prices.

This study investigates the role of durability to generate the substantial effect
of money on output and inflation. Following the strand of New-Keynesian research,
price stickiness is introduced into the model so that money has a non-negligible real
effect. we construct a dynamic stochastic general equilibrium model with monopolis-
tic competition in the goods market. Specifically, the model consists of two sectors:
nondurable goods and durable goods, to focus on the implications of monetary policy
when some goods are durable. For analytical tractability, first we consider the case
in which durable goods last for only two periods. But the discussion will be extended
to the multi-period case later.

We will show that durability can change output and inflation dynamics in im-
portant ways. This effect happens through two channels. First, since households ob-
tain utility from the flow of services durable goods provide, durability causes current
marginal utilities and marginal rates of substitution to depend on past and future pur-
chases of durable goods. This fact implies that aggregate demand for durable goods
are determined by past and expected future purchases as well as current purchases.
Furthermore if we assume that nondurable and durable goods are non—separable in
utility, durability can affect the nondurable consumption path, that is intratemporal

substitution appears. Second, when firms set their optimal price, durability is one

38

of factors they refer to. Thus aggregate price level and inflation dynamics are deter-
mined partly by durability of goods. As we will see, inflation dynamics are seriously
affected by the rate of depreciation and the number of periods durable goods last.
The remainder of this paper is organized as follows. Section 2.2 constructs the
two sector dynamic general equilibrium model and fundamental structural equations
are derived. Section 2.3 considers the case that durable goods last more than two
periods and discusses the implication of durability to generate the inertia in inflation
and persistence in output. Section 2.4 implements simulation and sensitivity analysis.

Section 2.5 concludes.

2.2 The Model

2.2. 1 Households

The economy is composed of a continuum of infinitely—lived individuals, whose
total is normalized to unity. Consumers obtain utility from both nondurable goods
and durable goods. We denote a typical durable good as d and a typical nondurable
good as n. The representative household is assumed to have preferences over non-
durable goods consumption (Cm): the service flow from the durable good stock (St),
real money balances (9%) and leisure (It). A specific functional form for expected

utility is assumed

 

oo 1_
EtZfit —1-—wl 01—0, 1 2t 5“- V+-1-u> (I—IW (21)
1—0 ’t t 1—1/“2’t Pt ¢ 3’t t ’ ’

t—O

where g— is the elasticity of intertemporal substitution of the consumption bundle, %
is the elasticity of intertemporal substitution of leisure and fl is the utility discount
factor. The 112’s are disturbances in each argument. All disturbances are assumed to
follow stationary processes. The consumption bundle Ct is given by a Cobb-Douglas
functional form,

C, a (37 33—7, (2.2)

mt

39

where Cn,t is the consumption of nondurable goods and St is the durable stock. For
an analytical solution, the durable stock lasts for only two periods. Thus the stock

of durable consumption goods evolves as follows:
St = (1— (”Cit—1 + Cit? 0 < (l S 1 (2.3)

where Cd.t is the purchase of durable goods in period t and the (5 represents the rate of
depreciation. Cm and C,“ are assumed as Dixit-Stiglitz aggregates of differentiated

products as follows

9
6
1 9%: #1 1 9,11 9.1-1
Cmt: focnfiz) 'n dz . Q“: /Ocd,t(2) d dz , (2.4)

where Bj for j = n, d is the elasticity of substitution between any different variety of
the differentiated goods. It is also the price elasticity of demand for any single variety
of the differentiated goods. It follows from the above specification of preferences that
the minimum cost of obtaining a unit of the sectoral composite goods (CW and Cd,t)

is given by the sectoral price index:

1
1 1_9 m .
Pj,t E [0 pj’t(z) for] = n,d (2.5)

The optimal allocation of demand across the various differentiated goods by con-

sumers satisfies

 

p- ("l 4)].
Cjt = J’t ~ Cj.t for j = n,d, (2.6)
: Pj,t .

for each good 2 in sector j. The household’s nominal budget constraint in period t is

as follows,

Pn.tC‘n..t + Pd,th,t + [lift + Bt = ll"7tnt+ll'[t_1 + Et + Rt—lBt—l + TRt (2.7)

40

where Pn,t and Pd,t denote the price index of nondurable goods and durable goods
respectively, Mt is nominal money holding for next period, Bt is nominal bond holding
for next period, Wt is nominal wage, St is profit, Rt_1 is nominal interest rate of
previous period, and TRt is government transfer.

In every period t, each household maximizes its expected lifetime utility, eq. (2.1)
with respect to its choice of nondurable consumption, durable stock, real money
balances, bonds and its labor supply: subject to its budget constraint, eq.(2.7). The
budget constraint is denominated by general price level (Pt) as defined properly. The

first order conditions for each choice variable are given by

.. , 1— —1 (1—7)(1-0) P .t
’7’t“’1,tC;,(t 0’ [(1 - 5)Cd,t—1 + Cd,t] = M72:- (28)
PdJ 7(1— 0) (1‘7)(1—0)-1
a7? =(1—w>w.1tC,., [<1— 6>C.1,._1+ Cat]
'71(— a) (1—7)(1—0)-1
+13(1—5)(1—7)E,z.;-1.,+IC,{,H [(1—5)Cd,,+cd,,+1] (2.9)
Alt , P
t‘2,t (fit—V) — /\t - /3Et/\t+lp;:—l— (2.10)
_ IV
um"? I = M735: (2'11)
, P
At = (3RtEt/\t+1rp_t, (2-12)
t+1

where At denotes the marginal utility of nominal income in period t and (1:25;) rep-
resents relative price of sector 2' denominated by Pt. Equation (2.8) states the effi-
ciency condition of nondurable goods consumption. Equation (2.9) is the condition
of durable goods services. Since we assumed that the durable stock lasts for only two
periods, only two periods of marginal utility terms are considered in the left hand side
of equation (2.9). Equations (2.10), (2.11) and (2.12) show the optimality conditions
for money demand, labor supply and bonds respectively.

By using a log-linear approximatirm and steady state conditions with flexible

41

prices, we can derive intertemporal IS equations in both sectors from the above first
order conditions. X represents the percent deviation of variable X from its steady

state value under flexible prices.

Yn,t = EtYn,t+1 — (1’1 [(1 - CAI/at + EtAi/d,t+1]

—(I>2Et [(Rt — 7ft) — Ain,t+1 + AIZ’I,t+1]

(1-7)(1-C) q, = 1
1-70-0)’ 2 1-70-01

 

 

where (D1 = (2.13)

I’d): = EtYd,t+1+‘1>3[AYd,t+BEtAYd,t+2 -‘1’4Et [AYn,t+1+fi(1-5)AYn,t+2l

4’5 [Et (Rt - 7Tt+1) - EtAid,t+1l - (I’GEt [A¢1,t+1+fi(1-5)A¢1,t+2j
_ 1—5 <1» _ y(1——0)(1+(1—-6))
— 2. 4 — , 2 , .

1+fi(1—5) (1+/3(1-6) )(1-7(1—0))
= (1+ fi(1 - 5))(l + (1 - 6))
5 (1+M1—eau—vu—o»’

(1 + (1 — 6))

1+ ,{3(1 — 6)?)(1— 7(1— 0)).

 

 

where (P3

 

 

(D6 = (2.14)

(
The above two equations represent the aggregate spending relationship, correspond-
ing to a traditional IS function. Eq. (2.13) represents aggregate demand in the
nondurable sector while Eq. (2.14) is the aggregate demand of durable goods sector.
The standard results are confirmed in the sense that each sector’s aggregate output
depends negatively on real interest rate (Rt — Wmt) and positively on the one period
ahead expected future own output gap. Because we consider two sectors, relative
price (133$) is included as an argument.

The key result of the model is that current purchases of the two goods depend on
past and expected future purchases. In other words, the model generates persistent
dynamics of output by including the past output gaps of the durable goods sector.
This relationship is due to durability of one good. Because households obtain the
utility of the flow of services over two periods from durable goods, the current pur-
chase decision of durable goods affects purchases of both goods in the next period.

Note that if we assumed all goods totaly depreciated in one period ((5 = 1), the above

42

two equations collapse to the traditional two sector IS equations.

2.2.2 Firms

Differentiated goods and monopolistic competition are assumed. The firms use
only one variable input: labor. This implies that durable goods are used only in
consumption. Labor is assumed to be homogeneous in both sectors. The production
technologies are the same in both sectors and operate under a linear technology as

follows:

yj’t(z) = ”$4”,th forj = n,d. (2.15)

where 2 represents an individual good producer. #243“ represents a technology shock.
The technology shock is assumed to follow stationary processes. As an essential part
of the model, firms’ price setting decisions are assumed to be sticky. Specifically, we
follow the Calvo—style staggered price setting rule in assuming that in each period a
fraction 1 — aj for j: n, d of producers in each sector is offered the opportunity
to choose a new price, independent of the length of time since the price was set and
of what the particular good’s current price may be, while the remaining producers
have to maintain whichever price they charged before. A firm’s profit maximization

problem is

 

 

_g,. _9.
00 P- (2) J w {P- (z) 2
, k at t+k ,t
MaxEt 0'13) AH k P‘t(2) Y'.t k—I Y't k
E J ’+ 3’ Pj,t+k 3" + W4,t+k\Pj,t+k 3’ +

(2.16)
where (aj [3)“At,t+ k represents a stochastic discount factor. The At is marginal utility
of income as defined in the previous section. The left hand side of the bracket rep-
resents the revenue which satisfies the demand condition. Since the goods market is
operated under monopolistic competition, an individual firm producing the product

19100—6.
.2 faces the demand, Pl’_ I/ .. for ' = n, d. The ri ht hand side re resents the
j,t+k “H” J g p

43

nominal cost. The first order condition to maximize profit can be written as

0- w, k
P-.t(z) — J + (2.17)
3' 9) — 1w4,t+k

 

 

t(Z)
Et 2(0’ 0.7/3) kAt t+k (Pjit 6ij¢+k
.7:

k_ 0 t+k

 

According to the above condition, each firm sets its price Pj’l‘t(z) equal to a markup

0 .

ME y—é-f) over its nominal marginal cost. This is the standard result in a model of
.7

monopolistic competition. Because the adjusting firms were selected randomly from

among all firms in period t—I, the average price in period t satisfies

Pj,t = (1P?— jt-— 1 + (1 — a)Pj,t for J = n,d. (2.18)
Two equations (2.17), (2.18) can be approximated around a zero average inflation
steady state equilibrium to derive the New-Keyensian Phillips curve. By using a log-
linear approximation and the definition of each sector’s price level index, we can derive

the aggregate supply equation or New—Keynesian Phillips curve for each sector.1

1
”Tut = [$1 (Yn‘t — Ygt) — K2 2(1 _ 6)] (Yd,t—j - Ygt-j)
i=0

_n3 (£3th — 555$) + fiEth,t+l (2.19)

 

 

where K1 = (l—an)(1-anfi)(¢- (1—0))
01n(1+6n(¢" 1)) ’
_ (l-an)(1—anfi)(1— v)(1—C)
“2 ‘ an(1+6n(¢— 1)) ’
n3 = (1—an)(1—anfi)

 

an(1+ 912025 — 1)).

where X n denotes percent deviation from variable X ’s steady state under flexible
price. The output gap is defined as YTM ——l77?t. The above equation expresses inflation
in the nondurable sector as a function of its sectoral output gap (Yet — 177%), the

other sector’s output gap (17,” — 175%), relative price gap (jimt — if: t) and expected

 

1For detailed derivation of aggregate supply equations, see Appendix A.

44

future inflation. Since two goods are non-separable in utility and durable stocks last
for only two periods, the durable good’s output gap is included in this equation.
While high aggregate output increases inflation in that sector, relative price (@t—t)
decreases inflation in that sector. Note that with complete depreciation (621) the

above equation is the same as conventional two sector aggregate supply equations.

”at = N4 (Yet-lift) + K5 [(Yd.t—1 - 3221-1) - fiEt (Yd.t+1 - Ydrft+1)]

1
7‘6: 53(1—6let(Yn,t+j ‘ Yritt+j> ’“3(5€d,t 43%) +3Et7rd,t+1 (2.20)

 

3:0
when, ,, z (l—O‘dlil“'9'de—(1—7")(1-0))(1+5(1‘5)2)
'4 ad(1+ 66(6 - 1))(1+ 60— 6)) ’
<1— 6.1m — 6.1mm — 7(1- 6))(1— 6)

 

ad(1+ 9.1(6 — 1))(1+ 60— 6))
K = (1- Odlfl - ad6)7(1 ‘- 0)
'6 ad(1+ 9d(d> — 1)(1+ 60— 6))

 

The durable goods sector’s inflation looks more complex. But we can notice
that the number of lagged and lead output gaps depends on the numberof period’s
the durable goods lasts. Durable good inflation dynamics are determined by two
sector output gaps, relative prices and expected future inflation. The impact of its
output gap and expected inflation, a positive effect, is the same as conventional N ew-
Keynesian business cycle models. Because durable goods purchased in the current
period depreciate totally after two periods, purchase decisions made last period affect
the current purchase decision. Suppliers consider this fact when they decide on their
product price. That is why the aggregate durable goods supply equation includes the
lagged aggregate outputs by length of durability. Also when the rate of depreciation
increases, the coefficient n4 increases whereas n5 decreases. This implies that as
durable goods deteriorate more rapidly, the persistent effect of output on inflation
decreases.

These equations are different from the conventional New—Keynesian Phillips curve

45

in two ways. First, when price stickiness is not same across sectors, relative price
fluctuation becomes another transmission mechanism, which does not exist in a one
good model. In the face of an unexpected monetary shock and change of relative
prices, households and firms adjust their optimization behavior. In fact, the pressure
of relative prices reduce the inflationary effect in that sector because of substitution
between two goods. Second, durability generates non-negligible endogenous dynamics
for sectoral inflations. Since durability introduces time non-separability in the utility
function into the model, durability provides the model with substantial persistence.
Therefore, this assumption can help to explain a persistent output effect on inflation.

But one problem with this model is that it does not show the persistent inflation
dynamics in the sense that inflation does not incorporate own past inflation. Because
we assumed that firms’ pricing setting decisions are based on only expected future
variation of marginal revenue and cost with currently available information, their
own expected future product price and aggregate conditions matter. Thus there is

no room for past inflations to go into this model like some New-Keynesian literature.

2.3 Multi—Periods Case

Since our interest is in the role of durability for substantial real effects of monetary
policy, we need to look into implications of durability in more detail. To do this, we
extend the periods the goods lasts and then investigate how output and inflation
dynamics change. For analytical purpose, in this section we consider the case in
which durable goods last for three periods. Then we will extend it to more general

N-periods case.

2.3.1 Three Periods Case

Let us assume that the purchased durable goods lasts for three periods. Then

durable stock evolves as follows:

St = <1 — 6)2Cd,t..2 + <1 — 6)C.),._1 + Cd,t (2.21)

46

Except for the evolution of the durable stock, the other components of the model are
the same as before. We apply the same steps we used to derive aggregate demand
and supply equations in the two period case to the three period case as well. We can
obtain output and inflation dynamics in the case that the durable good lasts for three

periods as follows:

2.3.2 Aggregate Demand and Supply Equation

Because the functional form of aggregate demand is almost the same as previous
case, we omit the aggregate demand equations. Instead, we report aggregate supply

equations.

2
m, = K, (YE, -— Ygft) — fig 230— 6)] (Yd,t— j " Yalft—j)
'=0

—K.3 (ilet — 533$) + fiEtW-n,t+l (2.22)

(1 — an)(1 - an.3)(¢ - 7’0 - 0))

 

 

where K1 = 0171(1 + 67201) _ 1)) ,
K = (l—anXl—anfiXl-VXI—a)
2 an(1+ 07m — 1))

n __ (l—an)(1—anfl)
3 " an(1+6n(6—1))'

 

Eq.(2.22) represents the dynamics of inflation in the nondurable goods sector when
durable goods last for three periods. Compared to the two periods case, the sectoral
inflation depends on more lagged durable sector’s output gaps and has the same coef-

ficients of its argument as before. But in the case of durable goods sector, coefficients

47

of variables are different as durability changes as below,

7Id,t = “4(Yd,t_l>£t)+"5[(1+/3(1‘6)2)(Yd,t—1“IA/(12-1)+(1'6)(Yd,t—2—Ydr:t_2)

+/’3(1+/3(1-5)2)Et(yd,t+1-Y£t+1)+l32(1_")Et(Yd»t+2_’>£t+2)l

2
46 2: [31(1 —5)JE, (Yth—Ygfij) — n3 (ed,,—5:g,,) + sandy +1(2.23)
'=0

(1—0‘d)(1-a'd/3)(¢-(1-7)(1-0))(1+B(1—5)+52(1-5)4)

 

 

 

“here “4 _ ad(1+6d(d>—1))(1+fl(1—6)+[32(1—6)2) ’
K = (1-ad)(1-adfl)(1-(1-7)(1-0))(1-5)
5 ad(1+ 6..)(6 — me + 60— 6) + fi2(1 — 6)2)’
,6 z (l—adxl—adahu—o)

aa<1+ 64(6 —- 1)((1+/3(1— 6) + 62(1 — 6)?)

Equation (2.23) show that durable good sector inflation is determined by the same
arguments as in the two period case. The number of lagged output gaps equal to
durability show up in the equation. Therefore, it is confirmed that higher durability
causes inflation to depend on longer periods of aggregate output gaps. While the
change of the durable sector aggregate output gap is related to inflation positively,
the change of the nondurable sector aggregate output gap is related to that of the
durable goods sector negatively because of substitution. The sensitivity analysis of
the response of coefficients of current aggregate output gaps shows how the impact
of own current aggregate output gap (K4) changes by durability compared to the
coefficients of two period case. The impact of current aggregate output gaps on

inflation decreases as durability becomes longer.

2.3.3' N-Period Case

Now we generalize the period of durability to N-periods case. Even though we
have difficulty in interpreting the implication of coefficients, there is an advantage to

obtain general understanding how durability changes inflation dynamics in important

48

ways. The durable stock in period t evolves as follows:

N—
=jZ(1—6)10d,_j_., (2.24)

Because the derivation procedure of aggregate demand and supply is the same as
before, we drop the steps. Instead, we report the result here. Eq. (2.25) represents

nondurable good sector’s aggregate supply in the case of N-period case.

N—1
7Tn,t = K1 (Yn,t — Yrift) - "2 Z (1 — 5)] (Yet—2' ‘ Yclit—j)
i=0
_,.3 (6...: — 6.2,.) + 61616....“ (2.25)

where the parameters H’s are the same as before. As we expected, the sectoral inflation
is affected by durability of durable goods. The degree of output gap persistence on
sectoral inflation, which is defined as the number of lagged and lead output gaps,
exactly depends on the number of periods durable goods provide a service flow. But
notice that only past aggregate durable good output gaps can affect the nondurable
goods sector inflation dynamics. As will see, this result does not apply to durable
goods sector case.

Eq.(2.26) represents the durable good sector inflation as follow:

q

 

—1
71¢, =n3 2 611—6)” (ray—173,) (2.26)
'=0
N—l . (N—l—z' . ,
+n4 Z (1 — 6)’ Z 33(1 - (5)23 (YdJ-i - Ydjt—i)
i=1 _ j=1
N—l _ . N—l—i
+I~t4 2 62(1 — 6)z fij(15)2j Et (yd,t+i _ Y£t+i>
i 1 j=1
N . .
—54 Z (3](1 — 5)] Et (Yn,t+j — 37731“) r “‘1 (idj — 63,1) + (3Et71d,t+1)
"=0

49

l—ad (I—adfixas—(l—vxl-a»
ad (1+ 9d(¢ — 1)) 23:31 6111— 6)J' ’

1— ad (1— adfi)(1 — (1 — 1x1 — 6))
ad (1+9.)(6 —1))2,; 0151(61— )'

 

where K3 =

 

K4:

As we can see, durability can affect inflation dynamics in the same way in the case
of the nondurable sector. But in contrast to nondurable sector, its own output gaps
are included in the equation. Because durable goods provide a flow of service for
N-periods, current purchase is determined by expected future marginal valuation of
durable goods. Then suppliers of durable goods incorporate this fact as they set their
product price. As a result, durable goods sector inflation includes the past and future

output gaps as components by the length of durability.

2.4 Simulation

2.4. 1 Stylized Facts

In this section, we simulate the model and conduct sensitivity analysis. Before we
simulate the model, we need to discuss some stylized facts about the business cycle. In
particular, because we focus on the role of durability in the context of New-Keynesian
business cycle model, we summarize some regularities about durable and nondurable
goods. For more extensive stylized facts, see Stock and Watson(1999) and King and
Rebelo (1999). It is well known that consumption of nondurable goods is less volatile
than output. In contrast, consumption of durable goods is strongly procyclical and
is more cyclically volatile than real GDP or the other consumption measures. For
nominal variables, the price level is countercyclical, but rates of inflation of prices,
for example the Consumer Price Index (CPI) and the GDP deflator, are procyclical
and lag the business cycle. Nominal interest rates are contemporaneously procycli-
cal. Finally, all macroeconomic aggregates display substantial persistence. We will
investigate whether durability can generate volatility, persistence and comovement of

sectoral and aggregate outputs and inflations.

50

2.4.2 Monetary Policy

To close the model, we need to add the monetary policy rule of a central bank
to the structural model. Much recent literature has addressed the question of the
type of policy rule to which a central bank should commit itself by asking which rule
would be the best within some parametric family 0f simple rules. The most famous
of such instrument rules is the Taylor rule. Taylor (1993) showed that the behavior of
the federal funds interest in the Unite States from the mid-19803 through 1992 could
be fairly well matched by a simple rule of the form
T)

Rt = CUlClit + 072(7Tt —- 7T + 7'* + Q,

T was the target level of average inflation, r* was the equilibrium real rate

where 7r
of interest rate and :IIt was the output gap which is defined as the difference‘between
actual output and flexible price equilibrium output. In this simulation, we use a
variation of the Taylor rule because we consider two sectors. Specifically, we assume

that target output gap and inflation are zero and the central bank commits to the

following monetary policy rule,

R, = 0.5 (66",, + 6rd,) + 2 (Mt + 7rd,) + ct, (2.27)

where subscripts, n and (1 represent the nondurable sector and durable sector re-
spectively. The random variable, ct represents an exogenous monetary policy shock.
Recently, many economists have argued that the federal funds rate has been the core
monetary policy instrument in the US. and also suggest that unforecasted changes
in the federal funds rate may provide good estimates of policy shocks. This view
has been argued by the ”structural VAR” literature on the identification of monetary
policy shocks, for example Bernanke and Blinder (1992) and Sims, Leeper, and Zha
(1996). So following this practice, we assume that monetary policy shock can be
identified with movements in the Federal funds rate that cannot be predicted given

information. According to the above policy rule, the central bank responds to sec-

51

toral output gaps and inflations instead of aggregate output gap and inflation. Like
the Taylor rule, the central bank responds to sectoral inflations more aggressively.
Specific coefficient value of output gap ranges from .18 to .99, that of inflation ranges
from 1.5 to 2.15 in the literature. Here as a base line case, we choose the response
coefficient of output gap as .5 and that of inflation as 2. We will consider the case in
which the central bank responds to the two sectors differently later.

Now we have a complete structural model to implement quantitative analysis. The
complete model consists of sectoral demand and supply equations, and the central
bank’s monetary policy rule. Also we define aggregate output as the sum of two
sector’s output, that is, Yt = Yn,t + Yd,t- Aggregate price index, Pt, is defined as
the weighted sum of sectoral price indexes, that is, Pt 2 YnP,” + Yde,t where Yn,
Yd are steady state level of output in each sector. For convenience we rewrite the

complete model as follows:

.. , 1— —1 (1-“')(1-0) P .t
1"W1,tCri.(t 0’ [(1 - 6)Cd.t—1 + Cd,t] I = 61—73,— (228)
P(Lt , 7(1—0) (1"?)(1—0l—1
At—P; = (1 — 7)’U11,tCn,t [(1 — 6)Cd,t_1 + Ca]
, 1— (l-m)(1-0)—1
+ 6(1— 7’)Et1¢1’1,t+1C;/,,(t+10) [(1 — 5)Cd,t + 0.1.11.1] ’ (2.29)
P
/\t = fiRtEtAtHF-t-s (2-30)
t+1

7Tn,t = "31 (Yn,t " Yritt) _ K2 (Yd,t—1 — Yalft—l) — K3 (Yd,t — Yclft)

~K4 (336,1 - flit) + fiEth,t+1 (2-31)

52

716.: = K5 (Yd.t - Kit) + “'6 [(th6—1 — Vii—1) ‘ (’Et (YdatH ‘ Y£t+lll

A

1
_,.,7 2 [33(1 — 6)] Et (Ynjfl' _ Ygtfl’)

i=0
—).<4 (em—6:3,) +13Et7rd3t+1 (2.32)
Rt : 0'5I7Lt + 0'5Id,t + 2701.1 + 271,“ + Q, (2.33)
. Yn . Yd .
Yt = 7 n,t + 71”,”, (2.34)
7ft = YnIn (”mt + int—1) + ded (7rd,t + field—1) . (2.35)

where all 2 represents the percent deviation from their steady state values. Eqs.(2.28)
to (2.30) are aggregate demand equations where A is Lagrange multiplier. At equi-
librium, Cm = 1’",me = Yd.t- Eq.(2.31) and (2.32) represent sectoral supply
equations where the coefficients KS are nonlinear functions of structural parameters.
Eq.(2.33) is the monetary policy rule where ct is monetary policy shock. Eqs.(2.34)
and (2.35) are derived from the definitions of total aggregate output and the general
price index.

Next, we need to choose the length of period and structural parameters for the
model economy, The length of a model period is one quarter, and the discount factor,
[3, is set to .99. The parameter 0 which is the inverse of elasticity of intertemporal
substitution, is set to .16. The leisure preference parameter, (I) is 2.5, the preference
weight parameter of durable and nondurable goods, 7 is .85. The quarterly depre-
ciation rate of the durable stock 6 = .025, consistent with an annual depreciation
rate of 10 percent. The price markup parameter, 6, is assumed to be the same across
sectors and is set to mag, = 1.15), which means that an average markup in the
goods market is 15%. We assume that an average fixed price duration, 0, is .56. As
the base line, we consider the case that durable goods last for only two periods. The

responses are those to a 1% innovatirm in ct.

2.4.3 Main Results

Figure 2.1 shows the impulse responses of output gaps and inflations to a one
standard deviation innovation to the monetary policy shock when durable goods have
different durability. In the figure, the “yo” represents the dynamics of output gap
when there is no durability and the “yg” the dynamics of output gap when durability
is two periods and so on. The first panel shows the dynamics of output gaps where the
effects of a shock last for about 10 quarters. Even though the initial responses to the
monetary policy shock are different over durabilities, the convergence to the steady
state level shows almost identical patterns and the effect of the shock disappears after
10 quarters. In other word, durability does not improve the persistence in the case
of the output gap. One reason for the result could be as follows. By using eq. (2.28)

to (2.30), for convenience, we rewrite eq.(2.13) and (2.14) as follows:

YTLJ : EtYn,t+l — (1’1 [(1 - 6)AYd,t—l + EtAYd3t+1]

r¢2Et [(Rt — 710- Aim“ + A631¢+1l ,

Yd,t = EtYd,t+1+‘I’3 [AYd,t+3EtAYd,t+2]—¢4Et [Ayn,t+1+/3(1—6)Ai/n,t+2]

4’5 (E: (Rt - 7111+1) - EtAde¢+1l — ‘PsEt [Aw1,t+1+fi(1—5)Aw1,t+2l -

where (D’s are nonlinear functions of structural parameters. As we can see, the output
gap of each sector is expressed by differences of lagged own variables, real interest
rate and relative prices. These differences may offset the effect of the monetary policy
shock on output dynamics.

The second panel of Figure 2.1 shows the dynamics of inflations in response to the
shock. As we can see, in this case the durability generates more persistent inflation
dynamics. With no durability, initial impact is lowest and then goes to the steady
state level. As durability increases, the initial impact and the periods the shock
lasts increase. In particular, when the durability is four periods, the initial impact

decreases to .07 percent and even decreases for two quarters and then goes to the

54

Impulse Responses of Output Gap

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o . ,2..- ._____ . - --._-__...---
.. {1" 3-- ---- yo
-0.1 ,/’I — Y2 _
v3
. W y4
-0.2 _
-0.3 _
-0.4 ..
-O.5 _
-0.6 ’- —(
-o_7 l J 1 1 1
0 S 10 15 20 25 30
Impulse Responses of Inflation
0 v _ , L ,_.,..,..u.m..__
”-3.1295417" — _4,_,. ---4--- '"‘ ---- info
4) 01 '/ — ir"2 t
_ - - - inf3
'0-02 , -_ inf‘ a
—o.03 -
-0.04 ..
‘0.05 —(
~0-06 _
.0-07 -
-0.08 ..
.009 l 1 1 l 1
0 S 10 15 20 25 30

Figure 2.1: The Impulse Responses of Output Gaps and Inflations

steady state more slowly. We can notice that as durability increases, the amplitude
and persistence of inflation increases. Durability contributes to generate substantial
inflation dynamics in this case.

The stylized facts say that durable consumption accounts for about 1500 of total
consumption and the durable goods sector is more volatile than nondurable goods
sector. Because the portion of nondurable goods is greater than that of durable
goods in total consumption, it is natural to assume that the central bank responds to
the nondurable goods sector more aggressively. If we assume that the central bank
put more a weight on the nondurable goods sector, for example .85, then monetary

policy rule could be written as follows:
Rt 2 0-425113n,t + 0-0754’7d,t + 267m + 27rd,t- (2.36)

One the other hand, let us suppose that the central bank responds more aggressively

to the volatile sector. The specific monetary policy reaction function is assumed to

be
Rt = 0-3In,t + 0.717,” + 175701.15 + 2.2571,”. (2.37)

According to the above monetary policy reaction function, the central bank puts a
higher weight on the durable goods sector to stabilize the economy. In the face of
uncontrolled positive monetary policy shock, when the output gap and inflation in
the durable goods sector increase given output gap and inflation in the nondurable
sector, the central bank increases the nominal interest rate more than in the opposite
case.

Figure 2.2 shows impulse responses of output gaps and inflation when the central
bank uses the adjusted new monetary policy rule to the monetary policy shock where
the “112 base” represents the output gap under the base line monetary policy rule and
two periods of durability and “y2 wgt” is impulse response under the monetary policy

rule, eq (2.36), and so on. The first. three panels compare the varicms monetary policies

56

on output. In the case of two and three periods of durability, the output impulses
with the monetary policy rule, one which puts more weight on the nondurable goods
sector are greater than other two cases. But when the durability is extended to four
periods, there is no significant difference over the monetary policies. When durability
is short relatively, the policy rule which puts more weight on the durable goods sector
is more effective in the sense that output’s fluctuation decreases.

The stabilizing effect appears in the inflation dynamics more dramatically (Fig
2.3). In the case of two and three periods of durability, the effect of the monetary
policy rule which puts more weight on the nondurable goods sector on inflation is
substantial. When the durability is four, the policy rule which puts more weight on
the durable goods sector stabilizes inflation. In this experiment, we can notice that
as durability is longer, the weighted new policy, which puts higher weight on the
durable goods sector, is more efficient than the base line policy in the sense that the
new monetary policy rule stabilizes the economy more than the base line monetary

policy and one puts more weight on the nondurable goods sector.

2.4.4 Sensitivity Analysis

In this model, the rate of depreciation(6)plays a role in generating persistence in
output and inertia in inflation. To investigate the other implications of the model.
we change the rate of depreciation (6) to study how the model responds. The default
value was 10%. So base line value of 6 is set to .1 and then we would change it to .3,
.5, and .7 respectively. Figure 2.4 shows the responses of output gaps and inflations
to this experiment where “yol” represents the dynamics of output gap when 6 = .1
and two periods of durability. As we can see, output gaps do not respond to variation
in the depreciation rate. Initially, output gaps decrease to about 3.3 percent from
their steady state level. The effect of shocks disappear after about ten quarters. On
the other hand, inflations show small differences over the change of the parameter.
The initial impact depends on the rate of depreciation and converges to steady state

level proportionally. We can notice that the higher rate of depreciation leads to weak

deviation

96

deviation

9%

deviation

°/o

-O.1
v0.2
-O.3
o0.4
-0.5
'0.6
-O.7
-0.8

o0.9

-0.06

-0.1

-0.16

~02

-0.26

~O.3

-035

-0.05
-0. 1
-0.15
—0.2
-O.26
-O 3
-O.36
.04
43.45

-0.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

quarters

- - - - yzbeso
—— yzwgt
_ yznew
.1, _
i- n:
0 5 10 15 20 25 30
matters
JF - - - - yabaso
— Yaw
__ yam
-(
1
.4
1
..(
, . . . quarters
O 5 1O 15 20 25 30
was
":::;:~:T::”“""-T ---- y‘baso
-— Y4W9‘
__ y‘new
7
o 5 10 15 20 25 30

Figure 2.2: The Impulse Responses of Output Gaps with New l\1‘lonetary Policy Rule

58

 

-0.01

 

 

-0.02

-0.03

-0.04

deviation

-0.05

‘70

 

 

 

30

 

 

 

- - - - infabaso i

-o oos —— unfawgt
inf3new

 

-0.01

.0015

-0.02

-0.025

deviation

-0.03

°/o

-0.035

.004

 

 

 

 

 

. . - . lnY‘bOSO
— inf‘wot H
_. inf‘now

-0.01

 

 

43.02

-0.03

v0.04

-0.05

deviation

 

60.08

°/o

.0.07 - 4

'0-09 '- ‘\J-’ -(

 

 

 

-o 09 A A 1 m l
0 5 1 0 1 5 20 25 30
quarters

Figure 2.3: The Impulse Responses of Inflations with New Monetary Policy Rule

59

deviation

°/o

deviation

°/o

 

 

 

 

 

 

 

0
0'1)-

10

 

-0-005
.001
.0015
.002 L1
.0025 )-
.o.03 (

-0-035

I

 

-o.04 )-

 

-0.045

 

 

30

 

 

 

Figure 2.4: The Impulse Responses to Change of Depreciation Rate (6)

 

quarters

60

20

30

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-O.1
'0-2 .1 .(
C
O
'; -0.3)- a
.9
>
0 ~01!
'0
-O.5 P -
o\°
-O.6 - -
25 30
an inf36 i
__ infsfi
__ inf76
c:
O ; I
'1: ':
113 :
> 3, ‘
0 :
u 3 ,
o -0.08 -; 5’ -
o\ '- 5
4-1 )- 3. —(
-o.12 I 1 I l L
0 5 10 15 20 25 30

quarters

Figure 2.5: The Impulse Responses to Change of Relative Price Stickiness (a)

61

initial impact and small response to the convergent path.

When we simulate the model, we assumed that both sectors have the same degree
of price stickiness, in our model. a. The parameter a represents a fraction of producers
in both sectors which is not offered the opportunity to choose a new price in each
period. As a base line case. we pick up an and 01d as .66 following Rotemberg and
Woodford ( 1997). To incorporate the effect of differences in price stickiness, we choose
the parameter value of durable goods sector, ad as .36, .56 and .76 with on = .36 fixed
which means that the price stickiness in the durable goods sector increases relative
to that in the nondurable sector. Figure 2.5 plots the responses of output gaps and
inflations over variation in price stickiness where 3156 represents the output gap when
on = .36 and ad = .56 and so on. Figure 2.5 illustrates that output gaps do not
show substantial differences, but inflations respond to the monetary policy shocks
more persistently as relative price stickiness increases. For example, in the case that
on = .36 and ad = .76, the effect of the shocks lasts beyond 25 quarters.

In summary, we have investigated the dynamics of sectoral and total output gaps
and inflation as durability changes. Durability is not successful in generating the
persistent and substantial responses of output gaps except for in the durable goods
sector. However we have shown that the persistence of inflation depends importantly
on durability of goods. As durability increases, the effect of monetary policy shocks
over inflation is more persistent and substantial. Also we have recognized that a
change in relative price stickiness can affect the dynamics of inflation rather than
output gaps. As relative price stickiness increases, inflations become more persistent

and initial impacts of the monetary policy shock decreases.

2.5 Conclusion

We considered the role of durability to explain the substantial real effect of money
in the context of New-Keynesian model. Our main conclusions can be summarized
as follows. First, durability changes aggregate demand in important ways. Because

of the intrinsic characteristic of durable goods, the persistence of output gaps is

62

generated by the number of periods durable goods endure in addition to conventional
arguments. As durability increases, the persistent effect of output gaps increases.
Also the rate of depreciation is correlated with output persistence negatively. Second,
when durability of goods is incorporated into the price setting decision, aggregate
supply equations depend on both past and expected future output gaps of durable
goods. But one difference is that while nondurable goods sector inflation includes
only lagged output gaps of durable goods, durable goods sector inflation has both
past and expected future own output gaps as its arguments. It implies that the two
sectors would respond to monetary policy differently. Therefore, in contrast to the
one good model, when policy makers design any optimal monetary policy rule, they
should recognize that each sector could respond to policy differently and thus result
in unexpected policy outcomes. Finally, even if we consider durable goods, it does
not generate persistent inflation dynamics in a sense that inflation does not include

any past inflations.

63

Chapter 3

Econometric Policy Evaluation in

Two Sector Model

3.1 Introduction

Over the past 40 years, economic activity and inflation have become less volatile in
the US.1 This “lower volatility” in macroeconomic variables appears to be associated
with improved monetary policy (Clarida, Gali and Gertler (2000), Cecchetti, Flores-
Lagunes, and Krause (2004), Boivin and Giannoni (2003)).2 But even if we agree
with the argument, that is, monetary policy has successfully reduced the variance
of economic activity and inflation, whether the monetary policy was “optimal” or
not is an additional issue to be addressed. On the other hand, it is well known that
monetary policy can have different consequences across sectors. However, the recent
discussion about the optimal monetary policy has often ignored the sectoral impacts
of monetary policy actions since aggregate inflation and output are thought to be
main policy concerns.

The purpose of this paper is to evaluate the optimality of monetary policy in

a multi-sector economy. Specifically, this paper investigates whether it is optimal

 

lFor extensive evidence and explanation, see Stock and Watson (2002, 2003).

2In addition, other explanations might include changes in the structure of economy (McConnell
and Perez-Quiros (2000), Kahn, McConnell and Perez-Quiros (2002)) and reduction in the variance
of exogenous structural shocks (Stock and W'atson (2002, 2003)).

64

for the central bank to use discretionary monetary policies which take account of
sectoral impacts in response to structural shocks. Furthermore, this paper also tests
the hypothesis that if the central bank had used these discretionary policies, monetary
policy could have been more efficient in the sense that monetary policy would have
reduced the volatility of output and the inflation rate.

To address this issue, we estimate a New— Keynesian type structural model with two
sectors: durable goods and nondurable goods. The reason that we choose these two
sectors is that these sectors show dramatic differences in response to a change in the
nominal interest rate, which is the central bank’s monetary policy instrument. After a
rational expectation model is solved, the reduced form structural model is estimated
by F1111 Information Maximum Likelihood (FIML) estimation method, which is a
popular estimation strategy in the literature. One important thing to note is that
we must assume the central bank’s specific objective is to minimize the deviation
of sectoral or aggregated output and inflation from their targets since we have an
interest in the optimal monetary policy. In this paper our interests are limited to the
discretionary monetary policy case.

To evaluate the optimality of the monetary policy, the traditional approach is
to construct an output-inflation variability efficiency frontier. (Cecchetti et al 2004,
Fuhrer 1997, Rudebusch 2002, and Taylor 1979). Following the line of research, we
obtain the optimal monetary policy trade—off locus by changing policy weight param-
eters and by using the estimated model. When we define the discretionary optimal
monetary policy as the locus that achieves the lowest possible trade—off between
variabilities of inflation and output gap, we can study which discretionary monetary
policy regime is optimal, i.e., targeting disaggregated variables, or targeting aggre-
gate variables. This comparison also can help us to evaluate whether past monetary
policy was optimal.

The remainder of the paper is as follows. In section 3.2, we present the complete
structural model to be estimated. Section 3.3 describes the data and preliminary
estimation results. These results will be used as the starting values later when we

estimate the complete model with optimal monetary policy rules. In section 3.4, after

65

we choose the central bank’s objective function, we describe the procedure to obtain
the efficiency frontier for monetary policy. Section 3.5 presents and discusses the

main results.

3.2 The Structural Model

In this section, we present the structural model we estimate. The complete model
consists of the intertemporal IS equations, New-Keynesian Phillips curves, and the
central bank’s reaction function.3 The below two equations, (3.1) and (3.2), represent

the aggregate spending relationship, corresponding to a traditional IS equation.
imt = alEti’nJ-l-l + QQP‘nJ—l + 013AEt4I3d,t + O4A(Rt - 7rn,t+1) + umt, (3.1)

536,1 = asEtid¢+decidi—1+07EtAEtin,t+1”rflsEtA13r,t+1+09A(Rt—7Td,t+1Wat)

(3.2)
where $j,t is the output gap for sector j, defined as output relative to the equilibrium
level of output under flexible prices (E 177m — 1772,), A denotes the first-difference, for
example, Art = :rt — :rt_1, Rt is the nominal interest rate which the central bank’s
policy instrument, 7r“ is the inflation rate for sector j, PM is log relative price level
defined as ln(Pd’t/Pn’t) where PJ-J is price level for sector j. Finally, 11” represents
the demand shock for sector j.

Equation (3.1) represents aggregate demand in the nondurable sector depending
on its own expected future and lagged output, the first difference of the ex ante real
interest rate and durable goods’ output, and a demand shock. Equation (3.2) is
the demand of the durable goods sector. The aggregate demand for durable goods
depends on the same arguments except for the first difference of expected relative
price and expected nondurable goods’ output.

In contrast to traditional models based on individuals’ optimization problem, the

aggregate demand of each good is partly determined by the first difference of the ex

 

3For explicit derivations. refer to the previous chapter.

66

ante real interest rate rather than the level of ex ante real interest rate. The reason is
as follows. The representative household obtains utility from the service flow of the
durable stock, not the purchase of durable goods. Since the new purchase of durable
goods is determined by the difference between current and previous period’s durable
stock and the demand for nondurable goods depends on the demand for durable
goods, the aggregate demand for both goods are determined by the first difference of
arguments which include the ex ante real interest rate.

Note that the above specifications extend the theoretical model in two dimensions.
First, we allow for degree of backward-looking behavior (02in,t—1 and 0653d,t—1) in
order to explain the slow adjustment of output observed in the real world (Fuhrer and
Rudebusch (2004)) and to avoid inconsistent estimation caused by serially correlated
sectoral demand shocks and lagged dependent variables. Second, we add the forward
looking variable, Etid,t+1) to the equation (3.2) to take account of forward looking
behavior in the durable goods sector.

The following two equations represent sectoral New-Keynesian Phillips curves
7rn,t = 51in,t+)3271n,t—1+53id¢+fi4EtPnt+1+135Pr,t+1+fieEt7rn,t+1+€n,t (3-3)

716,: = fi7id,t+(3877d,t—1+59in,t+fi10EtPr,t+l+511Pr,t+512Et7Id,t+l+ed,t1 (3-4)

where the exogenous shock 63¢ for jzn, d is a cost shock.

The above two equations describe dynamics of sectoral inflations in both sectors.
While sectoral inflations depend on their own current output gaps and future inflations
like traditional New-Keynesian Phillips curves, they also are determined by current
and future expected relative price gaps and future expected nondurable goods’ output
gaps as well.

These equations are different from the conventional N ew-Keynesian Phillips curve
in two ways. First, when price stickiness is not the same across sectors, relative price
fluctuations become another transmission mechanism, which does not exist in the one

good aggregate model. In the face of an unexpected monetary shock and changes of

67

relative prices, households and firms will adjust their behavior. In fact, the pressure
of relative prices reduces the inflationary effect in that sector because of substitution
between the two goods. Second, durability might generate non negligible endogenous
dynamics for sectoral inflations. Since durability introduces time non-separability in
the utility function into the model, we can see substantial persistence of variables in

the model.

3.3 Data and Preliminary Estimation

This section describes data used in the estimation, preliminary estimation method-
ology and main results. We use quarterly data for the period from 1960Q1 to 2004Q4.
Data has been demeaned prior to estimation in order to eliminate constant terms in
. the structural equation. All data series are obtained from the Bureau of Economic
Analysis and the FRED database of the Federal Reserve Bank of St. Louis.

The output gap (it) is the percent deviation of sectoral real GDP (measured in
chained 2000 dollars) from sectoral potential GDP, i.e. ij,t E 100(ln(GDPj,t) —
potential GDPj,t).4 The inflation rate (at) is the annualized quarterly change in
the GDP chain-weighted price index, i.e. 7rt E 400(ln(Pt) —ln(Pt_1)). 5 The interest
rate (Rt) is the average of monthly rate on a Federal Funds Rate.

As a preliminary step, we estimate the structural model by limited information
methods. In particular we estimate Intertempotal IS equation (eq.(3.1) and (3.2))
and New-Keynesin Phillips curve (eq. (3.3) and (3.4)) separately by two stage least
squares (2SLS).6 We also estimate the system by three stage least squares(3SLS)

to exploit efficiency gain by using the contemporaneous covariance among structural

 

4Since sectoral real GDP data is not available, it is calculated from industry production data in
NIPA. After each industry is divided into durable and nondurable goods sector, then the ratio is
calculated. This ratio is used to obtain sectoral real GDP data from aggregated real GDP. For the
potential GDP, quadratic trend is used, that is, Co + clTrendt + CgTrendtz. But because of possible
measurement error, HP filter also is used.

5Since sectoral inflation data also is not available, sectoral price index from durable and non-
durable consumption goods are used as proxy for calculation of sectoral inflations.

6For 2SLS estimation, instrument set includes four lags of sectoral output gaps, inflations and
relative price index.

68

errors.7 This estimation methodology can help us to obtain initial values that can be
used for estimation of the complete structural model by the full information method
and to verify the overall specification of the structural model.

Table 3.1 shows the estimated results of the Intertemporal IS equation over the
durable and nondurable goods sectors. One remarkable result is that parameter esti-
mates and standard errors are stable over estimation methods. Parameter estimates
in which we have an interest are the forward-looking terms (071 and 075), which rep-
resent the effect of expected sectoral future output, and ea: ante real interest rate
sensitivity (04 and 09).

Table 3.1: Estimation Results of the Intertemporal IS Equation

in,t=011Et53n,t+1 + agin,t_1 + a3(id,t — id,t—1)A+ a4A(Rt — 7rn,t+1) + amt,
id,t=05Etid,t+1+06id,t—1+07EtAin¢+1+08EtAPr,t+1+093(Rt— "(Lt+1)+ud,t

 

 

 

 

 

 

ZSLS 3SLS
Coefficient I P-Value Coefficient L P-Value
6.1 0.589 (0.086) 0.000 0.589 (0.104) 0.000
(12 0.422 (0.081) 0.000 0.422 (0.100) 0.000
03 0.006 (0.027) 0.807 0.006 (0.035) 0.858
04 -0.028 (0.072) 0.698 -0.028 (0.073) 0.703
(15 0.590 (0.074) 0.000 0.590 (0.078) 0.000
06 0.434 (0.063) 0.000 0.434 (0.070) 0.000
07 -0555 (0.751) 0.383 0.543 (0.721) 0.373
08 0.197 (0.381) 0.604 0.196 (0.495) 0.692
69 -0030 (0.205) 0.885 0032 (0.187) 0.865

 

 

 

 

 

 

 

Note: Standard errors in parentheses.

The coefficient estimates of the forward-looking term across the two sectors are
0.589, which all are significantly different from zero. On the other hand, the estimated
degree of backward looking behavior in aggregated sectoral demand is 0.422, which
are all significant and implies persistence in sectoral outputs. This result indicates
that forward looking behavior seems as important as backward looking behavior. The
relative importance of forward looking behavior is a controversial issue in empirical
macroeconomic literature. By using a one good econometric model and full informa-

tion maximum likelihood estimation (FIML), Fuhrer and Rudebusch (2004) estimate

 

7If all equations are correctly specified, system procedure such as 3SLS is more efficient. than a
single-equation procedure such as 2SLS. But single-equation methods are more robust.

69

the degree of forward looking to be between 0 and 0.4. while they estimate the degree
of backward looking to be between 0.53 and 0.99. Then they conclude that rational
expectations of future output are not important for the determination of current out-
put. In addition, Lindé (2002) and Rudebusch (2002) obtain 0.43 and 0.30 for the
degree of forward looking behavior, while Siiderstriim et al (2005) estimate it to be
0.56 which is similar to our estimates.

Regarding parameters (074 and 019) that govern real interest sensitivity in both
sectors, the real interest rate coefficient estimates are of the correct sign, but are
not significantly different from zero over both estimations. In addition, absolute
value of the durable goods sector’s real interest sensitivity is greater than that of the
nondurable goods sector’s. This implies that the durable goods sector is a little more
sensitive to ex ante real interest than the nondurable goods sector. This finding is
also consistent with Mankiw (1985), Gali (1987).

Table 3.2 shows the estimation results of sectoral New-Keynesian Phillips curves
over durable and nondurable goods sectors. We also report the p-values for the J-
statistic, which all are not significant. Thus the instruments we have chosen appear
valid. The slope coefficients (61 and 67) have the correct signs over both sectors
and estimation methods. But coefficients of durable goods sectors are not significant.
These estimated coefficients appear to be consistent with earlier research. Those vary
from 0.015 to 0.13 (Fuhrer (1997), Gali and Gerther (1999), Lindé(2002), and Rude—
busch (2002)). In terms of the effect of the output gap on current sectoral inflation,
note that the output gap of the nondurable goods sector causes greater impact on
current sectoral inflation than that of the durable goods sector. The estimates of
the coefficients (67 and 614) on expected inflation are between 0.55 and 0.59. All
estimates are significant and greater than the estimates of past sectoral inflations,
i.e 62 and ,88. This evidence indicates that expected future inflation is slightly more
important than past inflation for the determination of inflation dynamics. Research
has shown conflicting evidence about relative importance of expected future and past
inflation. Gali and Gertler (1999) and Sbordone (2002) argue that forward looking

behavior, i.e expected future inflation, is quantitatively important while backward

70

Table 3.2: Estimation Results of the Phillips Curve
"mt = 6113712 + (32717151 + 63116,: + fi4Etlfr,t+1 + 651351 + fl6Et7In,t+1 + 871,5
716,5 5753d,t + fi8”d,t—1 + 5913712 + 510EtPr,t+1 + 511331 + 512Et77d,t+1 + 66,1

 

 

 

 

 

 

 

 

 

 

 

 

 

2SLS 3SLS
Coefficient I p-value Coefficient L p-value
(31 0.084 (0.042) 0.047 0.066 (0.035) 0.055
62 0.389 (0.119) 0.001 0.406 (0.087) 0.000
63 -0.027 (0.013) 0.039 -0.023 (0.010) 0.025
64 0.753 (0.245) 0.002 0.652 (0.211) 0.002
55 -0.694 (0.242) 0.004 -0.606 (0.209) 0.004
66 0.553 (0.115) 0.000 0.555 (0.085) 0.000
137 0.011 (0.012) 0.347 0.015 (0.011) 0.178
68 0.460 (0.051) 0.000 0.507 (0.037) 0.000
139 -0.070 (0.053) 0.189 -0.075 (0.054) 0.165
310 -0.947 (0.276) 0.001 -0.855 (0.260) 0.001
611 0.902 (0.263) 0.001 0.805 (0.251) 0.001
312 0.594 (0.065) 0.000 0.545(0.045) 0.000
J-test(p-value) Eq.(3): 0.534, Eq.(4): 0.396 0.579

 

 

Note: Standard errors in parentheses.

looking behavior, i.e., past inflation is of limited quantitative importance. On the
other hand, Fuhrer (1997), Robert (2001), and Rudebusch (2002) argue that the
New-Keynesian model with only forward looking behavior does not fit the US. data
and requires additional lags of inflation not implied under rational expectations. Our
results support the evidence that Gali and Gertler (1999) and Sbordone (2002) sug-
gested.

Finally, we close the structural model by estimating the reaction function of the
central bank. In what follows, we assume that the central bank uses the Federal

Funds Rate (Rt) as its instrument. The specific functional form is given by

Rt = PRt—l + (1 - (9)017 + uyfvt) + 5t (3-5)

where R is the Federal Funds Rate (the instrument of monetary policy), [17; is the
aggregate inflation rate and 3:15 is the aggregate output gap. This is the modified

Taylor rule with an additional lagged interest rate Rt.8 This lagged term can help

 

8For detailed derivation of the functional form, see Gah’ and Gertler (1999). Since we use demeand
data, This equation does not constant term.

71

to explain the large persistence in the nominal interest rate (see e.g., Clarida et al.
(2000), Woodford (1999)). We will use this form of reaction function as the baseline

monetary policy rule later.

Table 3.3: Estimation Results of the Reaction Function
Rt = pRt—l + (1 - Mum + Myrrt) + 8t

 

 

 

 

 

 

 

 

 

p p-value 11W p—value 11y p-value R2
Whole sample 0.907 0.000 1.257 0.034 0.836 0.070 0.921
(0.039) (0.595) (0.462)
Pre—1979:Q3 0.886 0.000 0.184 0.720 1.013 0.011 0.892
(0.038) (0.514) (0.397)
Post-1979Q3 0.859 0.000 2.053 0.001 0.483 0.143 0.934
(0.054) (0.592) (0.330)

 

 

Note: Standard errors in parentheses. RTdenotes the adjusted R2.
Whole sample period is 1960Q1-2004Q4.

Table 3.3 shows the estimation results of the modified Taylor rule by ordinary
least squares (OLS). Since the estimation results are sensitive to the choice of sample
period (e.g., Soderstrom et al. (2005) and US. monetary policy has been changed
dramatically in the late 1970s (Gali et al. (2000)), we also report the estimation
results with pre and post 1979Q3 sample periods.

Over three sample periods, the lagged interest rate explains the dynamics of the
interest rate well, which means that the short-term interest rate has substantial per-
sistence. The other thing to note is that the response coefficient (#77) to inflation is
relatively high and significant in the post 1979Q3 period. This result supports the
finding of Clarida, et al.(2000) who suggests that for the post 1979 rule the estimate
is significantly above unity. We will use the above rule as the baseline rule when we

evaluate other monetary policy rules.

3.4 Discretionary Policy and Loss Function

Given the empirical model described above, we examine the performance of three
specific discretionary policies in terms of the central bank’s objective function. Since
we consider two different sectors, it is assumed that the central bank’s objective func-

tion has sectoral output gaps and inflations as arguments. This approach is consistent

72

 

with that of Blinder and Mankiw (1984), Waller (1992), Duca and VanHoose (1990),
even though they did not consider inflation as an argument.9 As a baseline case, the

central bank’s objective function is assumed to be of the form:

. 1 0° -
Mm 50—813: 20%] . (36)
2'20
2 2 2 2
Lt = ”n,t+i+7rd,t+i+“”$n,t+i+“dxd,t+i’ (37)

where the parameter pj is the relative weight on output deviations in sector j, 6 is
the discount factor. This objective function assumes that target inflations and output
gaps in both sectors are zero. Therefore, expected loss equals the weighted sum of

unconditional variances,
E(Lt) = VaT(7rn,t) + VaT(7Td,t) + unVaT($n,t) + Hal/070111) (3-8)

In the literature concerning stabilization of the economy, many discussions have
been built on one good models. In this case, it is assumed that the central bank

minimizes the following loss function
1 °° .
Min 5(1—fi)Et 2521181 . (3.9)
i=0
Lt == 73+.+Aaw?+5 (3.10)

where /\a is the relative weight on the aggregate output gap.
Finally, we consider the policy to only target the durable goods sector (DGT).

Then the policy objective is given by
DGT __ 2 2

where )‘dg is the weight on output gap of the durable goods sector.

 

9We will examine the policy implication in next section, as the central bank’s objective function
depends on aggregated variables.

73

3.5 Estimation and Optimal Policy Frontier

In this section, we present our empirical results and interpretations. Since the
model includes rational expectation terms, we should solve the model for the reduced
form first before we implement estimation. In this paper, we solve the problem by
following Séderlind’s approach (1999) with the assumption that the central bank
implements discretionary monetary policy. Then after we specify the conditional log-
likelihood function, we can obtain the Full Information Maximum Likelihood (FIML)

estimates.

3.5.1 Parameter Estimates

F IML estimates are shown in Table 3.4 . Standard errors are obtained as the
inverse of the Hessian Matrix. Each column represents estimation results under dif-
ferent monetary policy regimes. For example, the first column (Case (1)) is the result
in which the central bank implements discretionary monetary policy to target the de-
viation of sectoral inflations (77mg and 7rd,t) and output gaps ($7M and de)’ While
the second column (Case (2)) reports the result under the assumption that the cen-
tral bank targets the deviation of aggregate inflation and output gap (at and act), the
last column (Case (3)) represents the result when the central bank targets only the
durable goods sector’s inflation (7rd,t) and output gap (10¢)-

In terms of coefficients of intertemporal IS equation (a ’8) across different mone-
tary policy regimes, estimates of the forward-looking term across the two sectors ((11
and a5) vary from 0.32 to 0.589, which all are significantly different from zero while
the estimates of backward looking behavior vary from 0.1 to 0.45. Across monetary
policy regimes, estimates of the nondurable goods sector’s IS equation implies that
forward looking behavior is more important than backward looking behavior while
the durable goods sector shows mixed results.

The results also show that coefficients associated with the real interest rate sen-
sitivity (a4 and 09) are estimated poorly. Size and sign of some coefficients are

not consistent with theoretical prediction as well. Therefore, a comparison of Table

74

 

 

 

 

 

 

 

(1) Lt=7rn,t+7rd,t+“nxn.t+#dxd,t (3) Lt:7rd,t+)‘d9xd,t
071 0.5890 (1.0000) 0.5895 (0.0000) 0.5890 (1.0000)
02 0.1831 (0.0005) 0.4398 (0.0358) 0.4338 (0.0006)
(13 -0.1634 (0.0019) 0.0253 (0.0203) 0.0229 (0.0005)
(14 -0.9217 (0.0006) -0.I262 (0.0044) 0.0130 (0.0000)
05 0.3218 (0.0001) 0.5429 (0.0055) 0.4598 (0.0002)
06 0.6128 (0.0000) 0.4602 (0.0167) 0.4502 (0.0004)
07 -0.2287 (0.0002) -0.6305 (0.0308) ~0.6425 (0.0003)
0'8 -0.3736 (0.0023) 0.1699 (0.0169) 0.2509 (0.0006)
09 0.4326 (0.0004) 0.0362 (0.0071) -0.0591 (0.0005)
(31 0.1431 (0.0002) 0.0232 (0.0280) 0.0427 (0.0000)
732 0.5057 (0.0001) 0.4319 (0.0200) 0.4578 (0.0000)
(33 —0.0334 (0.0001) -0.0244 (0.0073) -0.0275 (0.0000)
[34 1.0195 (0.0008) 0.6314 (0.0395) 0.5987 (0.0002)
[35 -0.8689 (0.0007) -0.6751 (0.0105) —0.5978 (0.0002)
{36 0.4511 (0.0001) 0.5068 (0.0434) 0.5630 (0.0000)
(’37 0.0734 (0.0001) 0.0246 (0.0074) 0.0197(0.0001)
(’38 0.6208 (0.0001) 0.5130 (0.0040) 0.4670 (0.0001)
[39 -0.3175 (0.0001) -0.0398 (0.0310) -0.0482 (0.0001)
[310 -1.4023 (0.0007) -0.8075 (0.0106) -0.7777 (0.0000)
6'11 1.2163 (0.0003) 0.8300 (0.0428) 0.8175 (0.0000)
612 0.1596 (0.0001) 0.5080 (0.0324) 0.5224 (0.0002)

 

 

 

 

Note: Standard errors in parentheses.

3.4 with Table 3.1 shows that FIML estimation is not always better than the single
equation estimation approach in contrast to Lindé(2002).

Finally, we can see that estimates from the single equation approach (Table 3.1)
are closer to those from FIML under the assumption that the central bank targets
the deviation of aggregate inflation and output gap (Case (2)). In other-words, this
result indicates that monetary policy targeting aggregate inflation and the output gap
explains historical data better than any other monetary policy regimes. It seems to
be consistent with the traditional view and assumption by Barro and Gordon (1982)
and Svensson (1997, 1999) about monetary policy objective.

In general, estimates of New-Keynesian Phillips curve (13’s) are stable across mon-
etary policy regimes in contrast to estimates of intertemporal IS equation. Size and
sign of estimated parameters are reasonable and consistent with the single equation

estimation (Table 3.2). Estimates of the forward—looking term across the two sectors

75

((36 and 612) vary from 0.15 to 0.56, which are all significantly different from zero
while the estimates of backward looking behavior (62 and 68) vary from 0.43 to 0.62.
In Case (1), backward looking behavior is more important than forward looking be-
havior in both sectors while Case (3) indicates that forward looking behavior is more
important and Case (2) shows mixed result across sectors. These results indicate that
the monetary policy regimes could be a factor in determining the relative importance

between forward and backward looking behavior.

3.5.2 Optimal Policy Frontier

In this subsection, we compute the “optimal policy frontier”: the set of efficient
combinations of inflation variance and output variance attainable by policymakers.
But note that the frontier says nothing about what combinations are desirable. Then
we evaluate monetary policy regimes using the policy frontier.

Given the structure of economy and the monetary policy regime, each optimal
monetary policy frontier is calculated and compared. In this paper, the more efficient
monetary policy is defined as the combinations of standard deviation close to the
origin of policy frontier. The values of standard deviations depends on the shocks
experienced by the economy as well. In this paper, since we assume that all structural
shocks are same over monetary policy regimes, we can exclude the possibility of change
of policy frontier curve caused by shocks (See, for example Cecchetti, Flores-Lagunes
and Kraus (2004), and Stock and Watson (2003)). In other words, with the same
amount of structural shock, the monetary policy which shifts the policy frontier close
to origin is more efficient.

Each point on a frontier corresponds to a different relative weight on aggregate
(or disaggregate) inflation and output gap variability. Specifically, given the model
specification and parameter estimates, the monetary policy regime that targets disag-
gregate variables solves the optimization problem represented by equation (6) to (8).
The upper panel of Figure 3.1 represents the policy frontier over a grid for #71 and #d

from 0.0 to 1 in increments of 0.05, when the central bank implements the monetary

76

S. D. of Inflation

S. D. of Inflation

0.296

0.294

0.292

0.290

0.288

0.286

0.284

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00

 

 

 

 

 

 

 

 

 

I
1
l r I l
0.48 0.50 0.52 0.54 0.56 0.58
S. D. of Output Gap
d
-(
I l I i
0 0.2 0.4 0.6 0.8 1.2

S. D. of Output Gap

Figure 3.1: Optimal Policy Frontier

77

policy to seek to minimize the deviation of disaggregate inflations and output gaps
from their targets. For low relative weight on disaggregate output gaps, the cost to
reduce inflation in terms of standard deviation of aggregate output gap is very high.
One thing to note is that for some high relative policy weights, the policy frontier
shows positive relationship between standard deviations of aggregate inflation and
output gap. This implies that in this interval, the central bank does not face a policy
trad-off.

The bottom panel of Figure 3.1 represents the policy frontier over a grid for /\a
from 0.0 to 1 in increments of 0.05, when the central bank implements the monetary
policy to seek to minimize the deviation of aggregate inflations and output gap from
their targets (eq.(3.9) and (3.10). This policy frontier is consistent with conventional
wisdom (Taylor (1979), Fuhrer (1997) and Rudebusch (2002)) since we assumed that
the central bank minimizes the loss function depending on aggregate inflation and
output gap. According to the graph, we can see that the policy long run trade—off
relationship exists in the two goods model.

The main result of this experiment comes from the comparison of the above two
graphs. Considering the scale of the two graphs, the policy frontier in which the
central bank targets disaggregate variables (upper left panel) is closer to the origin
than policy frontier in which the central bank targets aggregate variables (upper right
panel). This implies that the past monetary policy could have been more effective if
the central bank had been concerned about sectoral stabilization. A crucial assump—
tion for this result is that the true loss function depends on sectoral inflations and
output gaps. Since we assumed that aggregate inflation and output gap are defined
as the linear combination of disaggregate inflations and output gaps, the stabilization
of disaggregate variables results in the low variability of disaggregate variables and
thus aggregate variables. On the other hand, the monetary policy to target aggregate
variables does not care about fluctuations of disaggregate inflations and output gaps.
Thus the policy results in higher volatility of aggregate variables even if the policy
objective of central bank is targeting aggregate variables.

Under the assumption that the central bank implements the monetary policy to

78

 

target only one sector (in our case, the durable goods sector, eq.(3.11)), Figure 3.2
represents the policy frontier of durable goods sector’s inflation and output gap. In
contrast to previous two cases, the locus represents the combinations of durable goods
sector’s inflation and output gap. In this policy regime, the trade-off relationship
between aggregate inflation and output gap dose not exist. Thus it is possible to
obtain the lowest variability of inflation and output gap. In our experiment, the

relative weight on durable sector’s output gap ( Adg) is 1.

1.4

 

1.2

1.0

0.8

L

0.6

S. D. of Inflation

0.4

 

 

0.2 ,,

 

 

 

I I I

0 0.2 0.4 0.6 0.8 1 1 .2
S. D. of Output Gap

Figure 3.2: Optimal Policy Frontier(DGT)

3.5.3 Sensitivity Analysis

This section implements the robustness analysis of the computed optimal policy
frontier with respect to the exact specification. Figure 3.3 represents the changed
policy frontier (dashed line) with respect to the change of impact of relative price gap
on the aggregate demand (Intertemporal IS equation).10 Specifically, the new policy
frontier is calculated under the assumption that the impact of relative price gap(c18)

is zero.

 

10The original policy frontier is represented by the solid line.

79

S. D. of Inflation

S. D. of Inflation

0.300

0.295

0.290

0.285

0.280

0.275

0.270

0.265

0.260

0.255

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00

 

 

 

 

Y I ‘U

0.2 0.4 0.6 0.8
S. D. of Output Gap

 

 

 

 

V I

0.5 1 1.5 2 2.5
S. D. of Output Gap

Figure 3.3: Sensitivity Analysis of Policy Hontier

80

S. D. of Inflation

S. D. of Inflation

0. 305

0.300

0.295

0.290

0.285

0.280

0.275

0.270

0.265

0.260

0.45

0.40

0.35

0.30

0.25

0.20

 

 

 

 

 

 

 

 

 

h
‘5‘
..I
I I I
0.2 0.4 0.6 0.8
S. D. of Output Gap
"1
'I
'l
.l
'I
a
0‘.
I"
"-‘
' x
I‘__
x
I.“
1.
a
I I I l
1 2 3 4 5

S. D. of Output Gap

Figure 3.4: Sensitivity Analysis of Policy Frontier

81

The upper panel is the policy frontier in which the central bank seek to minimize
the deviation of disaggregated inflations and output gaps from their targets. Since
we ignore the effect of relative price on aggregate demand, combinations of standard
deviations of aggregate inflation and output gap shift to the origin. In other words,
the policy trade—off that the central bank faces is improved as we expect. The bottom
panel is the policy frontier in which the central bank’s objective is to minimize the
deviations of aggregate variables from their targets. In this case, the policy frontier
is relatively insensitive to the absence of relative price effect. The comparison of
two graphs shows that the policy frontier in which the central bank targets disaggre-
gated variables achieves the lower combinations of volatility of aggregate inflation and
output gap. This results suggests that the monetary policy targeting disaggregated
inflations and output gaps has a possibility that the policy trade—off relationship the
central bank faces could be improved.

The Figure 3.4 represents the new policy frontier (dashed line) in which the
structure of the economy has no backward looking term in aggregate demand, that
is, £12 and 06 are equal to zero. The upper panel represents the policy frontier in
which the central bank targets disaggregate inflations and output gaps while the right
panel is the case that the central bank targets aggregate inflation and output gap.
In both cases, the policy frontier shifts to the right side. But the comparison of the
two graphs shows that even with no ”backward-lookingness”, discretionary monetary
policy targeting disaggregate variables can achieve lower combinations of volatilities of
aggregate inflation and output gap than the discretionary policy targeting aggregated

inflation and output gap.

3.6 Conclusion

In this paper, we estimate a two sector New-Keynesian structural model and
evaluate alternative monetary policy regimes. The estimated two sector model and
alternative policy regimes are used to calculate the optimal monetary policy frontier.

W’e find that changes in monetary policy responses to aggregate or disaggregate

82

inflations and output gaps can imply substantial differences in long—run inflation and
output variances. More interestingly, the location of the optimal monetary policy
frontier implies that the past monetary policy could have been more effective if the
central bank had been concerned about sectoral stabilization.

But we have to note one thing. The optimal policy frontier is just attainable
combinations of inflation and output gap variances. Thus the monetary policy to
care about sectoral stabilization can achieve the location close to the origin does not
mean that it is more effective than the policy to care about aggregated variables.
The result of this paper suggests simply that the former provides the central bank
with the available opportunity set of combinations of lower volatilities of inflation
and the output gap. Considering the uncertainty about the structure of economy and
data used, the result of this paper shows that sectoral stabilization is as important

as traditional stabilization policy if people care about their own sector or industry.

83

Appendix A

Appendix

F irm’s profit maximization problem is

 

 

oo "‘6 _6
. Pdt(Z) Wt kfpdtle
Max E, 50)"), k P (z) ’ m k— + ’ Ydt k

(A.1)
F.O.C

 

 

Pt+k 9 - 1 Pt+k Pd,t+k 8943+}.
(A.2)

—0
0" P (2')
k d,t
Et 2 (073) At,t+k( ) Yd,t+k

Pd,t(2) 9 Wt+k Pt+k 1 ]=0
[:20 Pt+k

 

By using household’s first condition,

 

 

—0 I ¢—1

k d,t pd,t 3,t+k t+k
E —— Y . A - - =0. A.3
t E (afl) ( + ) d,t+I. t,t+l. Pd,t+k 6—1 8941+]: ( )

Log-linearization: LHS of bracket term of above equation, If we know the fact that
Pn t(Z) P71 t(Z) P71 t

 

 

 

j t = 1’n,t 75;—
. , (57(1— (3(1— 6) - 730—5)
A = — — Y -+ ° A4
t,t+k xd,t+k 1 __ 6(1— (5)2 dat‘f’t (1_/3(1_5)2) ( )
. . 1—6 . .
(“OI/11.,t+k+1+PR,t+k+1] + (1—13(1—-6)2) [-UYnJ+k—1+PR.t+k—1]
_)(1-.3(1-5)) (1—6) -

(1—(1—5)L)132,t+

 

 

'U1’1,t—1a

(1—/3(1_6)2) (1530—6)?)

84

Z
where pdt(z=log(?§1%(t—)).

RHS of bracketed term of above equation: First, by using production and demand

function,

 

 

8—1 —0(<b—1 )
1/13,t+k"t+k Pt+k =¢3¢+k Pt+k (136862)) Y3—1(A-5)

¢4¢+k Pd,t+k ‘1’ Pd,t+k Pd,t+k 0””
4,t+k

% 1133,t+k-¢¢4,t+k—id,t+k+(¢ - llyd,t+k—0(¢1{Pdt 2: 7rd ,t+i}

Substitute above two log-linearized equations into FCC and use marginal utility of

durable goods and solve for pd,t(z)

 

 

 

 

 

 

1+0¢ 1 81 5 . .
( 1—(a003»P‘“1):E’,::(0WWl 1:150:11)? )+¢‘1)Yd.t+k—¢“/J4.t+k
1—5 .
+(1—fi(1—0)2) {0Yn,t+k—1_Pr,t+k-I}
1:
1—5 . . ,
+(1-fifi((1—c)5)2) {OVEN/8+1 ‘ Pow/9+1} + (1+9(<f>-1))ZM,1+1 +w3.t+k
i=1
7(1—50—6» _ ’- _ 1-5 I.)

where L represents the one period lag operator. Let denote 2:” represents the natural

rate of variable X. The equation (A6) can be written as

00

1—0161)”13(1 5) ‘ ‘n
= (1+9? )E‘tZéafi) WW 1_ --fl(1 (5)2 +¢‘1)(Yd,t+k-Yd,t+k)

 

 

 

[:2
+ Y” )— (P — P" )
(1_ :(1— 6M2 (Yn,t+k— 1 n,t+k—l r,t+k—-1 r,t+k—l

 

 

n A ”n
(1— 313(1—fl55):2){( Ynt+k+l_ Yn,t+k+1)_(Pr,t+k+1‘Pr,t+k+1)}

00

+(1—aB)Et Z (amk 2: 7rd,”, (A.7)
k: '—

85

By some algebra and calculation, following relationship is satisfied:

00 k 00
1
23W 2er = —<1 .. am 80/387151 (A8)

and

 

Pd’t(z) = 7rd,t (A.9)

1 — 0
Substituting above equation into equation (A.7), we obtain New-Keynesian Phillips

curve of the durable sector in the text.

86

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