2.
2 A. Razin, C.-W. Yuen / Economics Letters 75 (2002) 1 – 9the 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 O b [u(C , M /P ; j ) 2E v(h ( j); j ) dj] ` t E0 t t t t t t t 50 0where 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 ) Ct 5 3E0 ( t E c t ( j) u 21 ) / u dj 1 c * ( j)(u 21 ) / u dj n 4and 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) 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 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 0where 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 3foreign borrowing, ft21,t the forward exchange rate for foreign currencies purchased / sold at time t 2 1for 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: 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 andconsumption 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: vh (h t ( j); j t ) w t ( j) ]]]] 5 ]] (2) u c (Ct ; j t ) Ptand 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 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 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)) 21where 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. Imposingsymmetry 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 nY 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 nand Y t 5 e0 ((´t p * ( j)y t ( j)) /Pt ) dj as corresponding production indices for home goods and foreign tgoods. The goods markets are monopolistically competitive. A fraction g of the ﬁrms sets their pricesﬂexibly at p1t , supplying y 1t ; whereas the remaining 1 2 g of ﬁrms sets their prices one period inadvance (in period t 2 1) at p2t , supplying y 2t . In the former case, the price is marked up above themarginal 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) PtIn 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 2twhere we have used the inverse demand function from Eq. (4) for y 2t and the inverse productionfunction 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 naturallevel, 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 nAmong 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 candenote 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 5When the economy is completely closed in terms of both commodity trade and capital ﬂows (n 5 1and 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 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 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 ] ] ˆCt 5C. Deﬁne x t 5 log(x t /x) t tdeterministic 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 ]] ucLog-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 realexchange rate as e t ; ´t P t* /Pt . We show in Appendix A how these price relations can be combined toobtain 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 t3.1. Perfect capital mobility When capital is perfectly mobile, consumption smoothing can be achieved and, given the ˆ ˆnassumption 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 213.2. Closing the capital account In the absence of capital ﬂows, consumption smoothing can no longer be achieved and consumption ˆ ˆH ˆn ˆnwill ﬂuctuate with domestic output (i.e. Ct 5 Y t and C t 5 Y t ). As a result, the Phillips curve assumesthe 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 t3.3. 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
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 twhich 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 2g )(1 1 uv ), 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 1 uv ),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.Therefore, successive opening of the economy will ﬂatten the Phillips curve.14. Short-run aggregate supply As a corollary to our analysis of the output-inﬂation tradeoff, we can also examine how exogenousshocks 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 relativeresponses of domestic output and producer prices. From the Phillips curve Eq. (7), we can show thatthe sensitivity of log(Y H ) 2 log(Y n ) with respect to innovations in the exogenous process, viz., t tlog(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 Dwhile 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 Dand 1 Obviously, 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.
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 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: 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 byy 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 9From 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 ) tSubstituting 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 JReplacing log( p1t ) in the above expression by (A.1a9) yields an open-economy Phillips curve of theform 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 ˆFEq. (7) in the text can be obtained by noting that Y t 5 nY t 1 (1 2 n)Y t .ReferencesBall, L., Mankiw, N.G., Romer, D., 1988. The new Keynesian economics and the output-inﬂation tradeoff. Brookings Papers on Economic Activity 19, 1–65.Blanchard, O., Kiyotaki, N., 1987. Monopolistic competition and the effects of aggregate demand. American Economic Review 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.
Be the first to comment