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Economics Letters 75 (2002) 1–9www.elsevier.com/ locate /econbase

The ‘New Keynesian’ Phillips curve: closed economy versusopen economy

a b ,*Assaf Razin , Chi-Wa YuenaTel Aviv University, Cornell University, NBER, CEPR, and CES-Ifo, Tel Aviv, Israel

bSchool 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rigidities, Chapter 3 of Interest and prices:foundations of a theory of monetary policy, Princeton University, 2000; unpublished manuscript] analysis of theclosed economy Phillips curve to an open economy with both commodity trade and capital mobility. We showthat consumption smoothing, which comes with the opening of the capital market, raises the degree of strategiccomplementarity among monopolistically competitive suppliers, thus rendering prices more sticky andmagnifying 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 rigidityin the domestic economy to affect the output-inflation tradeoffs as well as the volatilities of output andinflation 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 anopen-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 economymacroeconomic 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 thatcountries 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: [email protected] (C.-W. Yuen).

0165-1765/02/$ – see front matter 2002 Elsevier Science B.V. All rights reserved.PI I : S0165-1765( 01 )00588-2

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 thelabor market is common or segmented. Similarly, the degree of price stickiness can be affected by theopenness 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 continuumof goods-specific skills — uniformly distributed on the unit interval [0, n] — to be supplied to adifferentiated 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]). Thehousehold seeks to maximize a discounted sum of expected utilities:

n`

tE O b [u(C , M /P ; j ) 2E v(h ( j); j ) dj]0 t t t t t tt50

0

where b is the subjective discount factor, C is the Dixit and Stiglitz (1977) index of householdconsumption, P the Dixit–Stiglitz price index, M /P the demand for real balances, j a preferenceshock, and h( j) the supply of type-j labor to the production of good of variety j. Like Obstfeld andRogoff (1996), we define the consumption index and its corresponding price index, respectively, as

n 1 u / (u 21)

(u 21) /u (u 21) /u*C 5 E c ( j) dj 1E c ( j) djt t t3 4n0

and

n 1 1 / (12u )

12u 12u*P 5 E p ( j) dj 1E [´ p ( j)] dj (1)t t t t5 6n0

where c( j) represents domestic consumption of the jth domestically produced good, c*( j) domesticconsumption of the jth foreign-produced good, p( j) the domestic-currency price of c( j), p*( j) theforeign-currency price of c*( j), ´ the nominal exchange rate (domestic-currency price of foreigncurrency), u . 1 the elasticity of substitution among the different goods, and n the fraction of goodsthat are produced domestically.

In nominal terms, the budget constraint facing the household is given by:

n 1

it* * ]] *E p ( j)c ( j) dj 1 ´ E p ( j)c ( j) dj 1 M 1 B 1 ´ BS Dt t t t t t t t t1 1 itn0

n n

* *5 M 1 (1 1 i )B 1 f (1 1 i )B 1E w ( j)h ( j) dj 1E P ( j) djt21 t21 t21 t21,t t21 t21 t t t

0 0

where B is the domestic-currency value of domestic borrowing, B* the foreign-currency value of

A. Razin, C.-W. Yuen / Economics Letters 75 (2002) 1 –9 3

foreign borrowing, f the forward exchange rate for foreign currencies purchased /sold at time t 2 1t21,t

for delivery at time t, i and i* the domestic and foreign interest rates, w( j) the wage rate per unit laborof type j, and P( j) profit income from firms of type j. With perfect capital mobility, covered interestparity prevails:

ft,t11* ]]1 1 i 5 (1 1 i )S Dt t ´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 wouldnot 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, consumerutility is assumed to be separable between consumption and real money balances.

For our purpose, the relevant utility-maximizing conditions include an intratemporal condition forthe choice of labor supply of type j:

v (h ( j); j ) w ( j)h t t t]]]] ]]5 (2)Pu (C ; j ) tc t t

and an intertemporal condition for the consumption-saving choice:

u (C ; j )c t t]]]]] 5 b(1 1 r*) (3)u (C ; j )c t11 t11

where r* is the world real rate of interest, assumed for simplicity to be time-invariant. This latterequality is a consequence of the covered interest parity and the Fisher equation. As in the Dixit andStiglitz (1977) model, demand for good j satisfies

2up ( j)t]]c ( j) 5 C (4)S Dt t Pt

The production function assumes the form

y ( j) 5 A f(h ( j))t t t

21where A is a random productivity shock. The variable cost of supplying y ( j) is w ( j)f ( y ( j) /A ),t t t t

which implies a (real) marginal cost of

w ( j)t]]]]]]]s ( j) 5t 21P A f 9( f ( y ( j) /A ))t t t t

Using Eq. (2), we can replace the real wage above by the marginal rate of substitution. Imposingsymmetry across firms (so that we can drop the index j), the above equation can be rewritten as

21v ( f ( y /A); j )h]]]]]]]s( y, C; j, A) 5 (5)21u (C; j )Af 9( f ( y /A))c


Trade-wise, price-making firms face world demand for their products so that Eq. (4) implies

2up ( j)tW]]y ( j) 5 Y (49)S Dt t Pt

where y ( j) is the quantity of good j supplied by the firm to meet the world demand andtW H F H nY 5 Y 1 Y the index for all goods produced around the world, with Y 5 e (( p ( j)y ( j)) /P ) djt t t t 0 t t t

F n *and Y 5 e ((´ p ( j)y ( j)) /P ) dj as corresponding production indices for home goods and foreignt 0 t t t t

goods.The goods markets are monopolistically competitive. A fraction g of the firms sets their prices

flexibly at p , supplying y ; whereas the remaining 1 2 g of firms sets their prices one period in1t 1t

advance (in period t 2 1) at p , supplying y . In the former case, the price is marked up above the2t 2t

marginal cost by a factor of m ( 5u /(u 2 1) . 1) so that

p1t]2 ms( y , C ; j , A ) 5 0 (6a)1t t t tPt

In the latter case, p will be chosen to maximize expected discounted profit2t

1]]]E ( p y 2 w h )FS D Gt21 2t 2t t t1 1 it21

1 W u 12u 21 W u 2u]]]5 E Y P p 2 w f (Y P p /A )f gHS D Jt21 t t 2t t t t 2t t1 1 it21

where we have used the inverse demand function from Eq. (4) for y and the inverse production2t

function for h . One can show that p satisfiest 2t

p1 2tW u 21]]] ]E Y P 2 ms( y , C ; j , A ) 5 0 (6b)HS D JF Gt21 t t 2t t t t1 1 i Pt21 t

Given p and p , the aggregate price index (1) can be rewritten as:1t 2t

12u 12u 12u 1 / (12u )*P 5 n[gp 1 (1 2 g )p ] 1 (1 2 n)(´ p ) (19)h jt 1t 2t t t

In the extreme case where all prices are fully flexible (i.e. g 5 1), output will attain its naturalnlevel, Y , implicitly defined byt

pt n n]]]]]]]]]] 5 ms(Y , C ; j , A )12u 12u 1 / (12u ) t t t t*np 1 (1 2 n)´ pf gt t t

n nAmong other things, Y depends on the level of home consumption under flexible prices (C ),t t

*domestic and foreign prices ( p and p ), as well as the exchange rate (´ ). For later purpose, we cant t tn n ndenote s(Y , C ; j , A ) as s .t t t t t

n nIn the absence of capital flows, C 5 Y so that the natural output level is defined byt t

pt n n]]]]]]]]]] 5 ms(Y , Y ; j , A )12u 12u 1 / (12u ) t t t t*np 1 (1 2 n)´ pf gt t t


When the economy is completely closed in terms of both commodity trade and capital flows (n 5 1n nand C 5 Y ), the equation above further simplifies tot t

n n1 5 ms(Y , Y ; j , A )t t t 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 byFriedman (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 steadystate. 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 5 0 and A 5A with ´ 5´, p 5p*, andt t t t] ] ] ]ˆC 5C. Define x 5 log(x /x) . (x 2x) /x as the proportional deviation of any variable x from itst t t t t]deterministic steady state value x. We can then log-linearize Eq. (5) around the deterministic steady

state equilibrium to getn nn 21ˆ ˆ ˆˆ ˆ ˆs 2 s 5 v(y 2 Y ) 1 s (C 2 C ) (59)t t t t t t

where

v 5 v 1 vw p

]]v (y /A)hh]]]v 5w v f 9h

]21 ]f 0( f (.))(y /A)]]]]]v 5 2p 21f 9( f (.))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 n21ˆ ˆ ˆˆlog( p ) 5 log(P ) 1 v(y 2 Y ) 1 s (C 2 C ) (6a9)1t t 1t t t t

andn n21ˆ ˆ ˆˆlog( p ) 5 E log(P ) 1 v(y 2 Y ) 1 s (C 2 C ) (6b9)f g2t t21 t 2t t t t

From the definition of the aggregate price index (19), we can derive the following approximation

*log(P ) 5 n[g log( p ) 1 (1 2 g ) log( p )] 1 (1 2 n) log(´ p ) (10)t 1t 2t t t


Define the inflation rate p 5 ln(P /P ) so that p 2 E (p ) 5 log(P ) 2 E log(P ), and the realt t t21 t t21 t t t21 t

*exchange rate as e ; ´ P /P . We show in Appendix A how these price relations can be combined tot t t t

obtain the open-economy Phillips curve as follows:

g nv H nˆ ˆ]] ]]]p 2 E (p ) 5 (Y 2 Y )HS DS Dt t21 t t t1 2 g 1 1uv

21(1 2 n)v sF n nˆ ˆ ˆ ˆS D JF]]]G ]]]1 (Y 2 Y ) 1 (C 2 C )t t t t1 1uv 1 1uv

1 2 n 1S]]D ]]1 log(e ) 2 E [log(e )] (7)HS D Jt t21 tn 1 2 g

3.1. Perfect capital mobility

When capital is perfectly mobile, consumption smoothing can be achieved and, given thenˆ ˆassumption that b(1 1 r*) 5 1, consumption will be trendless (see Eq. (3)). As a result, C 5 0 5 C .t t

The Phillips curve therefore simplifies to

g nv H nˆ ˆ]] ]]]p 2 E (p ) 5 (Y 2 Y )HS DS Dt t21 t t t1 2 g 1 1uv

(1 2 n)v F nˆ ˆF]]]G J1 (Y 2 Y )t t1 1uv

1 2 n 1S]]D ]]1 log (e ) 2 E [log (e )] (79)HS D Jt t21 tn 1 2 g

3.2. Closing the capital account

In the absence of capital flows, consumption smoothing can no longer be achieved and consumptionH n nˆ ˆ ˆ ˆwill fluctuate with domestic output (i.e. C 5 Y and C 5 Y ). As a result, the Phillips curve assumest t t t

the form

21g nv 1 s H nˆ ˆHS D]] ]]]p 2 E (p ) 5 (Y 2 Y )S Dt t21 t t t1 2 g 1 1uv

21(1 2 n)s F nˆ ˆF G J]]]]1 (Y 2 Y )t t1 1uv

1 2 n 1S]]D ]]1 log(e ) 2 E [log(e )] (70)HS D Jt t21 tn 1 2 g

3.3. Closed economy

If we further close the trade account, the economy will be self-sufficient and n 5 1. In this case, thePhillips curve will take an even simpler form


21g v 1 s H nˆ ˆS D]] ]]]p 2 E (p ) 5 (Y 2 Y ) (7-)S Dt t21 t t t1 2 g 1 1uv

which is exactly identical to Eq. (1.23) in Woodford (2000).

3.4. A comparison

21The difference in the output-inflation tradeoff coefficients between (79) and (70) lies in gs /(1 2

g )(1 1uv), which captures the sensitivity of inflation to consumption spending. This term willdisappear in the presence of consumption smoothing, as will be achieved under perfect capitalmobility. The difference in the same coefficients between (70) and (7-) is g(n 2 1)v /(1 2 g )(1 1uv),where n represents the fraction of world consumption that is produced domestically in the case oftrade openness whereas 1 stands for the same fraction (i.e. 100%) in the case of a closed economy.

1Therefore, successive opening of the economy will flatten the Phillips curve.

4. Short-run aggregate supply

As a corollary to our analysis of the output-inflation tradeoff, we can also examine how exogenousH Hshocks to nominal GDP, defined as n[gp y 1 (1 2 g )p y ] 5 P Y ; Q , would affect the relative1 1t 2t 2t t t tt

responses of domestic output and producer prices. From the Phillips curve Eq. (7), we can show thatH nthe sensitivity of log(Y ) 2 log(Y ) with respect to innovations in the exogenous process, viz.,t t

log(Q ) 2 E [log(Q )], in the case of perfect capital mobility ist t21 t

1open]]]]]]]output-elasticity 5 g v

]] ]]]1 1 S DS D1 2 g 1 1uv

H Hwhile the sensitivity of log(P ) 2 E log(P ) ist t21 t

g v]] ]]]S DS D1 2 g 1 1uvopen

]]]]]]]price-elasticity 5 g v]] ]]]1 1 S DS D1 2 g 1 1uv

Similarly, the sensitivity parameters in the case of a closed economy are given by

1closed]]]]]]]]output-elasticity 5 21

g v 1 sS D]] ]]]1 1S D1 2 g 1 1uv

and

1Obviously, our conclusion here is valid only if the parameters involved in the various versions of the Phillips curve arestable and invariant to changes in trade and capital mobility regimes. The same condition applies to our results in the nextsection.


21g v 1 sS D]] ]]]S D1 2 g 1 1uvclosed

]]]]]]]]price-elasticity 5 21g v 1 sS D]] ]]]1 1S D1 2 g 1 1uv

As discussed in Woodford (2000), these sensitivity parameters are related to the degree of strategiccomplementarity among price setters. In turn, the latter depends on the organization of markets. Forinstance, strategic substitutability (complementarity) will prevail if all factor prices are (cannot be)instantaneously equalized across suppliers of different goods, the case of common (segmented) factormarkets. In our case, we show another example where the organization of the world capital marketmatters — 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 degreeof strategic complementarity, thus rendering prices more sticky and magnifying output responses.

Appendix A

Let us start with the two price-setting equations:

n n21ˆ ˆ ˆˆlog( p ) 5 log(P ) 1 v(y 2 Y ) 1 s (C 2 C ) (A.1a)1t t 1t t t t

andn n21ˆ ˆ ˆˆlog( p ) 5 E log(P ) 1 v(y 2 Y ) 1 s (C 2 C ) (A.1b)f g2t t21 t 2t t t t

WLog-linearizing the demand functions facing the firm (Eq. 4) (where we can replace c and C byt tWy and Y , respectively), we gett t

Wˆy 5 Y 2u [log( p ) 2 log(P )], j 5 1,2 (A.2)jt t jt t

Substituting (A.2) into (A.1a) and (A.1b) and rearranging terms, we have

v 1W n n21ˆ ˆ ˆ ˆ]]] S]]]Dlog( p ) 5 log(P ) 1 (Y 2 Y ) 1 s (C 2 C ) (A.1a9)S D1t t t t t t1 1uv 1 1uv

and

v 1W n n21ˆ ˆ ˆ ˆF ]]] S]]]D Glog( p ) 5 E log(P ) 1 (Y 2 Y ) 1 s (C 2 C ) (A.1b9)S D2t t21 t t t t t1 1uv 1 1uv

Together, (A.1a9) and (A.1b9) imply that

log( p ) 5 E [log( p )] (A.3)2t t21 1t

From the aggregate price index Eq. (19), we have an approximate relation of the following kind

*log(P ) 5 n[g log( p ) 1 (1 2 g ) log( p )] 1 (1 2 n) log(´ p ) (A.4)t 1t 2t t t


From this and (A.3), the unanticipated rate of inflation is given by

log(P ) 2 E log(P ) 5 ng [log( p ) 2 log( p )]f gt t21 t 1t 2t

* *1 (1 2 n) log(´ p ) 2 E log(´ p ) (A.49)h f gjt t t21 t t

(A.4) also implies that

1]]] *log( p ) 5 [log(P ) 2 ng log( p ) 2 (1 2 n) log(´ p )]F G2t t 1t t tn(1 2 g )

*Substituting this into (A.49) and defining the real exchange rate as e ; ´ P /P , we havet t t t

g]]log(P ) 2 E log(P ) 5 [log( p ) 2 log(P )]S Dt t21 t 1t t1 2 g

1 2 n 1S]]D ]]1 log(e ) 2 E [log(e )]HS D Jt t21 tn 1 2 g

Replacing log( p ) in the above expression by (A.1a9) yields an open-economy Phillips curve of the1t

form

21g v sW n nˆ ˆ ˆ ˆF S D G]] ]]] ]]]log(P ) 2 E log(P ) 5 (Y 2 Y ) 1 (C 2 C )S DS Dt t21 t t t t t1 2 g 1 1uv 1 1uv

1 2 n 1S]]D ]]1 log(e ) 2 E [log(e )]HS D Jt t21 tn 1 2 g

W H Fˆ ˆ ˆEq. (7) in the text can be obtained by noting that Y 5 nY 1 (1 2 n)Y .t t t

References

Ball, L., Mankiw, N.G., Romer, D., 1988. The new Keynesian economics and the output-inflation tradeoff. Brookings Paperson Economic Activity 19, 1–65.

Blanchard, O., Kiyotaki, N., 1987. Monopolistic competition and the effects of aggregate demand. American EconomicReview 77, 647–666.

Dixit, A., Stiglitz, J.E., 1977. Monopolistic competition and optimum product diversity. American Economic Review 67,297–308.

Friedman, M., 1968. The role of monetary policy. American Economic Review 58, 1–17.Lane, P.R., 2001. The new open economy macroeconomics: a survey. Journal of International Economics 54, 235–266.Loungani, P., Razin, A., Yuen, C.-W., 2001. Capital mobility and the output-inflation tradeoff. Journal of Development

Economics 64, 255–274.Obstfeld, M., Rogoff, K., 1996. Foundations of International Macroeconomics. MIT Press, Cambridge, MA, Chapter 10.Phelps, E.S., 1970. Microeconomic Foundations of Employment Theory. Norton, New York.Roberts, J.M., 1995. New Keynesian economics and the Phillips curve. Journal of Money, Credit, and Banking 27, 975–984.Woodford, M., 2000. Optimizing models with nominal rigidities, Chapter 3 of Interest and Prices: Foundations of a Theory

of Monetary Policy, unpublished manuscript, Princeton University.

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