Do R&D subsidies necessarily stimulate economic growth?

Transcription

1 MPR Munich Peronal RePEc rchive Do R&D ubidie necearily imulae economic growh? Ping-ho Chen and Hun Chu and Ching-Chong Lai Deparmen of Economic, Naional Cheng Chi Univeriy, Taiwan, Deparmen of Economic, Tunghai Univeriy, Taiwan, Iniue of Economic, cademia Sinica, Taiwan ugu 2015 Online a hp://mpraubuni-muenchende/66061/ MPR Paper No 66061, poed 13 ugu :42 UTC

2 Do R&D Subidie Necearily Simulae Economic Growh? Ping-ho Chen Deparmen of Economic, Naional Cheng Chi Univeriy, Taiwan Hun Chu Deparmen of Economic, Tunghai Univeriy, Taiwan Ching-chong Lai Iniue of Economic, cademia Sinica, Taiwan Deparmen of Economic, Naional Cheng Chi Univeriy, Taiwan Iniue of Economic, Naional Sun a-sen Univeriy, Taiwan ugu 2015 brac Thi paper analyze he growh effec of ubidy policie in a modified R&D-baed growh model of Romer (1990), in which boh innovaion and capial accumulaion are engine of long-run economic growh We how ha, under cerain condiion, ubidizing he R&D ecor may be growh-impeding 1 Inroducion R&D ubidy policie are now commonly adoped in developing and developed counrie he world over Popular view are ha R&D ubidie direc reource o innovaive aciviie, and hu can imulae economic growh Thi view ha been eified wihin he framework of claic innovaion-led endogenou growh model (Romer, 1990; Groman and Helpman, 1991; ghion and Howi, 1992) Thee and numerou ubequen udie baically uppor ha R&D ubidie have in general poiive effec on long-run growh Empirical evidence, on he oher hand, are le 1

3 clear abou he poiive effec of hee policie on produciviy growh (ee, eg, Beaon and Weinein, 1996; Wemore, 2013) In hi paper, we analyze he effec of ubidy policie on long-run growh in an expanding-variey R&D-baed growh model, developed by Romer (1990), wih boh innovaion and capial accumulaion being he engine of long-run economic growh (eg, Chu e al, 2012; Iwaiako and Fuagami, 2013) The ubidy policie under conideraion include a ubidy for he co (of he employmen of worker) in hree ecor: he final-good ecor, he R&D ecor, and he capial-producing ecor 1 Our analyi how ha ubidizing he final-good ecor i growh-impeding However, ubidizing he oher wo ecor ha uncerain effec on long-run growh Thi finding implie ha he ypical view ha a ubidy for R&D lead o faer growh doe no necearily hold Inuiively, he R&D ecor and he capial-producing ecor are boh conribuive o economic growh Given he fac ha he wo ecor compee over labor, when an R&D ubidy i implemened, an increaed R&D invemen in he form of an expanion in R&D worker end o crowd ou available inpu for he capial-producing ecor Thi lead o wo conflicing effec on growh, and he overall effec hen hould hinge upon he relaive imporance of he wo ecor will be hown below, if he produciviy of he capial-producing ecor i dominan, ubidizing R&D may depre long-run growh Our udy i relaed o he lieraure on he effec of R&D ubidy policie in R&D-baed growh model Davidon and Segerrom (1998) conider wo ype of 1 Subidizing producion co of R&D i an approach ha have been mo commonly adoped in he lieraure (eg, Zeng and Zhang, 2007; Gromann and Seger, 2013; Gromann e al, 2013; Chu e al, 2015) for he ubidy o he final-good ecor, we conider a ubidy o he hiring of final-good worker, imply for he purpoe of eay comparion Our main reul will no change if we conider oher ype of ubidie for final good producion 2

4 R&D (innovaive R&D and imiaive R&D), and find ha ubidie on differen ype of R&D reul in differen growh effec Segerrom (2000) employ he Howi (1999) model wihou cale effec, and how ha R&D ubidie can have ambiguou effec on growh Zeng and Zhang (2007) and Gómez and Sequeira (2014) provide quaniaive evaluaion for he effec of R&D ubidie on boh growh and welfare By adoping a emi-endogenou growh model of Jone (1995), Gromann and Seger (2013) and Gromann e al (2013) explore he opimal R&D ubidizaion, bu heir udie are aben from he long-run growh effec due o he naure of a emi-endogenou growh model The preen udy conribue o hi rand of lieraure by conidering boh R&D and capial accumulaion a engine of long-run growh, and by howing ha he growh effec of an R&D ubidy depend on he relaive produciviy beween hee wo ecor 2 The model We modify he baic model of Chu e al (2012) by (i) inroducing ubidie, (ii) removing money, and (iii) auming inelaic labor upply We now briefly decribe he model rucure 21 Houehold There i a uni coninuum of houehold The populaion i aionary The lifeime uiliy i U e ρ u d 0 =, (1) where u = ln C, C i he conumpion of final good, and ρ >0 i he ubjecive dicoun rae The oal labor upply of each houehold i fixed and normalized o uniy 2 Thu, he houehold budge conrain i a = r a + w C T, where a 2 To keep he analyi imple, we aume ha he oal labor upply i inelaic, bu our reul are 3

5 i he houehold ae, r i he inere rae, w i he wage rae, 3 and T i he lump-um ax The uual eyne-ramey rule i: C C = r ρ (2) 22 Final good Final good (he numeraire) are produced by compeiive firm uing labor and a coninuum of inermediae good: 1 α α, 0 = L x ( i) di, (3) where L, i labor in final good producion, x ( i ) i he inermediae good of ype i ( i [0, ]), and i he number of varieie of inermediae good Denoing p ( i ) a he price of x ( i ) relaive o final good, he profi funcion of he final good firm i π = (1 ) w L p ( i) x ( i) di, (4),, 0 where i he ubidy on he employmen of final-good labor The condiional demand funcion are: L, (1 α ) = (1 ) w, (5) x ( i) 1 1 α α = L, p ( i) (6) 23 Inermediae good There i a coninuum of differeniaed inermediae good x ( i ), i [0, ] Each inermediae firm i owned by a monopoli who ue one uni of capial k o qualiaively robu o a more general uiliy funcion u= ln C+ η ln(1- L ) where L denoe he endogenou labor upply Deviaion are available from he auhor upon reque 3 We aume ha labor i perfecly mobile acro ecor, which implie a unified wage rae 4

6 produce one uni of inermediae good, ie, x ( i) = k ( i) Thu, he monopoliic profi i π x, ( i) = p ( i) x ( i) qk ( i), where q i he capial renal price Profi maximizaion yield he familiar pricing rule p ( i) = q / α, which implie ha he inermediae firm are ymmeric Therefore, we can drop noaion i for variable { x, p, k, π } x, The profi hen can be implified o: π 1 α = ( ) q k (7) α x, The marke-clearing condiion for capial good i x ( i ) di = x =, where 0 i aggregae capial For fuure ue, i i alo helpful o derive he condiion from (6) and (7) ha q = α and π = ( α ) α 2 x, 1 24 R&D In he compeiive R&D ecor, he value of a variey, denoed a v,, follow he no-arbirage condiion: rv = π + v, (8), x,, which ae ha he reurn of invemen in R&D will be equal o he monopoliic profi π x, plu he capial gain v, The R&D firm employ labor o produce new varieie wih he echnology =ϕ L,, where he parameer ϕ deermine he R&D produciviy and L, i labor ued in R&D The governmen may provide ubidie for he employmen of R&D worker The profi of R&D i: π = v (1 ) w L (9),, The zero-profi condiion implie: v ϕ = (1 ) w (10) 25 Capial producion Le u denoe he value of one uni of capial a v, The no-arbirage 5

7 condiion for v, i: rv = q+ v, (11),, which ae ha he reurn of invemen in capial producion i equal o i renal price q plu he capial gain v, Capial good are produced by a uni of coninuum compeiive firm ha employ labor L, The correponding producion echnology i =δ L,, where δ i a parameer reflecing he produciviy in he capial-producing ecor 4 The governmen may provide ubidie for he capial-producing firm o hire labor The profi of a capial-producing firm i: π = v (1 ) w L (12),, The zero-profi condiion implie: v, δ = (1 ) w (13) 26 The governmen, marke clearing, and aggregaion The governmen levie a lump-um ax on he houehold o finance i ubidy policie: T= w L + w L + w L (14),,, The marke-clearing condiion for capial good and he labor marke are: = x ( i) di= x, (15) 0 L + L + L = (16),,, 1 The houehold ae a conain he invemen in R&D and in capial producion, ie, a= v, + v, ccordingly, he reource conrain for final good can be calculaed a = C 3 Long-run growh effec of ubidy policie 4 Chu e al (2012) pecify ha = δωl,, where Ω reflec he echnology level To permi uained growh, hey furher aume Ω = o capure he capial exernaliy in he model 6

8 On he balanced growh pah, he allocaion of labor are aionary, which can be derived a (a ilde denoe he eady-ae value): = 1+ξ, (17a) 1 + Φ L (1 ) 1 L α + ξ ρ =, (17b) (1 ) 1+ Φ ϕ 2 (1 ) 1 L α + ξ ρ = (1 )(1 α) 1+ Φ δ, (17c) where ξ ρ δ ϕ and 1 α Φ (1 ) α + 1 (1 α )(1 ) are compoie parameer To enure ha L and L are non-negaive, we impoe he following rericion on he wo produciviy parameer: Condiion 1 ϕ ϕˆ = ρ(1 )(1 + Φ) α(1 )(1 + ξ ) and δ δˆ = ( ) ( ξ ) ρ(1 α )(1 ) 1+ Φ 2 α (1 ) 1+ The fir inequaliy of Condiion 1 enure ha L 0 and he econd enure ha L 0 From (17a)-(17c), he following lemma hold: Lemma 1 The effec of ubidie on equilibrium labor allocaion are: ~ L ~ L ~ L ~ ~ L L > 0 ; < 0 ; < 0, (18a) ~ ~ L L > 0 ; < 0 ; < 0, (18b) ~ ~ L L > 0 ; < 0 ; < 0 (18c) Proof Sraighforward from differeniaing (17a)-(17c) wih repec o,, and 7

9 Lemma 1 how ha, when an R&D ubidy i implemened, an increaed R&D invemen in he form of an expanion in R&D worker end o crowd ou available inpu for he capial-producing and final good ecor The ame reul applie o boh and Now we move o he effec of ubidy policie on balanced growh By uing x ( i) = x and (15), he aggregae producion funcion can be arranged a: = 1 α L 1 α, α (19) Taking log and differeniaing wih repec o ime yield he balanced growh rae, denoed by g ( / ), a: g ~ ~ ~ ~ ~ = (1 α ) ~ + α ~ = (1 α) ϕl + L αδ (20) The above equaion clearly how ha he balanced growh rae i deermined by boh R&D and capial accumulaion ccording o Condiion 1 and (20), we can infer ha if ϕ= ϕˆ, he R&D ecor hu down uch ha economic growh i driven only by capial accumulaion, a in he -ype endogenou growh model In conra, if δ= δˆ, he capial producion hu how; in hi cae, economic growh i driven only by R&D and hu our model reduce o he andard Romer model To eaily convey our reul, we uppoe ha he governmen iniially doe no implemen any ubidy policie Equipped wih (17b), (17c), (20) and Lemma 1, we can elaborae he growh effec of ubidy policie by he following propoiion: Propoiion 1 The effec of ubidie on balanced growh rae g are a follow: (i) g i alway decreaing in ; (ii) g i increaing in 3 2 if and only if ϕ / δ > α /(1 α )(1 α + α ) ; (iii) g i increaing in if and only if ϕ / δ < (1+ α)/(1 α) 8

10 Proof Inering (17b) and (17c) ino (20) and differeniaing wih repec o and,, ubidy o he final-good ecor decreae he labor in he R&D and capial-producing ecor, boh of which are he engine of growh Therefore, i alway depree growh Wheher a ubidy o R&D and capial-producing ecor i growh-enhancing or no depend on heir relaive produciviie When he relaive produciviy beween he R&D and he capial-producing ecor ϕ / δ i relaively large, he R&D ecor i more producive Under hi iuaion, i i beer o ubidize he R&D ecor When ϕ / δ i relaively mall, he capial-producing ecor i more producive; hen a ubidy o hi ecor i more likely o imulae growh ppendix (No for publicaion) In hi appendix we provide he derivaion of he labor allocaion on he balanced growh pah (17a)-(17c) By uing equaion (5) and (10), we can obain he expreion ϕv, (1 ) L, = (1 α )(1 ) Differeniaing he log of hi expreion wih repec o ime, and inering = C yield: v C = + v C,, (1) Then, by inering / =ϕ L and /, C C = r ρ ino (1), ogeher wih (8), (10) and he condiion π ( ) x, 1 α α =, we obain: (1 ) α L L ρ =, (2) 1 ϕ Following a imilar algorihm, we can uilize (5), (13), and he condiion q = α 2 o derive: 9

11 2 (1 ) α L L ρ = (3) (1 )(1 α ) δ Finally, equaion (2) and (3) plu he clearing condiion for labor marke, (16), give u he cloed-form labor allocaion (17a)-(17c) in he main ex 10

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