The paper extends Woodford's (2000) analysis of the closed economy Phillips curve to an open economy with both commodity trade and capital mobility. We show that consumption smoothing, which comes with the opening of the capital market, raises the degree of strategic complementarity among monopolistically competitive suppliers, thus rendering prices more sticky and magnifying output responses to nominal GDP shocks.

Assaf Razin

Chi-Wa Yuen

English

Research Papers in Economics

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1=*39 93A* ,,39
6<4/;!"B%!%1 Introduction
In this paper, we examine how open capital market policies would interact with the degree of
price rigidity in the domestic economy to aﬀect the output-inﬂation tradeoﬀs and, similarly,
the volatilities of output and inﬂation in response to nominal shocks. The analysis will
be conducted in an optimization-based “New Keynesian” framework al aBlanchard and
Kiyotaki (1987). In the discussion, we extend to an open-trade and open-capital economy
the succinct exposition of Woodford (2000), which is conducted in the context of a closed
economy.
Why is such extension potentially useful? Evidently, the degree of price stickiness is
related to the organization of markets–for instance, whether the labor market is common
or segmented. Similarly, the degree of price stickiness can be aﬀected by the openness of
the economy both in commodity trade and capital mobility.
As an illustration, consider the evidence in Figure 1 below. The left panel measures
the extent to which 4 groups of countries restrict capital movements based on the IMF’s
Annual Report on Exchange Rate Arrangements and Exchange Restrictions. The right
panel provides their corresponding average output-inﬂation tradeoﬀ parameters as estimated
by Ball, Mankiw, and Romer (1988). The ﬁgure shows clearly that countries with greater
restrictions on capital mobility tend to have steeper Phillips curves. This ﬁnding has been
recently substantiated by econometric estimations (see, Loungani, Razin, and Yuen (2001)).
2 The analytical framework
Consider a small open economy with a representative household that is endowed with a
continuum of goods-speciﬁc skills–uniformly distributed on the unit interval [0,n]–to be
supplied to a diﬀerentiated product industry. As a consumer, the representative household
has access to consumption of both domestic (distributed on [0,n]) and foreign goods (dis-
1 
 
 
Figure 1: Capital controls and the output-inflation tradeoff
The greater the intensity of capital controls, the steeper is the Phillips curve
Average intensity of capital controls
0
0.2
0.4
0.6
0.8
I II III IV
Output-Inflation Tradeoff
0
0.1
0.2
0.3
0.4
I II III IVtributed on (n,1]). The household seeks to maximize a discounted sum of expected utilities:
E0
∞ ￿
t=0
β
t[u(Ct,M t/Pt;ξt) −
￿ n
0
v(ht(j);ξt)dj],
where β is the subjective discount factor, C is the Dixit-Stiglitz index of household consump-
tion, P the Dixit-Stiglitz price index, M/P the demand for real balances, ξ a preference
shock, and h(j) the supply of type-j labor to the production of good of variety j. Like
Obstfeld and Rogoﬀ (1996), we deﬁne the consumption index and its corresponding price
index respectively as
Ct =
￿￿ n
0
ct(j)
θ−1
θ dj +
￿ 1
n
c
∗
t(j)
θ−1
θ dj
￿ θ
θ−1
,
and
Pt =
￿￿ n
0
pt(j)
1−θdj +
￿ 1
n
[εtp
∗
t(j)]
1−θdj
￿ 1
1−θ
, (1)
where c(j) represents domestic consumption of the jth domestically produced good, c∗(j)
domestic consumption of the jth foreign-produced good, p(j) the domestic-currency price
of c(j), p∗(j) the foreign-currency price of c∗(j), ε the nominal exchange rate (domestic-
currency price of foreign currency), θ>1 the elasticity of substitution among the diﬀerent
goods, and n the fraction of goods that are produced domestically.
The budget constraint facing the household is given by:
￿ n
0
pt(j)ct(j)dj + εt
￿ 1
n
p
∗
t(j)c
∗
t(j)dj +
￿ it
1+it
￿
Mt + Bt + εtB
∗
t
= Mt−1 +( 1+it−1)Bt−1 + ft−1,t(1 + i
∗
t−1)B
∗
t−1 +
￿ n
0
wt(j)ht(j)dj +
￿ n
0
Πt(j)dj,
where B is the domestic-currency value of domestic borrowing, B∗ the foreign-currency value
of foreign borrowing, ft−1,t the forward exchange rate for foreign currencies purchased/sold
at time t − 1 for delivery at time t, i and i∗ the domestic and foreign interest rates, w(j)
the wage rate per unit labor of type j, and Π(j) proﬁt income from ﬁrms of type j. With
perfect capital mobility, covered interest parity prevails:
1+it =( 1+i
∗
t)
￿
ft,t+1
εt
￿
.
2>From now on, we shall focus on the relation between aggregate supply of goods and
consumption smoothing made possible by international capital mobility. For this purpose,
we would not be concerned about the details of aggregate demand (including the demand for
money), international commodity trade, and the determination of the exchange rate. For
simplicity, separability between consumption and real money balances is assumed for the
utility function.
The relevant utility-maximizing conditions for our purpose include an intratemporal
condition for the choice of labor supply of type j:
vh(ht(j);ξt)
uc(Ct;ξt)
=
wt(j)
Pt
(2)
and an intertemporal condition for the consumption-saving choice:
uc(Ct;ξt)
uc(Ct+1;ξt+1)
= β(1 + r
∗), (3)
where r∗ is the world real rate of interest, assumed for simplicity to be time-invariant. This
latter equality is a consequence of the covered interest parity and the Fisher equation.
As in the Dixit-Stiglitz model, demand for good j satisﬁes
ct(j)=Ct
￿
pt(j)
Pt
￿−θ
. (4)
The production function assumes the form
yt(j)=Atf(ht(j)),
where A is a random productivity shock. The variable cost of supplying yt(j) is wt(j)f−1(yt(j)/At),
which implies a (real) marginal cost of
st(j)=
wt(j)
PtAtf￿(f−1(yt(j)/At))
.
Using (2), we can replace the real wage above by the marginal rate of substitution. Imposing
symmetry across ﬁrms (so that we can drop the index j), the above equation can be rewritten
3as
s(y,C;ξ,A)=
vh(f−1(y/A);ξ)
uc(C;ξ)Af￿(f−1(y/A))
. (5)
Trade-wise, price-making ﬁrms face world demand for its products so that equation
(4) implies
yt(j)=Y
W
t
￿
pt(j)
Pt
￿−θ
. (4￿)
where yt(j) is the quantity of good j supplied by the ﬁrm to meet the world demand and
Y W
t = Y H
t +Y F
t the index for all goods produced around the world, with Y H
t =
￿ n
0
pt(j)yt(j)
Pt dj
and Y F
t =
￿ n
0
εtp∗
t(j)yt(j)
Pt dj as corresponding production indices for home goods and foreign
goods.
The goods markets are monopolistically competitive. A fraction γ of the ﬁrms sets
their prices ﬂexibly at p1t, supplying y1t whereas the remaining 1−γ of ﬁrms sets their prices
one period in advance (in period t − 1)a tp2t, supplying y2t. In the former case, the price
is marked up above the marginal cost by a factor of µ(= θ
θ−1 > 1) so that
p1t
Pt
− µs(y1t,C t;ξt,A t)=0 . (6a)
In the latter case, p2t will be chosen to maximize expected discounted proﬁt
Et−1
￿￿
1
1+it−1
￿
(p2ty2t − wtht)
￿
= Et−1
￿￿
1
1+it−1
￿￿
Y
W
t P
θ
t p
1−θ
2t −wtf
−1(Y
W
t P
θ
t p
−θ
2t /At)
￿￿
,
where we have used the inverse demand function from (4) for y2t and the inverse production
function for ht. One can show that p2t satisﬁes
Et−1
￿￿
1
1+it−1
￿
Y
W
t P
θ−1
t
￿p2t
Pt
− µs(y2t,C t;ξt,A t)
￿￿
=0 . (6b)
Given p1t and p2t, the aggregate price index (1) can be rewritten as:
Pt =
￿
n[γp
1−θ
1t +( 1−γ)p
1−θ
2t ]+( 1−n)εtp
∗
t
1−θ
￿ 1
1−θ . (1￿)
4In the extreme case where all prices are fully ﬂexible (i.e., γ =1 ), output will attain
its natural level Y n
t implicitly deﬁned by
pt
￿
np
1−θ
t +( 1− n)εtp∗
t
1−θ
￿ 1
1−θ
= µs(Y
n
t ,C
n
t ;ξt,A t). (6a￿)
Among other things, Y n
t depends on the level of home consumption under ﬂexible prices
(Cn
t ), domestic and foreign prices (pt and p∗
t), as well as the exchange rate (εt). For later
purpose, we can denote s(Y n
t ,Cn
t ;ξt,A t) as sn
t .
In the absence of capital ﬂows, Cn
t = Y n
t so that the natural output level is deﬁned
by
pt
￿
np
1−θ
t +( 1− n)εtp∗
t
1−θ
￿ 1
1−θ
= µs(Y
n
t ,Y
n
t ;ξt,A t). (7)
When the economy is completely closed in terms of both commodity trade and capital ﬂows
(n =1and Cn
t = Y n
t ), (6a￿￿) further simpliﬁes to
1=µs(Y
n
t ,Y
n
t ;ξt,A t). (8)
In this last case, equilibrium output is completely independent of monetary policy.
3 The Phillips curve
This section derives the expectations-augmented Phillips curve of the kind hypothesized by
Friedman (1968) and Phelps (1970) for both open and closed economies.
In order to obtain a tractable solution, we log-linearize the equilibrium conditions
around the steady state. We assume that β(1+r∗)=1 , which is necessary for the existence
of a steady state. In particular, we consider a deterministic steady state where ξt =0and
At = A with εt = ε, p∗
t = p∗, and Ct = C. Deﬁne ￿ xt = log(xt
x ) ￿ xt−x
x as the proportional
deviation of any variable xt from its deterministic steady state value x. We can then
log-linearize equation (5) around the deterministic steady state equilibrium to get
￿ st − ￿ s
n
t = ω(￿ yt − ￿ Y
n
t )+σ
−1( ￿ Ct − ￿ C
n
t ), (5)
5where ω = ωw +ωp,ω w =
vhh(y/A)
vhf￿ ,ω p = −
f￿￿(f−1(.))(y/A)
f￿(f−1(.))f￿(.) , and σ = −
uccy
uc . Log-linearizing the
two price-setting equations (6a) and (6b) using (5￿), we obtain
log(p1t)=l o g ( Pt)+ω(￿ y1t − ￿ Y
n
t )+σ
−1( ￿ Ct − ￿ C
n
t ), (6a￿)
and
log(p2t)=Et−1
￿
log(Pt)+ω(￿ y2t − ￿ Y
n
t )+σ
−1( ￿ Ct − ￿ C
n
t )
￿
, (6b￿)
>From the deﬁnition of the aggregate price index (1￿), we can derive the following
approximation
log(Pt)=n[γ log(p1t)+( 1− γ)log(p2t) ]+( 1− n)log(εtp
∗
t). (1￿￿)
Deﬁne the inﬂation rate πt =l n ( Pt/Pt−1) so that πt−Et−1(πt)=l o g ( Pt)−Et−1log(Pt),
and the real exchange rate as et ≡ εtP ∗
t /Pt. We show in the Appendix how these price
relations can be combined to obtain the open-economy Phillips curve as follows:
πt − Et−1(πt)=
￿
γ
1 − γ
￿￿￿ nω
1+θω
￿
(￿ Y
H
t − ￿ Y
n
t )+
￿
(1 −n)ω
1+θω
￿
(￿ Y
F
t − ￿ Y
n
t )9 (1)
+
￿
σ−1
1+θω
￿
( ￿ Ct − ￿ C
n
t )
￿
+
￿1 − n
n
￿￿￿
1
1 − γ
￿
log(et) − Et−1[log(et)]
￿
.
3.1 Perfect capital mobility
When capital is perfectly mobile, consumption smoothing can be achieved and it will be
trendless given the assumption that β(1 + r∗)=1 . As a result, ￿ Ct =0= ￿ Cn
t . The Phillips
curve therefore simpliﬁes to
πt − Et−1(πt)=
￿
γ
1 −γ
￿￿￿ nω
1+θω
￿
(￿ Y
H
t − ￿ Y
n
t )+
￿
(1 − n)ω
1+θω
￿
(￿ Y
F
t − ￿ Y
n
t )
￿
9￿
(2)
+
￿
1−n
n
￿￿￿
1
1−γ
￿
log(et) − Et−1[log(et)]
￿
.
63.2 Closing the capital account
In the absence of capital ﬂows, consumption smoothing can no longer be achieved and
consumption will ﬂuctuate with domestic output (i.e., ￿ Ct = ￿ Y H
t and ￿ Cn
t = ￿ Y n
t ). As a result,
the Phillips curve assumes the form
πt − Et−1(πt)=
￿
γ
1 −γ
￿￿￿
nω + σ−1
1+θω
￿
(￿ Y
H
t − ￿ Y
n
t )+
￿
(1 − n)σ−1
1+θω
￿
(￿ Y
F
t − ￿ Y
n
t )
￿
9￿￿
(3)
+
￿
1−n
n
￿￿￿
1
1−γ
￿
log(et) − Et−1[log(et)]
￿
.
3.3 Closed economy
If we further close the trade account, the economy will be self-suﬃcient and n =1 .I n t h i s
case, the Phillips curve will take an even simpler form
πt − Et−1(πt)=
￿
γ
1 − γ
￿￿
ω + σ−1
1+θω
￿
(￿ Y
H
t − ￿ Y
n
t ), (9￿￿￿)
which is exactly identical to equation (1.23) in Woodford (2000).
3.4 A comparison
The diﬀerence in the output-inﬂation tradeoﬀ coeﬃcients between (9￿) and (9￿￿) lies in
γσ−1/(1 − γ)(1 + θω), which captures the sensitivity of inﬂation to consumption spend-
ing. This term will disappear in the presence of consumption smoothing as will be achieved
under perfect capital mobility. The diﬀerence in the same coeﬃcients between (9￿￿)a n d
(9￿￿￿)i sγ(n − 1)ω/(1 − γ)(1 + θω), where n represents the fraction of world consumption
that is produced domestically in the case of trade openness whereas 1 stands for the same
fraction (which is 100%) in the case of a closed economy. Therefore, successive opening of
the economy will ﬂatten the Phillips curve.
74 Short-run aggregate supply
This section examines how exogenous shocks to nominal GDP deﬁned as n[γp1ty1t +( 1−
γ)p2ty2t]=P H
t Y H
t ≡ Qt would aﬀect the relative responses of domestic output and producer
prices. From the Phillips curve equation (9), we can show that the sensitivity of log(Y H
t )−
log(Y n
t ) with respect to innovations in the exogenous process, viz., log(Qt) − Et−1[log(Qt)],
in the case of perfect capital mobility is
output-elasticity
open =
1
1+
￿
γ
1−γ
￿￿
ω
1+θω
￿,
while the sensitivity of log(PH
t ) − Et−1log(PH
t ) is
price-elasticity
open =
￿
γ
1−γ
￿￿
ω
1+θω
￿
1+
￿
γ
1−γ
￿￿
ω
1+θω
￿.
Similarly, the sensitivity parameters in the case of a closed economy are given by
output-elasticity
closed =
1
1+
￿
γ
1−γ
￿￿
ω+σ−1
1+θω
￿,
and
price-elasticity
closed =
￿
γ
1−γ
￿￿
ω+σ−1
1+θω
￿
1+
￿
γ
1−γ
￿￿
ω+σ−1
1+θω
￿.
As discussed in Woodford (2000), these sensitivity parameters are related to the de-
gree of strategic complementarity among price setters. In turn, the latter depends on the
organization of markets. For instance, strategic substitutability (complementarity) will pre-
vail if all factor prices are (cannot be) instantaneously equalized across suppliers of diﬀerent
goods, the case of common (segmented) factor markets. In our case, we show another exam-
ple where the organization of the world capital market matters–in particular, the integra-
tion or not of the domestic capital market into the world market. Consumption smoothing,
which comes with the opening of the capital market, will increase the degree of strategic
complementarity, thus rendering prices more sticky and magnifying output responses.
85 Appendix
Let us start with the two price-setting equations:
log(p1t)=l o g ( Pt)+ω(￿ y1t − ￿ Y
n
t )+σ
−1( ￿ Ct − ￿ C
n
t ), (A.1a)
and
log(p2t)=Et−1
￿
log(Pt)+ω(￿ y2t − ￿ Y
n
t )+σ
−1( ￿ Ct − ￿ C
n
t )
￿
. (A.1b)
Log-linearizing the demand functions facing the ﬁrm (4) (where we can replace ct and
CW
t by yt and Y W
t respectively), we get
￿ yjt = ￿ Y
w
t − θ[log(pjt) − log(Pt)],j=1 ,2, (A.2)
where ￿ Y w
t = n ￿ Y H
t +( 1− n)￿ Y F
t . Substituting (A.2) into (A.1a) and rearranging terms, we
have
log(p1t)=l o g ( Pt)+
￿ ω
1+θω
￿
(￿ Y
W
t − ￿ Y
n
t )+σ
−1
￿ 1
1+θω
￿
( ￿ Ct − ￿ C
n
t ), (A.1a￿)
and
log(p2t)=Et−1
￿
log(Pt)+
￿ ω
1+θω
￿
(￿ Y
W
t − ￿ Y
n
t )+σ
−1
￿ 1
1+θω
￿
( ￿ Ct − ￿ C
n
t )
￿
, (A.1b￿)
Together, (A.1a￿) and (A.1b￿) imply that
log(p2t)=Et−1log(p1t). (A.3)
>From the aggregate price index equation (1￿), we have an approximate relation of
the following kind
log(Pt)=n[γ log(p1t)+( 1− γ)log(p2t) ]+( 1− n)log(εtp
∗
t). (A.4)
From this, the unanticipated rate of inﬂation is given by
log(Pt) − Et−1[log(Pt)] = nγ {log(p1t) − Et−1[log(p1t)]} +( 1− n){log(εtp
∗
t) − Et−1[log(εtp
∗
t)]}
= nγ[log(p1t) − log(p2t) ]+( 1− n){log(εtp
∗
t) − Et−1[log(εtp
∗
t)]},
9where we have used (A.3) to get the second equality. (A.4) also implies log(p2t)=
￿
1
n(1−γ)
￿
[log(Pt)−
nγ log(p1t) − (1 −n)log(εtp∗
t)] so that
log(Pt) −Et−1log(Pt)=
￿
γ
1 − γ
￿
[log(p1t) −log(Pt)]
+
￿1 − n
n
￿￿￿
1
1 −γ
￿
log(et) − Et−1[log(et)]
￿
,
where et ≡ εtP∗
t /Pt is the real exchange rate. Substituting (A.1a￿) into the above expression
yields an open-economy Phillips curve of the form
log(Pt) − Et−1log(Pt)=
￿
γ
1 − γ
￿￿￿ ω
1+θω
￿
(￿ Y
W
t − ￿ Y
n
t )+
￿
σ−1
1+θω
￿
( ￿ Ct − ￿ C
n
t )
￿
+
￿1 − n
n
￿￿￿
1
1 − γ
￿
log(et) − Et−1[log(et)]
￿
.
Equation (9) in the text can be obtained by noting that ￿ Y W
t = n￿ Y H
t +( 1− n)￿ Y F
t .
10References
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11

The "New Keynesian" Phillips Curve: Closed Economy vs. Open Economy

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