Financial Development, International Captial Flows, and Aggregate Output

Transcription

1 Sngapore Managemen Unversy Insuonal Knowledge a Sngapore Managemen Unversy Research Collecon School Of Economcs School of Economcs -23 Fnancal Developmen, Inernaonal Capal Flows, and Aggregae Oupu Hapng ZHANG Sngapore Managemen Unversy, hpzhang@smu.edu.sg Jürgen von Hagen Follow hs and addonal works a: hp://nk.lbrary.smu.edu.sg/soe_research Par of he Fnance Commons, and he Inernaonal Economcs Commons Caon ZHANG, Hapng and von Hagen, Jürgen. Fnancal Developmen, Inernaonal Capal Flows, and Aggregae Oupu. (23). Research Collecon School Of Economcs. Avalable a: hp://nk.lbrary.smu.edu.sg/soe_research/488 Ths Workng Paper s brough o you for free and open access by he School of Economcs a Insuonal Knowledge a Sngapore Managemen Unversy. I has been acceped for ncluson n Research Collecon School Of Economcs by an auhorzed admnsraor of Insuonal Knowledge a Sngapore Managemen Unversy. For more nformaon, please emal lbir@smu.edu.sg.

2 Fnancal Developmen, Inernaonal Capal Flows, and Aggregae Oupu Jürgen von Hagen and Hapng Zhang Ths Verson: Sepember 22 Frs Verson: November 28 Absrac We develop a racable wo-counry overlappng-generaons model and show ha cross-counry dfferences n fnancal developmen can explan hree recen emprcal paerns of nernaonal capal flows: Fnancal capal flows from relavely poor o relavely rch counres, whle foregn drec nvesmen flows n he oppose drecon; ne capal flows go from poor o rch counres; despe s negave ne nernaonal nvesmen posons, he Uned Saes receves a posve ne nvesmen ncome. Inernaonal capal mobly affecs oupu n each counry drecly hrough he sze of domesc nvesmen and ndrecly hrough he aggregae savng rae. Under ceran condons, he ndrec effec may domnae he drec effec so ha nernaonal capal mobly rases oupu n he poor counry and globally, alhough ne capal flows are n he drecon o he rch counry. We also explore he welfare and dsrbuonal effecs of nernaonal capal flows and show ha he paerns of capal flows may reverse along he convergence process of a developng counry. Our model adds o he undersandng of he benefs of nernaonal capal mobly n he presence of domesc fnancal frcons. Keywords: Capal accoun lberalzaon, fnancal developmen, foregn drec nvesmen, symmery breakng JEL Classfcaon: E44, F4 We apprecae he commens and suggesons from he edor and wo anonymous referees as well as he parcpans a he 4h Konsanz Semnar, he Economerc Socey NASM 29 n Boson, he SED 29 Annual Meeng n Isanbul, he 3h ZEI Summer School, he AEA 2 meeng n Alana, and semnar parcpans a he Unversy of Bonn, he Unversy of Illnos, Indana Unversy, Naonal Unversy of Sngapore, Queen s Unversy. Fnancal suppor from Sngapore Managemen Unversy and he German Research Foundaon (DFG) are sncerely acknowledged. Unversy of Bonn, Indana Unversy and CEPR. Lennesrasse. 37, D-533 Bonn, Germany. E-mal: vonhagen@un-bonn.de Correspondng auhor. School of Economcs, Sngapore Managemen Unversy. 9 Samford Road, Sngapore E-mal: hpzhang@smu.edu.sg

3 Inroducon Sandard nernaonal macroeconomcs predcs ha capal flows from capal-rch counres, where he margnal produc of capal (MPK, henceforh) s low, o capal-poor counres, where he MPK s hgh. Furhermore, here should be no dfference beween gross and ne capal flows, as capal movemens are undreconal. The paerns of nernaonal capal flows observed n he pas 2 years, however, sand n sark conras o hese predcons (Lane and Mles-Ferre, 2, 27b,c). Frs, snce 998, he average per-capa ncome of counres runnng curren accoun surpluses has been below ha of he defc counres,.e., ne capal flows have been uphll from poor o rch counres (Prasad, Rajan, and Subramanan, 26, 27). Second, many developng economes, ncludng Chna, Malaysa, and Souh Afrca, are ne mporers of foregn drec nvesmen (hereafer, FDI) and ne exporers of fnancal capal a he same me, whle developed counres such as France, he Uned Kngdom, and he Uned Saes exhb he oppose paern (Ju and We, 2). Thrd, despe s negave ne nernaonal nvesmen poson snce 986, he U.S. has been recevng a posve ne nvesmen ncome unl 25 (Gournchas and Rey, 27; Hausmann and Surzenegger, 27; Hggns, Klgaard, and Tlle, 27). Recen research offers wo man explanaons o hese emprcal facs. Devereux and Suherland (29) and Tlle and van Wncoop (2) focus on he cross-counry rsksharng nvesors can acheve by dversfyng her porfolos globally. Inernaonal porfolo nvesmen s deermned by he cross-correlaon paerns of aggregae shocks a he counry level. These models do no dsngush beween FDI and porfolo equy nvesmen and, herefore, offer no explanaon for he second paern. The oher srand of leraure focuses on domesc fnancal marke mperfecons (Aok, Bengno, and Kyoak, 29; Caballero, Farh, and Gournchas, 28; Smh and Valderrama, 28). Masuyama (24) shows ha, n he presence of cred marke mperfecons, fnancal marke globalzaon may lead o a seady-sae equlbrum n whch fundamenally dencal counres end up wh dfferen levels of per capa oupu, a resul he calls symmery breakng. Furhermore, fnancal capal flows from poor o rch counres n he seady sae. However, Masuyama (24) does no address FDI flows. Mendoza, Quadrn, and Ros-Rull (29) analyze he jon deermnaon of fnancal capal flows and FDI n a heerogeneous-agen model wh unnsurable dosyncrac endowmen and nvesmen rsks. The precauonary savngs move plays he crucal role. Ju and We (2) show n a sac model ha, when boh FDI and fnancal capal flows are allowed, all fnancal capal leaves he counry where cred marke mperfecons are more severe, whle FDI flows no hs counry. Thus, capal mobly allows nvesors o fully bypass he underdeveloped fnancal sysem. The models menoned above explan only one or wo of he hree facs. 2

4 Whle he leraure does no explcly address he mplcaons of nernaonal capal mobly for aggregae oupu, seems nuvely plausble ha, due o he declnng MPK, uphll capal flows make he poor counres and he world economy poorer. The polcy mplcaons seem o be clear: The world would be beer off whou nernaonal capal movemens beween rch and poor counres. We exend he second srand of leraure and explan smulaneously all hree emprcal facs. Followng Masuyama (24), we ake he ghness of he borrowng consrans as a measure of a counry s level of fnancal developmen. The wo counres n our model dffer fundamenally only n he level of fnancal developmen. Under nernaonal fnancal auarky (hereafer, IFA), neres raes are affeced by wo facors. Frs, for a gven level of fnancal developmen, a lower capal-labor rao mples a hgher MPK and hgher neres raes. We call hs he neoclasscal effec, as arses from he concavy of he neoclasscal producon funcon wh respec o he capal-labor rao. Second, for a gven capal-labor rao, a lower level of fnancal developmen mples he less effcen enforcemen of cred conrac and monorng of borrowers. In hs case, agens face gher borrowng consrans and he lower aggregae cred demand leads o a lower loan rae and a hgher equy rae. We call hs he fnancal-underdevelopmen effec. If aggregae savng s neres-elasc, domesc fnancal frcons dsor aggregae savng hrough he neres raes, leadng o he neffcenly low nvesmen and hgh MPK. Thus, domesc fnancal frcons affec neres raes drecly hrough he fnancal-underdevelopmen effec and ndrecly hrough he neoclasscal effec. In he less fnancally developed counry, he seady-sae loan rae s lower, as he fnancal-underdevelopmen effec domnaes he neoclasscal effec; as he wo effecs work n he same drecon, he seady-sae equy rae s srcly hgher. Suppose ha he wo counres are nally n he seady sae under IFA. Upon full capal mobly, he more fnancally developed counry receves ne capal nflows, hanks o s larger cred marke. In oher words, ne capal flows are uphll from he poor o he rch counry. The nal cross-counry neres rae dfferenals drve fnancal capal flows from he poor o he rch counry and FDI flows n he oppose drecon. Snce he rch counry receves a hgher reurn on s FDI asses han pays on s foregn debs, ges a posve ne nvesmen ncome despe s negave ne nernaonal nvesmen poson. Inuvely, by exporng s superor fnancal servces hrough wo-way capal flows, he rch counry receves a posve ne reward, accordngly. Thus, our model predcons are conssen wh he hree emprcal facs menoned above. Buldng upon hs model, we make four conrbuons o he leraure. Frs, we show ha full capal mobly can rase oupu n he poor counry as well as globally, despe uphll ne capal flows. Inuvely, fnancal frcons depress he reurn on and, hence, he level of aggregae savng. Allowng for nernaonal capal mo- Masuyama (24) and von Hagen and Zhang (2) show ha hs may ndeed be he case. 3

5 bly provdes domesc households wh beer reurns on savngs. Thus, by amelorang he neres rae dsorons, capal mobly ndrecly rases aggregae savngs n he less fnancally developed counry. If savng s suffcenly neres-elasc, he rse n aggregae savng may exceeds ne capal ouflows so ha aggregae nvesmen and oupu n he less fnancally developed counry as well as globally can be hgher han under IFA. The neres-elasc savng s key o oupu gans n our model and deserves specal aenon. Gven he Cobb-Douglas preference, he ncome effec and he subsuon effec of neres raes on savng exacly offse each oher. The neres-elasc savng n our model resuls from he posve fuure labor ncome, whch s defned as he human wealh effec by Summers (98). Our model predcs ha, n he counry wh a hgher growh rae of he labor ncome, aggregae savng s more neres-elasc so ha full capal mobly s more lkely o rase oupu. The neres elascy of savng has been he focus of he debaes on he effecveness of ax reform (Bernhem, 22; Evans, 983; Summers, 98), fnancal lberalzaon (Bandera, Capro, Honohan, and Schanarell, 2), and oher publc polces (Corbo and Schmd-Hebbel, 99) on capal accumulaon. The emprcal evdences on he magnude of he neres elascy of savngs are raher mxed (Govannn, 983; Loayza, Schmd-Hebbel, and Serven, 2). In parcular, Ogak, Osry, and Renhar (996) provde he emprcal evdences ha savngs are more responsve o raes of reurn a hgher ncome levels. Insead of argung for he emprcal sgnfcance of he neres elascy of savng, our analyss complemens he exsng leraure by emphaszng he heorecal relevance of he neres-elasc savng o he oupu mplcaons of capal accoun lberalzaon polcy. As our second conrbuon, we show ha fnancal capal flows affec he owners of cred capal and equy capal n oppose ways and so do FDI flows. Capal flows also affec he nergeneraonal ncome dsrbuon. Our model pons ou such dsrbuonal effecs of capal flows and offers an explanaon for why capal accoun lberalzaon ofen encouners boh suppor and opposon n a gven counry. Thrd, we also analyze a scenaro where one counry s more fnancally developed and n s seady sae, whle he oher counry s less fnancally developed and below s seady sae before capal accoun lberalzaon. We sudy he neracons of nernaonal capal flows and he economc convergence of he second counry and show ha he paern of nernaonal capal flows may reverse along he convergence process of he less fnancally developed counry. We assume ha he mass of ndvduals who can produce s fxed n each counry, whle he nvesmen sze of each producer s endogenously deermned. Thus, aggregae nvesmen occurs on he nensve margn nsead of on he exensve margn as n Masuyama (24). Counres wh dencal fundamenals have he same, unque, and sable seady sae under capal mobly n our model. As our fourh conrbuon, we show ha Masuyama s symmery-breakng depends crcally on he assumpon of he fxed 4

6 projec sze and hus, nvesmen occurs along he exensve margn. Our model dffers from he exsng leraure n he followng aspecs. The sac model of Ju and We (2) s useful for analyzng he mmedae mpacs of capal accoun lberalzaon, whle our OLG model faclaes he shor-run and he long-run analyss. Devereux and Suherland (29); Mendoza, Quadrn, and Ros-Rull (29); Tlle and van Wncoop (2) capure nernaonal capal flows n he sengs wh aggregae or dosyncrac uncerany, whle our model feaures nernaonal capal flows n he deermnsc seng. Angeleos and Panous (2); Buera and Shn (2); Carroll and Jeanne (2); Sandr (2); Song, Soresleen, and Zlbo (2) address uphll fnancal capal flows, whle we focus on he jon deermnaon of fnancal capal and FDI flows. Caballero, Farh, and Gournchas (28); Mendoza, Quadrn, and Ros-Rull (29) analyze he jon deermnaon of fnancal capal and FDI flows n an endowmen-economy model, whle endogenous capal accumulaon s crucal n our model. Caballero, Farh, and Gournchas (28) assume ha foregn drec nvesors from he more fnancally developed counry have an advanage n capalzng he reurn on nvesmen n he hos counry and Mendoza, Quadrn, and Ros-Rull (29) assume ha nvesors from he more fnancally developed counry can nsure her foregn drec nvesmen usng he beer rsk-sharng opporunes n her home counry. We do no need hese exra assumpons. Carroll and Jeanne (2); Sandr (2) feaure he precauonary savngs channel n a model wh dosyncrac rsk and ncomplee markes, whle neres-elasc savngs n our model resul from lmed commmen. Casell and Feyrer (27) presen alernave esmaes of cross-counry MPK dfferences o assess he mporance of nernaonal cred marke frcons. They mplcly assume away domesc fnancal frcons so ha he MPK s he rae of reurn o nvesors and he drvng force behnd nernaonal capal flows. They fnd ha, f one focuses on reproducble capal and adjuss for he hgher relave prces of capal goods n poor counres, he MPK does no dffer much beween developed and developng counres. Thus, hey conclude ha nernaonal cred marke frcons canno go far n explanng observed capal flows beween hese counres. Our analyss absracs from nernaonal cred marke frcons and focuses on domesc fnancal frcons whch creaes a wedge beween he prvae raes of reurn (.e., he raes of reurn o cred capal and equy capal) and he socal rae of reurn (.e., MPK). The prvae raes of reurn are he drvng forces behnd nernaonal capal flows n our model, whch allows us o dsngush beween fnancal capal and FDI flows. The res of he paper s srucured as follows. Secon 2 ses up he model and shows he dsorons of fnancal frcons on neres raes and oupu under IFA. Secon 3 analyzes he oupu and welfare mplcaons of capal mobly. Secon 4 concludes wh some remarks. Appendx collecs he echncal proofs and relevan dscussons. 5

7 2 The Model under Inernaonal Fnancal Auarky The world economy consss of wo counres, N (Norh) and S (Souh), whch are fundamenally dencal excep n he level of fnancal developmen as specfed laer. In he followng, varables n counry {N, S} are denoed wh he superscrp. A fnal good can be consumed or ransformed no capal goods. The fnal good s nernaonally radable and chosen as he numerare, whle capal goods are non-radable. Indvduals lve for wo perods, young and old. There s no populaon growh and he sze of each generaon s normalzed o one n each counry. Each ndvdual s endowed wh one un of labor when young and ɛ uns of labor when old, whch are suppled o aggregae producon. Aggregae labor supply s L = + ɛ n each perod. A he begnnng of each perod, fnal goods Y are produced wh capal goods K and labor L n a Cobb-Douglas fashon. Capal goods fully deprecae afer producon. Capal goods and labor are prced a her respecve margnal producs. To summarze, ( ) K Y α ( ) α = L, where α (, ), () α α R K = αy and ω L = ( α)y, (2) where ω denoes he wage rae and R denoes he MPK. There s no uncerany n he economy. In hs secon, we assume ha nernaonal capal flows are no allowed. Each generaon consss of wo ypes of ndvduals, enrepreneurs and households, of mass η and η, respecvely. They have he Cobb-Douglas preference over consumpon, ( ) c,j β ( ) u,j y, c,j β o,+ =, (3) β β where superscrp j {e, h} denoes he deny of enrepreneur or household; c,j y, and c,j o,+ denoe ndvdual j s consumpon when young and when old; β (, ) s he paence facor,.e., a larger β means ha ndvduals are more paen and care more abou consumpon when old. If β =, hey only consume when old, u,j = c,j o,+. An ndvdual j born n perod and counry receves a labor ncome ω, consumes c,j y,, and saves s,j = ω c,h y, a a gross neres rae of R,j n perod. In perod +, afer recevng he fnancal ncome R,j s,j and a labor ncome ɛω+, he ndvdual consumes s oal wealh c,j o,+ = R,j consran s c,j y, + c,j o,+ R,j s,j + ɛω + and exs from he economy. Is lfeme budge = W,j, where W,j ω + ɛω + R,j denoes s dscouned lfeme wealh when young. The componen ɛω + capures he human wealh defned by Summers R,j (98). Gven he Cobb-Douglas preference, s opmal consumpon-savng choces are c,j y, = ( β)w,j and c,j o,+ = R,j βw,j, (4) s,j = ω c,j y, = βω ( β) ɛω +. (5) R,j 6

8 Plug he soluons o consumpon back no he uly funcon (3), he ndvdual s ndrec lfeme uly funcon s u,j = W,j (R,j ) β. Households and enrepreneurs may ge dfferen neres raes on her savngs and he deermnaon of neres raes s key o our resuls. We assume ha only enrepreneurs can use fnal goods o produce capal one-o-one and he producon akes one perod. Thus, he gross rae of reurn o he enrepreneural nvesmen made n perod s equal o he MPK n perod +, R+. Wh no oher nvesmen opporuny avalable, households lend her enre savngs o he cred marke a he gross neres rae R,h n perod. As long as R+ R,h, an enrepreneur prefers o fnance s nvesmen usng loans d,h. However, due o lmed commmen, he enrepreneur can borrow only up o a fracon of s fuure projec revenues, R,h d,h = R,h ( d,e ) θ R+. (6) where d,e denoes he enrepreneur s own funds n he projec. In oher words, an enrepreneural projec wh he nvesmen sze demands for equy capal d,e and cred capal d,h. Followng Masuyama (24, 27), we use θ [, ] as a measure of fnancal developmen or he severy of cred marke mperfecons n counry. I capures a wde range of nsuonal facors and s hgher n counres wh more sophscaed fnancal and legal sysems, beer credor proecon, and more lqud asse marke, ec. Defne he equy rae as he rae of reurn o he enrepreneural equy capal, R,e R + R,h d,h d,e = R+ + (R+ R,h )(λ ) R,h, (7) where λ denoes he nvesmen-equy rao. For a un of equy capal nvesed, d,e he enrepreneur can borrow (λ ) uns of loan n perod. In perod +, receves he ne reurn from he leveraged nvesmen, (R+ R,h )(λ ), n addon o he margnal produc of s equy capal, R+. Iff R+ > R,h, he enrepreneur borrows o he lm defned by (6) o fully explore he leverage effec; afer repayng he deb n perod +, ges ( θ )R + and he equy rae s R,e = ( θ )R + d,e = ( θ )R + d,h = ( θ )R + θ R + R,h > R,h. If R,h = R+, he enrepreneur does no borrow o he lm; afer repayng he deb n perod +, ges R+d,e and he equy rae s R,e = R+. The non-negave leverage effec ensures ha he equy rae s no less han he loan rae and nequaly (7) hus marks he enrepreneur s parcpaon consran. In he follow, he socal rae of reurn refers o he MPK, whle he prvae raes of reurn refer o he loan rae and he equy rae. The markes for cred capal, equy capal, and he fnal goods clear smulaneously, S,h = ( η)s,h K + = η = D,h = D,h = ηd,h, and S,e = ηs,e = D,e = ηd,e, (8) + D,e, and C + K+ = Y (9) 7

9 where S,h and D,h denoe he aggregae cred supply and demand, S,e and D,e denoe he aggregae equy supply and demand, and C η(c,e y, + c,e o,) + ( η)(c,h y, + c,h o,) denoes aggregae consumpon n counry and perod. Defnon. Gven he level of fnancal developmen θ, a marke equlbrum n counry {, 2,..., N} under IFA s a se of allocaons of households, {c,h, c,h y,, s,h o,}, enrepreneurs, {, c,e y,, s,e, c,e o,}, and aggregae varables, {Y, K, ω, R, R,h, R,e }, sasfyng equaons ()-(2), (4)-(9), 2. The Model Soluon For noaonal convenence, we defne some auxlary parameers, ρ α, m ( β)ɛ, α (+ɛ)ρ R (+ɛ)ρ ( + m), θ η, A θ θ, β η B + θ θ. η Gven he Cobb-Douglas preference, he ncome effec and he subsuon effec of neres raes cancel ou so ha an ndvdual saves a fracon ( β) of s lfeme wealh when young. ɛ > makes s lfeme wealh neres-elasc hrough he human wealh effec. Thus, ff ɛ > and β <, s consumpon when young s neres-elasc and so s s savng. m capures he jon mpacs of he human wealh effec (ɛ > ) and mpaence (β < ) on he neres elascy of savng. See Lemma for he relaonshp beween m and he neres elascy of savng. θ s a crcal value. As shown below, for θ θ, he borrowng consran s slack so ha he socal and he prvae raes of reurn are equal o R n he seady sae. For θ [, θ), he borrowng consran s bndng, A and B measure he wedge beween he prvae and he socal raes of reurn wh < A < < B and A > > B. θ θ The aggregae rewards o capal n perod + s dsrbued o ndvduals as he reurns o her savngs, ( η)s,h R,h + ηs,e R,e = R+K +, where R+K + = ρlω+, we ge accordng o equaons (2). Use equaon (5) o subsue away s,j ( η)r,h whch s called as he reward splng rule. + ηr,e = ω + ω R, () In he followng, we frs show he model soluon n he case of he bndng borrowng consrans and hen dscuss he condon under whch s rue. 2 R,h = ω + ω Le X denoe he seady-sae value of varable X under IFA. The model soluon s, [ K+ = βω m( ] A )(B ), () m + (m + A )(m + B ) ( ) R,e = ω + R + B, (2) ω m + R ( ) A, (3) m + 2 See he proof of Proposon n he appendx for echncal dervaons of he model soluon. 8

10 [ R+ = ω + R + m( ] A )(B ), (4) ω (m + )(m + A B ) ψ R,h ω + = ln Λ θ = R + = ψif A = ( A )B, (5) m + B ) α, where Λ = Λ = (m + A B )(m + ) (m + A )(m + B ), (6) ( Λ R ω m(b ) (m + A B )(m + A ) A θ m( A ) (m + A B )(m + B ) B θ. (7) ψ denoes he relave loan rae and Λ denoes he aggregae effcency ndcaor. Boh are me-nvaran. As oupu s proporonal o wage, Y = (+ɛ)ω, he model dynamcs ( α) are characerzed by he dynamc equaon of wages (6). Gven α (, ), here exss a ( unque and sable seady sae wh he wage a ωif A = Λ R Now, we show nuvely ha θ s he crcal value for he borrowng consrans o be bndng. If θ = θ, A = B = and hus, R,h = R+ = ω + R, so ha he borrowng ω consrans are weakly bndng. In hs case, he aggregae cred demand s srong enough o push he loan rae equal o he socal rae of reurn, ψ = ; accordng o equaon (7), he zero spread mples ha R,e = R+ = R,h = ω + R = R α ρ α( α) ( K L ) α( α). Inuvely, n he counry wh a lower capal-labor rao K, he growh rae ω + s L ω hgher and so are he neres raes. We call hs he neoclasscal effec, as arses from he concavy of he neoclasscal producon funcon wh respec o he capal-labor rao. For θ > θ, enrepreneurs do no have an ncenve o borrow o he lm and he equlbrum allocaon s dencal as n he case of θ = θ. In boh cases, aggregae savngs βω s ransformed by enrepreneurs no capal so ha he aggregae effcency +m ndcaor s Λ =. In he seady sae, he wage s ω = R ρ, and he neres raes are R,j = R = R. Iff θ < θ, holds ha A < < B. Accordng o equaons (3) and (4), R,h < ω + R < R ω + so ha he borrowng consrans are srcly bndng. In subsecon 2.2 and 2.3, we focus on he case of θ [, θ) and analyze he dsorons of fnancal frcons n he presence of nelasc savng (m = ) and elasc savng (m > ), respecvely. The ndvduals savng raes are, ω ) ρ. s,h ω s,e ω = β = β [ [ ( β)ɛ ω+ β ω ( β)ɛ ω+ β ω R,h R,e ] = βa, and ff m >, m + A ] = βb, and ff m >, m + B s,h ω θ > ; (8) s,e ω θ <. (9) Defne he aggregae savng rae as he rao of aggregae savng S ( η)s,h over aggregae labor ncome of young ndvduals n counry, + ηs,e 9

11 S ω = β ( β)ɛ ω + ω ( η R,h + η ) R,e = β(m + A B S ) (m + A )(m + B ) ; ff m >, ω >. θ (2) 2.2 The Equlbrum wh Inelasc Savngs m = f ndvduals are fully paen (β = ) or f here s no human wealh effec (ɛ = ). Accordng o equaons (8)-(2), he ndvdual s and aggregae savng raes are consan a s,j = S ω = β. The bndng borrowng consrans depress aggregae cred demand and ω he loan rae falls below he socal rae of reurn o clear he cred marke. Accordng o equaon (7), he posve spread makes he equy rae hgher han he socal rae of reurn. Thus, fnancal frcons creae a wedge beween he prvae and he socal raes of reurn, ψ = R,h = A < < R,e R+ = B. The smaller θ, he larger he neres rae R+ wedge. We call hs he fnancal-underdevelopmen effec and measure by ψ. Beng neres nelasc, aggregae savng s no affeced by fnancal frcons. Thus, aggregae nvesmen s effcen K + = βω m+ and so s aggregae oupu, Λ =. 2.3 The Equlbrum wh Elasc Savngs m > f ndvduals are mpaen (β < ) or f here s he human wealh effec (ɛ > ). Accordng o equaons (8)-(2), he savng raes are neres elasc. Besdes dsorng he neres raes hrough he fnancal-underdevelopmen effec, fnancal frcons also dsor aggregae savng, nvesmen, and oupu. Accordng o equaons (8)-(9), he dsored neres raes depress household savng and rase enrepreneural savng hrough he ndvduals human wealh channel. Accordng o equaon (2), a lower θ leads o a lower aggregae savng rae, mplyng ha neffcenly low household savng mus domnae neffcenly hgh enrepreneural savng. Wha s he economc nuon behnd ha? Le R,j ω ω + R,j denoe he neres rae normalzed by he he gross growh rae of wage. Defne an auxlary funcon, M(x, x 2, p) ( η)x p + ηx p 2. The aggregae savng rae s rewren as S = β ( β)ɛm(r,h, R,e, ), where ɛm(r,h, R,e, ) capures ω he aggregae human wealh effec. Whou loss of generaly, we assume ha counry N s more fnancally developed, < θ S < θ N < θ. As dscussed above, he loan rae s hgher bu he equy rae s lower n counry N han n counry S. Accordng o he reward splng rule (), he normalzed neres raes are lnearly relaed, ( η)r,h + ηr,e = R. Pons S and N n fgure represen he neres raes n he wo counres, whch are on he same reward splng lne (he downward-slopng sold lne). M(R,h, R,e, ) s shown by he convex soquan. Accordng o he Jensen s nequaly heorem, he lower he soquan, he larger

12 R,e S N O R,h Fgure : Graphc Illusraon of he Aggregae Human Wealh Effec he aggregae human wealh effec and he lower he aggregae savng rae. Thus, fnancal frcons reduce he aggregae savng rae hrough he neres raes channel. We call hs he elasc savng effec. Le υ,j ln S ln R,h ln s,j ln R,j denoe he neres elascy of savng for ndvdual j and Υ denoe he elascy of aggregae savng wh respec o he loan rae under IFA. Lemma. υ,h = m A and υ,e = m B are lnear n m. Iff θ < θ, Υ > and rses n m. In a counry wh a hgher ɛ or a lower β, m s larger and, accordng o equaon (5), ndvduals save less when young. Changes n he neres raes end o have larger mpacs on aggregae savngs. Thus, m s a key parameer affecng he neres elascy of savng and crucal for he aggregae mplcaons of capal mobly n secon 3. Snce aggregae nvesmen s fnanced by domesc savng under IFA, fnancal frcons dsor aggregae nvesmen and oupu. Accordng o equaon (7), Λ > and Λ θ reaches s maxmum of one, when he borrowng consrans are weakly bndng a θ = θ. Accordng o equaon (5), he same paern exss for he relave loan rae, ψ. Thus, we can use ψif A o measure he dsorons on he neres raes and oupu.3 Proposon. For θ [, θ), he borrowng consran s bndng ( ) and here s a unque and sable seady sae n counry wh he wage a ωif A = Λ ρ. R There s a wedge beween he prvae and socal raes of reurn, R,h < R+ < R,e. In he seady sae, he loan rae rses and he equy rae falls n θ. If β = or ɛ =, aggregae oupu s ndependen of θ. If β < and ɛ >, aggregae oupu s below he effcen level and rses n θ. 3 von Hagen and Zhang (29, 2) develop a model wh heerogenous projecs and show ha fnancal frcons dsor aggregae nvesmen among projecs wh dfferen producvy and hus, aggregae oupu s neffcenly low. Alhough oupu s dsored hrough dfferen channels n he curren paper and n von Hagen and Zhang (29, 2), he mplcaons of capal mobly are dencal.

13 3 Inernaonal Capal Mobly Under full capal mobly, ndvduals are allowed o lend and make drec nvesmens globally. Whou loss of generaly, we assume ha he borrowng consrans are bndng n boh counres under IFA and counry N s more fnancally developed, θ S < θ N θ. We frs solve he equlbrum allocaon analycally and show ha he seadysae paerns of nernaonal capal flows under full capal mobly n our model are conssen wh he hree emprcal facs menoned n he nroducon. Le Φ and Ω denoe he aggregae ouflows of fnancal capal and FDI from counry n perod, respecvely, wh negave values ndcang capal nflows. Fnancal capal ouflows reduce he aggregae cred capal used for domesc nvesmen, D,h = ( Φ, whle FDI ouflows reduce he aggregae equy capal used for domesc η)s,h nvesmen, D,e = ηs,e Ω. Therefore, FDI flows rase he aggregae cred demand n he hos counry and reduce ha n he paren counry. 4 Wh hese changes, he analyss n secon 2 carres hrough for he cases of capal mobly, due o he (log-)lneary of preferences, projecs, and borrowng consrans. Fnancal capal flows equalze loan raes and FDI flows equalze equy raes n he wo counres. Cred and equy markes clear n each counry as well as globally. To summarze, Φ S + Φ N = Ω S + Ω N =, R S,h K + = ( η)s,h + ηs,e = R N,h = R,h, R S,e = R N,e = R,e, (Φ + Ω ) = λ (ηs,e Ω ). The remanng condons for marke equlbrum n each counry are same as under IFA. A he world level, aggregae revenue of capal n perod + s dsrbued o households and enrepreneurs as he reurns o her respecve savngs, ( η)r,h s,h + + ηr,e s,e + = R+K + = ρ( + ɛ) {N,S} {N,S} Usng equaon (5) o subsue away s,j, we ge {N,S} {N,S} ω +. ( η)r,h + ηr,e = ωw + ω w R, where ω w ωs + ω N 2. (2) We call hs he reward splng rule a he world level. Lemma 2. Under full capal mobly, here s a unque and sable seady sae. 4 In he case of deb defaul, he projec lqudaon value depends on he effcency of he legal nsuon, he law enforcemen, and he asse marke n he hos counry. Thus, we assume ha enrepreneurs makng FDI borrow only from he hos counry and are subjec o he borrowng consrans here. Alernavely, we can assume ha enrepreneurs may borrow only n her paren counry no maer where hey nves, snce he fnancal nsuons n her paren counry have beer nformaon on he cred record, socal nework, and busness acves of he enrepreneurs. The realsc case should be a hybrd of hese wo. Our resuls hold under he wo alernave assumpons. 2

14 Le X F CM denoe he seady-sae value of varable X under full capal mobly. Defne a me-nvaran auxlary varable ZF CM (ψf CM ψ )m+b m+ soluon o he equlbrum allocaon s, (ψ F CM ψ )m+b m+ +B η ( η) R,e. The R,e = ωw + (R,e ω w R,h = ωw + ω w Z F CM), (22) ), (23) ( R,h + η η Z F CM ψ = ψ F CM = ( θ )R,h F CM Φ = ( η)βω Ω = ηβω Ω + Φ = βω { [ ( θ ω+ = R,e [ ω + R,e F CM ω + ω ω ω + ω + θ R,h R,e R,e [ + θ, (24) ] R,h R,h ] η R,e R,e, (25), (26) + ( η) R,h R,h ]}, (27) ) ρ. (28) Under full capal mobly, he seady-sae neres raes and capal flows are, R,e F CM = R,e Z F CM, Φ F CM = ( η)βω F CM Ω F CM = ηβω F CM ( Φ F CM + Ω F CM = ηβω F CMZ F CM R,h F CM = R,h ( ) R,h R,e R,e F CM R,h F CM ) (R,e F CM R,h + η η Z F CM, (29) = ηβω F CM = ηβω F CM F CM ) R,e F CM R,h F CM ZF CM, (3) R,h F CM ZF CM R,e, (3) F CM. (32) Proposon 2. In he seady sae under full capal mobly, he world neres raes are R,h F CM (RS,h, RN,h ) and R,e F CM (RN,h, RS,h ), mplyng he paral convergence n he relave loan rae, ψif S A < ψs F CM < ψn F CM < ψn. Aggregae oupu s hgher n counry N han n counry S. The gross and ne capal flows are Φ S F CM > > ΦN F CM, Ω S F CM < < ΩN F CM, and ΦS F CM + ΩS F CM > > ΦN F CM + ΩN F CM. The gross nernaonal nvesmen reurn sums up o zero n each counry, Φ F CM R,h F CM + Ω F CM R,e F CM =. Wh a hgher level of fnancal developmen, counry N mpors fnancal capal, expors FDI, and receves ne capal nflows. Snce he rae of reurn on s foregn asse (FDI ouflow) exceeds he neres rae pad for s foregn lably (fnancal capal nflow), R,e F CM > R,h F CM, counry N receves he posve ne nernaonal nvesmen 3

15 ncomes, Φ N F CM (R,h F CM ) + ΩN F CM (R,e F CM ) = ΦN F CM R,h F CM + ΩN F CM R,e F CM (ΦN F CM + Ω N F CM ) = (ΦN F CM + ΩN F CM ) >, despe s negave nernaonal nvesmen posons, Φ N F CM + ΩN F CM <. Thus, our model predcons are conssen wh he hree emprcal evdences menoned n he nroducon. In he followng, we use hs analycal framework o address he aggregae mplcaons of capal mobly. Subsecons 3. and 3.2 focus on he oupu and welfare mplcaons, f boh counres are nally n he seady sae under IFA before capal mobly s allowed from perod = on. Subsecon 3.3 analyzes how he paerns of capal flows may change or even reverse along s convergence pah f counry S s nally below s seady sae under IFA. Subsecon 3.4 shows ha Masuyama s symmery-breakng propery depends crcally on he fac ha aggregae nvesmen akes place n he exensve margn. 3. The Oupu Implcaons of Capal Mobly Le us sar wh he case of nelasc savng (m = ), whch resuls from eher ɛ = or β =. Snce he oupu mplcaons of capal mobly are qualavely dencal n he case of eher ɛ = or β =, we focus on he case of ɛ = as follows. Indvduals save a fracon β of he labor ncome when young and fnancal frcons do no affec oupu under IFA, YIF A = α R ρ. Upon full capal mobly n perod =, aggregae savng s same as under IFA, S = βω = βωif A, and ne capal flows drecly reallocae he funds for nvesmen from counry S o counry N, whch has wo consequences on oupu. Frs, oupu n counry S (N) s lower (hgher) n perod = han before; second, gven he concave aggregae producon wh respec o he capal-labor rao a he counry level, world oupu s lower han under IFA, because ne capal flows are n equlbrum from counry S where he MPK s hgher o counry N where he MPK s lower. Corollary. In he case of nelasc savng, from perod = on, world oupu s lower han s seady-sae value under IFA. Under IFA, fnancal frcons do no producon and seady-sae oupu s same n he wo counres, even hough he wo counres dffer n he level of fnancal developmen. Capal mobly breaks he nal symmery n he wo counres n he sense ha capal, n he ne erm, flows uphll from he poor o he rch counry n he new seady sae, leadng o world oupu losses, whch s also presen n Masuyama (24). Ths s a ypcal resul of he heory of second bes. In he presence of domesc fnancal frcons, capal accoun lberalzaon causes capal o flow o he counry wh he hgher neres raes raher han o he counry wh he hgher MPK. The oupu responses a he counry and he world level depends on he sze of ne capal flows, Ω + Φ. In he case of elasc savng (m > ), besdes he drec mpac on oupu hrough cross-counry capal reallocaon, full capal mobly also has an ndrec mpac on oupu hrough aggregae savng. Take counry S as an example. Fnancal capal ouflows 4

16 reduce he domesc cred supply and FDI nflows rase he domesc cred demand. Boh forces push up he loan rae and nduces domesc households o save more. Ne capal ouflows reduces he domesc cred supply and he rsng compeon from foregn enrepreneurs reduces he MPK. Boh forces push down he equy rae and nduce domesc enrepreneurs o save less. The oppose apples for counry N. Thus, changes n he ndvdual s savng depends on he sze of gross capal flows, Ω + Φ. aggregae savng rae n counry s, S ω = ( η)s,h ω + ηs,h = β ( β)ɛ ω + ω ( η R,h The + η ) R,e. (33) As shown n subsecon 2.3, a hgher level of fnancal developmen gves rse o a hgher aggregae savng rae under IFA, SN > SS ωif N. Under full capal mobly, he crosscounry equalzaon of he loan rae as well as he equy rae leads o he A ωif S A cross-counry equalzaon of he aggregae savng rae n he seady sae,.e., he aggregae savng rae rses (declnes) n counry S (N), SS < SS ωif S F CM = SN A ωf S F CM < SN CM ωf N. Thus, by rasng CM ωif N A (reducng) aggregae savng and hence, he oal funds avalable for domesc nvesmen, full capal mobly ndrecly affec oupu n counry S (N). Lemma 3 summarzes he overall effec on seady-sae oupu n he case of elasc savng m >. Lemma 3. If η (,.5), defne κ 4m 2 ( η)η < and here are hree scenaros: 2 2. f m (, ), YF S CM > Y IF S A holds for θs (, κ), and YF N CM > Y IF N A θ N (κ, θ); holds for 2. f m (, 2 η( η) ), Y S F CM > Y S holds for θs (, κ) ( κ, θ), and Y N F CM > Y N holds for θn (κ, κ); 3. f m > 2 η( η), Y S F CM > Y S If η (.5, ), here are wo scenaros: always holds.. f m (, ), YF S CM > Y IF S A holds for θs (, κ), and YF N CM > Y IF N A θ N (κ, θ); 2. f m >, Y S F CM > Y S always holds. holds for Pu planly, a larger m mples ha aggregae savng s more neres-elasc. The rse n domesc savng n counry S s more lkely o exceed ne capal ouflows so ha domesc nvesmen s hgher han under IFA and so s oupu. Full capal mobly affecs world oupu also hrough he drec and ndrec channels. Frs, uphll ne capal flows drecly lead o cross-counry capal reallocaon, whch wdens he cross-counry oupu gap. The drec effec on world oupu s negave, dependng on he sze of ne capal flows. Second, boh fnancal capal and FDI flows 5

17 ndrecly affec aggregae savng a he counry level. Gven θ S < θ N, he rse n aggregae savng of counry S domnaes he declne n counry N so ha world savng rses and so does world oupu. The ndrec effec on world oupu s posve, dependng on he sze of gross capal flows. Two-way capal flows mply ha gross flows sgnfcanly exceed ne flows. Thus, s possble ha full capal mobly rases world oupu, despe uphll ne capal flows. Snce he ndrec effec essenally resuls from he elasc savng, he sze of he ndrec effec naurally depends on he neres elascy of aggregae savng. Accordng o Lemma, he hgher m, he more elasc he aggregae savng, he larger he ndrec effec, he more lkely full capal mobly rase world oupu. Oupu Levels (m=.53) Oupu Levels (m=.8).6 Y N FCM 2.5 Y N FCM.4.2 Y N IFA 2 Y N IFA Y S FCM.5 Y S IFA Y S FCM Y S IFA ^ S S N _ =.5 ^ S _ S N = 25 % Changes n World Oupu (m=.53) 2 % Changes n World Oupu (m=.8) Y W S _ N =.5 ~ ~ S Y W S S 2 _ N = Fgure 2: Comparng Seady-Sae Oupu under IFA and under Full Capal Mobly For llusraon purpose, we se up a numercal example and show ha he world oupu mplcaons of capal mobly depend on m as well as he cross-counry dfference n fnancal developmen. We se he populaon share of enrepreneurs a η = %, he share of labor ncome n aggregae oupu, α = 64%, and ndvduals pu more weghs on consumpon when young, β =.6 > β =.4. We consder wo alernave cases wh ɛ {,.2} and correspondngly, m {.53,.8}. The upper-lef and upper-rgh panels of fgure 2 show he seady-sae oupu levels n he wo counres under full capal mobly versus under IFA, wh θ S [, θ) on he horzonal axes, gven θ N = θ. Gven he parameer values, full capal mobly srcly rases seady-sae oupu n counry N, whle rases seady-sae oupu n 6

18 counry S f θ S s below a hreshold value ˆθ S, confrmng our resuls n Lemma 3. The boom-lef and boom-rgh panels show he percenage changes ) of seady-sae world oupu under full capal mobly versus under IFA,. If m s suffcenly ( Y w F CM Y w hgh, e.g., m =.53 n our example, he oupu gans n counry N always exceed he oupu losses (f any) n counry S so ha world oupu s hgher han under IFA; f m s small, e.g., m =.8 n our example, here exss wo hreshold values θ S and θ S 2 such ha, for θ S ( θ S, θ S 2 ), full capal mobly reduces seady-sae world oupu, whle, for θ S (, θ S ) ( θ S 2, θ), rases seady-sae world oupu..53 A ~ S FCF B m ~ S FCM.8 E ~ S FDI O D S C N _ = Fgure 3: Threshold Values under Three Scenaros of Capal Mobly Gven m (,.53) and θ N = θ, we compue θ S for world oupu under full capal mobly as well as under he wo alernave scenaros,.e., free mobly of fnancal capal under whch ndvduals are allowed o lend abroad bu enrepreneurs are no allowed o make drec nvesmens abroad, and free mobly of FDI under whch enrepreneurs are allowed o make drec nvesmens abroad bu ndvduals are no allowed o lend abroad. 5 Fgure 3 shows hese hreshold values n he parameer space (θ S, m), where he sold curve denoed by θ F S CM, he dash curve denoed by θ F S CF, and he dash-do lne denoed by θ F S DI refer o he hreshold values under he scenaros of full capal mobly, free mobly of fnancal capal, and free mobly of FDI, respecvely. In each scenaro, capal mobly rases he seady-sae world oupu f he parameers are n he regon above he respecve curve. As menoned above, he ndrec effec, whch conrbues posvely o world oupu, depends crucally on elasc savng. Gven θ N and θ S, a larger ɛ leads o a larger neres elascy of savngs, represened by a larger m. In hs case, 5 See he echncal analyss of he wo scenaros n appendx A and B, respecvely. 7

19 he oupu dsoron of fnancal frcons under IFA s more severe. By amelorang he oupu dsoron, capal mobly generaes a sronger ndrec effec hrough elasc savng and world oupu s more lkely o be hgher han under IFA. Le us frs compare he scenaros of full capal mobly and free mobly of fnancal capal. Under free mobly of fnancal capal, fnancal capal flows from counry S o counry N. Uphll capal flows drecly wden cross-counry oupu gap, leadng o world oupu losses; by equalzng he loan rae across he border, fnancal capal flows ndrecly nduce households n counry S (N) o save more (less) and aggregae savng a he world level s hgher, leadng o world oupu gans. The cross-counry dfference n θ has o be suffcenly large so ha he ndrec effec can be srong enough o overrde he drec effec. In our example, he parameers need o be n regon A. Under full capal mobly, wo-way capal flows mply ha gross flows are sgnfcanly larger han ne flows. Thus, even f he cross-counry dfference n θ s small, as n regon B and C, he ndrec effec may sll domnae he drec effec. Thus, full capal mobly domnaes free mobly of fnancal capal n generang world oupu gans. Turnng o free mobly of FDI alone, for parameers n regon C, full capal mobly rases world oupu, whle free mobly of FDI reduces world oupu. However, for parameers n regon E, he oppose apples. Thus, full capal mobly does no necessarly domnae free mobly of FDI n generang world oupu gans. Consder parameers n regon C. Snce he cross-counry oupu gap under IFA s small n hs case, free mobly of FDI reverses he oupu gap hrough cross-counry capal reallocaon and he drec effec on world oupu s negave. The ndrec effec, whch depends on gross capal flows, s small here. Under full capal mobly, gross flows are sgnfcanly larger han ne flows so ha he ndrec effec easly domnaes he drec effec and world oupu s hgher. Consder parameers n regon E where wo counres dffer modesly n θ. Gven he relavely large nal cross-counry oupu gap under IFA, free mobly of FDI drecly narrows he cross-counry oupu gap hrough cross-counry capal reallocaon, mplyng a posve drec effec on world oupu. Thus, free mobly of FDI srcly rases world oupu. In conras, under full capal mobly, uphll ne capal flows mply ha he drec effec s always negave and full capal mobly reduces world oupu. Here, elasc savng s a crcal channel hrough whch full capal mobly may rase oupu n he less fnancally developed counry as well as globally. Shung down eher fnancal capal or FDI flows may undermne such world oupu gans. 3.2 The Welfare Implcaons of Full Capal Mobly As shown before, β and ɛ are wo key parameers affecng he neres elascy of savng and he oupu mplcaons of capal mobly. We address here he welfare mplcaons of full capal mobly n he cases of nelasc and elasc savng, respecvely. Case I: ɛ = and β. 8

20 Wh no labor endowmen when old (ɛ = ), an ndvdual s lfeme wealh s smply s labor ncome when young, W,j = ω. If he ndvdual s fully paen (β = ), does no consume when young bu saves s enre labor ncome. In hs case, he lfeme welfare only depends on s consumpon when old, funded fully by s fnancal ncome, u,j = c,j o,+ = ωr,j. If s mpaen (β < ), consumes a fracon ( β) of s labor ncome when young and save he res. In hs case, s welfare depends on s consumpon n boh perods of lfe and he fnancal ncome has smaller welfare mpacs. In hs sense, mpaence reduces he welfare mpacs of neres raes, u,j = ω(r,j ) β. As a suffcen condon for m =, ɛ = leads o neres-nelasc savng so ha capal mobly reduces (rases) oupu and wage n counry S (N) and world oupu s lower han under IFA. β = or β < does no change hs resul qualavely. For generaon =, gven he predeermned labor ncome, ω = ωif A, capal mobly makes households beer (worse) off and enrepreneurs worse (beer) off n counry S (N) hrough he neres rae channel. For generaon, he declnes (rses) n labor ncome and he equy rae make enrepreneurs n counry S (N) worse (beer) off han under IFA; as labor ncome and he loan rae move n he oppose drecon, he welfare mplcaons o households are ambguous. Inuvely, paence (a larger β) enhances he welfare mpacs of neres raes and he neres rae effec s more lkely o domnae he labor ncome effec. Usng equaon (28) o subsung away ωf CM, we rewre he long-run household welfare as [ u,h F CM = ω F CM(R,h F CM )β = ( θ ) R,h F CM R,e F CM + θ ] ρ (R,h F CM )β ρ. (34) The loan rae converges across he border and so does he equy rae,.e., R S,h R,h F CM < RN,h, and RS,h R S,e < R,h F CM R,e F CM < RN,h R N,e <. Thus, β ρ s a suffcen condon for households n counry S (N) o be beer (worse) off n he long run han under IFA. Fgure 4 shows he percenage dfferences n welfare under full capal mobly versus under IFA n he case of( ɛ = and ) β =. The dashed lnes show he welfare u,j changes for generaon =,, and he sold lnes for generaon, u ),j. The upper (boom) panels show he relevan varables n counry S ( u,j F CM u,j (N) and he horzonal axes denoe θ S (, θ). The parameer values are same as n he numercal example n subsecon 3., excep β = and ɛ =. Changes n he welfare of generaon = ( ) reflec he shor-run (long-run) welfare mplcaons. Fgure 5 shows he welfare changes n he case of ɛ = and β =.4. Gven α =.36, f β =, β > ρ so ha households n counry S (N) are srcly beer (worse) off n he long run, as shown n fgure 4; f β =.4, β < ρ so ha households n counry S (N) may be worse (beer) off n he long run, as shown n fgure 5. The oher measures of ndvduals welfare have he qualavely same responses n he wo cases. The socal welfare of generaon s defned as he weghed sum of he welfare of 9

21 Household (S) Long Run Shor Run 2 4 Enrepreneurs (S) 2 Socal Welfare (S) S N _ = 6 8 S N _ = 4 S N _ = Household (N) Enrepreneurs (N) Socal Welfare (N) S N _ = 3 2 S _ N = S N _ = Fgure 4: Percenage Changes n he Shor-Run and Long-Run Welfare: ɛ = and β = 3 2 Household (S) Long Run Shor Run 2 4 Enrepreneurs (S) 5 Socal Welfare (S) S _ N = 6 S N _ = S _ N = Household (N) Enrepreneurs (N) Socal Welfare (N) 5 5 S N _ = 5 S _ N = 5 5 S _ N = Fgure 5: Percenage Changes n he Shor-Run and Long-Run Welfare: ɛ = and β =.4 ndvduals born n perod, U ( η)u,h +ηu,e = ωm(r,h, R,e, β), where M(x, x 2, p) s he auxlary funcon defned n subsecon 2.3. Full capal mobly affecs socal welfare hrough he labor ncome, ω, and a compose of neres raes n he form of he weghed average wh he power β, M(R,h, R,e, β). Upon capal mobly, he responses n labor ncome are unambguous, whle he responses n he compose of neres raes depend on β, whch s analyzed as follows. Fgure 6 shows he compose of neres raes n he space of (R,h, R,e ). Pon S (N) denoes he neres rae combnaon n counry S (N) n he seady sae under IFA, pon A denoes ha n perod =, and pon L denoes ha n perod,.e., n he seady sae under full capal mobly. 6 Accordng o equaons () and (2), he 6 Under full capal mobly, he loan rae converges across he border and so does he equy rae. 2

22 LR and SR Allocaon ( =) Long Run Allocaon ( <) Shor Run Allocaon ( <) R,e R,e R,e S S S A L N L N A N O R,h O R,h O R,h Fgure 6: Graphc Illusraon of M(R,h, R,e, β) under Full Capal Mobly versus IFA reward splng rules n he seady sae under IFA and under full capal mobly are ( η)r,h + ηr,e = R = ( η)r,h F CM + ηr,e F CM. Thus, pon S, N, and L are on he same soquan (he hn sold sragh lne). As capal mobly reduces world oupu, he world-average wage n perod = falls. Gven he reward-splng rule (2) n perod =, ( η)r,h + ηr,e = ωw R < R, pon A s on an soquan (he hck sold sragh ω w lne) below he prevous one. M(R,h, R,e, β) can be shown as he soquan n he space of (R,h, R,e ). Le us sar wh he case of β = where he soquan of M(R,h, R,e, ) s a downward-slopng sragh lne and concdes wh he one represenng he reward splng rule. See he lef panel of fgure 6. In perod =, M(R,h, R,e, ) = ωw R < R, whle n he seady sae under ω w IFA and under full capal mobly, M(R,h, R,e, ) = M(R,h F CM, R,e F CM, ) = R. Thus, he compose of neres raes declnes n perod = and converges back o s prevous level n he long run, whch s purely drven by he world-average growh effec. Le us hen consder he case of β < where he soquan of M(R,h, R,e, β) s convex and downward-slopng. The dashed curves and he sold curve n he mddle panel of fgure 6 are he soquans of M(R,h, R,e, β) n he seady sae under IFA and under full capal mobly. Due o he Jensen s nequaly heorem, M(R S,h, RS,e, β) < M(R,h F CM, R,e F CM, β) < M(RN,h, RN,e, β). The dashed curves and he sold curve n he rgh panel of fgure 6 show he soquans of M(R,h, R,e, β) before and n perod =, respecvely. The world-average growh effec reduces M(R,h, R,e, β), whle he Jensen s nequaly effec reduces M(R S,h, RS,e, β). If β s suffcenly small, he Jensen s nequaly effec domnaes so ha M(R,h, R,e, β) > M(R S,h, RS,e, β); f β s suffcenly close o one, he world-average growh effec domnaes so ha M(R,h, R,e, β) < M(R S,h, RS,e, β). Neverheless, M(R,h, R,e, β) < M(R N,h, RN,e, β) always holds. Now, we are ready o analyze he responses of socal welfare. For generaon =, gven he predeermned labor ncome, ω = ωif A, socal welfare s drven purely by he Thus, he neres raes n perod = and n perod mus be n he regon o he boom-rgh of pon S and o he upper-lef of pon N. 2

23 compose of neres raes M(R,h, R,e, β). Thus, he socal welfare n counry N declnes whle he responses of socal welfare n counry S depends on β. For generaon, snce he changes n he labor ncome and he compose of neres raes are oppose, he socal welfare mplcaons are ambguous, dependng on β. Le us compare he socal welfare responses n he cases of β =.4 versus β = (he hrd columns of fgures 5 and 4). For a declne n β from o.4, he shor-run socal welfare responses n counry S changes from negave o posve and so does he long-run socal welfare responses for θ S close o zero. Thus, (m)paence s an mporan facor affecng he welfare mplcaons of capal mobly. Case II: ɛ > and β <. An ndvdual s lfeme welfare s u,j = W,j (R,j ) β = ω [ + ɛ ω + ω ] R,j (R,j ) β. (35) Compared wh case I, allowng ɛ > nroduces he human wealh componen, ɛ ω +. ω R,j An ncrease n he relevan neres rae affecs he ndvdual s welfare posvely hrough he fnancal ncome channel as menoned n case I and negavely hrough he human wealh channel. A larger ɛ or a larger β amplfes he welfare mpacs of neres rae. Furhermore, a rse n he wage growh rae posvely affec he ndvdual s welfare hrough he human wealh channel and a larger ɛ magnfes s welfare mpacs. As shown n subsecon 3., allowng eher a posve human wealh (ɛ > ) or mpaence (β < ) does no change qualavely he oupu mplcaons of capal mobly as savng s neres-nelasc; combnng hem makes savngs neres-elasc so ha full capal mobly may generae oupu gans n counry S and globally. Here, we focus on he welfare mplcaons n he case of oupu gan n counry S,.e., θ S s small. Take enrepreneurs n counry S as an example. Upon full capal mobly n perod =, and he declne n he equy rae, R S,e < R S,e, ogeher wh he posve wage growh, >, rase he human wealh, parally offseng s negave welfare effec hrough he ω S ω S fnancal ncome channel. Compared wh case I, he welfare declne of enrepreneurs s much smaller. In perod, he wage growh vanshes ωs + equy rae rases he human wealh, ɛ R,j F CM ω S and he declne n he, parally offseng s negave welfare effec hrough he fnancal ncome channel, (R,j F CM )β. Furhermore, n he presence of long-run oupu gans, ωf S CM > ωs has a posve welfare effec. For a suffcenly small β, he fnancal ncome effec can be domnaed by he human wealh effec so ha enrepreneurs of generaon can be beer off han under IFA, n conras o case I. Le us consder socal welfare of generaon. Rewre he socal welfare as [ ] U = ( η)u,h + ηu,e = ω M(R,h, R,e, β) + ɛ ω + M(R,h, R,e, β ). (36) ω 22