This document summarizes and extends Woodford's analysis of the New Keynesian Phillips curve from a closed economy to an open economy with trade and capital mobility. It finds that capital mobility, which enables consumption smoothing, increases the degree of strategic complementarity among price-setting firms. This makes prices more rigid and amplifies the response of output to nominal GDP shocks. The document presents a model of an open economy with monopolistic competition and some firms that set prices flexibly and others that set prices one period in advance. It log-linearizes the model's equilibrium conditions to derive expectations-augmented Phillips curves for both closed and open economies.

1. Economics Letters 75 (2002) 1–9
www.elsevier.com / locate / econbase
The ‘New Keynesian’ Phillips curve: closed economy versus
open economy
Assaf Razin a , Chi-Wa Yuen b , *
a
Tel Aviv University, Cornell University, NBER, CEPR, and CES-Ifo, Tel Aviv, Israel
b
School of Economics and Finance, University of Hong Kong, Pokfulam Road, Hong Kong, China
Received 27 May 2001; accepted 6 June 2001
Abstract
The paper extends Woodford’s [Optimizing models with nominal rigidities, Chapter 3 of Interest and prices:
foundations of a theory of monetary policy, Princeton University, 2000; unpublished manuscript] analysis of the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. © 2002 Elsevier Science B.V. All rights reserved.
Keywords: Phillips curve; New Keynesian; Trade; Capital mobility
JEL classification: E12; F41
1. Introduction
In this paper, we examine how open market policies would interact with the degree of price rigidity
in the domestic economy to affect the output-inflation tradeoffs as well as the volatilities of output and
inflation in response to nominal shocks. The analysis will be conducted in an optimization-based
‘New Keynesian’ framework a la Blanchard and Kiyotaki (1987). In the discussion, we extend to an
open-trade-account and open-capital-account economy the succinct exposition of Woodford (2000)
conducted in the context of a closed economy. [For a useful survey of the new open economy
macroeconomic approach we adopt for our analysis in this paper, see Lane (2001).]
Why is such extension potentially useful? Empirically, Loungani et al. (2001) have found that
countries with greater restrictions on capital mobility tend to have steeper Phillips curves. Evidently,
* Corresponding author. Tel.: 1852-2859-1051; fax: 1852-2548-1152.
E-mail address: cwyuen@econ.khu.hk (C.-W. Yuen).
0165-1765 / 02 / $ – see front matter © 2002 Elsevier Science B.V. All rights reserved.
PII: S0165-1765( 01 )00588-2

2. 2 A. Razin, C.-W. Yuen / Economics Letters 75 (2002) 1 – 9
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 in both commodity trade and capital flows.
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 consump-
tion of both domestic goods (distributed on [0, n]) and foreign goods (distributed on (n, 1]). The
household seeks to maximize a discounted sum of expected utilities:
n
O b [u(C , M /P ; j ) 2E v(h ( j); j ) dj]
`
t
E0 t t t t t t
t 50
0
where b is the subjective discount factor, C is the Dixit and Stiglitz (1977) index of household
consumption, P the Dixit–Stiglitz price index, M /P the demand for real balances, j 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
n 1 u / (u 21 )
Ct 5
3E0
(
t E
c t ( j) u 21 ) / u dj 1 c * ( j)(u 21 ) / u dj
n
4
and
n 1 1 / (12u )
Pt 5
5E0
pt ( j)
12u
tE
dj 1 [´t p * ( j)]
n
12u
dj
6 (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), ´ the nominal exchange rate (domestic-currency price of foreign
currency), u . 1 the elasticity of substitution among the different goods, and n the fraction of goods
that are produced domestically.
In nominal terms, the budget constraint facing the household is given by:
n 1
E p ( j)c ( j) dj 1 ´ E p*( j)c*( j) dj 1S]]DM 1 B 1 ´ B *
t t t
n
i
11i t t
t
t
t t t t
0
n n
* *
5 Mt21 1 (1 1 i t 21 )Bt 21 1 ft21,t (1 1 i t21 )B t21 1 w t ( j)h t ( j) dj 1 Pt ( j) dj E E
0 0
where B is the domestic-currency value of domestic borrowing, B* the foreign-currency value of

3. A. Razin, C.-W. Yuen / Economics Letters 75 (2002) 1 – 9 3
foreign borrowing, ft21,t the forward exchange rate for foreign currencies purchased / sold at time t 2 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 P ( j) profit income from firms of type j. With perfect capital mobility, covered interest
parity prevails:
1 1 i t 5 (1 1 i t* ) ]] S D
ft,t11
´t
[cf. first-order conditions of the household with respect to B and B*.]
From this point 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, consumer
utility is assumed to be separable between consumption and real money balances.
For our purpose, the relevant utility-maximizing conditions include an intratemporal condition for
the choice of labor supply of type j:
vh (h t ( j); j t ) w t ( j)
]]]] 5 ]] (2)
u c (Ct ; j t ) Pt
and an intertemporal condition for the consumption-saving choice:
u c (Ct ; j t )
]]]]] 5 b (1 1 r*) (3)
u c (Ct11 ; j t11 )
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 and
Stiglitz (1977) model, demand for good j satisfies
S D
pt ( j)
c t ( j) 5 Ct ]]
Pt
2u
(4)
The production function assumes the form
y t ( j) 5 A t f(h t ( j))
21
where A is a random productivity shock. The variable cost of supplying y t ( j) is w t ( j)f ( y t ( j) /A t ),
which implies a (real) marginal cost of
w t ( j)
s t ( j) 5 ]]]]]]]
Pt A t f 9( f 21 ( y t ( j) /A t ))
Using Eq. (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 as
vh ( f 21 ( y /A); j )
s( y, C; j , A) 5 ]]]]]]] (5)
u c (C; j )Af 9( f 21 ( y /A))

4. 4 A. Razin, C.-W. Yuen / Economics Letters 75 (2002) 1 – 9
Trade-wise, price-making firms face world demand for their products so that Eq. (4) implies
S D
pt ( j)
y t ( j) 5 Y W ]]
t Pt
2u
(49)
where y t ( j) is the quantity of good j supplied by the firm to meet the world demand and
W H F H n
Y t 5 Y t 1 Y t the index for all goods produced around the world, with Y t 5 e0 (( pt ( j)y t ( j)) /Pt ) dj
F n
and Y t 5 e0 ((´t p * ( j)y t ( j)) /Pt ) dj as corresponding production indices for home goods and foreign
t
goods.
The goods markets are monopolistically competitive. A fraction g of the firms sets their prices
flexibly at p1t , supplying y 1t ; whereas the remaining 1 2 g of firms sets their prices one period in
advance (in period t 2 1) at p2t , supplying y 2t . In the former case, the price is marked up above the
marginal cost by a factor of m ( 5 u /(u 2 1) . 1) so that
p1t
] 2 m s( y 1t , Ct ; j t , A t ) 5 0 (6a)
Pt
In the latter case, p2t will be chosen to maximize expected discounted profit
Et21FS]]]D( p y 2 w h )G
1
11i t 21
2t 2t t t
5 E HS]]]DfY P p 2 w f J
1 u 12u
(Y tW P tu p 2u /A t )g
W 21
11i
t21
t21
t t 2t t 2t
where we have used the inverse demand function from Eq. (4) for y 2t and the inverse production
function for h t . One can show that p2t satisfies
Et21 HS]]]DY
1
11i t 21
W
t t F
p2t
P u 21 ] 2 m s( y 2t , Ct ; j t , A t )
Pt GJ 5 0 (6b)
Given p1t and p2t , the aggregate price index (1) can be rewritten as:
Pt 5hn[g p 1t u 1 (1 2 g )p 2t u ] 1 (1 2 n)(´t p t* )12uj 1 / (12u )
12 12
(19)
In the extreme case where all prices are fully flexible (i.e. g 5 1), output will attain its natural
level, Y n , implicitly defined by
t
pt
]]]]]]]]]] 5 m s(Y n , C n ; j t , A t )
fnp t 1 (1 2 n)´t p t*12ug 1 / (12u )
12u t t
n n
Among other things, Y t depends on the level of home consumption under flexible prices (C t ),
domestic and foreign prices ( pt and p t* ), as well as the exchange rate (´t ). For later purpose, we can
denote s(Y n , C n ; j t , A t ) as s n .
t t t
In the absence of capital flows, C n 5 Y n so that the natural output level is defined by
t t
pt
]]]]]]]]]] 5 m s(Y n , Y n ; j t , A t )
fnp t 1 (1 2 n)´t p t*12ug 1 / (12u )
12u t t

5. A. Razin, C.-W. Yuen / Economics Letters 75 (2002) 1 – 9 5
When the economy is completely closed in terms of both commodity trade and capital flows (n 5 1
and C n 5 Y n ), the equation above further simplifies to
t t
1 5 m s(Y tn , Y tn ; j t , A t )
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 closed and economies [cf. Ball et al. (1988) and Roberts
(1995)].
In order to obtain a tractable solution, we log-linearize the equilibrium conditions around the steady
state. We assume that b (1 1 r*) 5 1, which is necessary for the existence of a steady state. In
]
particular, we consider a deterministic steady state where j t 5 0 and A t 5A with ´t 5], p t* 5p*, and
´ ]
] ] . (x 2x) /x as the proportional deviation of any variable x from its
] ]
ˆ
Ct 5C. Define x t 5 log(x t /x) t t
deterministic steady state value ] We can then log-linearize Eq. (5) around the deterministic steady
x.
state equilibrium to get
ˆ ˆn ˆn 21 ˆ ˆn
s t 2 s t 5 v (yt 2 Y t ) 1 s (Ct 2 C t )
ˆ (59)
where
v 5 vw 1 vp
] ]
vhh (y /A)
vw 5 ]]]
vh f 9
] ]
f 0( f 21 (.))(y /A)
vp 5 2 ]]]]]
f 9( f 21 (.))f 9(.)
and
]
u ccc
s 5 2 ]]
uc
Log-linearizing the two price-setting Eqs. (6a) and (6b) using Eq. (59), we obtain
n
ˆ
log( p1t ) 5 log(Pt ) 1 v (y1t 2 Y t ) 1 s
ˆ 21 ˆ ˆn
(Ct 2 C t ) (6a9)
and
ˆn 21 ˆ ˆn
log( p2t ) 5 Et 21flog(Pt ) 1 v (y2t 2 Y t ) 1 s (Ct 2 C t )g
ˆ (6b9)
From the definition of the aggregate price index (19), we can derive the following approximation
log(Pt ) 5 n[g log( p1t ) 1 (1 2 g ) log( p2t )] 1 (1 2 n) log(´t p * )
t (10)

6. 6 A. Razin, C.-W. Yuen / Economics Letters 75 (2002) 1 – 9
Define the inflation rate pt 5 ln(Pt /Pt21 ) so that pt 2 Et 21 (pt ) 5 log(Pt ) 2 Et 21 log(Pt ), and the real
exchange rate as e t ; ´t P t* /Pt . We show in Appendix A how these price relations can be combined to
obtain the open-economy Phillips curve as follows:
g nv
S
pt 2 Et 21 (pt ) 5 ]]
12g DHS]]]D(Yˆ 2 Yˆ )
1 1 uv
H
t
n
t
1F]]]G(Y 2 Y ) 1S]]]D(C 2 C )J
21
(1 2 n)v ˆ F s n n
ˆ ˆ ˆ
1 1 uv t1 1 uv t t t
1S]]DHS]]D log(e ) 2 E [log(e )]J
12n 1
(7)
n 12g t t21 t
3.1. Perfect capital mobility
When capital is perfectly mobile, consumption smoothing can be achieved and, given the
ˆ ˆn
assumption that b (1 1 r*) 5 1, consumption will be trendless (see Eq. (3)). As a result, Ct 5 0 5 C t .
The Phillips curve therefore simplifies to
g nv
S
pt 2 Et 21 (pt ) 5 ]]
12g DHS]]]D(Yˆ 2 Yˆ )
1 1 uv
H
t
n
t
1F]]]G(Y 2 Y )J
(1 2 n)v ˆ F n
ˆ
1 1 uv t t
1S]]DHS]]D log (e ) 2 E J
12n 1
[log (e t )] (79)
n 12g t t 21
3.2. Closing the capital account
In the absence of capital flows, consumption smoothing can no longer be achieved and consumption
ˆ ˆH ˆn ˆn
will fluctuate with domestic output (i.e. Ct 5 Y t and C t 5 Y t ). As a result, the Phillips curve assumes
the form
S DHS]]]D(Yˆ 2 Yˆ )
21
g nv 1 s H n
pt 2 Et 21 (pt ) 5 ]]
12g 1 1 uv t t
1F]]]]G(Y 2 Y )J
21
(1 2 n)s F n
ˆ ˆ
1 1 uv t t
1S]]DHS]]D log(e ) 2 E [log(e )]J
12n 1
(70)
n 12g t t21 t
3.3. Closed economy
If we further close the trade account, the economy will be self-sufficient and n 5 1. In this case, the
Phillips curve will take an even simpler form

7. A. Razin, C.-W. Yuen / Economics Letters 75 (2002) 1 – 9 7
S DS]]]D(Yˆ
21
g v 1s H
ˆ n
pt 2 Et 21 (pt ) 5 ]] 2Yt ) (7-)
12g 1 1 uv t
which is exactly identical to Eq. (1.23) in Woodford (2000).
3.4. A comparison
The difference in the output-inflation tradeoff coefficients between (79) and (70) lies in gs 21 /(1 2
g )(1 1 uv ), which captures the sensitivity of inflation to consumption spending. 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 (70) and (7-) is g (n 2 1)v /(1 2 g )(1 1 uv ),
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 (i.e. 100%) in the case of a closed economy.
Therefore, successive opening of the economy will flatten the Phillips curve.1
4. Short-run aggregate supply
As a corollary to our analysis of the output-inflation tradeoff, we can also examine how exogenous
shocks to nominal GDP, defined as n[g p1 t y 1t 1 (1 2 g )p2t y 2t ] 5 P tH Y tH ; Q t , would affect the relative
responses of domestic output and producer prices. From the Phillips curve Eq. (7), we can show that
the sensitivity of log(Y H ) 2 log(Y n ) with respect to innovations in the exogenous process, viz.,
t t
log(Q t ) 2 Et21 [log(Q t )], in the case of perfect capital mobility is
1
output-elasticity open 5 ]]]]]]]
g v
S
1 1 ]] ]]]
1 2 g 1 1 uv DS D
while the sensitivity of log(P H ) 2 Et21 log(P tH ) is
t
g v
S]]DS]]]D
1 2 g 1 1 uv
price-elasticity open 5 ]]]]]]]g v
1 1S]]DS]]]D
1 2 g 1 1 uv
Similarly, the sensitivity parameters in the case of a closed economy are given by
1
output-elasticity closed 5 ]]]]]]]]
g
12gS
1 1 ]] ]]] DS
v 1 s 21
1 1 uv
D
and
1
Obviously, our conclusion here is valid only if the parameters involved in the various versions of the Phillips curve are
stable and invariant to changes in trade and capital mobility regimes. The same condition applies to our results in the next
section.

8. 8 A. Razin, C.-W. Yuen / Economics Letters 75 (2002) 1 – 9
g
S
]] ]]]
12g DS
v 1 s 21
1 1 uv
D
price-elasticity closed 5 ]]]]]]]]
11
g
S DS
]] ]]]
12g
v 1 s 21
1 1 uv
D
As discussed in Woodford (2000), these sensitivity parameters are related to the degree of strategic
complementarity among price setters. In turn, the latter depends on the organization of markets. For
instance, strategic substitutability (complementarity) will prevail 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 example where the organization of the world capital market
matters — in particular, the integration 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.
Appendix A
Let us start with the two price-setting equations:
ˆn 21 ˆ ˆn
log( p1t ) 5 log(Pt ) 1 v (y1t 2 Y t ) 1 s (Ct 2 C t )
ˆ (A.1a)
and
ˆn 21 ˆ ˆn
log( p2t ) 5 Et 21flog(Pt ) 1 v (y2t 2 Y t ) 1 s (Ct 2 C t )g
ˆ (A.1b)
W
Log-linearizing the demand functions facing the firm (Eq. 4) (where we can replace c t and C t by
y t and Y tW , respectively), we get
ˆ ˆW
y jt 5 Y t 2 u [log( pjt ) 2 log(Pt )], j 5 1,2 (A.2)
Substituting (A.2) into (A.1a) and (A.1b) and rearranging terms, we have
Sv
1 1 uv
ˆW ˆn D 1
1 1 uv
ˆ ˆnS
log( p1t ) 5 log(Pt ) 1 ]]] (Y t 2 Y t ) 1 s 21 ]]] (Ct 2 C t ) D (A.1a9)
and
F v
S
1 1 uv
ˆW ˆnD 1
1 1 uv
ˆ S
ˆn
log( p2t ) 5 Et 21 log(Pt ) 1 ]]] (Y t 2 Y t ) 1 s 21 ]]] (Ct 2 C t ) D G (A.1b9)
Together, (A.1a9) and (A.1b9) imply that
log( p2t ) 5 Et 21 [log( p1t )] (A.3)
From the aggregate price index Eq. (19), we have an approximate relation of the following kind
log(Pt ) 5 n[g log( p1t ) 1 (1 2 g ) log( p2t )] 1 (1 2 n) log(´t p * )
t (A.4)

9. A. Razin, C.-W. Yuen / Economics Letters 75 (2002) 1 – 9 9
From this and (A.3), the unanticipated rate of inflation is given by
log(Pt ) 2 Et 21flog(Pt )g 5 ng [log( p1t ) 2 log( p2t )]
1 (1 2 n)hlog(´t p * ) 2 Et 21flog(´t p t* )gj
t (A.49)
(A.4) also implies that
F 1
G
log( p2t ) 5 ]]] [log(Pt ) 2 ng log( p1t ) 2 (1 2 n) log(´t p * )]
n(1 2 g ) t
Substituting this into (A.49) and defining the real exchange rate as e t ; ´t P * /Pt , we have
t
g
S D
log(Pt ) 2 Et 21 log(Pt ) 5 ]] [log( p1t ) 2 log(Pt )]
12g
12n
1 ]]
n
S 1
DHS D
]] log(e t ) 2 Et21 [log(e t )]
12g J
Replacing log( p1t ) in the above expression by (A.1a9) yields an open-economy Phillips curve of the
form
g
S
log(Pt ) 2 Et 21 log(Pt ) 5 ]]
12g DFS D
v ˆt ˆt s 21
]]] (Y W 2 Y n ) 1 ]]] (Ct 2 C n )
1 1 uv 1 1 uv
ˆ S
ˆt D G
12n
1 ]]
n
S DHS D
1
]] log(e t ) 2 Et21 [log(e t )]
12g J
ˆW ˆH ˆF
Eq. (7) in the text can be obtained by noting that Y t 5 nY t 1 (1 2 n)Y t .
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