Globalization and Synchronization of Innovation Cycles

Transcription

1 Globalizaion and Synchronizaion of Innovaion Cycles By Kiminori Masuyama, Norhwesern Universiy, USA Iryna Sushko, Insiue of Mahemaics, Naional Academy of Science of Ukraine Laura Gardini, Universiy of Urbino, Ialy Yale Macro Lunch November, 05 Page of 5

2 Inroducion Page of 5

3 Theoreical Moivaion: How does globalizaion affec macro co-movemens across counries? Mos economiss address his quesion by assuming ha some exogenous processes drive produciviy movemens in each counry. Bu, globalizaion (a rade cos reducion) can affec o produciviy growh raes, as already shown by endogenous growh models o synchroniciy of produciviy flucuaions, as we show in an endogenous cycle model Empirical Moivaion: Counries ha rade more wih each oher have more synchronized business cycles o Paricularly among developed counries (EU, OECD, ec) o No so beween developed and developing counries Difficul o explain his rade-comovemen puzzle in models wih exogenous shocks o Common shocks would cause synchronizaion regardless of he rade inensiy o Wih counry-specific shocks, more rade lead o less synchronizaion o Aemps o resolve i by global supply chains me limied success; also awkward Easier in models of endogenous flucuaions. No need o appeal o global supply chains Page 3 of 5

4 Inuiion We Wan o Capure o Two srucurally idenical counries o Each counry (in auarky) is subjec o endogenous flucuaions, due o sraegic complemenariies in he iming of innovaion among firms compeing in he same marke o Wihou rade, flucuaions in he wo counries are obviously disconneced. o Trade inegraion makes firms based in differen counries compee agains each oher and respond o an increasingly global (hence common) marke environmen. o Sraegic complemenariies in he iming of innovaion across counries o Even wih parial inegraion, his causes an alignmen of innovaion incenives, synchronizing innovaion aciviies and produciviy flucuaions across counries Wha We Do To capure his inuiion in a simples manner, we develop a -counry model of endogenous innovaion cycles wih wo building blocks Judd (985; sec.4), also Deneckere & Judd (99), for endogenous innovaion cycles Unique equilibrium pah exhibis flucuaion; which can be obained by ieraing a Dnoninverible PWL map, commonly called a skew-en map Helpman & Krugman (985; ch.0) for inra-indusry rade wih iceberg rade cos, which is used as a coupling parameer. Concepually, his is a sudy of Synchronizaion of (Weakly) Coupled Oscillaors Page 4 of 5

5 Synchronizaion of (Weakly) Coupled Oscillaors Naural Science: A Major Topic. Thousands of examples: Jus o name a few, Chrisiaan Huygens pendulum clocks The Moon s roaion and revoluion London Millennium Bridge Also, search videos Synchronizaion of Meronomes on Youube! Bu, we canno use he exising sudies of coupled skew-en maps. Wihou microfoundaions, we canno give srucural inerpreaion o heir synchronizing forces nor coupling parameers. Subjec o he Lucas criique. In GE, innovaion incenive migh change wih rade. Economics: None? To he bes of our knowledge, his is Firs -counry, dynamic GE model of endogenous flucuaions Our companion piece, Inerdependen Innovaion Cycles o Two-secor, closed economy o Each secor produces a Dixi-Sigliz composie, as in DJ o CES preferences over he wo composies o Flucuaions in he wo secors are decoupled for Cobb-Douglas o Synchronized (asynchronized) if EoS increases (decreases) from one. Page 5 of 5

6 The Two Building Blocks Page 6 of 5

7 Judd (985); Dynamic Dixi-Sigliz monopolisic compeiive model; Innovaors pay fixed cos o inroduce a new (horizonally differeniaed) variey Judd (985; Sec.); They keep heir monopoly power. Unique seady sae globally sable due o ineremporal smoohing of innovaion aciviies Main Quesion: Wha if hey have monopoly for a limied ime? o Each variey sold iniially a monopoly price; laer a compeiive price o Impac of an innovaion, iniially mued, reach is full poenial wih a delay o Pas innovaion discourages innovaors more han conemporaneous innovaion o Temporal clusering of innovaion, leading o aggregae flucuaions Judd (985; Sec.3); Coninuous ime and monopoly lasing for 0 < T < o Delayed differenial equaion wih an infinie D sae space o For T > Tc > 0, he economy oscillaes beween he phases of acive innovaion and of no innovaion along any equilibrium pah for almos all iniial condiions. Judd (985; Sec.4); also Deneckere & Judd (99; DJ for shor) o Discree ime and one period monopoly for analyical racabiliy o D sae space (he measure of compeiive varieies inheried from pas innovaion deermines how sauraed he marke is) o Unique equilibrium pah generaed by a D PWL noninverible (i.e., skew-en) map o When he unique seady sae is unsable, converging o a -cycle or o a chaoic aracor from almos all iniial condiions. Page 7 of 5

8 Deneckere-Judd (DJ) in a Nushell n : (Measure of) compeiive varieies inheried per labor supply Noninverible PWL (Skew Ten) map n f ( n ) f f L H ( n ( n ) ) ( ) n n if if n n 45º (0,), Survival rae of varieies due o obsolescence (or exogenous labor supply growh) (, e), increasing in σ (EoS) Marke share of a compeiive variey relaive o a monopolisic variey > 0: he delayed impac of innovaions O Acive Innovaion No Innovaion Page 8 of 5

9 A Unique Aracor: Sable seady sae for Sable -cycle for Robus chaoic aracor (of various ypes) for Effecs of a higher δ Page 9 of 5

10 Bifurcaion diagram in he (σ, δ)-plane and is magnificaion Endogenous flucuaions wih a higher σ (more subsiuable, srong incenive o avoid compeiion) a higher δ (more pas innovaion survives o crowd ou curren innovaion). We focus on he sable -cycle case,. Page 0 of 5

11 Helpman & Krugman (985; Ch.0): Trade in horizonally differeniaed (Dixi-Sigliz) goods wih iceberg rade coss beween wo srucurally idenical counries; only heir sizes may be differen. In auarky, he number of firms based in each counry is proporional o is size. As rade coss fall, o Differeniaed goods produced in he wo counries muually penerae each oher s home markes (Two-way flows of goods). o Firm disribuion becomes increasingly skewed oward he larger counry (Home Marke Effec and is Magnificaion) Two Parameers: s & s s [/,) : Bigger counry s share in marke size sn s [0,) : Degree of Globalizaion: inversely relaed o he iceberg cos, / s n : Bigger counry s share in firm disribuion O s/s ρ Page of 5

12 A Two-Counry Model of Endogenous Innovaion Cycles Page of 5

13 Our Main Resuls: By combining DJ (99) and HK (985): D sae space: (Measures of compeiive varieies in he wo counries) Unique equilibrium pah obained by ieraing a D-PWS, noninverible map wih four parameers: θ & δ & s & One uni of compeiive varieies = θ (> ) unis of monopolisic varieies One uni of foreign varieies = ρ (< ) uni of domesic varieies In auarky (ρ = 0), he dynamics of he wo are decoupled. Wheher hey converge o synchronized or asynchronized -cycles depends on how you draw he iniial condiion As rade coss fall (a higher ρ), hey become more synchronized: o Basin of aracion for asynchronized -cycles shrinks and disappears o Basin of aracion for synchronized -cycles expands. Full synchronizaion occurs wih parial rade inegraion (i.e., ρ < ) o Fully synchronized a a larger rade cos if counry sizes are more unequal o Even a small size difference speeds up synchronizaion significanly o The larger counry ses he empo of global innovaion cycles, wih he smaller counry adjusing is rhyhm Page 3 of 5

14 D Dynamical Sysem; n F( n ) n (0 < δ < ; < θ < e; 0 ρ < ; / s < ) R wih, n s ( ) ( ) n n s ( ) ( ) n if D n n n n if D n n n h ( n ) ( ) n if n h ( n ) ( ) n n n if n n ; n n, n LL n n, n HH R n j s j ( ) R n j h j ( nk n n n D HL ), R n s( ); n h ( n ) n n n D LH s s where s ( ) s( ) min,, 0.5 s s ; s j sk h j ( n k ) 0 defined implicily by. h ( n ) n h ( n ) n / j k k j k, R n h ( n ); n s ( ) k Page 4 of 5

15 Sae Space & Four Domains for he Symmeric Case: s / s 0 (ρ = 0) (ρ = ) Innovaion Acive in D LH DHH No Innovaion (ρ = 0) Innovaion Acive in Boh D LL DHL O Innovaion Acive in (ρ = ) Page 5 of 5

16 Sae Space & Four Domains for he Asymmeric Case: s / s 0 Innovaion Acive in DHH No Innovaion DLH Innovaion Acive in Boh O DLL D HL Innovaion Acive in Page 6 of 5

17 Synchronized vs. Asynchronized -Cycles in Auarky: 0 As a D-map, his sysem has * An unsable seady sae; n,n A pair of sable -cycles * * * * o Synchronized; n L, nl n H, nh, Basin of Aracion in red. * * * * o Asynchronized; n L, nh n H, nl, Basin of Aracion in whie A pair of saddle -cycles: * * * * * * n, n n n n n * * L H, ;, H n, nl * Kiminori Masuyama, Globalizaion and Synchronizaion of Innovaion ;, Page 7 of 5

18 Symmeric Synchronized & Asynchronized -Cycles: s 0. 5;. 5; Red (Sync. -cycle) becomes dominan. Sym. Async. -cycle becomes a node a ρ =.87867, a saddle a ρ = Page 8 of 5

19 Asymmeric Synchronized & Asynchronized -Cycles s 0. 7,. 5; By ρ =.65, infiniely many Red islands appear inside Whie. By ρ =.9, he sable asynchronized -cycle collides wih is basin boundary and disappears, leaving he Synchronized -cycle as he unique aracor. Page 9 of 5

20 A Smaller Reducion in Trade Coss Synchronizes Innovaion Cycles wih Counry Size Asymmeries Criical Value of ρc a which he Sable Asynchronized -cycle disappears (as a funcion of s ) I declines very rapidly as s increases from 0.5. I hardly changes wih δ. Page 0 of 5

21 Four Basins ofaracion ( s 0. 7,. 5, 0. 75) Kiminori Masuyama, Globalizaion and Synchronizaion of Innovaion As ρ rises, Red invades Whie, and Azure invades Gray, and verical slips of Red and Azure emerge. Page of 5

22 Three Effecs of Globalizaion: Home Marke Effec Produciviy Gains Synchronizaion Page of 5

23 Concluding Remarks Page 3 of 5

24 Summary: s aemp o explain why globalizaion migh synchronize endogenous produciviy flucuaions Key Mechanism: Globalizaion Innovaors from everywhere compeing agains each oher in more inegraed (hence common) marke Alignmen of Incenives o Innovae Synchronizaion Capured in a -counry model of endogenous innovaion cycles, buil on DJ and HK o In auarky, innovaion dynamics of he wo counries are decoupled. o As rade cos falls and inra-indusry rade rise, hey become more synchronized. o Full synchronizaion a a larger rade cos wih more unequal counry sizes. o The smaller counry adjuss is rhyhm o he rhyhm of he bigger counry. Adding endogenous sources of flucuaions helps o undersand he radecomovemen puzzle. Technical Conribuions o s wo-counry model of endogenous flucuaions o A New Model of Coupled Oscillaors o Applicaion of D noninverible, PWS, discree ime dynamic sysem Page 4 of 5

25 Nex Seps: Synchronizaion of Chaoic Flucuaions Many Counries Differen Models of Endogenous Innovaion Cycles: o My conjecure: Globalizaion should cause synchronizaion as long as i causes innovaors based in differen counries o operae in a common marke environmen. o The assumpion of srucural similariy seems crucial. Wha if wo counries are srucurally dissimilar? Differen Models of Trade: For example, o Wha if he wo counries become verically specialized?; e.g., global supply chains o Two Indusries: Upsream & Downsream, each produces DS composie as in DJ. o One counry has comparaive advanage in U; he oher in D o My conjecure: Globalizaion leads o an asynchronizaion Empirically consisen, as he evidence for he synchronizing effec of rade is srong among developed counries, bu no so bw developed and developing counries Page 5 of 5