Labor s Shares in a Model of Induced Innovation

Transcription

1 bor s Shres in Model of Induced Innovtion Hernndo Zulet * Deprtment of Economics Universidd del Rosrio Americn University in Bulgri hernndo.zulet@gmil.com Andrew T. Young ollege of Business nd Economics West Virgini University Morgntown, WV ph: em : Andrew.Young@mil.wvu.edu test Version: Februry 00 JE odes: O, O30, O4 eywords: bor's Shre, Fctor Shres, Development, Bised Technicl hnge, pitl Intensity We thnk Michele Boldrin nd im Ruhl for comments on previous version of this pper. We lso thnk Stefn ruse nd other prticipnts t the Emory University seminr series; John onlon nd other prticipnts t the University of Mississippi seminr series; Dniel Mejí, rlos Estebn Posd nd other prticipnts t the entrl Bnk of olombi seminr series. We thnk Andrés Grcí for excellent reserch ssistnce. * orresponding uthor.

2 bor's Shres in Model of Induced Innovtion Abstrct: The reltive stbility of ggregte lbor's shre constitutes one of the gret mcroeconomic rtios. However, reltive stbility t the ggregte level msks the unblnced nture of sectorl lbor's shres. We present two-sector (mnufcturing nd services model with induced innovtion tht cn rtionlize these phenomen s well s severl other empiricl regulrities of ctul economies. Specificlly, long the trnsition pth (i mnufcturing becomes incresingly cpitl-intensive over time while (ii there is n increse in the reltive price nd production shre of services nd (iii ggregte lbor's shre converges from bove to non-zero vlue. At the sectorl level (iv lbor s shre in mnufcturing trends towrds zero. Notbly, (v the model my trnsition to either neoclssicl stedy-stte or long-run endogenous growth, so it hs the potentil to ccount for wide rnge of growth experiences. JE odes: O, O30, O4 eywords: bor's Shre, Fctor Shres, Development, Bised Technicl hnge, pitl Intensity

3 . INTRODUTION Aggregte lbor's shre displys no upwrd or downwrd trend over time. This is one of Nichols ldor's (96 stylized fcts of economic growth. However, relity is more complex thn this gret mcroeconomic rtio would suggest. In the cse of the US, ggregte lbor s shre hs remined between 60 nd 70 percent from 960 through 005, but there does pper to be downwrd trend (figure. Behind ggregte lbor s shres, sectorl lbor s shres follow notbly distinct pths. Figure presents mnufcturing nd services lbor s shres for the sme 960 through 005 time period nd tble give some summry sttistics for the two series. Services lbor s shre is reltively stble, decresing by less thn 4 percent over the 45 yer period. bor s shre in mnufcturing, lterntively, flls by over percent over the sme time period. stly, in recent yers mnufcturing lbor s shre hs fllen below tht of services. As is well known, services hve become n incresing shre of US vlue-dded while mnufcturing s vlue-dded shre hs fllen (figure 3. To the extent tht we cn consider the evolution US ggregte lbor s shre to be consistent with blnced growth, it must be reconciled with unblnced growth t the sectorl level (uznets (965. The stbility of services lbor s shre, coupled with the increse in services vlue-dded The US experience my be peculir in this wy. Echevrri (997, for exmple, notes tht lbor s shre tends to be positively correlted to its totl output. However, she notes tht this correltion my hve diminished over time. Furthermore, Gollin (00 demonstrtes tht, once the income of the self-employed is ccounted for properly, there is no reltionship t ll between income levels nd lbor s shres cross countries. In previous version of this pper we presented figures nd tbles bsed on mnufcturing, services, nd griculture sectors seprtely. omments on tht erlier drft suggested tht we focus on two sectors: services nd non-services. Bsed on this we could hve ( combined griculture nd mnufcturing or (b dropped griculture. We chose the lter becuse (i griculture is such tiny prt of US production between 4. percent nd.0 percent for our entire smple; (ii the griculture sector s lbor s net chnge is negtive from 960 to 005. These fcts, (i nd (ii, imply tht the key fetures of the dt in compring mnufcturing nd services would be unchnged by including griculture. 3

4 shre, hs contributed to the reltive (to mnufcturing stbility of ggregte lbor s shre. Severl theoreticl models hve been introduced to ccount for both ggregte blnced nd unblnced sectorl growth. Exmples include ongsmut, Rebelo nd Xie (00, Ngi nd Pissrides (007, nd Acemoglu nd Guerrieri ( However, none of these models re designed to ccount specificlly for the evolution of both ggregte nd sectorl lbor s shres. In this pper we develop model tht cn ccount for lbor s shres, both ggregte nd sectorl, bsed on the theory of induced innovtion. In doing so we hope to not only ccount for the observed evolution of lbor s shres in the US nd elsewhere. We lso hope to provide useful frmework for thinking bout how lbor-sving innovtions my ffect on the income distribution cross productive fctors s economies grow. The model hs two-sectors. One sector (services uses lbor nd cpitl in eontief production function. In the production of services, lbor nd cpitl re highly complementry. The other sector (mnufcturing uses lbor nd cpitl in obb- Dougls production function nd is chrcterized by induced innovtion. 4 5 bor nd 3 Echevrri (997 summrizes set of useful stylized fcts of unblnced growth for smple of countries while ongsmut et l. (00 do the sme for the US in prticulr. 4 A generl explntion of the possible links between technologicl progress nd fctor shres is present in Acemoglu (00 nd 007. Acemoglu shows tht when the elsticity of substitution between fctors is different from one, fctor ugmenting technologicl chnge genertes chnges in fctor shres. The recent literture on bised innovtions provides severl models where technologicl chnge is modeled s increses in the shre of reproducible fctors. (For exmple, see Zeir (005, Peretto nd Seter (006 nd Zulet (008. In these models, gents try to reduce the need for scrce fctors nd increse the use of bundnt fctors. 5 Guscin (006 mkes n empiricl exercise in order to identify the determinnts of the chnges in lbor shres for the OED countries nd find tht, for the post-globliztion/post-it revolution er, percentge point increse in lbor productivity of the totl economy (Prod reduces the lbor s shre in ntionl by percentge points. 4

5 cpitl re, in mnufcturing, substitutble nd technologicl progress cn be lborsving. In the model, long the trnsition pth (i mnufcturing becomes incresingly cpitl-intensive over time while (ii there is n increse in the reltive price nd production shre of services nd (iii ggregte lbor's shre converges from bove to non-zero vlue. At the sectorl level (iv lbor s shre in mnufcturing trends towrds zero. Notbly, (v the model my trnsition to either neoclssicl stedy-stte or longrun endogenous growth, so it hs the potentil to ccount for wide rnge of growth experiences. This pper proceeds s follows. Section positions this pper in terms of the existing literture. This is followed by n intuitive discussion our model s ssumptions in Section 3. The model is then presented in Section 4. Sections 5 nd 6 discuss long-run growth pths nd trnsitionl dynmics respectively. Section 7 concludes.. MODES OF BOTH BAANED AND UNBAANED GROWTH Recent yers hve seen resurgence of models ccounting for the unblnced nture of growth t the sectorl level while remining consistent with blnced growth in the ggregte. For exmple, ongsmut, Rebelo nd Xie (00 focus on chnges in the mrginl rte of substitution in consumption between different sectors' outputs. 6 They ssume representtive gent with Stone Gery preferences over three goods: griculture (A, Mnufcturing (M nd Services (S. With these preferences, the income elsticity of substitution is less thn unity for A, unity for M, nd greter thn unity for S. As the 6 Other exmples include Murphy, Shleifer nd Vishny (989, Mtsuym (99, Echevrri (997, itner (000, selli nd olemn (000 nd Gollin, Prente nd Rogerson (00. 5

6 economy grows, output nd employment shres of A, M, nd S decrese, remin constnt, nd increse respectively. 7 Acemoglu nd Guerrieri (008, lterntively, demonstrte tht, given different cpitl intensities in different sectors, unblnced growth ccompnies cpitl deepening if sectorl outputs re gross complements in consumption. As cpitl ccumultes, the reltive price of the more cpitl-intensive sector's good flls. As it does, both other sectorl cpitl stocks nd employment shres converge towrds unity. Aggregte lbor's shre converges to constnt from below. Given tht they model ech sector with obb-dougls production function, the implied sectorl lbor s shres re constnts. Our model, however, predicts tht ggregte lbor s shre converges to constnt from bove nd cn mtch the dynmics of sectorl lbor s shres. Also, Ngi nd Pissrides (007 focus on (exogenous differences in sectorl totl fctor productivity (TFP growth rtes. Specificlly, outputs from m sectors enter ES consumption ggregte. Since goods re gross complements in consumption, employment shres nd reltive prices re inversely-relted to TFP growth rtes while growth in the ggregte cn be blnced. Our model provides different perspective on ggregte blnced nd sectorl unblnced growth. We focus on induced innovtion s source of both. 8 In this sense our work complements the existing literture. We lso extend the existing literture by ccounting for, specificlly, the distribution of income cross fctors, both ggregte nd sectorl. As will be seen in the model below, successful lbor-sving innovtion in one 7 Though the model chieves blnced growth, the evolution of ggregte lbor's shre need not be (pproximtely blnced depending on the rnge of vlues covered during the trnsition. 8 Studies of lbor-sving innovtions in reltion to growth nd development generlly constitute substntil literture. Erly exmples re ennedy (964, Smuelson (965, Drndkis nd Phelps (966; more recent exmples include Acemoglu (00, Boldrin nd evine (00 nd Zeir (998. 6

7 sector of the economy my be consistent with reltively constnt income distribution cross fctors. 3. INTUITION There re two sectors in our model tht (roughly correspond to services nd mnufcturing in rel economy. In services, lbor nd cpitl re both essentil to production nd re used in fixed proportions. There is no possibility for lbor-sving innovtions. While this ssumption is extreme, we hope to cpture the distinction between goods production nd services production tht Bumol (967, p. 45 rticulted. In the former, "lbor is primrily n instrument"; in the lter, "lbor is n end in itself". In services, lbor is reltively (to mnufcturing essentil nd the opportunities to substitute cpitl re reltively limited. Our ssumption is lso consistent with csul observtions bout the production of mny services. For exmple, hirstylist works with one chir nd one pir of shers. New, better shers cn be invented (tht re shrper nd/or open nd close more smoothly; new chir tht djusts more quickly nd/or is more comfortble cn lso be invented. But the scope for djusting the cpitl to lbor rtio seems reltively limited to, sy, the mnufcturing of crs where, over time, ssembly lines hve become incresingly utomted with robots performing wht were previously distinctly humn tsks. For mny services, the lbor is fundmentl nd, in our present exmple, one stylist per hircut per hour is reltively binding constrint. 9 9 One cn, of course, imgine robot hirstylist. Another wy to think bout the ssumption is tht lbor, displced from sectors where lbor-sving innovtions hve become possible, tend to flow to whtever sectors t tht point in time re more fundmentlly dependent on humn lbor. We would cll those sectors services. (Once you cn buy robot to cut your hir, hircuts re then more directly ssocited with mnufcturing. 7

8 In mnufcturing, on the other hnd, there re reltively good potentils for substitution nd innovting in wy tht sves lbor (uses cpitl. Since lbor is not reproducible (t lest in per cpit sense it becomes incresingly scrce reltive to reproducible cpitl inputs. The potentil for lbor-sving innovtion becomes incresingly vluble over time. On growth pth, competition leds to wge nd rentl rtes equl to the mrginl productivities of lbor nd cpitl, respectively, in mnufcturing. In the production of services, on the other hnd, (perfect complementrity of lbor nd cpitl prevent this equliztion of fctor prices nd mrginl products. Insted, fctor prices re determined by their opportunity costs, i.e, the mrginl productivity of lbor nd cpitl in mnufcturing. onsequently, s the economy grows nd wges increse the lbor s shre of services lso grows towrds unity. At the sme time, lbor s shre in mnufcturing is flling towrds zero s lbor-sving innovtions re dopted. Services employment shre is rising. Despite innovtions only occurring in mnufcturing, diminishing mrginl utility nd the limited supply of lbor imply tht the reltive price of services increses over time (the celebrted Bumol-Bowen (966 effect A TWO-SETOR MODE OF UNBAANED GROWTH WITH INDUED INNOVATION 0 lyuev (005 presented model where reltively high cpitl intensity in mnufcturing sector yields both the Bumol-Bowen effect nd n incresing employment shre in services. Bsed on the greter cpitl intensity, cpitl ccumultion lone drives the results. lyuev noted tht his motivtion for focusing on cpitl ccumultion lone ws in prt tht models ssuming fster TFP growth in mnufcturing thn in services counterfctully predict decresing employment shre for services. By incorporting lbor-sving innovtions, our two sector model reconciles the ide of fster technicl chnge nd decresing employment shre in mnufcturing (i.e., "deindustriliztion" see Bumol et l. (989 nd Rowthorn nd Rmswmy (999. 8

9 Assume n economy with two sectors. Sector one (mnufcturing uses both lbor nd cpitl in obb-dougls production function. Sector two (services produces, ccording to constnt eontief technology using cpitl nd lbor. bor-sving innovtions cn be pursued in the mnufcturing. Mnufcturing nd services re indexed by i,. Output, lbor input, nd cpitl input in sector re denoted by, respectfully, Y i, i, nd i. Output consumed from sector is denoted by i. Firms The production function for mnufcturing is, ( Y, I A where I is investment nd (. Totl lbor input vilble t ny instnt is normlized to unity. An impliction of this is tht ech sector s lbor input is identiclly its employment shre. The fctor elsticity prmeter,, will be vrible nd determined by innovtive ctivity (discussed below. The production function for services is, ( Y min( B,, where B is n efficiency prmeter nd re the sector's cpitl nd sector's lbor input respectively. Note tht services re lwys consumed while mnufcturing output cn be consumed or invested. We ssume tht firms re minimizing costs so (3 B ( pitl nd lbor re brod ctegories ment to encompss reproducible (e.g., both physicl nd humn cpitl nd non-reproducible (e.g., rw lbor nd lnd inputs. The model below builds off of Zulet (008. Other wys of modeling fctor sving innovtions cn be found in Zeir (006 nd Peretto nd Seter (005. 9

10 Eqution (3 implies tht there is no idle mchinery or useless employment in services. For services, we ssume tht fctor prices re determined by the opportunity cost of fctors. Therefore, fctor shres, nd Y Y nd r P, (4 w ( P where P is the reltive price of services. fctors,, re vrible nd fctor prices re given by, In mnufcturing, fctor prices re determined by the mrginl productivity of w A nd (5 ( r A We ssume tht lbor cn freely move cross sectors such tht (4 nd (5 imply tht, (6 ( ( A P. B onsumers A representtive consumer fces logrithmic instntneous utility function nd mximizes lifetime utility tking fctor prices s given. 0 ρt (7 mx e log( s.t. r w P, where λ λ, 0 < λ <, ρ > 0 is discount fctor, is consumption nd re ssets (i.e., clims on cpitl tht the consumer cn ccumulte. 3 At ech instnt the consumer is confronted by the stte of the economy nd mkes consumption/svings choices. 4 From the first order conditions it follows tht, 3 Time rguments re omitted for ese of exposition. 0

11 (8 r ρ λ (9 P λ Equtions (8 nd (9 re stndrd results in this type of model. The growth rte consumption of given good is equl to the interest rte minus the discount rte. Also, the rtio of consumption of both goods is constnt. Technologicl hnge Output from mnufcturing cn be invested in cpitl deepening or towrds the doption of more cpitl intensive production methods. We ssume tht investment decisions re mde by the shre holders (i.e., the representtive consumer. We lso ssume tht mrkets re competitive so the consumer chooses the technology tht mximizes the output of the firm tking fctor prices s given. There exists set of technologies, differentited by the elsticity of output with respect to cpitl, on the intervl (0,. 5 To undertke lbor-sving innovtions some frction of I must be llocted towrds the instlltion of new production methods, reorgniztion of existing productive structures, nd replcement/refurbishing of obsolete cpitl. 6 The entire spectrum of technologies, (0,, is vilble t every instnt. However, lbor-sving innovtions re costly in terms of foregone. eeping constnt 4 We ignore corner solutions for ese of exposition. 5 Assuming tht ll technologies "exist" t ll times is for simplicity nd does not mtter for our results if we interpret the required investments for innovtion s providing for the discovery of more cpitl intensive-methods. See below. 6 onsidering cpitl brodly, the investment cn lso be thought of in terms of trining for nd djustment to previously unused production methods.

12 hs no cost but incresing hs positive cost. This cost depends on the size of the chnge nd the current vlue of. The ssumption tht the cost of chnging depends positively on its vlue implies decresing returns to scle in the production of. 7 The stock of cpitl in sector one is given by δ (, where is the mount of ssets in sector one, 0 < δ ( nd δ '( 0. Specificlly, we include the cost of chnging ssuming production function of the following form: (0 δ ln( ln(. ( 0 Where 0 is the existing technology while is the new technology. Note tht this ssumption implies tht, I nd ( ( ξ or ξi I, where 0 < ξ <. This ssumption embodies severl desirble properties. First, ( 's mximum I ξ vlue is unity (consistent with constnt returns to scle. Second, ( 0 so it becomes incresingly costly to increse s it pproches unity. Finlly, ( ξ ( I is never counterproductive. 8 0 ; so positive investment in instlltion/reorgniztion/replcement <, 7 This ssumption my be justified by diminishing returns to innovtion (Jones (995. On the other hnd, relxing this ssumption does not brek the min predictions of the model. However, if there were no diminishing returns in innovtion, rich economies would rech the A production function in finite period (see Peretto nd Seter ( Seter (005 presents growth model tht similrly hs obb-dougls specifiction with n evolving prmeter. However, the prmeter evolution in Seter's model is exogenous; lso his model is onesector model. Young (004 considers prmeter chnges in the obb-dougls specifiction of rel business cycle model.

13 In ny cse, there is n dditionl problem of how to llocte resources between cpitl widening nd cpitl deepening: ( Mx A s. t. ( (ln( ln( 0 Where is the totl mount of ssets used in mnufcturing. From the first order condition it follows tht ( ln. ln First, note tht the production function is one of constnt returns in nd so the sum of fctors income is equl to totl income. Second, the production function is concve in. Third, depends on the cpitl lbor rtio of the firm so there is no technologicl dvntge derived from the size of the firm. 9 Equilibrium Note tht the interest rte pid by the firms pplies to but when technology is chnging <. Therefore, in equilibrium r A( effectively received by investors r is given by, /. (3 r A( so the interest rte / Given tht cpitl is mobile cross sectors, from (5 nd (3 it follows tht, 9 A complete proof of the concvity of the problem is vilble by request to the uthors. 3

14 Y (4 A P. ombining (6 nd (4 we get, (5 ( ( B. Replcing from eqution ( yields, (5 ( B ln. Proposition follows from (5 nd (5 PROPOSITION. IF or then the lbor shre in sector two increses s the cpitl lbor rtio in sector one grows. It is immedite to see tht if then is constnt nd s grows decreses. 0 We lso use numericl methods to simulte eqution (5. Figure 4 illustrtes the reltion between nd. As stted in proposition when the cpitl to lbor rtio is high in mnufcturing then lbor s shre in services increses s the cpitl to lbor rtio in mnufcturing grows. Furthermore s ( / goes to infinity goes to zero. Therefore, cn be initilly higher thn but with the growth process lph grows while decreses. 0 A forml proof is presented in the ppendix. For the simultion we ssume B3,5. 4

15 Now, combining (5, (0 nd (4 yields, (6 δ ( A ρ, nd combining (3, (5 nd (7 yields, (7 ( ( λ A λ B. Equtions (6 nd (7 re stndrd results in this type of model. The growth rte of consumption of mnufcturing output is equl to the mrginl productivity of cpitl minus the discount rte nd the rtio of consumption spending in the two goods is constnt. It is strightforwrd to see tht if fctor shres re constnt then there is stedy stte, tht is, there is no long run growth. 5. ONG-RUN GROWTH PATHS The previous section delt with equilibrium conditions for the model. Bsed on those conditions, this section focuses on the model s long-run pths. We begin this section with proposition. PROPOSITION. The model cn support both neoclssicl stedy-stte where 0, 0 * <, nd 0 < Y < ; or endogenous growth where 0 nd > 0, *, nd Y 0. 5

16 Totlly differentiting (4 nd mnipulting leds to the expression,. (8 ( The equtions (4 nd (8 give us insights into the model's stedy-stte properties. If 0 nd 0 * <, then it must be the cse tht, (9 0 A stedy-stte with 0 is possible nd, if 0 in the long-run (which must be the cse for 0, then it must lso be the cse tht 0. On the other hnd, if we llow tht converges to unity ( * then, the cpitl growth condition for this model is, (0 A. ( 0. Indeed, is constnt so δ(. Additionlly, s long s > the growth rte of is negtive nd its bsolute vlue converges to zero in the long run. Therefore, in the long run nd 0 It cn be demonstrted tht the rtio of to goes to ρ, so with, > 0 s long s ρ < A. So there re two bsic types of long-run equilibrium tht the model cn support. In the former cse, * <, true stedy-stte (in ll the vribles' levels is chieved; in 6

17 the lter cse, the production of sector one in the economy converges to "A", *, nd endogenous growth is chieved. Wht do these two long-run possibilities imply for ggregte lbor's shre (SH? 3 ( ( SH. ( PROPOSITION 3. Aggregte lbor's shre, SH, chieves stedy-stte vlue greter thn 0 nd less thn unity; if endogenous growth is chieved then 0 < SH <. In neoclssicl stedy-stte there re three determinnts of SH:, nd. determines how lbor is split between sector one nd sector two. The prtil derivtives SH SH re < 0, < 0 SH nd < 0. When endogenous growth results, ( cnnot be evluted t nd 0 nd, insted, the limiting vlue must be considered. We cn do this by using, (4 P λ. λ SH then becomes, The bseline endogenous growth models of this type were provided by Jones nd Mnuelli (990 nd Rebelo (99. 7

18 SH. P P ( I λ λ I λ λ which simplifies to, (3 SH λ. I λ Given tht I/ is constnt in the long-run 4, (3 is constnt between 0 nd despite the growing cpitl to lbor rtio in endogenous growth. PROPOSITION 4. In endogenous growth the reltive price of services, P, increses while its reltive shre in vlue-dded equls ggregte lbor's shre. As well, becuse > 0 nd 0, by (4 P must grow t the sme rte s. So the economy displys n ever-incresing reltive price of services widely-recognized feture of mny rel economies (e.g. De Gregorio et l. (994 nd Bumol nd Bowen (966. This ever-incresing reltive price of services, long with the ever-decresing shre of services in "physicl" output, results in constnt long-run vlue-dded shre for services (SSH. 5 Specificlly, in the long-run 4 In the long run Y A nd ρ so I A ρ ρ 5 "Physicl" here though perhps vgue in terms of services is ment to distinguish between shres in the totl Y Y s opposed to shres in vlue s determined by reltive prices. 8

19 (4 SSH SH. λ A λ ρ This connection between SSH nd SH is tied to the shre of totl lbor employed in the services sector going to unity. Tble reports, for vrious possible prmeteriztions, implied long-run lbor's shres for the model. Prmeteriztions re nchored to two bseline vlues for the prmeter ρ: 0.05 nd In generl, for lbor's shre to be in "conventionl" rnge (i.e., between 0.6 nd 0.8 the prmeter λ is implied to be below 0.5. However, humn cpitl considertions (which re not present in the model my dmit considerbly lower rel-world lbor's shres (e.g., s suggested by Mnkiw et l. (99. In ny cse, λ vlue below 0.5 is not t ll implusible nd tble does not suggest ny cler quntittive shortcomings of the model. We lso note tht, during endogenous growth, the growth rtes of nd re identicl while λ. Evluting (6 t then implies tht, (6 A ρ. nd λ( A ρ Aggregte consumption grows more slowly thn the cpitl stock, brodly conceived. 6. TRANSITIONA DYNAMIS In this section we elborte on the trnsition of the model economy to neoclssicl stedy-stte or endogenous growth pth. The expression for chnges in is 9

20 given by (8. The reltion between cpitl ccumultion nd the sectorl lloction of lbor is fundmentl to the dynmics of. Now, differentiting (6 nd (7 nd combing with (8 we get n expression for the growth rte of lbor llocted to sector one 6, ( ( (7. ( ( It cn be proved tht, strting from ny initil, 0, the growth rte of lbor in sector one is negtive then 0. 7 Implying tht, in generl, long the trnsition lbor migrtes from the production of good one to the production of good two. ike stndrd growth model, diminishing returns imply tht the incentives for investments (in both cpitl nd cpitl intensity vnish s ( A ρ pproches zero. Whether the economy settles into neoclssicl stedy-stte or chieves endogenous growth depends on whether converges to unity before ( A ρ converges to 0. In propositions 5 nd 6 we identify sufficient conditions for stgntion nd long-run growth to be optiml. PROPOSITION 5. If the initil cpitl lbor rtio for sector one is bellow one nd the initil technology is such tht 0 < (ρ/a then the economy does not present long run growth. 6 Detiled derivtions re provided in the ppendix. 7 From proposition we know tht long the trnsition there is negtive reltion between nd. 0

21 From eqution (6 it follows tht if the cpitl shre is constnt in stedy stte then the stedy stte cpitl lbor rtio is given by ( ρ * A. Now, from eqution ( it follows tht if then there re no incentives to increse the cpitl shre so is constnt. Finlly, if 0 < (ρ/a the cpitl lbor rtio of sted stte is smller thn one so the economy will never hve incentives to increse the cpitl shre. PROPOSITION 6. There exists criticl level of cpitl in the mnufcturing sector, **, such tht if the initil stock of cpitl for sector one is bove the criticl level, > ** then the economy present long run growth. First, note tht consumption growth rte depends on the interest rte. Now, s the stock of cpitl goes to infinity cpitl shre in sector two converges to one nd the growth rte of consumption in sector one converges to A ρ. Note lso tht when cpitl shre is endogenous the interest rte increses s the economy grows. Indeed, since A r the growth rte of the interest rte is given by, ( r r which cn be simplified to ( r r

22 r Therefore if < 0, 5 nd then 0 r nd If 0, 5 then ( 0, 5 so if 0, 5 nd, 3334 then r r 0 Since the cpitl lbor rtio in sector one depends positively in the welth of the economy propositions 5 nd 6 imply tht economies which re initilly rich converge to BGP while economies which re initilly poor converge to stedy stte. We now employ the bove dynmics to describe the evolution of SH. PROPOSITION 7. Aggregte lbor's shre, SH, converges to its stedy-stte vlue from bove. Eqution (8 cn be rewritten s, (8 SH Y X Y, Using eqution (0: SH ln k Y Y X Y, such tht the dynmics of SH depend on the sign of, ( (, which is lwys positive.

23 Strting from below the economy's stedy-stte/endogenous growth pth, ggregte lbor's shre converges to its long-run, constnt vlue from bove. This is not inconsistent with the pttern of US lbor's shre pictured in Figure. 8 Furthermore, during the trnsition, lbor's shre in mnufcturing flls while it grows in services. This is the cse despite the fundmentl role tht sector two plys in preventing ggregte lbor's shre from going to zero. Despite SH's trnsitionl decrese, the vlue-dded shre of services increses. PROPOSITION 8. Services shre in vlue-dded, SSH, converges from below to its stedystte vlue. The shre of services is, SSH (6, P P ( I which is notbly identicl to the expression for SH during long-run endogenous growth (but not for SH in generl. Expression (6 cn, s in Section IV, be mnipulted into, (7 SSH λ. I λ I/ decreses during the trnsition, so SSH increses. This is consistent with the US experience s evidenced by figure 3. 8 Beyond the US evidence is mixed on this point. Gollin (00 suggests tht there is no reltion between the level of lbor's shre nd the level of economic development. Also, Torrini (005 reports tht Itly's lbor's shre declined from the mid-970s through the mid-990s; nd Grrido Ruiz (005 reports tht Spin's lbor's shre incresed from 955 through

24 While the model ccounts for the reltive price nd vlue-dded shre of services incresing over time, it implies tht the quntity of services reches stedy-stte. Figure 5 shows tht, over the 960 to 005 time period, the increse in the rtio of services to mnufcturing vlue-dded ws the result of the increse in both the reltive (to mnufcturing price nd quntity of services. Buer nd boski (009 present similr evidence for US services reltive to the totl economy. (See their figure 7. However, s Buer nd boski (p. 6, in mny cses the mesurement of rel service quntities is only implicit. More importntly, perhps, our model bstrcts from ny technologicl chnge in service sectors nd is, on tht dimension, clerly counterfctul. 7. ONUDING REMARS The process of economic development is fmously chrcterized by certin gret mcroeconomic rtios, e.g. cpitl to output rtios, the return to cpitl, nd lbor's shre. These rtios hve displyed surprising stbility, trnscending both countries nd time periods. In the cse of ggregte lbor's shre, we hve motivted this pper by demonstrting tht, for the US cse, lbor s shre in mnufcturing hs been consistently flling while being offset by stble lbor s shre nd incresing vlue-dded shre in services. Blnced growth in the ggregte msks unblnced growth t the sectorl level. In this pper we develop model tht cn ccount for lbor s shres, both ggregte nd sectorl, bsed on the theory of induced innovtion. The theoreticl story cptures intuitively plusible beliefs bout rel economies. The process of industriliztion cretes incentives for mnufcturing firms to dopt lbor-sving 4

25 innovtions s wges rise. As this occurs, incresing mounts of lbor flow into service sectors. Despite the fct tht technologicl progress is often most evident in industril mchinery, service sectors constitute nd growing shre of the economy. Our model hs two-sectors: services where lbor nd cpitl re used ccording to eontief production function nd mnufcturing where production is obb-dougls t ny instnt but induced (lbor-sving innovtion cn occur. The model ccounts for severl fetures of the US economy: (i mnufcturing becomes incresingly cpitlintensive over time while (ii there is n increse in the reltive price nd production shre of services nd (iii ggregte lbor's shre converges from bove to non-zero vlue. At the sectorl level (iv lbor s shre in mnufcturing trends downwrd. 5

26 REFERENES Acemoglu, D. (00 Directed Technicl hnge. The Review of Economic Studies, 69 (4, pp Acemoglu, D. (007 EQUIIBRIUM BIAS OF TEHNOOGY Econometric, 75, (5, Acemoglu, D. nd Guerrieri, V. (008, "pitl Deepening nd Non-blnced Growth." Journl of Politicl Economy. 6, (3 pp Bumol, W. J. (967 "Mcroeconomics of Unblnced Growth: The Antomy of Urbn risis." Americn Economic Review, 57 (3, pp Bumol, W. J. nd Bowen, W. G. (966 Performing Arts: The Economic Dilemm. New York: Twentieth entury Fund. Boldrin, M. nd evine, D.. (00, "Fctor Sving Innovtion." Journl of Economic Theory, 05 (, pp Buer, F. J. nd boski, J. P. (009, The Rise of the Service Economy. NBER Working Pper 48. selli, F. nd olemn, J. (00, "The U.S. Structurl Trnsformtion nd Regionl onvergence: A Reinterprettion." Journl of Politicl Economy, 09, pp Drndkis, E. M. nd Phelps, E. S. "A Model of Induced Invention, Growth nd Distribution." Economic Journl, 76 (304, pp Echevrri,. (997, "hnges in Sectorl omposition Associted with Economic Growth." Interntionl Economic Review, 38, pp

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28 uznets, S. (965, "Quntittive Aspects of Economic Growth of Ntions: II." Economic Development nd ulturl hnge, 5 (Supplement, pp. 3-. itner, J. (000 "Structurl hnge nd Economic Growth." Review of Economic Studies 67, pp Mnkiw, N. Gregory, Dvid Romer, nd Dvid N. Weil (99, A ontribution to the Empirics of Economic Growth, Qurterly Journl of Economics 07, Mtsuym,. (99, "Agriculturl Productivity, omprtive Advntge nd Economic Growth." Journl of Economic Theory, 58, pp Murphy,., Shleifer, A. nd Vishny, R. (989, "Industriliztion nd the Big Push," Journl of Politicl Economy, University of hicgo Press, vol. 97(5, pges Murphy,., Shleifer, A. nd Vishny, R. (989b, "Income Distribution, Mrket Size nd Industriliztion." Qurterly Journl of Economics, 04, pp Ngi,. R. nd Pissrides,. A. (007, "Structurl hnge in Multi-Sector Model of Growth." Americn Economic Review, 97 ( pges Peretto, P. nd Seter J. J. (005, "Augmenttion or Elimintion?" Working Pper. Rebelo, S. (99, "ong-run Policy Anlysis nd ong-run Growth." Journl of Politicl Economy, 99 (3, pp Rowthorn, R. nd Rmswmy, R. (999, "Growth, Trde, nd Industriliztion." IMF Stff Ppers, 46, pp

29 Smuelson, P. A. (965, "A Theory of Induced Innovtion Along ennedy-weisäcker ines." Review of Economics nd Sttistics, November, 47 (4, pp Seter, J. J. (005, "Shre-Altering Technicl Progress." in Focus on Economic Growth nd Productivity. Huppuge: Nov Science Publishers. Torrini, R. (005 "Profit Shre nd Returns on pitl Stock in Itly: the Role of Privtistions Behind the Rise of the 990s." EP Discussion Pper No. 67. Young, A. T. (004 "bor's Shre Fluctutions, Bised Technicl hnge, nd the Business ycle." Review of Economic Dynmics, 7, pp Young, A. T. (006 "One of the Things We now tht Ain't So: Why US bor's Shre is not Reltively Stble." Working Pper, Jnury, Zeir, J. (998, "Workers, Mchines nd Economic Growth." Qurterly Journl of Economics, 998, 3 (4, pp Zeir, J. (006, Mchines s Engines of Growth Working Pper, Jnury 006. Zulet, H. (008 A Note on Scle Effects Review of Economic Dynmics, 004, 7 pp Zulet, H. (008 "Fctor Sving Innovtions nd Fctor Income Shres," Review of Economic Dynmics, 008, (4, pp Zulet, H. (007 "Why lbor income shres seem to be constnt?" Journl of Interntionl Trde & Economic Development, 0007, 6 (4, pp

30 FIGURES FIGURE. US AGGREGATE ABOR'S SHARE: Notes: lculted from ggregtion of 35 industries' dt. At the sector level, clcultions re of lbor's shre of vlue dded. At the ggregte level, industries weighted by their shre of totl vlue dded. 30

31 FIGURES (ONT. FIGURE. US MANUFATURING AND SERVIES SETOR ABOR'S SHARES Notes: Dt from 35-EM dtbse. Methodology described in Jorgenson et. l. (987. Mnufcturing includes "Food nd indred Products," Tobcco," "Textile Mill Products," "Apprel," "umber nd Wood," "Furniture nd Fixtures," "Pper nd Allied," "hemicls," "Petroleum nd ol Products," "Rubber nd Miscellneous Products," "ether," "Stone, ly nd Glss," "Primry Metl," "Fbricted Metl," "Nonelectricl," "Motor Vehicle," "Trnsporttion Equipment nd Ordinnce," "Instruments," nd "Miscellneous Mnufcturing" industries. Services include "Services," "Trde," nd "Finnce, Insurnce nd Rel Estte" industries. 3

32 FIGURES (ONT. FIGURE 3. US MANUFATURING AND SERVIES SETOR VAUE-ADDED SHARES Notes: Dt from 35-EM dtbse. Methodology described in Jorgenson et. l. (987. Mnufcturing includes "Food nd indred Products," Tobcco," "Textile Mill Products," "Apprel," "umber nd Wood," "Furniture nd Fixtures," "Pper nd Allied," "Print, Publishing & Allied," "hemicls," "Petroleum nd ol Products," "Rubber nd Miscellneous Products," "ether," "Stone, ly nd Glss," "Primry Metl," "Fbricted Metl," "Non-electricl Industry," "Electricl Industry," "Motor Vehicle," "Trnsporttion Equipment nd Ordinnce," "Instruments," nd "Miscellneous Mnufcturing" industries. Services include "Services," "Trde," nd "Finnce, Insurnce nd Rel Estte" industries. 3

33 FIGURES (ONT bor Shres 0.6 Sector One 0.4 Sector Two pitl-bor Rtio (Sector One FIGURE 4. ABOR SHARES AORDING TO THE MODE. 33

34 FIGURES (ONT. FIGURE 5. US REATIVE (TO MANUFATURING VAUE-ADDED, PRIE AND QUANTITY OF SERVIES Notes: Dt from 35-EM dtbse. Methodology described in Jorgenson et. l. (987. Mnufcturing includes "Food nd indred Products," Tobcco," "Textile Mill Products," "Apprel," "umber nd Wood," "Furniture nd Fixtures," "Pper nd Allied," "Print, Publishing & Allied," "hemicls," "Petroleum nd ol Products," "Rubber nd Miscellneous Products," "ether," "Stone, ly nd Glss," "Primry Metl," "Fbricted Metl," "Non-electricl Industry," "Electricl Industry," "Motor Vehicle," "Trnsporttion Equipment nd Ordinnce," "Instruments," nd "Miscellneous Mnufcturing" industries. Services include "Services," "Trde," nd "Finnce, Insurnce nd Rel Estte" industries. 34

35 TABES TABE SUMMARY STATISTIS FOR US MANUFATURING AND SERVIES SETORS Sttistic for Mnufcturing Services bor's Shre Men σ ρ x,mnufcturing ρ x,services Δ 960, Vlue-Added Shre Men σ ρ x,mnufcturing ρ x,services Δ 960, Notes: Dt from 35-EM dtbse. Methodology described in Jorgenson et l (987. Mnufcturing includes "Food nd indred Products," Tobcco," "Textile Mill Products," "Apprel," "umber nd Wood," "Furniture nd Fixtures," "Pper nd Allied," "Print, Publishing & Allied," "hemicls," "Petroleum nd ol Products," "Rubber nd Miscellneous Products," "ether," "Stone, ly nd Glss," "Primry Metl," "Fbricted Metl," "Non-electricl Industry," "Electricl Industry," "Motor Vehicle," "Trnsporttion Equipment nd Ordinnce," "Instruments," nd "Miscellneous Mnufcturing" industries. Services include "Services," "Trde," nd "Finnce, Insurnce nd Rel Estte" industries. 35

36 TABES (ONT. TABE BAANED GROWTH ABOR'S SHARES FOR VARIOUS PARAMETER VAUES A ρ 0.05 λ ρ Notes: bor's shres re clculted for different prmeter vlues nd eqution (. Reported vlue for A re bsed on the fct tht, for the existence of solution to the model, ρ < A < ρ. 36

37 Appendix A The growth rte of From eqution (5 it follows tht (A 0 Using eqution (8 nd rerrnging (A k ( k Where k. We know tht so ( ( Now, if 0, 38 then ( 0. Finlly from eqution ( if k, 85 then 0,38. 37

38 38 Appendix B The growth rte of ombining (6 nd (7, (B ( ( ( A B λ λ. Differentiting with respect to time: (B ln From equtions (7 nd (8, ln so ln nd ( cn be written s ( ( ombining with B (B3 ( ( k k A. Therefore, if 0 ( ( then 0.

39 39 Now, suppose tht 0 ( ( > nd 0 > then it must be the cse tht ( ( so ( (. B. Therefore, if 0 ( ( > nd ( ( then 0. Rerrnging eqution B3, (B4 ( ( ( (. Therefore, if 0 ( ( > nd ( ( then 0. From A, B nd it follows tht 0

40 40 From eqution (8 we know tht ( ( I ξ so (B5 ( ( (B6 ( ( δ ombining with 3 (B7 (. ( ( ( δ Rerrnging ( ( ( ( ( ( Therefore, ( ( ( ( ( ( ( ( ( ( ( (