DISCUSSION PAPER November 2009 RFF DP 09-47 Emissions Targes and he Real Business Cycle Inensiy Targes versus Caps or Taxes Carolyn Fischer and Michael R. Springborn 66 P S. NW Washingon, DC 20036 202-328-5000 www.rff.org
Emissions Targes and he Real Business Cycle: Inensiy Targes versus Caps or Taxes Carolyn Fischer and Michael R. Springborn Absrac For reducing greenhouse gas emissions, inensiy arges are aracing ineres as a flexible mechanism ha would beer allow for economic growh han emissions caps. For he same expeced emissions, however, he economic responses o unexpeced produciviy shocks differ. Using a real business cycle model, we find ha a cap dampens he effecs of produciviy shocks in he economy. An emissions ax leads o he same expeced oucomes as a cap bu wih greaer volailiy. Cerainyequivalen inensiy arges mainain higher levels of labor, capial, and oupu han oher policies, wih lower expeced coss and no more volailiy han wih no policy. Key Words: emissions ax, cap-and-rade, inensiy arge, business cycle JEL Classificaion Numbers: Q2, Q43, Q52, H2, E32 2009 Resources for he Fuure. All righs reserved. No porion of his paper may be reproduced wihou permission of he auhors. Discussion papers are research maerials circulaed by heir auhors for purposes of informaion and discussion. They have no necessarily undergone formal peer review.
Conens Inroducion... Deerminisic Model... 4 No Policy... 6 Inensiy Targe... 7 Emissions Cap... 8 Emissions Tax... 9 Summary and Comparison... 9 Numerical Model wih Sochasic Produciviy Shocks... Numerical Soluion and Simulaion Mehod... Resuls for he Deerminisic Case... 2 Resuls wih Sochasic Produciviy... 4 Sensiiviy Analysis: Produciviy Growh... 20 Sensiiviy Analysis: Developing-Counry Volailiy and Risk Aversion... 2 Conclusion... 23 References... 25
Resources for he Fuure Emissions Targes and he Real Business Cycle: Inensiy Targes versus Caps or Taxes Carolyn Fischer and Michael R. Springborn Inroducion Even hough consensus has grown on he need for dramaic reducions in anhropogenic emissions of greenhouse gases (GHGs), which conribue o global climae change, considerable debae coninues on which policies would bes serve ha goal. Many academics argue for carbon axes as he mos efficien domesic and global mechanism (Aldy e al. 2008), bu few governmens are seriously considering a carbon ax as a primary policy for slowing GHG emissions. Many counries, including hose of he European Union, have commied o or are proposing caps on GHG emissions. Oher counries, including Canada, are insead pursuing inensiy arges, which are also he basis for some prominen proposals o include developing counries in a global framework (Herzog e al. 2006). These arges would index emissions allowance allocaions o economic oupu, he idea being ha a flexible mechanism would beer allow for economic growh (e.g., Pizer 2005). How much of a boon is his flexibiliy? From a policy design sandpoin, one could equivalenly assign caps ha follow a growh pah or assign declining inensiy arges or carbon axes o mee a cap. Therefore, a growh pah is no an inheren feaure of inensiy arges, nor is a fixed emissions pah a defining characerisic of emissions caps. Furhermore, when he ulimae goal is reducing overall emissions and sabilizing amospheric concenraions, any policy would have o be racheed over ime. However, in he face of uncerain economic growh, he policies offer differen qualiies. Holding expeced allocaions consan, inensiy and emissions arges are likely o provoke differen economic responses o unexpeced produciviy shocks. This paper explores he impacs of such economy-wide emissions regulaions on he business cycle. Carolyn Fischer is a senior fellow a Resources for he Fuure; fischer@rff.org. Michael R. Springborn is an assisan professor in he Deparmen of Environmenal Science and Policy, Universiy of California, Davis. The auhors are graeful for he suppor of EPA/STAR (gran RD 830990) and NSF/IGERT (Program gran DGE- 04437).
Resources for he Fuure A long lieraure in environmenal economics, beginning wih Weizman s seminal 974 paper, has compared price and quaniy insrumens for regulaing emissions. More recenly, researchers have begun o also compare inensiy-based insrumens. Several of hese laer works, including Newell and Pizer (2008) and Quirion (2005), follow he parial equilibrium approach of Weizman. Ohers have aken a general equilibrium approach, focusing on he role of ax ineracions (Goulder e al. 999; Parry and Williams 999), he role of mulisecor and inernaional rade (Dissou 2005; Jozo and Pezzey 2007), or boh (Fischer and Fox 2007). Given ha uncerainy abou economic growh and he macroeconomic ransiion effecs of carbon policy is driving ineres in indexed emissions arges, surprisingly few sudies address hese aspecs direcly. Much of he previous heoreical analysis of inensiy arges and alernaive insrumens has focused on variance in abaemen and compliance coss as he criical meric. This lieraure, including Kolsad (2005), Quirion (2005), Pizer (2005), Jozo and Pezzey (2007), and a pre-publicaion version of Sue Wing e al. (2009), is reviewed by Peerson (2008) who observes ha a common hread is he imporance of he correlaion beween GDP and emissions in deermining wheher abaemen cos uncerainy is lower under an inensiy arge. This paper akes a broader approach, characerizing he response in a se of macro-level variables o economy-wide emissions regulaions via price, quaniy, and inensiy insrumens, operaing in he conex of an uncerain business cycle. In conras o he preceding prices-versus-quaniies lieraure, we use a dynamic sochasic general equilibrium (DSGE) model o compare he dynamic effecs of hese policy choices under produciviy shocks. We specify a dynamic Robinson Crusoe economy, wih choices over consumpion, labor, capial invesmen, and a polluing inermediae good. We consider hree policies for consraining emissions from he polluing facor: an emissions cap, an emissions ax, and an inensiy arge ha ses a maximum emissions-oupu raio. The economy is subjec o uncerain shocks o overall produciviy. We sar wih a simple approach o characerizing he response by solving analyically for he seady sae following a single, permanen shock; his is our SS model. To implemen he full real business cycle, RBC model, we specify a produciviy facor ha evolves according o a firs-order auoregressive process, Jensen and Rasmussen (2000) consider using a general equilibrium model of he Danish economy and find ha allocaing emissions permis according o oupu dampens secoral adjusmen bu imposes greaer welfare coss han grandfahered permis. 2
Resources for he Fuure which includes i.i.d. random shocks each period. To solve he RBC model numerically, we parameerize he model wih plausible values from he macroeconomics lieraure. Our analysis and an unpublished work by Heuel (2008) are he firs aemps of which we are aware o examine climae policy in an RBC framework ha is, in a DSGE model wih uncerainy over fuure produciviy. Heuel s focus is on he opimal dynamic ax or quoa policy, which adjuss each period in response o income and price effecs. Heuel finds ha price effec dominaes, driving increased emissions levels and prices during economic expansions. Our approach differs in ha we compare he performance of hree insrumens (ax, cap, and inensiy arge) in each se o achieve an exogenous and fixed level of expeced emissions reducion. Whereas we accoun for labor marke responses o policy and produciviy shifs and absrac from considering direc damages from emissions, Heuel ses aside labor flucuaions o concenrae on he ineresing dynamics of he opimal endogenous policy. 2 We incorporae labor for wo main reasons. Firs, since labor marke impacs are ofen highlighed in environmenal policy debaes, labor is a criical oucome variable in is own righ. Second, as we will furher discuss in he resuls below, he dynamic impulse response of labor o a produciviy shock in he full RBC model is, uniquely, no single-peaked. Our analyical resuls for variable levels in he SS model and expeced variable levels in he RBC model ell he same sory. Implemenaion of any of he hree insrumens leads all variable levels o fall, excep under he inensiy arge policy where labor remains unchanged from he no policy seing. This paricular consisency occurs because adjusmens in response o he inensiy arge policy in consumpion and producion exacly offse wihin he labor opimaliy condiion. In a comparison of levels under he hree insrumens, we find ha deerminisic oucomes under he cap and ax policies are idenical and, aside from emissions, lower han hose of he inensiy arge. Thus, given an idenical emissions reducion consrain, oal oupu is higher wih he inensiy arge han wih he cap or ax. This arises because addiional producion under he inensiy arge earns addiional permis, increasing he reurns o producion. Consequenly, he emissions inensiy arge mus be se below he emissions inensiy observed under he cap and ax policies. Considering volailiy, he SS model reveals ha he sensiiviy of oupu o a paricular produciviy shock is dampened by he cap. Similarly, when sochasic produciviy shocks are incorporaed in he RBC analysis, he cap policy leads o he lowes levels of volailiy for each 2 Oher modeling differences lie in he represenaion of abaemen opporunies. 3
Resources for he Fuure variable and herefore minimal variaion in producion and uiliy as well. The ax policy has he opposie effec. Opimal invesmen under he ax policy is much more sensiive o deviaions in he produciviy facor han under any oher policy. No surprisingly hen, he volailiy of each variable, and ulimaely producion and uiliy is greaes under he ax. Meanwhile, he sensiiviy o shocks under he inensiy arge is unchanged from he no policy case. Deerminisic Model Alhough he issues a play involve economic growh and uncerainy, much of he inuiion regarding he policy differences can firs be derived from a simple, deerminisic model wihou growh, by looking a he seady-sae responses o differen emissions policies and degrees of a one-ime produciviy shock. Consider a simple Robinson-Crusoe economy. Le C be he consumpion good, K be capial, L be labor, l be leisure, and M be a polluing inermediae good. The represenaive agen ges uiliy u(c,l) from consumpion and leisure. Toal producion Y is a funcion of capial, labor and polluing inpus F( K, M, L ), adjused by a produciviy facor Θ wih an expeced value of, where Y = Θ F( K, M, L). Capial depreciaes a rae δ and is augmened wih invesmen I, so K = I + ( δ ) K. Toal oupu is allocaed beween + consumpion, invesmen and inermediae inpus (C+ I + M Y ), and ime is allocaed beween leisure and labor ( l = L). Emissions are assumed o be proporional o he use of M and unis of emissions are chosen such ha he quaniy of emissions is equal o M. 3 For he remainder of he analysis we will refer o he level of he inermediae polluing good and he level of emissions inerchangeably. The emissions consrain requires ha M AY ( ), where A (.) is he permi allocaion, which may vary over ime and wih oupu. We assume he specific funcional forms of log uiliy and Cobb-Douglas consan reurns o scale echnology: u = lnc + ω ln( l ) F( K, M, L) = K M L α γ α γ The Lagrangian for he consrained uiliy maximizaion problem is 3 We absrac from economic growh, and we also ignore he implicaions of improvemens in abaemen echnology. We will relax his assumpion when considering an exension incorporaing growh in our sensiiviy analysis. 4
Resources for he Fuure [ln C + ω ln( L)] r + α γ α γ L = + λ[ ΘK M L C M K+ + ( δ) K)] () = 0 α γ α γ + φ[ A( ΘK M L ) M] Furhermore, le ˆ φ φ / λ be he effecive shadow value of emissions ha is, he nominal shadow value normalized by he marginal value of income. The firs-order condiions produce six equaions for he six variables in each ime period: C : λ = (2) ( + r) C α γ α γ ˆ λ, Y λ K : αθ K M L ( + φ A ) = + δ (3) M Θ K M L + ˆA + ˆ = (4) α γ α γ : γ ( φ, Y) ( φ) 0 ωc L : = ( α γ) Θ K M L ( + ˆ φ A ) α γ α γ, Y L (5) λ α γ α γ : K M L K+ ( δ) K C M Θ = + + (6) φ : M = AY ( ) (7) where A,Y represens he derivaive of A wih respec o Y. Furher subsiuing and rearranging, we deermine expressions for capial, emissions, and consumpion as shares of oupu and labor in erms of he labor-leisure raio K α ( ˆ + φa, Y) k = Y C ( + r) ( δ ) C M γ( + ˆ φa, Y) m = Y + ˆ φ + + ( δ ) Y (8) (9) Y c m k + k (0) L ( α γ)( + ˆ φa, Y) z = L ωc () 5
Resources for he Fuure wih oupu being deermined in equilibrium wih he policy consrain, Equaion (7). Noe ha z=l/(-l) is a monoonic, increasing, and convex funcion of L. Alernaively, rearranging (9), we solve for he shadow value of emissions: ˆ γ / m φ = (0) AY, γ / m cap Noe ha for he cap, ˆ φ = γ / m ; since emissions are fixed, he price adjuss o he level of oupu. For he ax, his shadow value is fixed by he policy. Wih he inensiy arge (IT), AY, = μ and m = μ, meaning he shadow value is also fixed, albei a a differen (higher) level, which we will discuss nex: ˆ φ IT = ( γ / μ )/( γ). Le us now absrac from he pah dynamics and focus on he seady sae, wih C+ = C = C, ec. (seady-sae levels will be denoed by he absence of a ime index) and he shadow values growing a he rae of ime preference. (The Lagrange mulipliers λ and φ are presen value mulipliers; when solving for seady-sae values, he curren value mulipliers will be consan, as will he raio of he presen value mulipliers, φˆ.) Le ˆ β /( r + δ ). Seady-sae equilibrium levels are given by k = ˆ βα( + ˆ φ A Y ) () ( + ˆ φ A Y ) m = γ (2) + ˆ φ c= m δ k (3) ( α γ ) z = ( + ˆ φ A Y ) (4) ωc Wih hese general resuls, we now urn o evaluaing he effecs of specific emissions policy choices. No Policy As an iniial benchmark, consider he absence of an emissions policy. Wihou any regulaion, we can drop he consrain on emissions, so φ = 0. Simplifying he above equaions, we have k = ˆ βα, m = γ, c = γ ˆ βδα, and α γ α γ z = or L=. Solving for producion, hen, we ge ω( γ ˆ βδα) α γ + ω( γ ˆ βδα) 6
Resources for he Fuure ( ˆ βα ) α γ α γ α γ α γ Y =Θ γ L, from which he percenage response o a shock in he produciviy dy { }/ Y facor is = ; ha is, he elasiciy of oupu is greaer han one. dθ/ Θ α γ Noe ha in he absence of an emissions policy, he seady-sae GDP shares of consumpion, capial, and emissions are invarian o he shock variable. Therefore, heir levels α γ will all vary in a posiive manner wih permanen produciviy shocks, proporional o Θ. Meanwhile, oal labor supply in he seady sae is uniquely indifferen o he shock parameer, since he effec of increased marginal produciviy of labor is exacly offse by he falling marginal value of income, λ (see Equaions (2) and (5)). Inensiy Targe Consider nex an inensiy arge of μ per uni of oupu, so AY ( ) = μy. We assume a binding arge, which implies m = μ < γ. Furhermore, in equilibrium, A=M. ( + ˆ φμ) Simplifying he seady-sae equaion for he emissions share, we ge m = γ = μ, + ˆ φ from which we derive he effecive shadow value of he emissions consrain: ˆ γ μ φ = μ( γ ) ( ) Subsiuing ino he remaining seady-sae equaions, we ge ˆ μ k = βα, ( γ ) ˆ ( μ ) ( ˆ ) ( μ c ) ( α γ) μ α γ = μ δβα = γ δβα, and z = =. ( γ ) ( γ ) ωc γ ω γ δβα ˆ (5) ( ) Thus, we observe again ha seady-sae consumpion, capial, and emissions shares of GDP are invarian o permanen produciviy shocks (he laer by definiion). Their levels are hen all procyclical, in he sense of responding in he same direcion as he change in he produciviy facor. Labor supply is also invarian, boh o shocks and o he policy sringency, since he effecs filer hrough he change in he marginal produciviy of labor (o produce final oupu and addiional permis) and he marginal value of income, which offse. Consequenly, we observe he same sensiiviy of seady-sae oupu o produciviy facor changes as wih no dy { }/ Y policy: = dθ/ Θ α γ. 7
Resources for he Fuure Ineresingly, capial as a share of oupu is increasing wih he sringency of he emissions consrain. The reason is ha addiional invesmen and producion also produce addiional emissions allocaions. The rae of consumpion also increases wih policy sringency, since he capial buildup does no absorb all of he decrease in he polluing inermediae good: dc γ δβα ˆ = > 0. dμ ( γ) Emissions Cap Wih an emissions cap, M is fixed. In his case, AY ( ) = M, so A Y = 0. The key seadysae condiions hen reduce o k = ˆ βα, m = γ + ˆ φ, γ c ˆ ˆ α γ = δβα, z =, and + φ ωc m= M / Y. We see ha he capial share is consan and idenical o he no-policy case, also implying i is sricly lower han ha under he inensiy arge. Labor supply also carries he same relaionship o he consumpion rae as in he no-policy case. On he oher hand, we also see ha he effecive shadow price of emissions is no longer independen of he produciviy variable, bu raher procyclical: ˆ γθf φ = (6) M In oher words, a posiive produciviy shock, which would oherwise increase emissions, raises he price of emissions permis o mainain he cap. As a resul, consumpion as a share of GDP reacs in a procyclical manner, since he cap prevens addiional oupu from being used as more of he inermediae good: c= M / Y δβα ˆ. Meanwhile, labor supply hen becomes counercyclical, o compensae for he inabiliy o * α γ expand emissions: L =. The increase in he marginal produciviy α γ + ω M / Y δβα ˆ ( ) of labor from a posiive produciviy shock, dampened under he cap consrain, is no longer srong enough o offse he decrease in he marginal value of income, so labor falls under he cap. Subsiuing hese values and solving for producion, we ge ( ˆ βα ) α γ α γ α α α α Y =Θ M L. Overall, seady-sae producion under he cap is less sensiive o a given permanen produciviy shock han in he preceding scenarios, boh since labor supply is counercyclical and since α α γ d { Θ } d{ Θ } <. dθ dθ 8
Resources for he Fuure Emissions Tax Suppose ha insead of emissions rading, we have a fixed price, as wih a carbon ax, wih he revenues rebaed in lump-sum fashion o he represenaive consumer. Le his price be fixed, so ˆ φ = τ (i.e., he ax is fixed in erms of he marginal value of income). The new problem is similar o he grandfahering problem, in which he permis are allocaed lump-sum, wih AM = AK = AL = 0. Bu in his case, he equilibrium value of he allocaion equals he emissions ax revenues; ha is, τ A = τ M. The key seady-sae condiions hen reduce o k ˆ γ γ = βα, m =, c = δβα ˆ, + τ + τ α γ and z =. Wih he emissions price fixed, labor supply and he consumpion, capial, and ωc emissions inensiies are all invarian o produciviy changes, as in he no-policy and inensiy arge scenarios. Summary and Comparison A summary of analyical resuls is presened in Table so ha he policy effecs can be seen side-by-side. Firs, i is useful o compare oucomes under cerainy, wih Θ=. In his case, we noice ha he emissions ax achieving he same emissions as he cap will replicae all he same prices and quaniies as he cap. The inensiy arge, on he oher hand, has imporan differences: he capial share is higher (since ( μ) /( γ ) > ), and he labor allocaion is also higher (since γ > m when emissions are consrained). Given he same oal emissions arge, hen, wih he oher facors of producion being larger, i mus be ha oal oupu is higher wih he inensiy arge han wih he cap or ax. As a consequence, he emissions inensiy arge mus be lower han he emissions rae under he oher policies o achieve he same level of oal emissions. 4 We also observe ha he consumpion rae is higher wih he inensiy arge han wih no policy, bu i is unclear wheher i is higher han wih he cap or ax policies. 4 These resuls echo hose in saic models, such as Fischer (2003) and Fischer and Fox (2007). 9
Resources for he Fuure Table. Comparison of Analyical Resuls m c k L/(-L) No Policy Inensiy Targe Emissions Cap Emissions Tax γ μ M γ M Y +τ = Y γ ˆ ( ˆ ) ( μ γ δβα ) βδα ( γ ) m δβα ˆ m δβα ˆ ˆ βα α γ ˆ ( μ) βα ( γ ) ( ˆ ) ω ( γ δβα ˆ ) ( ˆ ω ω m δβα ) ( m δβα ˆ ) ω γ βδα α γ ˆ βα α γ ˆ βα α γ dy { }/ Y dθ/ Θ α γ α γ Θ α L / L α ( α γ ) Y / Y α γ Oher differences arise in response o innovaions in he produciviy parameer. Under he emissions cap, obviously, emissions are fixed, and oupu is less responsive o a shock han he oher policies because of a counercyclical effec on labor supply and emissions inensiy. An imporan cavea in hinking abou he effec of produciviy shocks is ha he seadysae analysis considers a permanen produciviy shock, as opposed o ransiory ones. A permanen change in produciviy has he same (procyclical) effec on oupu, in percenage erms, in all bu he emissions cap policy. The oher seady-sae variables remain consan as a share of oupu; heir levels are hen procyclical in he same percenage erms as oupu. However, as we will see in he nex secion, hese resuls do no hold along a pah wih sochasic produciviy, when shocks are ransiory and heir cumulaive effec is also manifesed in he capial sock responses. We now urn o a numerical version of he model, incorporaing a sochasic process ino he overall produciviy facor. 0
Resources for he Fuure Numerical Model wih Sochasic Produciviy Shocks Numerical Soluion and Simulaion Mehod Because of he nonlinear form of he firs-order condiions, specifically he ineremporal Euler and labor equaions, we urn o a numerical mehod o calculae a firs-order approximaion o he equilibrium condiions. To begin, we parameerize he model using sandard calculaions from he real business cycle (RBC) lieraure and our own analyses (see Table 2). For producion parameers we sar wih King, Plosser, and Rebelo s (988) (hereafer KPR) calculaion of mean annual share of GNP o labor (verified wih curren daa). We decompose he oal capial share of oupu in our model ino energy inpus, M (o represen he inermediae polluing good), and all oher nonenergy capial, K. The baseline share of energy o oupu is se equal o he mean raio of annual energy expendiures o GDP. Finally, he share of nonenergy capial o oupu is se equal o one minus he labor and energy shares. The uiliy parameer, discoun facor, and depreciaion raes all reflec sandard RBC model assumpions. The produciviy facor is given by Θ = exp(z ), where z evolves according o a saionary, firs-order auoregressive process, z = η + ε (7) z and where ε is an i.i.d. normal random variable wih a mean of zero and sandard deviaion σ. Parameers of he produciviy facor process approximaely follow Presco (986) and much of he subsequen macroeconomic lieraure. Given hese parameer values, we linearize he efficiency condiions by aking a firsorder Taylor approximaion around he seady-sae levels of our variables. Using a sandard eigenvalue decomposiion mehod, we hen solve for he decision funcions ha ake he sae variables (K and Θ) a he beginning of he period and reurn he opimal levels of C, M, L, and capial invesmen. 5 To characerize he variance of he variables of ineres, we simulae,000 realizaions, each 00 years in lengh. In each simulaion he iniial capial sock is se o is seady-sae level 5 Noe ha his is a consrained opimum subjec o he relaxaion of linearizing he equilibrium condiions, and hence he decision rules, around he seady sae.
Resources for he Fuure for he paricular policy seing, and he produciviy facor is se o one. Subsequenly, he economy is subjeced o a new shock each period, afer which opimal decisions are made over he choice variables. As a robusness check, we also modify he model wih a labor-enhancing produciviy facor and perform he same analysis in he conex of exogenous growh in he baseline. The resuls, viewing he variables as shares of oupu along he growh pah, are essenially idenical o hose in he no-growh case, so we concenrae our reporing on he laer case. Table 2. Summary of Simulaion Parameer Values and Sources Parameer Level Source α γ Share of oupu going o L 0.58 Mean annual raio of oal employee compensaion o GNP (KPR 988 for 948 985, same resul calculaed for 970 200 using daa from NIPA 2005) γ Share of oupu going o M 0.09 Mean raio of oal energy expendiures o GDP (970 200), daa from EIA 2004 Convenional share of oupu 0.42 Calculaed as one minus he share o L going o oal capial (in models wihou M) α Share of oupu going o K 0.33 Convenional share o oal capial less share o energy capial ω Uiliy parameer 0.2 From KPR 988, chosen indirecly by specifying seady-sae hours worked (0.20) based on he average fracion of hours devoed o marke work in 948-985 β Discoun facor 0.95 From KPR 988, consisen wih he observed average real reurn o equiy, 948 98 δ Depreciaion rae 0.096 Calculaed assuming an invesmen-oupu raio of 25% and a capial sock-oupu raio of 2.6 η Auocorrelaion parameer 0.8 Annual analog of he quarerly rae of 0.95 (Presco 986) σ Sandard deviaion of random parameer ε 0.04 Annual analog of he quarerly level of 0.007 (Presco 986) Resuls for he Deerminisic Case Wih his parameerizaion, we begin by numerically solving for seady-sae values in he deerminisic case (Θ =), which reproduces he analyical approach above wih no shocks. Afer calculaing he benchmark case of No Policy, we consider he hree policy scenarios Inensiy 2
Resources for he Fuure Targe, Emissions Cap, and Emissions Tax and solve for he level of sringency such ha all mee he same emissions reducions (20 percen) as in he deerminisic seady-sae. The resuls are repored here and in Tables 3 and 4. In he absence of uncerainy, here is no difference beween he cap and he ax, as one would expec. The inensiy arge, on he oher hand, requires a more sringen inensiy level han he oher policies, and i also resuls in a 7 percen higher permi price. On he oher hand, consisen wih he analyical resuls, i generaes no decrease in employmen and increases capial as a share of oupu. Alhough he consumpion share is higher, oal consumpion is slighly lower. When we consider a single period a he new seady sae under a policy, he welfare coss, in erms of changes in uiliy, of reaching he emissions reducion goal wih he inensiy arge are less han hose wih he cap or he ax policy. 6 However, he ransiion dynamics in reaching ha new seady sae differ. The new seady-sae capial level for he cap and ax is lower han for he inensiy arge under he laer wo policies here is a longer period of relaxed invesmen and labor and elevaed consumpion along he ransiion o he new seady sae. From a presen value of uiliy perspecive, he cap and ax hen dominae he inensiy arge. There is ye a furher difference in he ransiion properies of he cap and ax. Once he cap is imposed, he new seady-sae level for M is achieved immediaely. The ax, which is se o achieve he same level for M a he deerminisic seady sae, resuls in emissions above he cap level, while he capial sock is above he seady sae. (The same is rue for he inensiy arge bu o a much lesser exen.) In a presen value analysis, he ax policy hen dominaes, hough i should be acknowledged ha his is made possible by elevaed emissions ha are no accouned for in he uiliy funcion. Recall from he analyical SS model resuls (Table ) ha wheher he consumpion share under he inensiy arge was greaer han for he cap and ax policies was ambiguous. Given our model parameers, we see ha he inensiy arge consumpion share is lower, since he proporional increase in producion, relaive o he cap or ax, ouweighs he same in consumpion. 6 Uiliy levels exclude damages from emissions, bu since emissions are equal across he policy scenarios, ha doesn change he relaive evaluaion. 3
Resources for he Fuure Table 3. Deerminisic Seady-Sae Consumpion, Capial, and Emissions Shares c L/Y k m No Policy 0.697 0.923 2.22 0.0900 Inensiy Targe 0.709 0.943 2.26 0.0735 Cap 0.72 0.95 2.22 0.0745 Tax 0.72 0.95 2.22 0.0745 Table 4. Seady-Sae Levels in he Deerminisic Case, wih Percenage Changes Relaive o No Policy C L K M Y U No Policy (NP) 0.609 0.806.94 0.079 0.87 0.825 change from NP 0% 0% 0% 0% 0% Inensiy Targe 0.607 0.806.93 0.063 0.86 0.828 change from NP 0.3% 0.00% 0.3% 20.0% 2.% Cap 0.602 0.803.88 0.063 0.84 0.833 change from NP.% 0.43% 3.3% 20.0% 3.3% Tax 0.602 0.803.88 0.063 0.84 0.833 change from NP.% 0.43% 3.3% 20.0% 3.3% Resuls wih Sochasic Produciviy Nex, o evaluae he effecs of uncerainy and volailiy in he produciviy parameer, we solve for he opimal linearized decision funcions, presened in Table 5. These funcions map he sae variables (K and Θ) ino invesmen, consumpion, and labor choices. The decision rules are calculaed in erms of proporional deviaion from seady sae (PDSS). 7 For example, he ' ' ' PDSS of he capial sock in period + under no policy is given by K =.8594* + 0.3372 θ 0 K *. + The decision funcions were used o conduc,000 sochasic 00-year simulaions for each emission policy. In Figure we presen example oupu under he four policies for a 30-period segmen of one simulaion. The sochasic produciviy facor pah is shown in he firs panel, and he remaining panels depic he response in producion, polluing inpu, and uiliy. 7 For example, if he seady-sae level of capial is given by K, hen K = (K K )/K. 4
Resources for he Fuure Figure. Variable Oucomes under No Policy (NP), Inensiy Targe (IT), Cap, and Tax, Given Pah of Produciviy Facor θ. Levels are normalized by he NP seady-sae level for Y, M, and U..04.02 θ (common o all policies).06.04.02 Y NP IT Cap Tax Levels (all excep θ relaive o no policy) 0.98 0.96 0 0 20 30 0.03 0.02 0.0 0-0.0-0.02 0 0 20 30 U 0.98 0.96 0.94 0 0 20 30..05 0.95 0.9 0.85 0.8 M 0.75 0 0 20 30 ime Our findings are summarized in wo key saisics for each variable, repored in Table 6. Firs, we presen he mean of he simulaion means (i.e., we ake he mean of each simulaion ime pah and hen ake he mean over all,000 simulaions). Comparison wih Table 4 shows ha he variable cenral endencies are virually idenical o he deerminisic seady-sae levels, as expeced. Second, we repor he mean simulaion sandard deviaion (in percenage erms) as a measure of expeced volailiy for any given realizaion of produciviy shocks (i.e., for any ime pah). 5
Resources for he Fuure Table 5. Decision Funcions for Choice Variables in Terms of Proporional Deviaion from Seady Sae Table 6. Simulaion Cenral Tendencies and Variabiliy Variable Policy Saisic C L K M θ Y U P - U *** NP No Policy msm* 0.609 0.806.94 0.079 0.87 0 mssd** 2.50% 0.27% 3.09% 3.32% 2.25% 3.32% 0.0242 Inensiy Targe msm 0.607 0.806.93 0.063 Same 0.86 0.00322 mssd 2.50% 0.27% 3.09% 3.32% 3.32% 0.0242 Cap msm 0.602 0.803.88 0.063 Same 0.84 0.0080 mssd 2.43% 0.22% 2.86% 0.00% 2.94% 0.0239 Tax msm 0.602 0.803.88 0.063 Same 0.84 0.0083 mssd 2.52% 0.27% 3.4% 3.34% 3.40% 0.0244 *Mean of simulaion means (msm): he mean over,000 simulaions of he 00-year simulaion mean. **Mean of simulaion sandard deviaions (mssd): he mean over,000 simulaions of he simulaion sandard deviaions, in percenage erms (excep for las column). ***Under U P - U NP, msm is calculaed over he deviaion of uiliy under he given policy from he no policy baseline. The saisic mssd is calculaed for levels of U p only. 6
Resources for he Fuure The expeced levels in he RBC model ell he same sory as he analyical resuls for variable levels in he SS model and he deerminisic case. Implemenaion of any of he hree insrumens leads all variable levels o fall excep under he inensiy arge policy, where labor remains unchanged from he no policy seing. This paricular consisency occurs because adjusmens in response o he inensiy arge policy in consumpion and invesmen exacly offse wihin he labor opimaliy condiion. As expeced from he deerminisic analysis, we find ha expeced levels under he cap and ax policies are idenical and lower han hose of he inensiy arge. Thus, given an idenical emissions reducion consrain, oal oupu is higher wih he inensiy arge han wih he cap or ax. Consequenly, we again see ha he emissions inensiy arge mus be se below he emissions rae observed under he cap and ax policies. We find ha uiliy a he seady sae is he same under a cap or ax, and lower han for uiliy under an inensiy arge (see Table 4). These resuls are essenially mainained in he seing wih sochasic produciviy shocks (see Table 6). Even hough he average sacrifice in uiliy for a period (he mean of simulaion means) from adoping he cap policy (lowes volailiy) is slighly smaller han for he ax policy (highes volailiy), we are no able o rejec ha he means are equal using he nonparameric Wilcoxon signed rank es (p = 0.20). Since opimal capial sock levels are lower under emissions consrains, here is a period of ransiion from he iniial no policy sae. Uiliy under he cap and ax policies is acually greaer over his period of ransiion because invesmen levels are deflaed o a larger exen han under he inensiy arge. The effec of his invesmen holiday is srong enough ha he inensiy arge acually performs he wors from a presen value of uiliy perspecive. This resul will be sensiive o he assumed 5 percen discoun rae and 00-year ime horizon of our analysis. Consisen wih he observaion ha here is greaer flexibiliy under he ax o ake advanage of elevaed capial levels over he ransiion period, we find ha he presen value of uiliy under he ax is significanly greaer han for he cap (p < 0.00). 8 Considering volailiy, in general, in boh he single permanen shock (SS) and repeaed ransiory shock (RBC) seings, he variables of ineres (emissions, consumpion, capial, and labor) are procyclical under each policy; ha is, hey move in he same direcion as he level of he produciviy shock. The excepions are emissions under he cap, which are fixed, and labor. 8 Noe ha in aking advanage of elevaed capial levels over he ransiion o he new seady sae, he ax policy will resul in greaer emissions han he cap policy, an effec ha is no incorporaed ino he uiliy funcion. 7
Resources for he Fuure Labor is invarian o shocks in he SS seing, excep under a cap, in which case i is counercyclical. In perhaps he sarkes divergence beween he wo seings, he RBC response of labor is procyclical for all policies. This resul is explored furher below. Oherwise, he SS resuls are qualiaively mainained in he RBC seing. In he SS model he sensiiviy of oupu o a paricular produciviy shock is dampened by he cap. Similarly, from he RBC analysis, Table 6 reveals ha he emissions cap, which by definiion has he leas volailiy in emissions, also has he leas volailiy in oupu and all he oher variables, including uiliy. When produciviy is high, he shadow value of he fixed emissions consrain becomes greaer, puing he brakes on he economy, and when produciviy is low, he effecive permi price drops, easing up on he economy. The ax policy has he opposie effec in he RBC seing. Opimal invesmen under he ax policy is more sensiive o produciviy facor deviaion han under any oher policy. This is eviden in he opimal linear decision funcions for choice variables from Table 5. The coefficien represening he effec of deviaion in he produciviy facor on nex period s capial is larges for he ax. This sensiiviy o sochasic produciviy is born ou dynamically in simulaions: he volailiy of each variable, and ulimaely producion and uiliy, is greaes under he ax (see Table 6). The inensiy arge, on he oher hand, does no change he sensiiviy of he economy o produciviy shocks: he decision funcions for no policy and inensiy arge are idenical and lead o a level of volailiy ha lies beween he cap and ax. A salien feaure of generalizing he SS model o a seing of repeaed ransiory shocks is ha he opimal decision in a ime period is aken wih respec o he curren capial sock as well as he curren level of he produciviy shock. The capial sock is essenially coninually divergen from he seady sae and reflecs he cumulaive response o he series of shock levels encounered up o he presen period. Since invesmen is procyclical, a posiive deviaion from he seady sae roughly reflecs a hisory ha, on balance, feaured posiive produciviy shock levels. Given ha background, we now reurn o he quesion of why he SS model shows no response or a counercyclical response o a produciviy shock while he RBC model resuls in a procyclical labor response. The RBC decision funcion for all polices shows ha he opimal labor choice is increasing in posiive deviaions in he curren produciviy level (procyclical) bu is decreasing in capial sock deviaions; ha is, he residual effec of pas produciviy levels (see he las decision funcion in Table 5). (The laer effec occurs because elevaed capial socks invoke elevaed consumpion, which reduces he marginal value of income and hence he 8
Resources for he Fuure marginal benefi of labor.) However, even once we consider he indirec effec (hrough capial) of a one-ime shock on labor in he RBC model, he immediae effec is sill procyclical. In Figure 2 we depic he RBC model response o a one-ime, ransiory produciviy shock (see he pah of Θ). In he op panel, while labor clearly follows he direcion of he shock, noe ha he long-erm response evenually becomes negaive as he procyclical direc effec of he deviaion in produciviy decays faser han he negaive indirec effec of he capial sock. In he boom panel of Figure 2 we see wha drives he labor effec hrough an examinaion of choice variables as shares of oupu. Recall from he SS model (see Equaion (3)) ha labor is eiher counercyclical because he consumpion share c is procyclical (cap policy) or invarian o he shock because c is consan (all oher policies). In conras, under he long-horizon, ransiory shock seing of he RBC model, he consumpion share falls while he invesmen share rises in response o a posiive shock. The boom panel of Figure shows his relaionship for he inensiy arge policy, hough a similar relaionship holds for each policy we consider. When shocks are ransiory, a posiive shock leads o a greaer relaive response in invesmen versus consumpion (hough consumpion is elevaed). In he ension beween a marginal produciviy of labor increase and marginal value of income decrease ha deermines he labor response o shocks, i is he former ha dominaes in he RBC model, leading o a procyclical response, a leas in he shor run. 9
Resources for he Fuure Figure 2. Example Response o One-Sandard-Deviaion Produciviy Shock under Inensiy Targe Policy. Top panel: impulse responses in percenage deviaion from seady sae. Boom panel: percenage deviaion of oupu shares from seady sae. 3 percenage deviaion from seady-sae 2.5 2.5 0.5 0 producion θ M labor capial consumpion percenage deviaion from seady-sae share of oupu -0.5 0 5 0 5 20 25 30 35 40 45 50 7 6 5 4 3 2 0 - -2 invesmen M consumpion -3 0 5 0 5 20 25 30 35 40 45 50 ime Sensiiviy Analysis: Produciviy Growh Recall from he baseline resuls discussed above ha even hough he inensiy arge is preferred o he cap and ax in erms of he seady-sae uiliy level, when we consider he presen value of uiliy over he enire horizon, saring from he seady sae under no policy consrain, he ax is preferred; i is closely followed by he cap. From a long-run, presen-value perspecive, hen, ransiions during which he capial level is diminished oward he new seady sae can be imporan. Alhough our baseline model absracs from produciviy growh, i is reasonable o suppose ha such growh migh influence he naure of he ransiion and herefore affec how insrumens perform. To explore his possibiliy, we incorporae labor-augmening, echnological progress ino he model: 20
Resources for he Fuure F α γ ( K, M, L ) = K M ( ρ L ) α γ where ρ is equal o one plus he growh rae of labor produciviy, which we se o equal 3.47 percen. This level achieves an inended 2 percen rae of overall growh (.0347 (-α-γ) =.02) which is he average per capia growh rae over he pas 50 years (Brock and Taylor 2008). The only oher parameer adjusmen is o he rae of depreciaion, which falls from 0.096 o 0.076 when accouning for a 2 percen rae of overall growh. We hen solve for he balanced growh pah (BGP) where, in he deerminisic case, all variables excep for labor and emissions grow a he consan rae of ρ (i.e., 0.0347). To ensure exisence of he BGP, i is necessary o assume ha abaemen echnology improves a a rae equal o overall growh ha is, emissions per uni of M fall over ime a he rae of growh. We address his srong assumpion, and he possibiliy of avoiding i, in our discussion of fuure research direcions below. As expeced, incorporaing produciviy growh shorens he ransiion, in his case from he no policy BGP o he new BGP for each policy. Alhough he ax s advanage over he cap is diminished somewha, he ordering based on he presen value of uiliy from he no-growh seing is mainained. Overall, afer economic growh is incorporaed ino he model, decision funcions show ha choice variables are less sensiive o capial deviaions and, excep for labor, more sensiive o deviaions in he produciviy facor. In oher words, he direc effecs of innovaions o he produciviy facor are greaer while he indirec effec of all pas produciviy deviaions on invesmen and consumpion, as manifesed in he capial sock, is diminished. The inuiion for his resul is ha accouning for growh effecively discouns he fuure marginal value of income (shadow value of he income consrain). However, he degree of hese differences is minor. Oher han a diminished ransiion and a small degree of convergence in he mean presen value of uiliy across insrumens, here is no significan change in qualiaive resuls vis-à-vis he nogrowh seup. Sensiiviy Analysis: Developing-Counry Volailiy and Risk Aversion Given he sysemaic differences in he volailiy of key variables beween policies, i is naural o ask o wha degree his second-order sochasic relaionship ranslaes ino a direc preference on expeced uiliy grounds, given preferences wih some degree of risk aversion. In paricular, o wha degree migh he cap policy uniquely generae a benefi in erms of reduced volailiy? Barlevy (2004) provides a useful survey of he benefis of economic sabilizaion and he welfare coss of business cycles. The imporance of hese deviaions from sable growh is 2
Resources for he Fuure debaable; argumens range from Lucas s (987) conclusion ha hey are a small concern o Soresleen e al. s (200) esimaion ha lifeime consumpion coss of volailiy are as high as 7.4 percen for individuals wihou savings. Recall ha alhough he cap policy feaures he lowes volailiy, is uiliy advanage over he ax for a given period on average was no significan (Table 6) and no sufficien o ouweigh he advanage of he ax over he ransiion o a new seady sae. Failure o find a significan sabilizaion benefi o he cap policy migh reflec low variabiliy in innovaions o he shock process, low risk aversion in he assumed uiliy funcion, or boh. We explore he effec of an increase in he sandard deviaion of produciviy facor innovaion process, (Equaion (6)) which also reflecs he sandard manner in which RBC models for developing counries ypically differ in heir parameerizaion (e.g., Neumeyer and Perri 2005). The issue of volailiy and sabilizaion is paricularly imporan for emerging economies. Pallage and Robe (2003, absrac) argue ha in many poor counries, he welfare gain from eliminaing volailiy may in fac exceed he welfare gain from an addiional percenage poin of growh forever. Using he midrange esimae from Neumeyer and Perri (2005), based on heir analysis of Argeninian daa as a case sudy, we adjus he baseline level of σ from 0.04 o 0.0204. We find again ha he previous ordering based on mean uiliy in a period is mainained: he inensiy arge performs bes, and he cap slighly dominaes he ax. As in he baseline seing, given ransiions, he ax again dominaes from a presen value perspecive, followed by he cap and hen he inensiy arge. Simply raising he variance of innovaions o he produciviy shock process fails, in his case, o generae much sronger evidence of a srong sabilizaion benefi o he cap. Nex we consider he sensiiviy of our resuls o he degree of risk aversion over consumpion. Noe ha our measure of uiliy over consumpion, lnc, is a special case of he consan relaive risk aversion specificaion, C -ψ /(-ψ), where he coefficien of relaive risk aversion, ψ, is se o. We consider an alernaive parameerizaion wih increased risk aversion, seing ψ o 2. Conrary o iniial expecaion, elevaing risk aversion over consumpion in his manner fails o produce a sabilizaion benefi o uiliy under he cap. Uiliy orderings for he insrumens based on he mean per period and he presen value are unchanged. An explanaion for his effec, a leas in par, is found in examining he surprising effec on labor volailiy. Under increased risk aversion over consumpion, here is an increased incenive o avoid flucuaions from he seady sae in general and o direc flucuaions in income away from consumpion and ino invesmen. Thus he decision funcions show a decrease in he sensiiviy 22
Resources for he Fuure o deviaions in he produciviy facor and a corresponding increase in sensiiviy o capial deviaions. Given ha opimal labor deviaions move opposie o capial deviaions, he volailiy of labor is increased. This shif is paricularly srong for he cap policy, where he inflexibiliy of choice over M already drives a high relaive sensiiviy o capial flucuaions. Ulimaely, his consrain under increased consumpion risk aversion leads o a reversal of our earlier finding of he cap policy as a sabilizing force: labor volailiy under he cap policy is acually slighly greaer han under he alernaives. Since he baseline uiliy measure over labor also includes a degree of risk aversion, i is no surprising ha consumpion sabilizaion benefis under he cap may be eroded. Conclusion Sabilizing greenhouse gas concenraions in he amosphere will require dramaic reducions in global carbon emissions. The choice among policies should be informed boh by heir expeced cos-effeciveness and by how hey respond o unexpeced evens along he pah. We find ha alhough a cap and a ax can produce equivalen oucomes in expecaion, a capand-rade program reduces economic volailiy, compared wih all oher policies and no policy, and a ax enhances volailiy. The cap funcions as an auomaic sabilizer, since he shadow price of he emissions consrain increases wih unexpeced increases in produciviy and decreases wih unexpeced economic cooling. We find ha an inensiy arge does indeed encourage greaer economic growh han a cap or a ax, since he allocaion of addiional permis serves as an inducemen for addiional producion. Furhermore, i seems neiher o dampen nor o exacerbae aspecs of he business cycle. Alhough emissions do remain volaile, for a sock polluan like GHGs, he iming of emissions is no generally imporan. Mos of he differences in volailiy seem o be raher small, given our parameers and policy arges; he noable excepion may be labor, which demonsraes more han 50 percen greaer variance under all oher policies relaive o he cap in our baseline scenario. Depending on one s perspecive and prioriies, here is reason o prefer each of he possible insrumens considered here. The inensiy arge achieves he emissions reducion a he lowes welfare cos in he seady sae, wih no reducion o he labor force. The emissions ax achieves he emissions goal wih he lowes welfare cos from a presen value of uiliy perspecive. These resuls are robus o consideraions of developing-counry levels of volailiy in produciviy and heighened risk aversion. Finally, he cap achieves he reducion wih a slighly higher presen value welfare cos han he ax bu ensures he cu is achieved wihou lag 23
Resources for he Fuure and feaures a lower level of labor variance han all oher policies considered. However, his labor sabilizaion resul does no hold when he volailiy of produciviy facor innovaions is raised o a level represenaive of emerging economies. All of hese policies deviae from opimal policy, in which boh emissions prices and quaniies should adjus (procyclically) o produciviy shocks (Heuel 2008). Alhough he emissions cap fixes quaniies, boh he ax and he inensiy arge feaure fixed emissions prices. In pracice, hose disincions may be less imporan in a more realisic, decenralized policy seing. The inensiy arge may no have he same producion incenive effec unless acors hemselves receive addiional allowance allocaions in proporion o heir oupu, as wih radable performance sandards or oupu-based allocaion. However, i does reain he feaure of allowing emissions levels o rise in an expansion. Meanwhile, commonly proposed cosconainmen feaures like banking, borrowing, or price caps end o make he emissions cap behave over ime more like a ax. These design elemens mus be considered in weighing he macroeconomic rade-offs of he differen policies. In fuure work we inend o exend he analysis using a more compuaionally inensive bu flexible backward inducion soluion approach o relax cerain model consrains on he resuls presened here. Our soluion approach of linearizing around he seady sae precludes he consideraion of policy anicipaion, racheing policy sringency over ime, and more realisic models of abaemen efficiency growh. The seady-sae echnique is no suied for anicipaion of he onse of a policy by economic agens, which would affec he dynamics of he ransiion pah. A dynamic policy ramp, where emissions consrains are racheed over ime, is beer capured by a nonseady-sae approach. Finally, when exended o consider he role of economic growh, he linearizaion echnique requires srong assumpions abou he rae of improvemen in abaemen echnology namely, ha i is equal o he rae of produciviy growh. Nex seps o advance his analysis should include decoupling produciviy and abaemen echnology and providing greaer flexibiliy in policy forma and agen expecaions overall. 24
Resources for he Fuure References Aldy, J.E., E. Ley, and I.W.H. Parry. 2008. A Tax-Based Approach o Slowing Global Climae Change. Naional Tax Journal, 6: 493 58. Barlevy, G. 2004. The Cos of Business Cycles and he Benefis of Sabilizaion: A Survey. NBER Working Paper W0926. Cambridge, MA: Naional Bureau of EconomicResearch. Brock, W.A., and M.S. Taylor. 2008. Economic Growh and he Environmen: A Review of Theory and Empirics. In P. Aghion and S. Durlauf (eds.), Handbook of Economic Growh. Amserdam: Norh-Holland, 749 82. Dissou, Y. 2005. Cos-effeciveness of he Performance Sandard Sysem o Reduce CO2 Emissions in Canada: A General Equilibrium Analysis. Resource and Energy Economics 27(3) (Ocober): 87 207. Energy Informaion Adminisraion (EIA). 2004. Annual Energy Review 2004. DOE/EIA- 0384(2004), July 2005. Washingon, DC: Deparmen of Energy. Fischer, C. 2003. Combining Rae-Based and Cap-and-Trade Emissions Policies. Climae Policy (3S2): S89 S09. Fischer, C., and A.K. Fox. 2007. Oupu-Based Allocaion of Emissions Permis for Miigaing Tax and Trade Ineracions. Land Economics 83: 575 99. Goulder, L.H., I. Parry, R. Williams III, and D. Burraw. 999. The Cos-Effeciveness of Alernaive Insrumens for Environmenal Proecion in a Second-Bes Seing. Journal of Public Economics 72(3): 329 60. Herzog, T., K.A. Baumer and J. Pershing. 2006. Targe: Inensiy an Analysis of Greenhouse Gas Inensiy Targes. WRI Repor. Washingon, DC: World Resources Insiue. Heuel, G. 2008. How Should Environmenal Policy Respond o Business Cycles? Opimal Policy under Persisen Produciviy Shocks. Manuscrip. Greensboro, NC: Bryan School of Business and Economics, Universiy of Norh Carolina. Jensen, J., and T.N. Rasmussen. 2000. Allocaion of CO 2 Emission Permis: A General Equilibrium Analysis of Policy Insrumens. Journal of Environmenal Economics and Managemen 40: 36. 25