Economic Growth & Development: Part 3 Horizontal Innovation Models: Applications. By Kiminori Matsuyama. Updated on , 6:12:26 PM

Transcription

1 iminori Masuyama Groh & Develomen Par-3 Economic Groh & Develomen: Par 3 orizonal Innovaion Models: licaions By iminori Masuyama Udaed on ::6 PM Page of 6

2 iminori Masuyama Groh & Develomen Par-3 Page of 6 Direced Technological Change Technological Change: Classificaions cemoglu; Ch.5. e ~ is linear homogenous in and and is he sae of echnology. n increase in is abor-augmening arrod-neural if Caial-augmening olo-neural; if TP-augmening icks-neural; if These classificaions should no be confused ih he relaed bu disinc noion of facor-biased. n increase in is abor-biased if 0 ~ ~ r Caial-biased if 0 ~ ~ r Unbiased if 0 ~ ~ r Clearly TP-augmening icks-neural change is unbiased. Bu ho abou labor- or caial-augmening changes?

3 iminori Masuyama Groh & Develomen Par-3 Page 3 of 6 CE examle: r k. If ε > -augmening change is -biased and -augmening change is -biased. If ε < -augmening change is -biased and -augmening change is -biased. If ε = -augmening and -augmening changes are boh unbiased. Inuiion for -augmening change is -biased hen ε <. n increase in labor roduciviy creaes caial shorage and excess suly of labor a he iniial facor rices. This causes a dro in he age/renal raio. When he scoe of subsiuion beeen he o facors limied his dro in he age/renal raio is more han he roduciviy gain and hence he overall effec is agains labor in favor of caial. The maer is more comlicaed because he relaive suly of facors migh also affec he direcion of echnological change.

4 iminori Masuyama Groh & Develomen Par-3 To-ecor ab-equimen Model cemoglu Ch.5.3: Consan inelasic sulies of o-yes of labor &. There are o secors -secor and -secor. The final good is roduced by combining he -good and -good. -ecor ousehold ecor -ecor -good C inal Good ecor -good x ν; 0 ν X Z Z X x ν; 0 ν -Inermediaes -Inermediaes R&D for R&D for Page 4 of 6

5 iminori Masuyama Groh & Develomen Par-3 Page 5 of 6 inal Good ecor: numeraire comeiive ih CR Technology hich combines he -good and -good: Relaive Demand for -good/-good: ih -Goods and -Goods Producion: comeiive ih CR echnology d x 0 ; d x 0 The sae of echnology is no o-dimension } {. orks only ih -inermediaes in he -secor. orks only ih -inermediaes in he -secor.

6 iminori Masuyama Groh & Develomen Par-3 Demand for an -inermediae: x rom Max 0 v x d. x. x -Inermediae roducers: unis of he final good are required o roduce one x x uni of each variey. ence for all ν and. / / x ; / Is scale of oeraion and is rofi boh increase ih he marke size effec and he rice effec. X / ; ; / can be vieed as he roduciviy of. is hence roorional o conrolling for bu ill change ih. imilar exressions hold for ; ence Page 6 of 6

7 iminori Masuyama Groh & Develomen Par-3 Page 7 of 6 Equilibrium Relaive Ouu Price in he hor Run: Relaive uly Relaive Demand here. oe. Relaive acor Price in he hor Run: / ence σ can be vieed as he derived elasiciy of subsiuion beeen &. -augmening change is -biased if σ > and -biased if σ <. -augmening change is -biased if σ > and -biased if σ <.

8 iminori Masuyama Groh & Develomen Par-3 Page 8 of 6 R&D ecors: Z ; Z here he reurns for innovaion are given by s ds du u r s ex ; s ds du u r s ex. long he BGP r & are consan hence so are &. ih is marke size effec & he rice effec. If 0 and 0 higher / cause -augmening change if σ > and -augmening change if σ <.

9 iminori Masuyama Groh & Develomen Par-3 Page 9 of 6 Relaive acor Price in he ong Run: long he BGP. The relaive demand curve is flaer in he long run han in he shor-run / henever because a higher / causes -biased echnological change hich shifs he demand curve ouard. Inuiion: When & are close subsiues σ > higher / causes -augmening change; -augmening change is -biased; ence i is -biased. When & are no so close subsiues σ < higher / causes -augmening change; -augmening change is -biased; ence i is -biased.

10 iminori Masuyama Groh & Develomen Par-3 Eiher ay a higher / induces -biased echnological change. Weak Equilibrium Bias in cemoglu s erminology lso if σ > Bias is so srong ha he relaive demand becomes uard-sloing. rong Equilibrium Bias in cemoglu s erminology cemoglu Ch.5 argue ha hese resuls hel o undersand: Unskill-biased echnological change in he 9 h cenury and more skill-biased echnological change in he 0 h cenury; Temorary decline in he college remium in he sevenies and subsequen rise in he remium in he eighies. This hoever requires σ >. More general lesson is ha a change in he relaive suly of skills no only resonds o biased echnological changes bu also could cause biased echnological changes. Exercise: Comlee he analysis by finding he condiions ensuring he exisence of BGP. oe on Transiion Dynamics: If 0 / 0 / * reaches he BGP. ikeise if 0 / 0 / * he BGP. 0 unil i 0 unil i reaches Page 0 of 6

11 iminori Masuyama Groh & Develomen Par-3 Page of 6 To-ecor noledge-illover Model cemoglu Ch.5.4: Modify he above model by: ouseholds have a consan suly of and. and are used only in - and -secors as before. cieniss are used only in he R&D secor as is only inus insead of he final good. The R&D echnologies are ; ;. here δ inroduces he ersisence in he direcion of R&D. long he BGP. oe: Convergence oards BGP requires σδ <. Too much ersisence and/or subsiuion leads o insabiliy.

12 iminori Masuyama Groh & Develomen Par-3 Page of 6 Relaive acor Prices: uard-sloing for σ > δ under he condiion less sringen han before. Groh Rae: ; ;. * g g * oes: The exisence of BGP is ensured by imosing resricions on arameers θ and ρ. The groh rae is maximized a indeenden of σ or γ /γ.

13 iminori Masuyama Groh & Develomen Par-3 Page 3 of 6 noledge-illover Case ihou cale Effec cemoglu Ch.5.5 o change he above model such ha ouseholds have an inelasic suly of & groing a he rae n. R&D echnology is given by ; ; ; long he BGP uard sloing if σ > λ less sringen condiion han before.

14 iminori Masuyama Groh & Develomen Par-3 -ugmening Technological Change and Endogenously Consan acor hares cemoglu Ch.5.6 kech of he idea no very rigorous: noledge-sillover models ih and insead of hich gros a a consan rae. ; r Wih σ < k / declines as / gros. More -augmening closer o arrod-neural. Bu no urely -augmening and no BGP. r Wih δ =. r/ is consan asymoically. BGP ih urely -augmening i.e. arrod-neural hich is globally sable. Inuiion: Wih σ < caial accumulaion makes he rice of labor and rofis from labor-augmening echnologies rise sufficienly faser hich causes he arrod-neural change keeing he effecive sulies of he o facors in balance. Page 4 of 6

15 iminori Masuyama Groh & Develomen Par-3 Develomen Tras Ciccone and Masuyama Page 5 of 6

16 iminori Masuyama Groh & Develomen Par-3 Endogenous Cycles Masuyama 999 Page 6 of 6