Synchronization of Innovation Cycles

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1 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Syhroizaio of Iovaio Cyles By Kimiori Masuyama, Norhweser Uiversiy, USA Based o wo proes wih Irya Sushko, Isiue of Mahemais, Naioal Aademy of Siee of Ukraie Laura Gardii, Uiversiy of Urbio, Ialy NYU Applied Theory Semiar November 6, 05 Page of 35

2 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Iroduio Page of 35

3 Kimiori Masuyama, Syhroizaio of Iovaio Cyles May models of oliear dyamis geeraig edogeous fluuaios (i iovaio, bu hey are all (effeively oe-oury, oe-seor models Need for muli-seor exesios (wih edogeous fluuaios i eah seor To evaluae he aggregae effes, we eed o kow how fluuaios a differe seors affe eah oher. How do seors o-move? Are hey syhroized o amplify fluuaios? Or asyhroized o moderae? No previous work o hese issues, eiher heoreially or empirially. We eed a oepual framework o guide our heoreial ad empirial researh. Need for muli-oury exesios (wih edogeous fluuaios i eah oury Theoreial Moivaio: Mos maroeoomiss sudy he effes of globalizaio i a model where produiviy movemes are drive by some exogeous proesses. Bu, globalizaio a hage Produiviy growh rae, as already show by edogeous growh models. Syhroiiy of produiviy fluuaios, i a model of edogeous yles Empirial Moivaio: More bilaeral rade leads o more syhroized busiess yles amog developed ouries, bu o bewee developed & developig ouries. Hard o explai his rade-omoveme puzzle i models wih exogeous shoks Easier o explai i models wih edogeous soures of fluuaios Page 3 of 35

4 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Our buildig blok: Deekere-Judd (99 oe-seor, losed eoomy model of edogeous iovaio fluuaios, haraerized by a skew-e map Mahemaially, our exesios geerae oupled skew-e maps. Coepually, his is a sudy of weakly oupled osillaors. Syhroizaio of Weakly Coupled Osillaors Naural Siee: A Maor Topi. Thousads of examples: Jus o ame a few, Chrisiaa Huyges pedulum loks The Moo s roaio ad revoluio Lodo Milleium Bridge Also, searh videos Syhroizaio of Meroomes o Youube! Bu, we ao use exisig models i he aural siee. They simply apped a addiioal erm ha apures syhroizig fores, muliplied by a ouplig parameer, ad sudy he effes of hagig a ouplig parameer. Wihou miro foudaios, o sruural ierpreaio a be give o he ouplig parameer. sube o he Luas riique. I geeral equilibrium, suh ouplig would hage iovaio ieives. Page 4 of 35

5 Kimiori Masuyama, Syhroizaio of Iovaio Cyles The Buildig Blok: Deekere-Judd (99 Page 5 of 35

6 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Judd (985; Dyami Dixi-Sigliz moopolisi ompeiive model; Iovaors pay fixed os o irodue a ew (horizoally differeiaed variey Judd (985; Se.; They ear he moopoly profi forever. Covergig o seady sae Mai Quesio: Wha if iovaors have moopoly oly for a limied ime? o Eah variey sold iiially a moopoly prie; laer a ompeiive prie o Impa of a iovaio, iiially mued, reah is full poeial wih a delay o Pas iovaio disourages iovaors more ha oemporaeous iovaio o Temporal luserig of iovaio, leadig o aggregae fluuaios Judd (985; Se.3; Coiuous ime ad moopoly lasig for 0 < T < o Delayed differeial equaio (wih a ifiie dimesioal sae spae o For T > T > 0, he eoomy aleraes bewee he phases of aive iovaio ad of o iovaio alog ay equilibrium pah for almos all iiial odiios. Judd (985; Se.4; also Deekere & Judd (99; DJ for shor o Disree ime ad oe period moopoly for aalyial raabiliy o D sae spae (he measure of ompeiive varieies iheried from pas iovaio deermies how sauraed he marke is o Uique equilibrium pah geeraed by D PWL oiverible (i.e., skew-e map. o Whe he uique seady sae is usable, fluuaios for almos all iiial odiios, overgig eiher o a -yle or o a haoi araor Page 6 of 35

7 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Page 7 of 35 Revisiig Deekere-Judd (99 Time: 0,,,... Fial (Cosumpio Good Seor: assembles differeiaed ipus a la Dixi-Sigliz ( d x X Y ( Demad for Differeiaed Ipus: P v p X v x ( (, where d p P ( Se of Differeiaed Ipus: a hage due o Iovaio ad Obsolesee. m ; Se of all differeiaed ipus available i : Se of ompeiively supplied ipus iheried i period. m : Se of ew ipus irodued ad sold exlusively by heir iovaors for oe period.

8 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Differeiaed Ipus Priig: uis of labor (he umeraire for produig oe ui of eah variey: p p p p ( ; x ( v x for m m m ( ; x ( v x for / x p ; x ; m m m θ (, e x p x p p m Aggregae Oupu ad Prie: Le m N ( N be he measure of / / m m / Y N x N x x m P N p N p m / M, ( M, where m M m N N. Oe ompeiive variey has he same effe wih > moopolisi varieies. is ireasig i σ, bu varies lile for a wide rage of σ e =.788 Page 8 of 35

9 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Iroduio of New Varieies: Iovaio os per variey, f m x f 0 m m m m p x ; N 0 f ; x M N Complemeary Slakess: Eiher e profi or iovaio has o be zero i equilibrium Resoure Cosrai: Fixed oal labor supply, L, m m m m m L N ( x N ( x f N ( p x N ( p x L M max, N. f x M Obsolesee of Old Varieies: δ (0,, he Survival Rae m N N M ( N N L max f ( N, N Aleraively, labor supply may grow a a osa faor, G /. Page 9 of 35

10 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Le (f N L : (Normalized measure of ompeiive varieies per labor supply Skew-Te Map f ( f f L H ( ( ( if if f L ( ( ( 45º (0,, Survival rae of eah variey due o obsolesee (or exogeous labor supply growh (, e, ireasig i σ (EoS Marke share of a ompeiive variey relaive o a moopolisi variey > 0: he delayed impa of iovaios * O Aive Iovaio f H No Iovaio ( Page 0 of 35

11 Kimiori Masuyama, Syhroizaio of Iovaio Cyles A Uique Araor: Sable seady sae for Sable -yle for Robus haoi araor wih m iervals (m = 0,, for Effes of a higher δ Page of 35

12 Kimiori Masuyama, Syhroizaio of Iovaio Cyles I he (σ, δ-plae Edogeous fluuaios wih a higher σ (more subsiuable; sroger ieive o avoid ompeiio a higher δ (more pas iovaio survives o rowd ou urre iovaio. We fous o he sable -yle ase,. Page of 35

13 Kimiori Masuyama, Syhroizaio of Iovaio Cyles A Two-Seor Model of Edogeous Iovaio Cyles Based o our Ierdepede Iovaio Cyles Page 3 of 35

14 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Two-Seor Exesio: o Eah seor produes a Dixi-Sigliz omposie, as i Deekere-Judd o CES over he wo omposies wih ε (EoS aross seors < σ (EoS wihi eah seor Resuls D sae spae (he measures of ompeiive goods i he wo seors deermie he urre sae of he eoomy Uique equilibrium pah geeraed by D-PWS, oiverible map Dyamis i he wo seors are deoupled for Cobb-Douglas (ε =. Wheher dyamis may overge o eiher syhroized or asyhroized -yles depeds o how you draw he iiial odiio As ε goes up from oe, fluuaios beome syhroized o Basi of araio for syhroized -yles expads ad overs he sae spae. o Basi of araio for asyhroized -yles shriks & disappears This ours before ε reahes σ. As ε goes dow from oe, fluuaios beome asyhroized o Basi of araio for syhroized -yles shriks o Basi of araio for asyhroized -yles expads Thus, perhaps surprisigly ad ouer-iuiively, ε > syhroizaio & amplifiaio ε < asyhroizaio & moderaio Page 4 of 35

15 Kimiori Masuyama, Syhroizaio of Iovaio Cyles -Dim Dyamial Sysem; F( / ( / ( R wih, for D for D g( ( for g( ( for, LL R, HH / R g( i D HL D LH, R / ; g(, R g( ; / where m g( m is defied by i ( m ( m ( m i wih (,. Page 5 of 35

16 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Idepede (Deoupled Skew Te Maps: Cobb-Douglas Case ( If, 0 ad g ( /. m i D sysem osiss of wo idepede D skew-e maps: D LH Iovaio Aive i D HH No Iovaio max{/, } (. / * D LL D HL * / Uique S.S.: / ( Iovaio Aive i Boh Iovaio Aive i A Uique Araor: O * / Sable seady sae for Sable -yle for Robus haoi araor wih m iervals (m = 0,,, for Page 6 of 35

17 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Idepede Sable -Cyles: ( 0 ; ( ( Eah ompoe D-map has * / o a usable seady sae, / ( * / * / o a sable -yle, L H ( ( As a D-map, his sysem has A usable seady sae; *, *. A pair of sable -yles: * * * * o Syhroized; L, L H, H, wih Basi of Araio i Red. * * * * o Asyhroized; L, H H, L, wih Basi of Araio i Whie. A pair of saddle -yles: * * * * * * * *,. L H, &, H, L The losure of he sable ses of he wo saddles forms he boudaries of he basis of araio of he wo sable -yles. Page 7 of 35

18 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Ierdepede (Coupled Skew Te Maps: ( 0 ompoes sill idepede i DLL ad DHH, whih iludes he diagoal. For ( 0: g ( is ireasig. More ompeiive goods i seor ( irease he marke size for seor (, eourage iovaio i i DLH (DHL. For ( 0 : g ( is dereasig. More ompeiive goods i seor ( dereases he marke size for seor (, disourage iovaio i i DLH (DHL. Complemes: ( 0 Subsiues: ( 0 DLH g( DHH g( / Iovaio Aive i No Iovaio g( / D LH DHH * DLL Iovaio Aive i Boh D HL Iovaio Aive i * DLL D HL g( O * / O * / Page 8 of 35

19 Ierdepede -Cyles: ( 0 Kimiori Masuyama, Syhroizaio of Iovaio Cyles, wih Eah ompoe D-map has: * * / o a usable seady sae, ( * * / * * / o a sable -yle, L L H H. ( ( As a D-map, As (or ireases, DLH & DLH shrik ad DHH expads. As (or dereases, DLH & DLH expad ad DHH shriks. * * * * Syhroized -yle, L, L H, H exiss ad sable; o affeed by (or. a a a a Symmeri Asyhroized -yle, L, H DLH H, L DHL, depeds o * * * * (or, ad o loger equal o L, H H, L. I exiss for all (or ; sable for ( ad usable for ( 0. Furhermore, oe ould see umerially, For, a higher expads he basi of araio for he syhroized -yle. Page 9 of 35

20 Kimiori Masuyama, Syhroizaio of Iovaio Cyles a a a a Symmeri Asyhroized -Cyle: L, H DLH H, L DHL a a a a a H ; ( L H H g H, where (, ad m g( mk solves ( m ( m Jaobia a his -yle: ( J, ( m a where g' ( H = ( (. Two Eigevalues: 4 Complex ougaed if ( ( 4( / ; a sable fous,as De ( J ( Real, boh posiive, less ha oe if 4( / ( ( ; a sable ode; Real, boh posiive, oe greaer ha oe if ( ( ; a usable saddle. ( ( for 0; ireasig i (0, wih ( (0 0 ad ( (. Hee, (0,, s.. his -yle is sable for ad usable for. k. Page 0 of 35

21 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Basis of -yles: Syhrozied (Red vs. Asyhroized (Whie The basi of he syhroized -yle expads as ad shriks as 0. Page of 35

22 Kimiori Masuyama, Syhroizaio of Iovaio Cyles A Two-Coury Model of Edogeous Iovaio Cyles Based o our Globalizaio ad Syhroizaio of Iovaio Cyles Page of 35

23 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Helpma & Krugma (985; Ch.0: Trade i horizoally differeiaed (Dixi-Sigliz goods wih ieberg rade oss bewee wo sruurally ideial ouries; oly heir sizes may be differe. I auarky, he umber of firms based i eah oury is proporioal o is size. As rade oss fall, o Horizoally differeiaed goods produed i he wo ouries muually peerae eah oher s home markes (Two-way flows of goods. o Firm disribuio beomes ireasigly skewed oward he larger oury (Home Marke Effe ad is Magifiaio Two Parameers: s & s s [/, : Bigger oury s share i marke size s s [0, : Degree of Globalizaio: iversely relaed o he ieberg os, / s : Bigger oury s share i firm disribuio O s/s ρ Page 3 of 35

24 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Our Mai Resuls: By ombiig DJ (99 ad HK (985: D sae spae: (Measures of ompeiive varieies i he wo ouries Uique equilibrium pah obaied by ieraig a D-PWS, oiverible map wih four parameers: θ & δ & s & Oe ui of ompeiive varieies = θ (> uis of moopolisi varieies Oe ui of foreig varieies = ρ (< ui of domesi varieies I auarky (ρ = 0, he dyamis of he wo are deoupled. Wheher hey may overge o eiher syhroized or asyhroized -yles depeds o how you draw he iiial odiio. As rade oss fall (a higher ρ, hey beome more syhroized: o Basi of araio for asyhroized -yles shriks ad disappears o Basi of araio for syhroized -yles expads Full syhroizaio is reahed wih parial rade iegraio (ρ < or τ > 0 o Fully syhroized a a larger rade os if oury sizes are more uequal o Eve a small size differee speds up syhroizaio sigifialy o The larger oury ses he empo of global iovaio yles, wih he smaller oury adusig is rhyhm. Page 4 of 35

25 Kimiori Masuyama, Syhroizaio of Iovaio Cyles D Dyamial Sysem; F( (0 < δ < ; < θ < e; 0 ρ < ; / s < R wih, s ( ( s ( ( if D if D h ( ( if h ( ( if ;, LL, HH R s ( R h ( k D HL, R s( ; h ( D LH s s where s ( s( mi,, 0.5 s s ; s sk h ( k 0 defied impliily by. h ( h ( / k k k, R h ( ; s ( k Page 5 of 35

26 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Sae Spae & Four Domais for he Symmeri Case: s / s 0 h ( (ρ = 0 (ρ = Iovaio Aive i 0.5 * Iovaio Aive i Boh D LH D LL * O 5 DHL DHH 0. Iovaio Aive i No Iovaio (ρ = 0 h ( (ρ = Page 6 of 35

27 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Sae Spae & Four Domais for he Asymmeri Case: s / s 0 s s s s ( ( Iovaio Aive i h DLH ( DHH No Iovaio s ( * Iovaio Aive i Boh DLL D HL h ( O s ( * Iovaio Aive i s s Page 7 of 35

28 Syhroized vs. Asyhroized -Cyles i Auarky: 0 As a D-map, his sysem has * A usable seady sae;, A pair of sable -yles * * * * o Syhroized; L, L H, H, Basi of Araio i red. * * * * o Asyhroized; L, H H, L, Basi of Araio i whie A pair of saddle -yles: * * * * * *, * * L H, ;, H, L * Kimiori Masuyama, Syhroizaio of Iovaio Cyles ;, Page 8 of 35

29 Symmeri Ierdepede -Cyles, s 0. 5, (0, Kimiori Masuyama, Syhroizaio of Iovaio Cyles, : Eah ompoe D-map has: * * / o a usable seady sae, & ( * * / * * / o a sable -yle, L L H. H ( ( As a D-map, * * * * Syhroized -yle, L, L DLL H, H DHH, is uaffeed by (0,. a a a a Symmeri Asyhroized -yle, L, H DLH H, L DHL, depeds o * * * * (0,, o loger equal o L, H H, L. I exiss for all (0, ; sable for 0, ad usable for,. ( ( Furhermore, oe ould see umerially, For, ( 0,, a higher expads he basi of araio for he syhroized - yle, ad redues ha for he asyhroized -yle. Page 9 of 35

30 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Symmeri Syhroized & Asyhroized -Cyles: s 0. 5;. 5; Red (Sy. -yle beomes domia. Sym. Asy. -yle beomes a ode a ρ =.87867, a saddle a ρ = Page 30 of 35

31 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Asymmeri Syhroized & Asyhroized -Cyles s 0. 7,. 5; By ρ =.65, ifiiely may Red islads appear iside Whie. By ρ =.9, he sable asyhroized -yle ollides wih is basi boudary ad disappears, leavig he Syhroized -yle as he uique araor. Page 3 of 35

32 Kimiori Masuyama, Syhroizaio of Iovaio Cyles A Smaller Reduio i τ Syhroizes Iovaio Cyles wih Coury Size Asymmeries Criial Value of ρ a whih he Sable Asyhroized -yle disappears (as a fuio of s I delies very rapidly as s ireases from 0.5. I hardly hages wih δ. Page 3 of 35

33 Four Basis of Araio ( s 0. 7,. 5, Kimiori Masuyama, Syhroizaio of Iovaio Cyles As ρ rises, Red ivades Whie, ad Azure ivades Gray, ad verial slips of Red ad Azure emerge. Page 33 of 35

34 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Three Effes of Globalizaio: Home Marke Effe Produiviy Gais Syhroizaio Page 34 of 35

35 Kimiori Masuyama, Syhroizaio of Iovaio Cyles Summary: A -seor exesio wih CES preferees over he wo seors o For Cobb-Douglas (ε =, iovaio dyamis of he wo seors are deoupled. o For ε >, syhroized o amplify fluuaios; for ε <, asyhroized o moderae A -oury exesio wih rade bewee sruurally ideial ouries, where he degree of rade globalizaio ρ as as a ouplig parameer o I auarky (ρ = 0, iovaio dyamis of he wo ouries are deoupled. o As rade os falls, hey beome more syhroized o Full syhroizaio ours a a srily posiive rade os (ad a a larger rade os wih more uequal oury sizes o The smaller oury aduss is rhyhm o he rhyhm of he bigger oury. More o Come: Syhroizaio of haoi fluuaios More seors or more ouries A -seor & -oury exesio o sudy he effes of globalizaio bewee wo sruurally dissimilar ouries o Two Idusries: Upsream & Dowsream, eah produes DS omposie as i DJ. o Oe oury has omparaive advaage i U; he oher i D o My oeure: Globalizaio leads o a asyhroizaio Cosise wih he empirial evidee (Trade auses syhroizaio amog developed ouries, bu o bewee developed ad developig ouries Page 35 of 35