The New Keynesian Phillips curve: closed economy versus open economy

Transcription

1 Ecoomics Leers 75 (2002) 9 locae/ ecobase The New Keyesia Phillips curve: closed ecoomy versus ope ecoomy a b, Assaf Razi, Chi-Wa Yue a Tel Aviv Uiversiy, Corell Uiversiy, NBER, CEPR, ad CE-Ifo, Tel Aviv, Israel b chool of Ecoomics ad Fiace, Uiversiy of Hog Kog, Pokfulam Road, Hog Kog, Chia Received 27 May 200; acceped 6 Jue 200 Absrac The paper exeds Woodford s [Opimizig models wih omial rigidiies, Chaper 3 of Ieres ad prices: foudaios of a heory of moeary policy, Priceo Uiversiy, 2000; upublished mauscrip] aalysis of he closed ecoomy Phillips curve o a ope ecoomy wih boh commodiy rade ad capial mobiliy. We show ha cosumpio smoohig, which comes wih he opeig of he capial marke, raises he degree of sraegic complemeariy amog moopolisically compeiive suppliers, hus rederig prices more sicky ad magifyig oupu resposes o omial GP shocks Elsevier ciece B.V. All righs reserved. Keywords: Phillips curve; New Keyesia; Trade; Capial mobiliy JEL classificaio: E2; F4. Iroducio I his paper, we examie how ope marke policies would ierac wih he degree of price rigidiy i he domesic ecoomy o affec he oupu-iflaio radeoffs as well as he volailiies of oupu ad iflaio i respose o omial shocks. The aalysis will be coduced i a opimizaio-based New Keyesia framework alablachard ad Kiyoaki (987). I he discussio, we exed o a ope-rade-accou ad ope-capial-accou ecoomy he succic exposiio of Woodford (2000) coduced i he coex of a closed ecoomy. [For a useful survey of he ew ope ecoomy macroecoomic approach we adop for our aalysis i his paper, see Lae (200).] Why is such exesio poeially useful? Empirically, Lougai e al. (200) have foud ha couries wih greaer resricios o capial mobiliy ed o have seeper Phillips curves. Evidely, Correspodig auhor. Tel.: ; fax: address: cwyue@eco.khu.hk (C.-W. Yue) / 02/ $ see fro maer 2002 Elsevier ciece B.V. All righs reserved. PII: (0)

2 2 A. Razi, C.-W. Yue / Ecoomics Leers 75 (2002) 9 he degree of price sickiess is relaed o he orgaizaio of markes for isace, wheher he labor marke is commo or segmeed. imilarly, he degree of price sickiess ca be affeced by he opeess of he ecoomy i boh commodiy rade ad capial flows. 2. The aalyical framework Cosider a small ope ecoomy wih a represeaive household ha is edowed wih a coiuum of goods-specific skills uiformly disribued o he ui ierval [0, ] o be supplied o a differeiaed produc idusry. As a cosumer, he represeaive household has access o cosumpio of boh domesic goods (disribued o [0, ]) ad foreig goods (disribued o (, ]). The household seeks o maximize a discoued sum of expeced uiliies: ` E O b [u(c, M /P ; j ) 2E v(h ( j); j )dj] where b is he subjecive discou facor, C is he ixi ad igliz (977) idex of household cosumpio, P he ixi igliz price idex, M/P he demad for real balaces, j a preferece shock, ad h( j) he supply of ype-j labor o he producio of good of variey j. Like Obsfeld ad Rogoff (996), we defie he cosumpio idex ad is correspodig price idex, respecively, as ad 3 4 u /(u) (u )/u (u )/u C 5 E c ( j) dj E c ( j) dj /(2u ) 2u 2u P 5 E p ( j) dj E [ p ( j)] dj () 0 where c( j) represes domesic cosumpio of he jh domesically produced good, c( j) domesic cosumpio of he jh foreig-produced good, p( j) he domesic-currecy price of c( j), p( j) he foreig-currecy price of c( j), he omial exchage rae (domesic-currecy price of foreig currecy), u. he elasiciy of subsiuio amog he differe goods, ad he fracio of goods ha are produced domesically. I omial erms, he budge cosrai facig he household is give by: E p ( j)c ( j)dj E p ( j)c ( j)dj i M B B 0 ]] i 5 M ( i )B f,( i )B E w ( j)h ( j)dje P ( j)dj 0 0 where B is he domesic-currecy value of domesic borrowig, B he foreig-currecy value of

3 A. Razi, C.-W. Yue / Ecoomics Leers 75 (2002) 9 3 foreig borrowig, f he forward exchage rae for foreig currecies purchased/ sold a ime 2, for delivery a ime, i ad i he domesic ad foreig ieres raes, w( j) he wage rae per ui labor of ype j, ad P( j) profi icome from firms of ype j. Wih perfec capial mobiliy, covered ieres pariy prevails: f, i5 ( i )]] [cf. firs-order codiios of he household wih respec o B ad B.] From his poi o, we shall focus o he relaio bewee aggregae supply of goods ad cosumpio smoohig made possible by ieraioal capial mobiliy. For his purpose, we would o be cocered abou he deails of aggregae demad (icludig he demad for moey), ieraioal commodiy rade, ad he deermiaio of he exchage rae. For simpliciy, cosumer uiliy is assumed o be separable bewee cosumpio ad real moey balaces. For our purpose, he releva uiliy-maximizig codiios iclude a iraemporal codiio for he choice of labor supply of ype j: v h(h ( j); j ) w ( j) ]]]] 5]] u (C ; j ) P c ad a ieremporal codiio for he cosumpio-savig choice: (2) u c(c ; j ) ]]]]] 5 b( r) (3) u (C ; j ) c where r is he world real rae of ieres, assumed for simpliciy o be ime-ivaria. This laer equaliy is a cosequece of he covered ieres pariy ad he Fisher equaio. As i he ixi ad igliz (977) model, demad for good j saisfies c ( j) 5 C p ( j) ]] P 2u The producio fucio assumes he form y ( j) 5 Af(h ( j)) (4) where A is a radom produciviy shock. The variable cos of supplyig y ( j) isw ( j)f ( y ( j)/a ), which implies a (real) margial cos of w ( j) s ( j) 5]]]]]]] PA f9( f ( y ( j)/a )) Usig Eq. (2), we ca replace he real wage above by he margial rae of subsiuio. Imposig symmery across firms (so ha we ca drop he idex j), he above equaio ca be rewrie as v h( f ( y/a); j ) s( y, C; j, A) 5]]]]]]] u (C; j )Af 9( f ( y/a)) c (5)

4 4 A. Razi, C.-W. Yue / Ecoomics Leers 75 (2002) 9 Trade-wise, price-makig firms face world demad for heir producs so ha Eq. (4) implies p ( j) y ( j) 5 Y W ]] P 2u where y ( j) is he quaiy of good j supplied by he firm o mee he world demad ad W H F H Y 5 Y Y he idex for all goods produced aroud he world, wih Y 5 e (( p ( j)y ( j)) /P )dj 0 F 0 ad Y 5 e (( p ( j)y ( j)) /P )dj as correspodig producio idices for home goods ad foreig goods. The goods markes are moopolisically compeiive. A fracio g of he firms ses heir prices flexibly a p, supplyig y ; whereas he remaiig 2 g of firms ses heir prices oe period i advace (i period 2 ) a p 2, supplyig y 2. I he former case, he price is marked up above he margial cos by a facor of m ( 5u/(u 2 ). ) so ha p P ] 2 ms( y, C ; j, A ) 5 0 (6a) I he laer case, p 2 will be chose o maximize expeced discoued profi F G H gj E ]]] ( p2 y22 wh) i W u 2u W u 2u 5 E ]]] fy P p2 2 wf (Y P p 2 /A ) i where we have used he iverse demad fucio from Eq. (4) for y fucio for h. Oe ca show ha p saisfies Give p H F GJ 2 2 (49) ad he iverse producio ]]] W u ] p2 E Y P 2 ms( y 2, C ; j, A ) 5 0 (6b) i P ad p, he aggregae price idex () ca be rewrie as: 2 P 5h[gp ( 2 g )p ] ( 2 )( p ) j (9) 2u 2u 2u /(2u ) 2 I he exreme case where all prices are fully flexible (i.e. g 5 ), oupu will aai is aural level, Y, implicily defied by p 2u 2u /(2u ) g ]]]]]]]]]] 5 ms(y, C ; j, A ) p ( 2 ) p f Amog oher higs, Y depeds o he level of home cosumpio uder flexible prices (C ), domesic ad foreig prices ( p ad p ), as well as he exchage rae ( ). For laer purpose, we ca deoe s(y, C ; j, A )ass. I he absece of capial flows, C 5 Y so ha he aural oupu level is defied by p 2u 2u /(2u ) g ]]]]]]]]]] 5 ms(y, Y ; j, A ) p ( 2 ) p f

5 A. Razi, C.-W. Yue / Ecoomics Leers 75 (2002) 9 5 Whe he ecoomy is compleely closed i erms of boh commodiy rade ad capial flows ( 5 ad C 5 Y ), he equaio above furher simplifies o 5 ms(y, Y ; j, A ) I his las case, equilibrium oupu is compleely idepede of moeary policy. 3. The Phillips curve This secio derives he expecaios-augmeed Phillips curve of he kid hypohesized by Friedma (968) ad Phelps (970) for boh closed ad ecoomies [cf. Ball e al. (988) ad Robers (995)]. I order o obai a racable soluio, we log-liearize he equilibrium codiios aroud he seady sae. We assume ha b( r)5, which is ecessary for he exisece of a seady sae. I ] paricular, we cosider a deermiisic seady sae where j 5 0 ad A 5A wih 5, ] p 5p, ] ad ] C 5C. efie xˆ 5 log(x /x) ]. (x 2x)/x ] ] as he proporioal deviaio of ay variable x from is deermiisic seady sae value ] x. We ca he log-liearize Eq. (5) aroud he deermiisic seady sae equilibrium o ge where sˆ 2 sˆ 5 v(yˆ 2 Y ˆ ) s (Cˆ 2 C ˆ ) (59) v 5 vw vp ] ] v hh(y/a) v w 5]]] v f 9 h ] ] f 0( f (.))(y/a) vp 52]]]]] f 9( f (.))f 9(.) ad u c] cc s 52]] uc Log-liearizig he wo price-seig Eqs. (6a) ad (6b) usig Eq. (59), we obai ad ˆ ˆ ˆ ˆ log( p ) 5 log(p ) v(y 2 Y ) s (C 2 C ) (6a9) f ˆ ˆ ˆ ˆ 2 2 log( p ) 5 E log(p ) v(y 2 Y ) s (C 2 C ) (6b9) g From he defiiio of he aggregae price idex (9), we ca derive he followig approximaio log(p ) 5 [g log( p ) ( 2 g ) log( p )] ( 2 ) log( p ) (0) 2

6 6 A. Razi, C.-W. Yue / Ecoomics Leers 75 (2002) 9 efie he iflaio rae p5 l(p /P ) so ha p2 E (p ) 5 log(p ) 2 E log(p ), ad he real exchage rae as e ; P /P. We show i Appedix A how hese price relaios ca be combied o obai he ope-ecoomy Phillips curve as follows: H g v H p 2 E (p ) 5 ]] ]]] (Yˆ 2 Y ˆ ) 2 g uv ( 2 )v F s F]]]G (Yˆ 2 Y ˆ ) ]]] (Cˆ 2 C ˆ ) J uv uv 2 ]] H]] log(e ) 2 E [log(e )] J (7) 2 g 3.. Perfec capial mobiliy Whe capial is perfecly mobile, cosumpio smoohig ca be achieved ad, give he ˆ ˆ assumpio ha b( r) 5, cosumpio will be redless (see Eq. (3)). As a resul, C5 0 5 C. The Phillips curve herefore simplifies o H g v H p 2 E (p ) 5 ]] ]]] (Yˆ 2 Y ˆ ) 2 g uv ( 2 )v F F]]]G(Yˆ ˆ 2 Y ) J uv 2 ]] H]] log (e ) 2 E [log (e )] J (79) 2 g 3.2. Closig he capial accou I he absece of capial flows, cosumpio smoohig ca o loger be achieved ad cosumpio H will flucuae wih domesic oupu (i.e. Cˆ 5 Yˆ ad Cˆ 5 Y ˆ ). As a resul, he Phillips curve assumes he form H ( 2 )s ˆ F F]]]] G ˆ J uv 2 ]] H]] J g v s H p 2 E (p ) 5 ]] ]]] (Yˆ 2 Y ˆ ) 2 g uv 3.3. Closed ecoomy (Y 2 Y ) log(e ) 2 E [log(e )] (70) 2 g If we furher close he rade accou, he ecoomy will be self-sufficie ad 5. I his case, he Phillips curve will ake a eve simpler form

7 A. Razi, C.-W. Yue / Ecoomics Leers 75 (2002) 9 7 g v s H p 2 E (p ) 5 ]] ]]] (Yˆ 2 Y ˆ ) (7-) 2 g uv which is exacly ideical o Eq. (.23) i Woodford (2000) A compariso The differece i he oupu-iflaio radeoff coefficies bewee (79) ad (70) lies i gs /(2 g )( uv), which capures he sesiiviy of iflaio o cosumpio spedig. This erm will disappear i he presece of cosumpio smoohig, as will be achieved uder perfec capial mobiliy. The differece i he same coefficies bewee (70) ad (7-) isg( 2 )v/(2g )( uv), where represes he fracio of world cosumpio ha is produced domesically i he case of rade opeess whereas sads for he same fracio (i.e. 00%) i he case of a closed ecoomy. Therefore, successive opeig of he ecoomy will flae he Phillips curve. 4. hor-ru aggregae supply As a corollary o our aalysis of he oupu-iflaio radeoff, we ca also examie how exogeous H H shocks o omial GP, defied as [gp y ( 2 g )p2 y 2] 5 P Y ; Q, would affec he relaive resposes of domesic oupu ad producer prices. From he Phillips curve Eq. (7), we ca show ha H he sesiiviy of log(y ) 2 log(y ) wih respec o iovaios i he exogeous process, viz., log(q ) 2 E [log(q )], i he case of perfec capial mobiliy is ope oupu-elasiciy 5]]]]]]] g v ]] ]]] 2 g uv H H while he sesiiviy of log(p ) 2 E log(p ) is g v ]] ]]] 2 g uv ope price-elasiciy 5]]]]]]] g v ]] ]]] 2 g uv imilarly, he sesiiviy parameers i he case of a closed ecoomy are give by closed oupu-elasiciy 5]]]]]]]] g v s ]] ]]] 2 g uv ad Obviously, our coclusio here is valid oly if he parameers ivolved i he various versios of he Phillips curve are sable ad ivaria o chages i rade ad capial mobiliy regimes. The same codiio applies o our resuls i he ex secio.

8 8 A. Razi, C.-W. Yue / Ecoomics Leers 75 (2002) 9 g v s ]] ]]] closed 2 g uv price-elasiciy 5]]]]]]]] g v s ]] ]]] 2 g uv As discussed i Woodford (2000), hese sesiiviy parameers are relaed o he degree of sraegic complemeariy amog price seers. I ur, he laer depeds o he orgaizaio of markes. For isace, sraegic subsiuabiliy (complemeariy) will prevail if all facor prices are (cao be) isaaeously equalized across suppliers of differe goods, he case of commo (segmeed) facor markes. I our case, we show aoher example where he orgaizaio of he world capial marke maers i paricular, he iegraio or o of he domesic capial marke io he world marke. Cosumpio smoohig, which comes wih he opeig of he capial marke, will icrease he degree of sraegic complemeariy, hus rederig prices more sicky ad magifyig oupu resposes. Appedix A Le us sar wih he wo price-seig equaios: ˆ ˆ ˆ ˆ log( p ) 5 log(p ) v(y 2 Y ) s (C 2 C ) (A.a) ad f ˆ ˆ ˆ ˆ 2 2 log( p ) 5 E log(p ) v(y 2 Y ) s (C 2 C ) (A.b) g Log-liearizig he demad fucios facig he firm (Eq. 4) (where we ca replace c ad C W y ad Y, respecively), we ge W ŷ 5 Yˆ 2u [log( p ) 2 log(p )], j 5,2 (A.2) j j ubsiuig (A.2) io (A.a) ad (A.b) ad rearragig erms, we have v W log( p ) 5 log(p ) ]]] (Yˆ 2 Y ˆ ) s ]]](Cˆ 2 C ˆ ) (A.a9) uv uv ad v W log( p F ]]] ˆ ˆ ]]] ˆ ˆ 2) 5 E log(p ) (Y 2 Y ) s (C2 C ) G (A.b9) uv uv Togeher, (A.a9) ad (A.b9) imply ha log( p ) 5 E [log( p )] (A.3) 2 From he aggregae price idex Eq. (9), we have a approximae relaio of he followig kid log(p ) 5 [g log( p ) ( 2 g ) log( p )] ( 2 ) log( p ) 2 W by (A.4)

9 A. Razi, C.-W. Yue / Ecoomics Leers 75 (2002) 9 9 From his ad (A.3), he uaicipaed rae of iflaio is give by log(p ) 2 Eflog(P ) g5 g [log( p ) 2 log( p 2)] ( 2 ) hlog( p ) 2 E flog( p ) gj (A.49) (A.4) also implies ha log( p 2) 5 F]]] G[log(P ) 2 g log( p ) 2 ( 2 ) log( p )] ( 2 g ) ubsiuig his io (A.49) ad defiig he real exchage rae as e ; P /P, we have g log(p ) 2 E log(p ) 5 ]] [log( p ) 2 log(p )] 2 g 2 ]] ]] log(e ) 2 E [log(e )] 2 g H J Replacig log( p ) i he above expressio by (A.a9) yields a ope-ecoomy Phillips curve of he form g v ˆ W ˆ s ˆ ˆ ]] F]]] ]]] G log(p ) 2 E log(p ) 5 (Y 2 Y ) (C 2 C ) 2 g uv uv 2 ]] H]] log(e ) 2 E [log(e )] 2 g J W H F Eq. (7) i he ex ca be obaied by oig ha Yˆ 5 Yˆ ( 2 )Y ˆ. Refereces Ball, L., Makiw, N.G., Romer,., 988. The ew Keyesia ecoomics ad he oupu-iflaio radeoff. Brookigs Papers o Ecoomic Aciviy 9, 65. Blachard, O., Kiyoaki, N., 987. Moopolisic compeiio ad he effecs of aggregae demad. America Ecoomic Review 77, ixi, A., igliz, J.E., 977. Moopolisic compeiio ad opimum produc diversiy. America Ecoomic Review 67, Friedma, M., 968. The role of moeary policy. America Ecoomic Review 58, 7. Lae, P.R., 200. The ew ope ecoomy macroecoomics: a survey. Joural of Ieraioal Ecoomics 54, Lougai, P., Razi, A., Yue, C.-W., 200. Capial mobiliy ad he oupu-iflaio radeoff. Joural of evelopme Ecoomics 64, Obsfeld, M., Rogoff, K., 996. Foudaios of Ieraioal Macroecoomics. MIT Press, Cambridge, MA, Chaper 0. Phelps, E.., 970. Microecoomic Foudaios of Employme Theory. Noro, New York. Robers, J.M., 995. New Keyesia ecoomics ad he Phillips curve. Joural of Moey, Credi, ad Bakig 27, Woodford, M., Opimizig models wih omial rigidiies, Chaper 3 of Ieres ad Prices: Foudaios of a Theory of Moeary Policy, upublished mauscrip, Priceo Uiversiy.