Abatement R&D, Market Imperfections, and Environmental Policy in an Endogenous Growth Model

Transcription

1 MPRA Munch Personal RePEc Archve Abatement R&D, Market Imperfectons, and Envronmental Polcy n an Endogenous Growth Model Hsun Chu and Chng-Chong La Academa Snca, Tawan November 2013 Onlne at MPRA Paper No , posted 10. January :23 UTC

2 Abatement R&D, Market Imperfectons, and Envronmental Polcy n an Endogenous Growth Model* Hsun Chu Insttute of Economcs, Academa Snca, Tawan Chng-Chong La Insttute of Economcs, Academa Snca, Tawan Department of Economcs, Natonal Cheng Ch Unversty, Tawan Insttute of Economcs, Natonal Sun Yat-Sen Unversty, Tawan November 2013 Abstract Ths paper develops an endogenous growth model featurng envronmental externaltes, abatement R&D, and market mperfectons. We compare the economc performances under three dstnct regmes that encompass publc abatement, prvate abatement wthout tax recyclng, and prvate abatement wth tax recyclng. It s found that the beneft arsng from the prvate conduct of abatement wll be larger f the degree of the frms monopoly power s greater. Wth a reasonably hgh degree of monopoly power, a mxed abatement polcy by whch the government recycles envronmental tax revenues to subsdze the prvate abatement R&D s a plausble way of reachng the hghest growth rate and welfare. Keywords: abatement R&D, market mperfectons, endogenous growth JEL classfcaton: H23, O32, Q56 Correspondence: Hsun Chu, Insttute of Economcs, Academa Snca, 128 Academa Road, Secton 2, Nankang, Tape, 115 Tawan ext hchu0824@gmal.com

3 1. Introducton An mportant envronmental problem facng polcy-makers concerns how to reconcle sustanable growth wth lmted polluton. On the one hand, endogenous growth theory requres that most economc factors grow unlmtedly. On the other hand, f polluton, an nput or a by-product of output, were to grow to become nfntely large, any lfe or economc actvtes could hardly exst. To ensure sustanable growth, t s therefore essental for polluton to be abated wthn a survvable level n the long run. In the US, for example, the estmated total annual abatement expendture represents between 1.5% and 2.5% of GDP (Berman and Bu, 2001). Recent studes dealng wth the relatonshp between polluton abatement and envronmental growth, such as van Ewjk and van Wjnbergen (1995), Bovenberg and Smulders (1995, 1996) and Fullerton and Km (2008), treat abatement as technology or knowledge that could be accumulated and developed n a separate sector (.e., the envronmental R&D sector). 1 Snce knowledge s non-rval and has the characterstc of a publc good, the costs assocated wth the use of abatement knowledge as an nput are zero, whle knowledge creaton and accumulaton, by contrast, requre rval nputs and are costly. 2 Ths mples that, as stressed n Bovenberg and Smulders (1995), n a perfectly compettve market abatement R&D could not be rewarded so that no nnovaton n abatement technologes would be undertaken wthout the government s nterventon. Therefore, ths strand of the lterature essentally assumes that abatement R&D actvtes are publcly conducted by the government. 3 1 Alternatvely, some studes treat abatement spendng as a flow varable whch cannot be accumulated. See Gradus and Smulders (1993), Lgthart and van der Ploeg (1994), Smulders and Gradus (1996), and Bovenberg and de Mooj (1997). 2 See Smulders (1995) for a detaled dscusson. 3 One excepton s van Ewjk and van Wjnbergen (1995), n whch the accumulaton of abatement 1

4 In realty, however, we often observe that prvate and publc abatement actvtes coexst. Moreover, t s usually observed that abatement technologes are developed and produced n a prvate upstream sector, whch then sells abatement equpment (or blueprnts) to downstream pollutng ndustres (OECD, 2000; Greaker and Rosendahl, 2008). In the US, the prvate abatement nvestment s even greater than the publc abatement nvestment (OECD, 2007, Table 3). 4 Based on these observatons, t s qute far to say that a satsfactory model should be able to consder both possbltes of publc and prvate abatement R&D. Ths s what we am to do n ths paper. To be more precse, we buld up a theoretcal framework whch enables us to compare economc performance under the prvate and publc abatement nvestment regmes. Another key feature of our model s that we ntroduce mperfect competton n the ntermedate good market. As mentoned above, prvate abatement R&D requres ncentves, whch are not avalable n a perfect market because, f they were, the compettve frms would not be left wth any quas-rent for abatement R&D. Hence, we should resort to a dfferent market structure, such as an mperfectly compettve market. In the 1980s, several studes (e.g., Hart, 1982; Mankw, 1985; Blanchard and Kyotak, 1987) noted that market power n the prvate sector plays a crucal role n the performance of government polcy. More recently, Judd (2002) has also argued that mperfect competton s a key feature of dynamc modern economes. The emprcal evdence, on the other hand, suggests that pollutng ndustres are often equpped wth monopoly power (Beccarello, 1996; Consdne, 2001). To reflect the observed facts, a consderable body of studes have developed envronmental economc models whch take market mperfectons nto account (e.g., captal s costless (a byproduct of the accumulaton of human captal); thus prvate abatement takes place even wthout polcy nterventon. As s evdent, our model s structure s completely dfferent from thers. Furthermore, van Ewjk and van Wjnbergen (1995) do not deal wth publc abatement nvestment. 4 See Hatzpanayotou et al. (2005) for more detaled dscussons on prvate and publc abatement n the US and the UK. 2

5 Fullerton and Metcalf, 2002; Greaker and Rosendahl, 2008; Chang et al., 2009). Followng n the footsteps of these studes, ths paper develops an envronmental endogenous-growth model that features market mperfectons. More specfcally, the market structure we consder s characterzed by three vertcally-ntegrated sectors. Abatement technologes are developed n an upstream sector, whch sells the abatement knowledge (deas) to the ntermedate sector. The ntermedate sector, whch generates polluton, can generate a postve proft by exhbtng monopoly power, but t has to pay fees to the upstream sector for the rght to use the abatement knowledge. The perfectly compettve downstream sector produces a sngle fnal output by employng ntermedate nputs. Under such a settng, we are able to deal wth varous regmes ncludng publc abatement (hereafter, GA), prvate abatement wthout tax recyclng (PA), and prvate abatement wth tax recyclng (PAR) regmes. Moreover, we compare the relatve superorty n terms of economc growth and socal welfare among varous regmes. In partcular, we hghlght whether market mperfectons play an mportant role n determnng the relatve superorty. An nterestng ssue n ths paper s whether the prvate provson of abatement knowledge leads to a hgher growth rate than publc abatement. Our analyss shows that the answer crucally depends on two factors, namely, the monopoly power of the pollutng frms and the type of government spendng. We fnd that the greater the degree of the frms monopoly power, the larger wll be the beneft arsng from the prvate mplementaton of abatement. The reason for ths result s that the ncentve for the upstream sector to engage n R&D s precsely determned by the ntermedate frms proft. It s also found that growth wll be enhanced f the government dstrbutes ts tax revenues to boost (or drectly engage n) abatement R&D. Ths fndng mples that f envronmental tax revenues are used to provde publc goods or other prvate servces, a subsdy on prvate R&D abatement wll possbly be a good 3

6 choce to acheve hgher economc growth and socal welfare. The analyss of ths paper s also related to recent studes on the effect of envronmental taxaton on economc growth. The conventonal wsdom n the lterature (e.g., Huang and Ca, 1994; Lgthart and van der Ploeg, 1994; Grmaud, 1999) s often that there s an unavodable conflct between economc growth and the conservaton of the envronment n the economy. However, n recent years a growng body of lterature that proposes a postve growth effect of envronmental taxaton has accumulated. For example, n ther frequently cted artcle, Bovenberg and Smulders (1995) fnd that envronmental taxaton has an ambguous effect on economc growth by assumng that envronmental qualty s benefcal to nput productvty. 5 In departng from ths strand of the lterature, our analyss assumes that the pollutng nputs are purchased from abroad at a non-barganng prce. Accordngly, a hgher envronmental tax wll reduce the polluton by way of an accumulaton of abatement R&D, but the pollutng nputs wll reman unchanged. Snce an envronmental tax does not decrease the level of pollutng nputs (and thereby the margnal productvtes of other nputs), t undoubtedly spurs economc growth through the postve envronmental productvty effect. The remander of ths paper proceeds as follows. Secton 2 descrbes the model and solves the frms and households optmzaton problems. Secton 3 deals wth three dstnct regmes assocated wth dfferent abatement polces. Secton 4 presents our numercal results and compares the growth rates and the welfare levels among the three regmes. The fnal secton presents some concludng remarks. Techncal dervatons are relegated to the Appendx. 5 Other justfcatons contrbutng to a postve (ambguous) envronmental tax effect on economc growth nclude a postve externalty of abatement actvtes (Smulders and Gradus, 1996), an elastc labor supply (Hettch, 1998; Chen et al., 2003), the nternatonal accumulaton of envronmental assets (Ono, 2003), tax revenues recycled to subsdze ntermedate goods R&D (van Zon and Yetkner, 2003; Nakada, 2004), and the exstence of an ndetermnate equlbrum path (Itaya, 2008). 4

7 2. The model The economy we consder s composed of three parts: the households, the producton sectors, and the government. The producton sectors are characterzed by a perfectly compettve market for fnal goods and a monopolstcally compettve market for ntermedate goods. Moreover, ntermedate frms nvest n abatement R&D to mprove polluton reducton technology. In what follows, we n turn descrbe the structure of the economy Producton sectors In lne wth Benhabb and Farmer (1994) and Farmer and Guo (1994), the producton sde of the economy conssts of two sectors: a perfectly compettve fnal good sector and a monopolstcally compettve ntermedate goods sector. There s a contnuum of ntermedate goods y, [0,1], whch are used by a sngle representatve frm to produce a fnal good Y. Followng Dxt and Stgltz (1977), we specfy that the producton of the fnal good exhbts the followng constant returns-to-scale technology: θ 1 θ 0 Y = y d, θ [0,1). (1) As we wll show later, θ ndexes the degree of monopoly of the ntermedate good frms. Let π Y denote the proft of the fnal good frm and q be the prce of the th ntermedate good n terms of fnal output. 6 The maxmzaton problem of the fnal good frm can be expressed as: θ θ Y = 0 0, (2) Maxπ y d q y d y 6 It should be noted that the fnal good s treated as the numerare n ths paper. 5

8 The frst-order condton for ths problem yelds the demand functon of the th ntermedate good: y ( q ) Y 1 θ =. (3) It s qute clear from Eq. (3) that the demand functon of the th ntermedate good has a constant prce elastcty 1 / θ. When θ = 0, ntermedate goods are perfect substtutes n the producton of the fnal good, mplyng that the ntermedate goods sector s perfectly compettve. However, f 0 < θ < 1, ntermedate good frms face a downward-slopng demand curve so that they can exert monopoly power. Snce the man concern of our paper les n the mutual nteractons among envronmental externaltes, abatement R&D, and market mperfectons, n the followng analyss we focus our attenton on the case n whch 0 < θ < 1. Based on the fact that the fnal market s perfectly compettve, substtutng Eq. (3) nto Eq. (2) and mposng the zero-proft condton yelds: 1 0 θ 1 θ q d= 1. (4) The technology for producng the th ntermedate good s gven by: y = A( N) k α 1 α β e ly, A ( N) > 0, (5) 7 where A s an envronment-productvty functon, N s envronmental qualty, and k, l y and e are the captal, labor and emsson nputs used by the th ntermedate frm, respectvely. To reflect the postve producton externalty arsng from the envronmental qualty, Eq. (5) specfes that the output level of the ntermedate goods rses wth a better natural envronment. The proft functon of the th ntermedate frm π can then be expressed as: 7 It s worth notng that n a monopolstcally compettve market, although the producton functon s n an ncreasng-returns-to-scale form, ths does not necessarly mply negatve profts as long as the monopoly power θ s large enough (see, e.g., Benhabb and Farmer, 1994). In fact, as wll be seen later n our numercal example, the proft-output rato of an ntermedate frm s around 2.8%. 6

9 π = q y rk me ω l τ p, (6) y P where r s the captal rental rate, ω s the real wage, m s the prce of the pollutng nput, and τ P denotes a tax (or prce of permts) that the government leves on actual polluton p. We assume that ths envronmental tax evolves wth the aggregate captal,.e., τ P = τ K, where τ s a (constant) polcy parameter. 8 It s also assumed that the ntermedate frm purchases pollutng nput e from abroad so that the nput prce m s treated as exogenous throughout the paper (e.g., the pollutng nput can be thought of as f t were petroleum) Envronmental qualty The polluton generated n the producton process of the th ntermedate frm s of the form: 1 ε e p =, (7) H where H s the stock of abatement knowledge, and 1/ ε ( ε > 0 ) s the elastcty of polluton producton wth respect to abated pollutng nputs. In Eq. (7), polluton s specfed to be postvely related to pollutng nput e and negatvely related to abatement knowledge H. Accordngly, the total polluton P n the economy s the sum of pollutng emssons generated by all ntermedate frms: P 1 = p 0 d. (8) Followng Tahvonen and Kuuluvanen (1991), Bovenberg and Smulders (1995) and Fullerton and Km (2008), the natural envronment s treated as a renewable 8 To prevent the aggregate polluton from growng to nfnty (n whch case nothng could survve), we have to assume that the envronmental tax grows over tme. Ths s a commonly used assumpton n the lterature on envronmental and endogenous growth (see, e.g., Bovenberg and Smulders, 1995; Nelsen et al., 1995; Ono, 2007; Fullerton and Km, 2008). Smulders (1995) provdes a detaled dscusson on ths pont. As for the realstc concern, the effectve tax rates on fuel ol, coal and gas ncreased gradually durng the perod n many European countres (Andersen and Ekns, 2009). 7

10 resource, and can hence be specfed to grow and deplete n the followng manner: N = bn(1 N) P, (9) where a dot denotes the rate of change wth respect to tme, b s a parameter that captures the degree of ecologcal regeneraton, and the term bn( 1 N) reflects the regeneraton capacty of the envronment, whch mght ntally ncrease wth a larger N but wll eventually declne when N exceeds a threshold value. Eq. (9) ndcates that a rse n the level of polluton s assocated wth a declne n envronmental qualty n the next perod. In the steady state, the envronmental qualty remans constant over tme snce polluton equals the regeneraton capacty of the envronment ( P = bn( 1 N)). We restrct our analyss to a symmetrc equlbrum n whch k = k, e = e, l y= l y, p = p, π = π, y = y, and q = q for all. As a result, from Eq. (1) we have θ 1 θ 0 Y = y d = y. Wth y= y and q q =, the proft of the fnal good frm stated n Eq. (2) can then be expressed by π = ( 1 q y. Gven that the Y ) fnal good sector s perfectly compettve, the representatve fnal good frm earns zero proft (.e., π = 0) n equlbrum. Y Accordngly, the zero-proft condton n the fnal good sector π Y= 0 requres that q = 1. Furthermore, let K, E, and L y denote the aggregate captal stock, aggregate emsson, and aggregate labor hred by the ntermedate frms. Then, we have: 1 0, K= k d= k 1 0, E= e d= e 1 Ly= l 0 yd= ly. As a consequence, the ntermedate frms frst-order condtons can be arranged as: Y ( 1 θ ) α = r, (10) K 8

11 Y ε 1 (1 θ )(1 α ) ε = τ P + mε HP, (11) P Y ( 1 θ ) β = ω. (12) L y Eqs. (10)-(12) ndcate that, gven the envronmental qualty and abatement knowledge, frms equate the margnal revenue of the captal, polluton and labor to ther respectve margnal cost. Of partcular note, the rght-hand sde of Eq. (11) represents the margnal cost of polluton, and contans two parts. The frst part s the envronmental tax mplemented by the government τ p. The second part means that, n addton to the taxaton, n rasng one unt of polluton the frm needs to purchase 1 ε HP ε unts of the drty nput, and thus pay the cost mε HP ε 1. It follows from Eq. (11) that a larger abatement knowledge rases the margnal cost of polluton; thereby reducng the use of t Households There s a contnuum of dentcal nfntely lved households, each of whch derves postve utlty from both consumpton C and envronmental qualty N. Populaton s statonary and normalzed to unty for smplcty. The representatve household utlty s gven by: η 1 σ ( CN ) 1 W = exp[ ρt ] dt, (13) 0 1 σ where W s the dscounted lfetme utlty of the representatve household, ρ s the subjectve tme preference rate, σ s the ntertemporal substtuton elastcty, and η denotes the weght n terms of the utlty attached to the envronment or, as proposed by Fullerton and Km (2008), the consumpton externalty n relaton to the envronment. 9 It s equvalent f the frm chooses the drty nput e nstead of polluton p. In ths case, Eq. (11) 1 ε should be rewrtten as (1 θ )(1 α ) Y / E = τ PP / ε H + m. Then, by mposng E= P ε H we can obtan the same result as reported n Eq. (11). 9

12 Each household s endowed wth a fxed amount of labor L, whch s allocated to producton between the ntermedate goods ( L y ) and research ( L H ). We assume that labor s homogeneous and perfectly moble across sectors. A unque wage rate must, as a result, hold. The representatve household receves ncome by supplyng labor and captal servces to frms. In addton, t receves profts π (n the form of dvdends) and lump-sum transfers G from the government. Fnally, a captal ncome tax rate τ K s leved on the captal rentals. Accordngly, the budget constrant faced by the representatve household can be expressed as: K = (1 τ K ) r K + ωl + π + G C. (14) The optmum condtons for the representatve household wth respect to consumpton and physcal captal are: σ η (1 σ ) C N = λ, (15) λ / λ = ρ (1 τ ) r, (16) K where λ s the shadow prce of the prvate captal stock Abatement R&D actvty As noted earler, polluton abatement technologes are regarded as knowledge and can thus be accumulated over tme. The creaton of knowledge requres efforts and tme so that nnovaton and nventon are acts of nvestment (Smulders, 1995). In lne wth Romer (1990) and Jones (1995), we assume that new deas are developed by the labor nput and the exstng stock of deas. To be more precse, abatement knowledge H s specfed to be created n the followng manner: H = δ L H, (17) H where δ s a productvty parameter and L H denotes the labor nput for R&D actvtes. In our model, for long-run growth to be feasble and sustanable, the balanced 10

13 growth path (BGP) n the steady state s characterzed by: Y C K H E = = = = = g, N = P = 0, (18) Y C K H E where envronmental qualty and polluton are lmted n a physcal sense, and all other economc varables grow at a common constant endogenous growth rate g. 3. Publc versus prvate abatement Two possble facts concernng the R&D actvtes and the government budget constrant are consdered n ths secton. by ether prvate frms or the government. Frst, the R&D actvtes can be conducted Second, f the R&D actvtes are engaged n by prvate frms, the government may or may not subsdze the R&D actvtes. Based on these two knds of possblty, our analyss can be classfed nto three dfferent regmes: publc abatement (GA), prvate abatement wthout tax recyclng (PA), and prvate abatement wth tax recyclng (PAR). Snce the government budget constrant vares wth each of the three regmes, the BGP may dsplay qute contrastng results among these three regmes. In what follows, we dscuss three types of regmes n turn Publc abatement Under the GA regme, the R&D actvtes are engaged n by the government. Under such a stuaton, the balanced budget constrant faced by the government can be expressed as follows: G + q H =τ rk + τ P, (19) H K P where new abatement knowledge Ḣ s produced accordng to Eq. (17), and q H s the prce of abatement knowledge relatve to fnal goods. Eq. (19) states that the government receves ts revenues n the form of captal taxes τ KrK and polluton taxes τ P P to fnance ts provson of lump-sum transfer payments to the household 11

14 G and publc abatement nvestment q H H. Eq. (19) s consstent wth the Fullerton and Km (2008) specfcaton, n whch abatement knowledge s regarded as a publc good and can be used freely by frms. Notce that snce labor s perfectly moble, the margnal revenue product of labor should be the same between two sectors. That s: Y H ( 1 θ )β = qh. (20) L L y H Usng Eqs. (17), (19), and (20) together wth the household budget constrant yelds the resource constrant of the economy: K = Y C me. (21) Imposng the condtons for a BGP and defnng the followng transformed varables: h = H / K, c = C / K, w = ω / K, and φ = G / K, the macroeconomy along the BGP equlbrum can then be descrbed by the followng set of equatons: 1 = (1 τ )(1 θ ) α ( ) ρ σ, (22) (1 α ) ε 1 α β g K A N P h Ly g δ ( L L ), (23) = y (1 α ) ε 1 α β y ( 1 θ )(1 α ) εa( N ) P h L = τp + εmh P, (24) ε (1 α ) ε 1 α β ( 1 θ ) βa( N ) P h Ly = w Ly, (25) c (1 α ) ε 1 α β ε = A N ) P h Ly g mh P (, (26) P = bn (1 N ), (27) τ K (1 θ ) αa( N ) P ( 1 α ) ε 1 α β h L + = + ( y τp φ w L Ly ), (28) where the superscrpt * denotes the steady-state value. The macroeconomc model expressed n the above seven equatons determnes seven unknowns,.e., h, c, P, N, L y, w, and g. Snce the system s n a 12

15 nonlnear form and s too complcated to enable a closed-form soluton to be obtaned, we present our results va numercal analyss Prvate abatement R&D Ths subsecton deals wth both the PA and PAR regmes. Under these two regmes, the R&D actvtes are undertaken by prvate frms. Accordngly, we frst need to formulate how abatement knowledge s produced n the R&D sector. To acheve ths purpose, n lne wth the standard R&D lterature ncludng Romer (1990) and Jones (1995), we assume that there are three vertcally-ntegrated sectors n ths economy. The abatement technology s developed and produced n an upstream R&D sector, whch hres labor to engage n nnovaton actvty and then sell the abatement technology (blueprnts) to the mdstream ntermedate (pollutng) sector. The downstream fnal good sector produces a sngle fnal output by employng a set of ntermedate nputs. In the R&D sector, at each moment there exsts an R&D frm producng and sellng the lcense for the rght to use the abatement technology. It s the frm that makes the latest development, namely, the state-of-the-art technology for H. 10 The R&D frm hres labor L H to develop the abatement technology accordng to the producton functon reported n Eq. (17). The proft functon of the R&D frm s: π = q H (1 s) ω L, (29) 11 H H H 10 In the vast lterature on R&D-based growth models, the products of R&D (knowledge or blueprnt) are not homogeneous but sector-specfc. A blueprnt may relate to a new varety or a better qualty of a gven varety, but n any case t wll be used by a unque monopolst. Ths mples that there are many frms n the R&D sector and the number of frms s determned by the zero proft condton. In the present paper, however, the abatement technology s a homogeneous good. Hence, for the R&D sector to be able to extract all the profts of the ntermedate frms (as wll be assumed below), t must be the case that at each moment there s only one frm that sells the abatement technology. We would lke to thank an anonymous referee for brngng ths pont to our attenton. 11 Snce the technology s non-rval, the margnal cost of supplyng Ḣ to one more ntermedate frm s zero. Ths means that the R&D sector wll sell ts product to each and all of the ntermedate frms. Therefore, n Eq. (29) the revenues of the R&D sector should be x qh Ḣ where x denotes the number of the ntermedate frms. Notce that we have assumed x= 1 and thus x s gnored n Eq.(29). 13

16 where s s the subsdy rate for the labor employment of the R&D sector. Followng the lterature on R&D-based endogenous growth models (Grossman and Helpman, 1991; Barro and Sala--Martn, 2004), two mportant assumptons are made. proft. 12 Frst, there s free entry nto the R&D sector so that the R&D frm earns zero Second, the R&D sector has prcng power; t charges a prce for ts product (blueprnt) at whch the ntermedate frms are ndfferent between buyng the blueprnt (to produce the ntermedate product) and not buyng t (to leave the market). Accordngly, n each perod the prce of technology q H must be set to the level at whch the technology generated n the R&D sector extracts all the proft of the ntermedate frms, whch can be expressed by: 1 H = π 0 d= π. (30) 13 q H Eq. (30) says that the lcense fee for new abatement knowledge must be equal to the net proft that a monopolstc frm can earn. 14 Notce that because we have a contnuum of (both R&D and ntermedate) frms n the nterval (0,1), the total payment to the R&D sector s the sum of all ntermedate frms profts. Under the PA regme, the government does not subsdze R&D actvtes, and hence ths regme corresponds to s = 0 n Eq. (29). Alternatvely, under the PAR regme, the government provdes R&D subsdes, and hence ths regme s assocated wth s > 0 n Eq. (29). We now deal wth these two regmes n turn Prvate abatement R&D wthout tax recyclng 12 As ponted out n Grossman and Helpman (1991), ths assumpton mplctly supposes that potental entrants or outsders can, va nspecton of the goods n the market, completely learn about the state of knowledge (due to the publc-good characterstcs of knowledge) to mount ther own research efforts and then replace the exstng R&D frm. 13 In the standard R&D-based endogenous models, the ntermedate frms make a one-off payment to the R&D sector for the rght to use the knowledge forever after. However, n our model the ntermedate frms need to make flow payments to use the abatement knowledge n every perod. In subsecton 5.1 we wll dscuss ths pont more n detal. 14 Accordng to Kamen and Tauman (1986), a patentee can lcense her nventon to an olgopolstc ndustry by means of a fxed fee or a per unt royalty. It should be noted that n ths paper the prce of abatement knowledge can be regarded as a fxed lcense fee that an ntermedate frm should pay to the R&D sector n exchange for the rght to use abatement knowledge. 14

17 Under the PA regme, the government nether nvests n R&D nor subsdzes t (.e., s = 0 ). Hence, the government budget constrant s gven by: G= τ rk+ τ P. (31) K P Snce the proft of the ntermedate frms s allocated to pay for the use of abatement knowledge, no dvdends are dstrbuted to the households. Accordngly, the household budget constrant can be rewrtten as: K = (1 τ K ) rk + ωl + G C. (32) Based on the above condtons, t can be shown that the resource constrant reported n Eq. (21) stll holds n the PA regme. At the BGP equlbrum, the economy s descrbed by Eqs. (22)-(27) together wth the followng condton (mathematcal dervatons are provded n Appendx A): g δ [ 1 (1 θ )( α + β) (1 θ )(1 α ) ε ] * δ (1 ε ) mh P = Ly (1 θ ) β w ε. (33) Prvate abatement R&D wth tax recyclng Under the PAR regme, the government subsdzes the prvate abatement R&D nstead of drectly conductng the R&D actvtes. Hence, the government budget constrant becomes: G+ sω L = τ rk+ τ P. (34) H K P After some manpulatons, Eqs. (33) and (34) can be modfed as: g δ[1 (1 θ )( α + β) (1 θ )(1 α ) ε ] = L (1 s )(1 θ ) β y δ (1 ε ) mh P (1 s ) w ε, (35) τ K (1 θ ) αa( N ) P (1 α ) ε h 1 α L * β y + τp = φ + s w ( L L ). (36) * y The BGP economy can then be descrbed by Eqs. (22)-(27), (35), and (36), where eght unknowns h, c, P, N, L y, w, g, and s are solved n eght equatons. 15

18 4. Quanttatve results A numercal analyss s presented n ths secton to trace how the growth rate and welfare level wll react followng a change n an envronmental polcy under the three regmes. To construct an llustratve example, we choose benchmark parameter values that are wthn the plausble ranges used n the lterature. Table 1 lsts the benchmark parameter values, and some nterpretatons concernng these parameter confguratons should be provded here. Frst, n lne wth Fullerton and Km (2008), we specfy the envronmental productvty functon as beng of the form A ( N) = γ N and set the followng parameters: γ = 0. 77, α = 0. 24, b = 0. 04, η = Second, the values σ = 1. 5, β = 0. 67, and ρ = are based on the calbraton exercses n Lucas (1990) and Stokey and Rebelo (1995). The monopoly power ndex θ= 0.35 s calbrated such that the resultng proft rato n our economy s 2.8%, and conforms to the proft rato of a typcal US ndustry; see, e.g., Basu and Fernald (1997) and Guo and Lansng (1999). 15 Table 1 : Baselne parameters Parameter Value Parameter Value α σ ε γ τ K τ m b β ρ η θ φ δ L Thrd, to reflect the model s plausblty we choose τ = (based on the K 15 We choose the GA regme as our baselne economy when calbratng. 16

19 estmate reported by Auerbach, 1996) and φ= 0.06 as polcy parameters. Ths n turn mples that the government s spendng as a proporton of output s around 8%, and hence ths numercal value les wthn the reasonable nterval n the lterature (see e.g., Gal, 1994). Fourth, the polluton tax relatve to the captal stock τ = τ P / K s 30 so that the rato between the tax revenues and output s about 17%. 16 Ffth, as for the polluton converson parameter, whle Bovenberg and Smulders (1995) smply assume that ε s equal to 1, Fullerton and Km (2008), however, relax ths assumpton and allow ε to vary from 0.6 to 0.9. A relatvely low value of ε means that the elastcty of polluton producton wth respect to abated pollutng nputs s hgh. That s, rasng the level of pollutng nputs wll not only ncrease polluton, but wll also accelerate the generaton process. More specfcally, the nvestment n abatement knowledge wll be more mportant f the elastcty s hgher. To hghlght the role of abatement nvestment, we set ε = 0. 6 as our parameter value. Fnally, the values of ( m, δ, L) are calbrated so that the balanced growth rate s 3.12%, whch s close to the average growth rate for the past 30 years n the US Comparson of three regmes Table 2 presents the key endogenous varables n the benchmark case. Our goal s to compare the steady state growth rate and the welfare level under the three regmes. As shown n Table 2, n the GA regme, the steady state growth rate s about 3.12%. In the PA regme, the government swtches the abatement spendng to a lump-sum transfer, and the ntermedate frms are forced to purchase the lcense fee for abatement knowledge from the R&D frms. Under such an arrangement, the growth rate declnes to 1.43% n response. However, f the tax revenues are recycled to subsdze the R&D sector, the growth rate of 3.55% s ranked the hghest among 16 Supposng that K = 1, n the steady state we have P = and Y = Accordngly, the rato of polluton tax revenues to output s (30)(0.0042)/ = 17%, whch s n lne wth the value 17.8% n Fullerton and Km (2008). 17

20 the three regmes. In addton, as shown n Table 2, the rank of the abatement knowledge among the three regmes s the same as that of the balanced growth rate. The ntuton behnd ths concdent rankng follows from the fact that, as ndcated n Eq. (17), an accumulaton of abatement knowledge unambguously enhances economc growth. Table 2: Comparson of three regmes Envronmental Polluton Abatement Growth Welfare qualty knowledge rate (%) GA PA PAR However, by comparng the value of polluton under the three regmes, t may be somewhat surprsng that a hgher abatement nvestment s assocated wth more polluton. The economc ntuton behnd ths result can be explaned as follows. Other thngs beng equal, a better envronment (less polluton) should be acheved f the frm has access to more abatement knowledge. However, once the government drectly provdes or ndrectly subsdzes abatement knowledge, the cost of polluton-reducng actvtes wll declne. Cheaper abatement knowledge gves the frms an ncentve to use more pollutng nputs, whch worsen the envronmental qualty. In our model, t seems that the latter effect domnates the former, and thus abatement knowledge and polluton receve the same rankng among the three regmes. We now turn to compare the level of welfare under the three regmes. We focus on the welfare along the BGP, denoted by W, whch s calculated by usng Eqs. (13) and (26): 18

21 1 1 1 σ η (1 σ ) 1 W = C0 N, (37) 1 σ (1 σ ) g ρ ρ (1 α ) ε 1 α β where C0 = [ A( N ) P h Ly g mh P ] K0 s the endogenously determned level of consumpton on the BGP, and K 0 s the ntal (predetermned) captal stock. ε Wthout loss of generalty, we set K 0 = 1 n our numercal model. We follow Barro (1990) to assume that the economy jumps to the BGP rght from the begnnng, whch means that gven a predetermned ntal amount of captal K 0, the levels of all endogenous varables (ncludng C 0 ) are smultaneously determned. Ths assumpton mples that the level of welfare expressed n Eq. (37) does not consder the transton dynamcs and thus our quanttatve results only apply to the BGP. The numercal values of socal welfare under the three regmes are reported n the last column of Table 2. It s clear that the rankng of the level of welfare among the three regmes s the PAR regme, the GA regme and the PA regme n that order. The polcy mplcaton s that, gven the baselne parameter values, the growth rate and welfare are the lowest f abatement actvtes are conducted prvately wthout government nterventon. Nevertheless, they could be both enhanced once the government engages n publc abatement or provdes ncentves for prvate abatement R&D. If the latter s the case, the growth rate and welfare could acheve the hghest levels Parameters wth polcy mplcatons It should be noted that the numercal results regardng the growth rate and welfare are examned only under the baselne parameter values. An nterestng concern s how our numercal results are related to the values of the parameters. To ths end, n what follows we propose three relevant parameters that need to be consdered by the polcy-makers Market mperfecton 19

22 An early but nsghtful pont of vew by Schumpeter (1942) s that more competton would erode the monopolstc rents, and thus reduce the ncentve to undertake R&D actvtes. We stand n lne wth ths perspectve and extend t to an economy n whch R&D nvestment s used to control the polluton. To be more specfc, n our model the decentralzed economy suffers from two market falures. The frst concerns the envronmental externalty. Polluton harms human health and productvty, but s not accounted for by the pollutng frms. The second has to do wth the market mperfectons regardng the supply of ntermedate goods. However, these mperfectons can become the motvaton for people to engage n R&D n the case where the pollutng frms need to pay a lcense fee to use abatement technologes, but not n the case where there s publc provson of free abatement knowledge. In other words, only n the regme of prvate abatement (PA and PAR) can the second market falure (mperfect competton) remedy the frst market falure (the envronmental externalty). Based on ths observaton, market mperfectons play a crtcal role when ntegratng abatement nvestment wth prvate ncentves. Fg. 1 exhbts the effects of varyng the monopoly power parameter (θ ). A rse n θ s assocated wth an ncrease n both the balanced growth rate and the level of welfare under both the PA and PAR regmes. To explan ths result, by usng Eqs. (29), (30) and π H= 0 we obtan π = ( 1 s) ωlh, where a hgher proft mples more employment of research workers. As noted prevously, the R&D frms can prce ther deas exactly to extract all the proft of the ntermedate frms. For ths reason, a hgher θ (as well as the proft of the ntermedate frms) means that more resources are contrbuted to hre labor n the R&D sector, thereby stmulatng the balanced growth rate. In the GA regme, on the contrary, the effects of θ on the long-term growth rate and welfare are almost neglgble. The reason for ths result stems from the fact that 20

23 n the GA regme abatement nvestment s undertaken only by the government, and thus has no drect relatonshp wth the frms proft. More specfcally, the numercal results depcted n Fg. 1 ndcate that, under both the PA and PAR regmes, the greater the degree of mperfect competton, the larger the beneft of prvate abatement wll become. When θ s large enough, both the balanced growth rate and socal welfare for the PA regme may possbly exceed those for the GA regme. Moreover, f the government can recycle ts tax revenues to provde ncentves for prvate abatement R&D, both economc growth and welfare wll be further enhanced The type of government spendng We now dscuss the parameter related to the publc sector. In ther recent study, Fullerton and Km (2008) show that government spendng on transfer payments (φ ) s a non-envronmental parameter wth mportant mplcatons for envronmental polcy. The effect of changng φ s depcted n Fg. 2. It s shown that, n response to an ncrease n φ, the growth rate and socal welfare declne n both the PAR and GA regmes but reman unchanged n the PA regme. The ntuton for ths result s straghtforward. In the PA regme all tax revenues are returned to the households. The abatement nvestment whch strs up economc growth comes only from the monopolstc rents so that φ has no role n economc actvtes. However, under both the PAR and GA regmes, economc growth becomes closely related to φ snce the government uses ts tax revenues to stmulate (or drectly conduct) abatement R&D. A postve value of φ ndcates that part of the revenues from the envronmental tax must be spent on transfer payments. The greater need for transfer payments mples that less tax revenue wll be used n abatement R&D, and hence wll lead to a deteroraton n the balanced growth rate. As s evdent, our results ndcate that the concluson n Fullerton and Km (2008) s vald under both the PAR and GA regmes but nvald under the PA regme. 21

24 The effect of an envronmental tax We now turn to nvestgate the effect of an envronmental tax polcy. It s shown n Fg. 3 that rasng an envronmental tax can stmulate economc growth as well as reduce the level of polluton. Bovenberg and Smulders (1995) have clearly ponted out the two opposng forces whereby the envronmental polcy affects the long-term growth rate. Frst, a lower level of pollutng nputs decreases the productvty of reproducble nputs, thereby lowerng economc growth. Second, a reducton n polluton mproves the envronmental qualty, whch benefts productvty and economc growth. As a result, Bovenberg and Smulders (1995) suggest that the envronmental tax has an ambguous effect on economc growth. In our model, however, by referrng to Eq. (6), the polluton nputs are purchased from abroad at a gven prce so that a hgher envronmental tax can smultaneously reduce the polluton p= p ) but keep the pollutng nputs e= e ) unchanged. ( Under such a stuaton, a tghter envronmental polcy no longer decreases the productvty of captal and labor, because a lower level of polluton n producton s ( offset by more abatement knowledge. Hence, our model only presents the second envronmental qualty effect. To hghlght the mportance of ths envronmental qualty effect, we consder the alternatve value γ = 0 to ndcate that producton gans no extra beneft from a better envronmental qualty. 17 The numercal results are depcted n Fg. 4. It can be seen that, n the absence of an envronmental externalty, rasng an envronmental tax has no effect on the long-term growth rate whle t reduces polluton. Comparng Fg. 3 wth Fg. 4 enables us to realze that whether or not envronmental polces affect economc growth crucally depends on the presence of a postve envronmental 17 It should be noted that γ=0 only removes the envronmental externalty n relaton to producton; nonetheless the externalty n regard to the households utlty s always present. 22

25 externalty. Now we deal wth the welfare analyss. Fg. 3 and Fg. 4 show that the welfare level s ncreasng wth the envronmental tax, regardless of whether a postve envronmental externalty s present or not. As dscussed earler, n the case of γ = 0 a tghter envronmental polcy has no effect on long-term growth. However, t can stll nfluence the level of welfare because, wth the growth rate unchanged, a hgher envronmental tax mproves the envronmental qualty and thus unambguously enhances the welfare level. If the representatve household does not care about the envronmental qualty ( η = 0 ), t s an obvous conjecture that envronmental tax cannot play any role ether n governng the balanced growth rate or the welfare level. 5. Dscussons and extensons In ths secton we provde two detaled dscussons of prevous settngs whch may need further debate. The frst one concerns the propertes of the abatement technology, and the second one has to do wth why our model makes a dstncton between polluton emssons and drty nputs. In addton, we also conduct two nterestng extensons. In the frst extenson we examne the effects of the envronmental tax under an alternatve settng of polluton. In the second extenson we nvestgate the mpact of an ncrease n tarffs that rases the prce of polluton nputs The propertes of the abatement technology/knowledge What s the abatement technology/knowledge? In our model, the concept of the abatement knowledge s not much dfferent from that n the prevous lterature, such as Bovenberg and Smulders (1995, 1996) and Fullerton and Km (2008). It generally represents the amount of resources that the 23

26 economy has devoted to developng or applyng the new techncal knowledge whch enables producton to occur n a less pollutng way. As for practcal concerns, the abatement technology mght, as an example, refer to the CO 2 capture and storage (CCS) system, and therefore the value of H represents the avalable resources for the adopton of the CCS technology. Wthn the model, a plausble way of thnkng how the abatement technology works mght be to consder that the ntermedate frms are endowed wth a common abatement machne, and that H s concerned wth the technology to operate t. As such, a hgher level of H s assocated wth a superor technology, and hence leads the ntermedate-goods frm to mplement the abatement machne better so as to further reduce polluton Non-rvalry Gerlagh et al. (2008) establsh an endogenous growth model ncorporatng the R&D, envronmental polcy and nnovaton polcy. (ntermedate) producers of abatement equpment. In ther model, there are many The upstream R&D frm creates new deas that expand the varetes of the ntermedate producers, and then sells the new technology emboded n these rval goods. It should be emphaszed that our settng s dfferent from thers because n our model the varety of the ntermedate goods s constant. The role of market mperfecton n ths economy s to allow ntermedate frms to have a postve proft such that they can pay for abatement R&D. New deas, the products of R&D, are about the technology/knowledge used to abate polluton, whch are featured wth non-rvalry due to the property of knowledge. It s not specfc for each ntermedate good and thus could be used by all ntermedate frms once produced. Due to non-rvalry, when the R&D frm produces the state-of-the-art technology Ḣ, t sells the same blueprnt to each and all of the ntermedate frms. After payng for Ḣ, an ntermedate frm has the rght to use that technology forever, but for the next perod t has to pay another fee for the rght 24

27 to use newly-generated technology. In other words, n each perod the frms pay for new technology Ḣ, but use the whole of the exstng stock of technology H to abate polluton Incentves and ndvsble technology It s worth dscussng the ncentves (or necessty) to use the abatement technology. Frst of all, we need to explan why ntermedate frms must pay all of ther profts to buy the abatement technology. In lne wth the lterature on R&D-based endogenous growth ncludng Romer (1990) and Jones (1995), the upstream R&D frms have the prcng power to determne the prce of ther blueprnts. Specfcally, the R&D frms unlaterally determne the prce of ther nnovatons, and the ntermedate frms then determne whether or not to buy blueprnts. Therefore, the R&D sector wll charge a prce that fully extracts the profts of the mdstream frms. We then turn to explan why the ntermedate frms could not choose to use dvsble technology. economc ratonales. Ths specfcaton can be justfed by the followng two The frst ratonale s that the government enforces the utlzaton of the latest abatement technology by, for example, mposng strcter polluton standards. Ths regulaton forces the frms to leave the market f they stop usng the latest abatement technology. 18 The second ratonale s that we can assume that the technology generated n each nstance has a property of ndvsblty. Ths assumpton rules out the possblty that the ntermedate frm chooses to use a partton of Ḣ. More specfcally, for the ntermedate frm, there are only two choces: to accept the prce of the blueprnt and use the ndvsble technology, or to 18 It would be nterestng to further examne the effect of ths knd of regulaton on macroeconomc performance. However, due to the space constrant, we would lke to leave ths to a future study. For an analyss on the mplementaton of the optmal path n a growng economy wth polluton permts, see, for example, Grmaud (1999). 25

28 reject the prce of the blueprnt and stop usng the abatement technology (and thus leave the market). 19 The ndvsblty of the abatement technology stems from the fact that new technology and old exstng technology are often hghly correlated. If a frm does not buy all of the new technology n ths perod, t wll be very costly for t to utlze (upgrade to) the newest technology n the next perod. analyss, we assume that ths cost s too hgh to be consdered. To smplfy the Hence, the frms actually confront an all-or-nothng decson regardng the use of the technology The dstncton between polluton emssons and drty nputs In our model, as mentoned above, a fxed mport prce of pollutng nputs ( m ) s the key to screenng out the tradtonal negatve polcy effect on long-term growth n the lterature. Hence, t s worthwhle dscussng why we need to make a dstncton between polluton emssons and drty nputs, and to ntroduce m nto our model. Theoretcally, although numerous studes model polluton based on the concept of a drty nput, there are several reasons for treatng them dfferently. 20 Frst, polluton (.e., drty ar, messy water or nose) s not drectly used n the producton process, whle the drty nputs (.e., petroleum or chemcals) are. Second, abatement knowledge can hardly play any role n the polluton transformaton process f we mx the two. Thrd, and most mportantly, polluton harms human health but s not nternalzed by the prvate agents and thus needs to be prced by the government, whle drty nputs should be prced by the market, because they are producton factors just lke other clean nputs. Hence, we allow for τ P and m to denote, respectvely, the prce of polluton and drty nputs. 19 Once a frm stops usng abatement technology, as tme goes on, the burden of the envronmental tax wll become nfntely large, thereby leadng the ntermedate frms to have a negatve proft and forcng them to leave the market. 20 Some studes (e.g., Lgthart and van der Ploeg, 1994; Smulders and Gradus, 1996; and Bréchet and Mchel, 2007), on the other hand, treat polluton as a by-product of captal or fnal output. However, under such a stuaton, snce an envronmental tax leved on polluton s equvalent to that leved on physcal captal or output, t mght be dffcult to tell whether economc growth s affected by an envronmental tax or by a smlar captal (output) tax. 26

29 To be more specfc, supposng that there s no pollutng nput prce, from Eqs. (5)-(7) and q = 1 (the zero-proft condton n the fnal good sector) we have: π α ε (1 α ) 1 α H β y = A( N) k p l rk ωl τ p. (38) y P One mplcaton stemmng from Eq. (38) s that, n the absence of any polcy nterference ( τ = 0 ), the cost of polluton becomes zero so that the ntermedate P frms wll use an nfntely large level of polluton. As a result, the envronmental qualty declnes to the bottom and the economy cannot survve even temporarly. To ths end, we ntroduce such a non-polcy cost of pollutng nputs to restrct the polluton to wthn a fnte level even n the absence of an envronmental tax. To be concerned wth practcalty, snce frms usually mport petroleum from abroad at a prce that they can not bargan for, we beleve that the assumpton of a gven prce of pollutng nputs s not very far from the real world An alternatve polluton settng There are some studes ntroducng a prvate cost of polluton n order to prevent polluton from growng to nfnty n the absence of polcy nterventon; see, e.g., Jouvet et al. (2005) and Ono (2007). The man departure between these studes and our paper s that they do not make a dstncton between polluton emssons and drty nputs. growth. Therefore, rasng the envronmental tax leads to a negatve mpact on In ths subsecton, we examne the effects of the envronmental tax under such an alternatve settng of polluton. To smplfy the analyss and hghlght the negatve growth effect, we temporarly remove the role of abatement technology. By denotng z as the prvate cost of polluton, the proft functon of an ntermedate frm can now be expressed as: π = q A( N, K) k α p ν l β rk ωl ( z + τ ) p. (39) y y P Notce that n A( N, K ), t s assumed that, n lne wth the approach adopted n Ono 27