Second-Best Instruments for Near-Term Climate Policy: Intensity Targets vs. the Safety Valve. Massachusetts Institute of Technology

Transcription

1 Seond-Best Instruments for Near-Term Climate Poliy: Intensity Targets vs. the Safety Valve Mort Wester, Ian Sue Wing, Lisa Jakoovits MIT Joint Program for the Siene and Poliy of Gloal Change, Massahusetts Institute of Tehnology Dept. of Geography & Environment, Boston University Keywords: Unertainty, limate hange, instrument hoie, safety valve, intensity target. Astrat Current proposals for greenhouse gas emissions regulations in the United States mainly take the form of emissions aps with tradale permits. Sine Weitzman s (974) study of pries vs. quantities, eonomi theory predits that a prie instrument is superior under unertainty in the ase of stok pollutants. Given the general elief in the politial infeasiility of a aron tax, there has een reent interest in two other poliy instrument designs: hyrid poliies and intensity targets. We extend the Weitzman model to derive an analytial expression for the expeted net enefits of a hyrid instrument under unertainty. We ompare this expression to one developed y Newell and Pizer (6) for an intensity target, and show the theoretial minimum orrelation etween GDP and emissions required for an intensity target to e preferred over a hyrid. We test the preditions y performing Monte Carlo simulation on a omputale general equilirium model of the U.S. eonomy. The results are similar, and we show with the numerial model that when marginal aatement osts are non-linear, an even higher orrelation is required for an intensity target to e preferred over a safety valve.

2 . Introdution As many ountries prepare to egin their implementation of the Kyoto Protool (Ellerman and Buhner, 6) and the United States egins more serious disussions of domesti limate poliy (Paltsev et al, 7) and potential future international frameworks (Stolerg, 7), interest in alternative regulatory instruments for greenhouse gas emissions is inreasing. Beause greenhouse gases are stok pollutants, we expet their marginal enefits for a given deision period (-5 years) to have a negligile slope. The seminal work y Weitzman (974, 978) and extended y Pizer () and Newell and Pizer (6) showed that under ost unertainty and relatively flat marginal damages that a aron tax equal to the expeted marginal enefit is superior to the optimal emissions ap. Given the experiene with an attempt at a BTU tax under the Clinton Administration, the prevailing view is that a aron tax is politially infeasile, at least in the United States (Washington Post, 7; Newell and Pizer, 6). This politial onstraint on instrument hoie, omined with the signifiant unertainty in aatement osts under a pure quantity instrument, has generated interest in two suoptimal instruments that are superior to quantity instruments in the presene of unertainty: a hyrid or safety valve instrument, and an indexed ap or intensity target. The safety valve is one in whih an emissions ap is set with tradale permits alloated, ut if the permit prie exeeds some set trigger prie, an unlimited numer of permits are autioned off at the trigger prie (Pizer 5; Jaoy and Ellerman, 5), thus reverting to a aron tax. An indexed ap is one in whih the quantity of permits alloated is set not to an asolute emissions target, ut rather is determined relative to some other measurale

3 quantity, for example GDP, whih is orrelated with emissions (Newell and Pizer, 6; Ellerman and Sue Wing, 3; Sue Wing et al., 6). Weitzman (974) originally developed an expression for the relative advantage of pries versus quantity instruments for a pollution externality in the presene of unertainty. Pizer () showed that the safety valve for a stok externality under unertainty is superior to a pure quantity instrument and as good as or etter than a pure prie instrument. There have een several studies of the ehavior of an indexed ap or intensity target under unertainty and its relative advantages and disadvantages to quantity and prie instruments, inluding Newell and Pizer (6), Quirion (5), and Sue Wing et al (6). In general, the advantages of index ap have een shown in the aove studies to e a funtion of the orrelation etween emissions and the indexed quantity, as well as the relative slopes of marginal osts and enefits, and the variane of the unertainty. However, there have een no diret omparisons in the literature etween indexed aps and hyrid instruments. Sine this hoie etween seond-est instruments is one key element in the urrent deate (Paltsev et al, 7), it is useful to demonstrate oth theoretially and empirially when indexed aps should e preferred to hyrid instruments or the reverse. In this study, we develop a rule that indiates when indexed aps will e the preferred instrument for regulating a stok pollutant under unertainty, in terms of expeted net enefits, to a safety valve instrument. We use the theoretial model of an externality developed y Weitzman (974) and extended y Newell and Pizer (6), whih we present in Setion. In Setion 3, we extend this model to first show the optimal trigger prie for a hyrid instrument, and then derive an expression for the 3

4 expeted net enefits under this optimal hyrid poliy. We then ompare this result to the expression derived y Newell and Pizer for an indexed ap, and derive a general rule for when the indexed ap is preferred over the safety valve. In Setion 4, we illustrate the results y onduting unertainty analysis on a stati omputale general equilirium (CGE) model of the US eonomy, and show that with the non-linear marginal osts of the CGE model that the hyrid is even more preferale. Setion 5 gives onlusions and disussion.. Model of Pollution Externality We egin y reviewing the asi Weitzman (974) model and results. Benefits and osts are modeled as seond order Taylor Series expansions aout the expeted optimal aatement quantity target q. Costs and enefits, respetively, are defined as: () () C( q) = θ q ( )( q q ) ( q ) B( q) = q ( q q ) ( q ) We assume that > and ; i.e., osts are stritly onvex and enefits are weakly onave. θ is a random shok to osts with expetation and variane σ. As in Newell and Pizer, we define θ suh that a positive shok redues the marginal ost of produing q. Taking the derivative of net enefits, taking the expetation, and setting to zero, we otain the onditions for the optimal quantity: (3) ( q q ) = ( q ) q 4

5 The optimal aatement will e q if and only if =. Sine the expansion is done around the optimal point, marginal osts equal marginal enefits at that emissions level. The expeted net enefits with an emission ap of q = q is: (4) E{ NBq} = For the prie instrument, emissions would e redued up to where marginal osts equal the tax: (5) p = θ ( q ) q Rearranging, emissions under the tax is (6) q( θ ) = q p θ Beause the optimal tax is equal to the marginal enefits, whih in turn is equal to the marginal ost, p = =, (7) q( θ =. θ ) q Sustituting (7) into the net enefits and taking the expetation yields: ( ) σ (8) E { NB p } = This is the lassi result from Weitzman (974). The net gain from a prie instrument relative to a quantity instrument is: ( ) σ (9) Δ p q = When the slope of the marginal osts exeeds the slope of the marginal enefits, a prie instrument is preferred. 5

6 3. Seond-Best instruments for Cost-Containment We now extend this model to represent a hyrid instrument or safety valve. We will first solve for the optimal trigger prie, given an emissions ap. We then derive the expression for the expeted net enefits of the safety valve. Finally, we derive the expressions for the net gain from an intensity target relative to a safety valve, and show the general onditions under whih eah instrument is preferred. a. Optimal Design of Hyrid Instrument A hyrid regulatory instrument onsists of oth a quantity and a prie instrument. An emissions ap is set, just as in a pure quantity instrument, and emissions permits are alloated among emitters, whih they are allowed to trade. In addition, the regulatory ageny will sell additional permits at some trigger prie p, for as many permits as are neessary. Thus p estalishes a eiling on the permit prie; it an never rise aove this level. If the permit prie is elow p, a rational agent will either uy a permit from the market or aate, and the regulation ehaves like a quantity regime. If the emissions limit is stringent enough for the permit prie to rise aove p, agents will uy additional permits from the government and, for the purposes of alulating net enefits, the regulation ehaves like a prie instrument. The resulting net enefits from the hyrid instrument, as for quantity and prie instruments, depend ritially on the hoie of the emissions limit and the trigger prie. As in Weitzman (974) and in Newell and Pizer (6), we wish to assume optimal hoies of these design variales. However, there is immediately a diffiulty: we know from the Weitzman result, as summarized aove, that the optimal hyrid instrument 6

7 onsists of an emissions limit of zero (i.e., no allowanes) and an optimal trigger prie equal to the optimal pure tax. A hyrid instrument with a non-zero emissions limit is inherently a seond-est instrument ompared with a pure prie instrument, ut may e neessary when a prie instrument is not politially feasile. We therefore proeed for the remainder of this paper under the assumptions that ) a pure emissions tax is not feasile, and ) the emissions limit for a hyrid instrument will e given as an outome of some politial proess. The question we address here is under what onditions is a hyrid instrument with some non-zero ap preferale to an intensity target with an equivalent ap. The first step is to solve for the optimal trigger prie under a non-zero emissions ap. We egin with a simplified version of the model from setion to motivate this result. Assume that the ost unertainty θ is a two-state disrete distriution: θ L = θ δ Pr =.5 θ = θ δ Pr =.5 H E{ θ} = θ = VAR{ θ} = σ = δ When θ = θ, the prie instrument will e in effet, sine the marginal ost is higher than L the expeted value. Conversely, when θ = θ H, marginal osts are lower, and the quantity instrument will e in effet. The seond assumption is that the emissions limit q under the hyrid instrument is the optimal quantity under the pure quantity instrument. When θ = θ H and the ap is in effet, the optimal emissions will e: q = in effet, the optimal emissions will e: q. When θ = θ L and the prie instrument is 7

8 () p q p q q L δ θ = =. The expeted net enefits of the hyrid instrument is: () [ ] = ) ( ) ( } { p p NB E sv δ δ δ Taking the derivative of this expression with respet to p, setting equal to zero, and multiplying through y gives () ( ) = δ δ p. And solving for p gives an expression for the optimal trigger prie, (3) ) ( δ = p. In the general ase, the optimal trigger prie will e a weighted average etween the marginal enefits and the marginal ost in the high ost ase, where the relative weight of the terms depends on the relative slopes of marginal osts and enefits. In general, the optimal trigger prie will e higher than the marginal enefits (the optimal prie for a pure prie instrument. However, in the speial ase of a stok pollutant, suh as greenhouse gases, it has een suggested (Pizer, 999) that an e treated as approximately zero (onstant marginal enefits). In this speial ase, the optimal trigger prie redues to simply. The optimal trigger prie for a hyrid instrument for a stok pollutant is the same as the optimal tax, equal to the marginal enefits. Beause the p = 8

9 optimal trigger prie does not depend on the hoie of emissions limit q, this result holds for any hoie of emissions limit q for the hyrid. Note that this result for the optimal trigger prie is not a new result. This is simply the eiling prie for the hyrid poliy of Roerts and Spene (976). Roerts and Spene showed that for a general pollution externality, the optimal instrument was a hyrid with an emissions ap, a eiling prie, and a floor prie (or susidy), whih is preferred over a pure ap or a pure tax. The intuition is that the step funtion reated y poliy approximates the marginal enefit funtion. Roerts and Spene noted that for the speial ase of onstant marginal enefits, their optimal hyrid onverges to a pure prie instrument equal to the marginal enefits.. Expeted Net enefits of Hyrid Instrument For the remainder of this paper, we will restrit our onsideration to pure stok pollutants (suh as long-lived greenhouse gases) for whih we will assume that the marginal enefits in any single period are essentially onstant; i.e., we assume equals zero. As the aove disussion has shown, for this ase the optimal trigger prie is equal to the marginal enefits at the expeted level of aatement (q ). We an now relax the assumption of a disrete distriution of the ost unertaintyθ, and allow any distriution suh that E{ θ} = and VAR( θ ) = σ. For any distriution of θ around zero, the trigger prie will e ativated with proaility π, and the emissions limit will e inding with proaility - π. The expeted net enefits of a hyrid instrument under these onditions is: 9

10 ( ) = ) ( ) ( ) ( ) ( ) )( ( } { q q q q E q q q q E NB E sv θ θ δ π θ π θ θ = ) ( ) ( E θ π θ θ π θ (4) ) ( σ π =. Thus the additional net enefit of a hyrid relative to a quantity instrument is: (5) q p q sv Δ = = Δ π σ π ) (. For example, if the distriution for θ is symmetri, then π = π =.5 and the advantage of the safety valve relative to a quantity instrument is exatly half the advantage of the prie instrument over the quantity instrument, q p q sv Δ = Δ.. Safety Valve Vs. General Indexed Quantity Newell and Pizer (6) extended the Weitzman model to represent intensity targets. Intensity targets, where the emissions limit is determined from the GDP whih is unertain and a desired emissions intensity ratio, fall under the general ategory of indexed quantity instruments. The most general form of indexed quantities, whih Newell and Pizer refer to as a General Indexed Quantity (GIQ) hooses emissions q as a linear funtion of another random variale x as (7) rx a x q = ) (

11 Where a and r are poliy design variales, and E { x} = x, var( x) = σ, and ov( x, θ ) = σ x. Newell and Pizer show that the optimal hoie of an indexed quantity is (8) ( x) = q r ( x x) q GIQ x where r = ( σ x / σ x ) /( ),and the resulting expeted net enefits are (9) E σ =. { NBGIQ} ρ x ( ) We are interested here in when a hyrid instrument is preferred over an intensity target or vie versa. When the distriution of θ is symmetri, the expeted net enefits of the hyrid is as given in equation (4). Comparing with (9), the indexed quantity will e preferred when σ ( ρ x > ( ) ) σ Rearranging to solve for ρ, the intensity target is preferred when ( )( ) () ρx > π For the ase of a stok pollutant, where, this simplifies to () ρ x > π. π For example, if the distriution is symmetri and the proaility of ativating the trigger prie is ½, then the intensity target would e preferred when the orrelation exeeds/.7. As one should expet, the indexed quantity instrument is preferred when the orrelation etween emissions and the index quantity (e.g., GDP) is high enough. If the orrelation were perfet, ρ =, then the indexed quantity is preferale. If ρ x

12 there was no orrelation, ρ =, the hyrid would e preferred. The orrelation for whih one should e indifferent etween the two instruments is the square root of the proaility of the trigger prie ativating under the hyrid. d. Safety Valve vs. Indexed Quantity The most ommon form of intensity target under onsideration in limate poliy disussions would not take the most general form of the indexed quantity as desried aove. Newell and Pizer point out that a GDP intensity target would set the variale a in equation (9) to zero. They refer to this instrument as an Indexed Quantity (IQ), in ontrast to the GIQ aove, and its optimal form is: () q IQ ( x) = r x Where r = ( v ) (( q / x) v r ) and x x v = σ x. Newell and Pizer show that x x / if ρ, the expeted net enefits for the indexed quantity is x (3) E{ NB IQ } = σ ( ρx ) v x v x ρ xv q where v = ( σ /( )). / q q Comparing the net enefits for the IQ (equation 3) with the net enefits for the hyrid (equation 4), the ritial orrelation where the relative net enefits of IQ are positive is a quadrati funtion of the ratio of the oeffiient of variation (the standard deviation relative to the mean) of the indexed quantity (GDP) to the oeffiient of variation of the emissions, v / x v q. We plot this relationship for a wide range of possile values of v and v for a distriution of θ where π =.5 (Figure ). If this ratio is less x q

13 than.5 or greater than.8, the hyrid instrument is always preferred. Thus the intensity target is most useful in ases where the magnitude of the unertainties in ost and the index are roughly omparale, as also suggested y Newell and Pizer. For ratios etween.5 and.8, the minimum orrelation for whih one would e indifferent etween the two instruments follows the urve in Figure. Note that a ratio of v x / v q =.7 (orresponding to v x /( v q ρ x ) = ), the indexed quantity has the same indifferene orrelation as the general indexed quantity, /. 4. Numerial Example We illustrate the aove analytial expressions y performing an unertainty analysis on a omputale general equilirium model of the U.S. eonomy, and show the onditions under whih an intensity target will e preferred to a safety valve or vie versa. We first riefly desrie the model and the unertainty analysis, then give the results from the model and ompare to the analytial model from the previous setion. a. Model Desription We test the preditions of the preferred instrument using a stati CGE model of the U.S. The model treats households as an aggregate representative agent with onstant elastiity of sustitution (CES) preferenes. Industries are onsolidated into the setoral groupings shown in Tale 3, and are treated as representative firms with nested CES prodution tehnology. For this purpose we adapt Bovenerg and Goulder s (996) KLEM prodution tehnology and parameterization, as shown in Figure. Additional details are given in the appendix. 3

14 The model s algerai struture is numerially alirated using U.S. data on interindustry eonomi flows, primary fator demands, ommodity uses and emissions in the year 4. We simulate pries, eonomi quantities, and emissions of CO in the year 5 y saling oth the eonomy s aggregate fator endowment and the oeffiients on energy within industries ost funtions and the representative agent s expenditure funtion. The proaility distriutions of these saling fators, when propagated through the model, give rise to proaility distriutions for the future value of aseline national inome, energy use and emissions. The parameters whih govern the malleaility of prodution are the elastiities of sustitution etween omposites of primary fators (KL) and intermediate inputs (EM), whih we denote σ KLEM ; etween inputs of apital (K) and laor (L), denoted y σ KL ; etween energy (E) and materials (M), indiated y σ EM ; and among different intermediate energy and material ommodities (e and m), denoted y σ E and σ M, respetively. In natural resoure-dependent setors (e.g., prodution of primary fuels suh as oal) the resoure is modeled as a fixed fator whih enters at the top of the prodution hierarhy, governed y the elastiity σ R. The eletri power setor enompasses two nested prodution strutures, one for primary eletriity generated from fixed fators (e.g., nulear, hydro and wind) whih exhiits features of resoure-dependent setors, and another representing fossil fuel generation whih exhiits features of non-resoure setors. Proaility distriutions for these seven parameters, when propagated through the model, generate proaility distriutions for the hanges in inome and emissions from their aseline levels in response to limate poliy. 4

15 . Parametri Unertainty For this analysis of near-term aron aatement poliies, we onsider unertainty in three ategories of parameters: the GDP growth rate of the eonomy etween 5 and 5, the rate of autonomous energy effiieny improvement (AEEI), and the elastiities of sustitution in the prodution funtions. We riefly summarize here the proaility distriutions for the unertainty parameters, and a detailed desription an e found in (Wester et al., 7). Annual GDP growth rates are modeled as a random walk with drift (Stok and Watson, 988; Shwartz and Smith, ). The volatility is estimated from GDP time series data for the U.S. eonomy from 97- (BEA, 7). For projeting from 5 to 5, instead of the historial mean growth rate, we use the referene EIA foreast (EIA, 7) growth rate of 3% per annum. Our estimated volatility results in a distriution of future growth rates with /- one standard deviation almost idential to the EIA high and low growth ases. The AEEI parameter has a referene (mean) value of.% p.a., onsistent with many other energy eonomi models (Azar and Dowlataadi, 999). The unertainty in AEEI is assumed to e normal with a standard deviation of.4% ased on several analyses (Sott et al., 999; Wester et al., ). The unertainties in the elastiities of sustitution are ased on literature survey of eonometri estimates with pulished standard errors. The details of this survey and the synthesis of the standard errors into a proaility distriution for eah elastiity are doumented fully in Wester et al (7). The empirial proaility distriutions for eah of these parameters are summarized in Tale, along with representative statistis. 5

16 . Results of CGE Model We perform Monte Carlo simulation on the CGE model, drawing random samples of parameter values. In addition to the referene (no poliy) ase, we impose four types of poliy onstraints: an emissions ap, a aron tax, a safety valve, and an intensity target. The stringeny of the emissions ap is defined as the expeted CO aatement under the MCain-Lieerman Senate Bill (Paltsev et al., 7) of Mt CO, leaving U.S. emissions in 5 at 5 Mt CO, and at a marginal ost of $3/ton CO. We define all other poliy instruments suh that they will e equivalent in the mean ase; the aron tax is $3/ ton CO, the trigger prie of the safety valve is $3/ton CO, and the intensity target requires an emissions/gdp ratio to e the same as that whih results under the quantity instrument in the mean ase. Finally, a ritial assumption in the results shown here is that the marginal enefit of CO aatement in 5 is assumed to e $3/ton CO ; i.e., we assume that the imposed poliies are all optimal in the nounertainty ase. The mean and standard deviations for key results are given in Tale. The expeted aatement of CO is the same for all instruments exept the safety valve, whih aates less than the others. The safety valve also has greater unertainty in the aatement than either the tax or intensity targets, ut less than the emissions ap. The unertainty in marginal osts of aatement are greatest for the ap and no unertainty for the tax (y definition), with the safety valve having the next smallest unertainty. Expeted net enefits (alulated assuming a marginal enefit of aatement of $3/ton) are, onsistent with theory, greatest for the tax and least for the ap. The safety valve and the intensity target have similar expeted net enefits, ut the intensity target is preferred. The 6

17 orrelation etween GDP and emissions in the no poliy ase is alulated as.87, so this is onsistent with the expressions in Setion 3. To further test the onsisteny etween the CGE and analytial models, we onstrut an experiment to artifiially vary the orrelation etween GDP and emissions in the Monte Carlo simulation. We annot diretly impose a orrelation, sine the emissions are an endogenous funtion of GDP growth and other fators. Instead, we artifiially inrease or derease the variane of the GDP growth rate unertainty, while holding onstant the variane of AEEI and the elastiities of sustitution. This proedure auses the orrelation etween GDP and emissions to vary aross different sets of random samples. Six different sets of random samples are drawn, with orrelation etween GDP and emissions ranging from.65 to.93. The value of orrelation for whih one would e indifferent etween the intensity and safety valve instruments is.86 (Figure 3). In ontrast, the oeffiients of variation for GDP and emissions from the CGE model are.79 and.84, respetively, giving a ratio v / equal to.94. The relationship plotted x v q in Figure predits an indifferene orrelation value of.74 for these parameter values. The divergene in the indifferene point orrelation etween the CGE model and the analytial model results from the non-linearity of the marginal aatement ost from the model. Our analytial model, like Weitzman s model, assumes linear marginal osts, whereas the marginal osts predited y the CGE model are approximately ui (Figure 4). A non-linear marginal ost urve favors a poliy in whih the expeted aatement is lower than the optimal aatement under ertainty (the referene ap), eause eyond the point of optimal aatement marginal osts are steeply inreasing. As an illustration, we 7

18 use the average marginal aatement ost urve from runs of the CGE model (Figure 5), and alulate the loss in net enefits from mmt more or less than optimal aatement; the net enefit loss in area B, $4,797B, is more than twie that of area A, $8,873B. A safety valve will always result in aatement less than or equal to the referene ap, while an intensity target may require aatement either aove or elow the referene ap. Non-linear marginal osts thus indue a ias in favor of the safety valve, as the instrument operates solely in the region where marginal osts are favorale. We should thus expet that the CGE model with ui marginal osts will predit a higher indifferene point orrelation than the analytial model, whih is what we see here. To test this hypothesis, one would ideally perform an idential experiment exept with linear marginal aatement osts. However, there is no simple way to modify a CGE model to indue gloal linearity. As an approximation, we impose a less stringent emissions target (6mmt) in the CGE model, suh that the relevant portion of the marginal ost urve is nearly linear. We repeat the aove Monte Carlo experiments, for several different assumed varianes for the GDP unertainty, and alulate the expeted net enefits under the hyrid and indexed instruments (Figure 3). Under the less stringent target, the ritial value of orrelation for whih the intensity target eomes preferred over the safety valve is.74, as predited y the analytial model. The preferred poliy instrument is thus dependent on the slope of the marginal ost urve over the span of potential aatement. Beause the atual eonomy is unlikely to have stritly linear marginal aatement osts, the range of onditions in whih the intensity target is preferale to the safety valve, espeially given a reasonaly stringent emissions target, is proaly quite narrow. 8

19 5. Disussion Given the unertainty in eonomi growth and the ost of aating CO emissions, an emissions ap hosen today for some future year has the potential for extremely high welfare loss. The preferale eonomi instrument for a stok pollutant, a aron tax, seems politially infeasile at least in the U.S. and perhaps in other ountries as well. This leads to interest in either a safety valve or an intensity target as a regulatory instrument that has less unertainty in the ost of aatement and welfare losses. Our analysis has shown that, if oth instruments are optimally designed, a high level of orrelation (at least.7 and often higher) etween the ost unertainty and the index unertainty are required to justify the hoie of an intensity target as a regulatory instrument over a safety valve. The design details of the atual poliy are ritial to the hoie etween instruments. For example, a hyrid with a trigger prie muh lower than the marginal enefits will e muh less effiient, and an intensity target may e superior. The analysis presented here fouses exlusively on a single period of relatively few years. For longer time frames divided into multiple periods, an additional question is how anking and orrowing of emissions permits would perform relative to either a safety valve or an intensity target. Finally, there is a question aout how a single period analysis that allows emissions to e higher or lower in response to unertainty an e made onsistent with a long-term target, suh as onentration stailization, where less aatement in one period must e ompensated y aatement in another period. 9

20 Aknowledgements This work was supported y a grant from the Doris Duke Charitale Foundation (#). The authors are grateful for helpful omments from Mustafa Baiker, Denny Ellerman, Karen Fisher-Vanden, Gi Metalf, and Marus Sarofim.

21 Referenes Armington, P.S. (969). A Theory of Demand for Produts Distinguished y Plae of Prodution (Une théorie de la demande de produits différeniés d'après leur origine) (Una teoría de la demanda de produtos distinguiéndolos según el lugar de produión). Staff Papers - International Monetary Fund 6 () (Mar., 969) pp Azar, C. and H. Dowlataadi (999). A Review of Tehnial Change in Assessment of Climate Poliy. Annual Review of Energy and the Environment, 4: Bovenerg, A.L. and L.H. Goulder (996). Costs of environmentally motivated taxes in the Presene of other taxes: general equilirium analyses, Amerian Eonomi Review 86: Brooke, A., D. Kendrik, A. Meeraus, and R. Raman (998). GAMS: A User s Guide, Washington DC: GAMS Development Corp. Bureau of Eonomi Analysis (7). Current-dollar and real GDP, National Eonomi Aounts. Dirkse, S.P. and M.C. Ferris (995). The PATH Solver: A Non-Monotone Stailization Sheme for Mixed Complementarity Prolems, Optimization Methods and Software 5: Ellerman, A.D., & B. Buhner (Deemer 6). Over-Alloation or Aatement? A Preliminary Analysis of the EU Emissions Trading Sheme Based on the 5 Emissions Data, Report No. 4, Joint Program on the Siene and Poliy of Gloal Change, MIT, Camridge, MA. Or see

22 Ellerman, A. D. and I. Sue Wing (3). Asolute vs. Intensity-Based Emission Caps, Climati Poliy 3 (Supplement ): S7-S. Energy Information Ageny (7). Annual Energy Outlook 7 with Projetions to 3. Harrison, G.W., D. Tarr and T.F. Rutherford (997). Quantifying the Uruguay Round, Eonomi Journal 7: Jaoy, H.D. & A.D. Ellerman (4). The Safety Valve and Climate Poliy, Energy Poliy 3 (4): Mathiesen, L. (985a). Computational Experiene in Solving Equilirium Models y a Sequene of Linear Complementarity Prolems, Operations Researh 33: 5-5. Mathiesen, L. (985). Computation of Eonomi Equiliria y a Sequene of Linear Complementarity Prolems, Mathematial Programming Study 3: Newell, R. G. and W. A. Pizer (6). Indexed Regulation, Resoures for the Future Disussion Paper DP Paltsev, S., J. Reilly, H. Jaoy, A. Gurgel, G. Metalf, A. Sokolov & J. Holak (April 7). Assessment of U.S. Cap-and-Trade Proposals, Report No. 46, Joint Program on the Siene and Poliy of Gloal Change, MIT, Camridge, MA. Or see Pizer, W. A. (). Comining prie and quantity ontrols to mitigate gloal limate hange, Journal of Puli Eonomis 85:

23 Pizer, W. A. (999). Optimal Choie of Poliy Instrument and Stringeny under Unertainty: The Case of Climate Change, Resoure and Energy Eonomis : Pizer, W. A. (5). Climate Poliy Design under Unertainty, Resoures for the Future Disussion Paper DP Quirion, P. (5). Does Unertainty Justify Intensity Emissions Caps? Resoure and Energy Eonomis 7: Roerts M. J. and M. Spene (976). Effluent Charges and Lienses under Unertainty. Journal of Puli Eonomis 5: Rutherford, T.F. (999). Applied General Equilirium Modeling with MPSGE as a GAMS Susystem: An Overview of the Modeling Framework and Syntax, Computational Eonomis 4: -46. Sarf, H. (973). The Computation of Eonomi Equiliria, New Haven: Yale University Press. Shwartz, E. and J. E. Smith (). Short-Term Variations and Long-Term Dynamis in Commodity Pries, Management Siene 46 (7): Sott, M. J., R. D. Sands, J. Edmonds, A. M. Lieetrau, and D. W. Engel (999). Unertainty in Integrated Assessment Models: Modeling with MiniCAM.. Energy Poliy 7 (4): 597. Stok, J. H. and M. W. Watson (988). Variale Trends in Eonomi Time Series, The Journal of Eonomi Perspetives (3):

24 Stolerg, S. G. (7). At Group of 8 Meeting, Bush Reuffs Germany on Cutting Emissions. New York Times, June 7, 7. file:///c:/douments%and%settings/mort/my%douments/researh/ent ICE/LISA/NYTimes%artile%-%EU%target.htm. Sue Wing, I., A.D. Ellerman & J. Song (6). Asolute vs. Intensity Limits for CO Emission Control: Performane under Unertainty Report No. 3, Joint Program on the Siene and Poliy of Gloal Change, MIT, Camridge, MA. Or see Sue Wing, I. (4). Computale General Equilirium Models and Their Use in Eonomy-Wide Poliy Analysis: Everything You Ever Wanted to Know (But Were Afraid to Ask), MIT Joint Program on the Siene and Poliy of Gloal Change Tehnial Note No. 6, Camridge MA. Sue Wing, I. (6). The Synthesis of Bottom-Up and Top-Down Approahes to Climate Poliy Modeling: Eletri Power Tehnologies and the Cost of Limiting U.S. CO Emissions, Energy Poliy 34: Wester, M.D., M. Baiker, M. Mayer, J.M. Reilly, J. Harnish, M.C. Sarofim, and C. Wang (). Unertainty in Emissions Projetions for Climate Models. Atmospheri Environment 36 () Wester, M. D., I. Sue Wing, L. Jakoovits, and T. Felgenhauer (7). Unertainty in osts and aatement from near-term aron redution poliies in the U.S. (working paper). Weitzman, M. L. (974). Pries vs. Quantities, The Review of Eonomi Studies 4 (4):

25 Weitzman, M. L. (978). Optimal rewards for Eonomi Regulation, Amerian Eonomi Review 68 (4):

26 Tale : Unertain Parameter Distriutions for Monte Carlo Simulations AEEI GDP Growth Elastiities of Sustitution (%/yr) (%/yr) f q kl em e m Mean Standard Deviation

27 Tale : Results of Monte Carlo Simulations Aatement (Mt CO) Caron Prie ($/ton CO) Net Benefits ($M) Mean St. Dev. Mean St. Dev. Mean St. Dev. Cap Tax Safety Valve Intensity

28 Minimum Correlation to Prefer Indexed Quantity Indexed Quantity Preferred Hyrid Preferred v x /v q Figure : Critial orrelation etween index and ost unertainty for indexed quantity instrument to e preferred over hyrid, as a funtion of the ratio of the oeffiients of variation for indexed quantity x and emissions q. 8

29 Y Y σ KLEM σ R KL EM v R KLEM v K σ KL v K E σ EM M KL σ KLEM EM σ E x e σ M x m v K σ KL v L E σ EM M σ E σ M x e x m A. Non-Primary Setors B. Primary (Resoure) Setors Y σ F-NF y NF y F σ R σ KLEM v NF KLM NF KL F EM F σ KLEM σ KL σ EM KL NF M NF v K,F v L,F E F M F σ KL σ M σ E σ M v K,NF v L,NF x m,nf x e,f x m,f C. Eletri Power Setor Figure. The Struture of Prodution in the CGE Model. 9

30 8 Differene in Net Benefits (Intensity Target - Safety Valve) Mt CO Cap 6 Mt CO Cap Correlation(GDP, Emissions) Figure 3: Relative advantage of intensity target to safety valve as a funtion of orrelation etween GDP and aseline emissions. For an emissions target of 5 mmt, a higher orrelation (at least.86) is neessary for the intensity target to e the preferred instrument. For a less stringent target (6 mmt), for whih the relevant portion of the MAC urve is nearly linear, the indifferene point etween the intensity target and safety valve ours at.74, as was predited y the analytial model. 3

31 Caron Prie ($/ton CO ) 5 5 Median 5% Bounds 9% Bounds Caron Aatement (mmt of CO ) Figure 4: Unertainty in marginal aatement osts in omputale general equilirium model as a result of unertainty in GDP growth, AEEI, and elastiities of sustitution. 3

32 8 MC Caron Prie ($/ton CO ) 6 4 A B MD 3 4 Aatement (mmt of CO ) Figure 5: Loss in expeted net enefits in CGE model from aatement mmt less than optimal and mmt more than optimal. Area A represents the net enefits lost from aating too little ($8,873B), whih is sustantially smaller than area B, the net enefits lost from aating too muh ($4,797B). 3

33 33

34 Appendix: Desription of the CGE Model The simulations in the paper are onstruted using a simple stati CGE simulation of the U.S. eonomy. The model treats households as a representative agent, aggregates the firms in the eonomy into industry setors, and solves for a stati equilirium in the year 5. A. Model Struture The model is a simplified version of that developed y Sue Wing (6). It represents the U.S. in the small open eonomy format of Harrison et al (997). Imports and exports are linked y a alane-of-payments onstraint, ommodity inputs to prodution or final uses are modeled as Armington (969) CES omposites of imported and domestially-produed varieties, and industries prodution for export and the domesti market are modeled aording to onstant elastiity of transformation (CET) funtions of their output. Commodities (indexed y i) are of two types, energy goods (oal, oil, natural gas and eletriity, denoted e i ) and non-energy goods (denoted m i ). Eah good is produed y a single industry (indexed y j), whih is modeled as a representative firm that generates output (Y) from inputs of primary fators (v) and intermediate uses of Armington ommodities (x). Households are modeled as a representative agent who is endowed with three fators of prodution, laor (L), apital (K) and industry-speifi natural resoures (R), indexed y f = {L, K, R}. The supply of apital is assumed to e perfetly inelasti. The endowments of the different natural resoures inrease with the pries of domesti output 34

35 in the industries to whih these resoures orrespond, aording to setor-speifi supply elastiities, η R. Inome from the agent s rental of these fators to the firms finanes her onsumption of ommodities, onsumption of a government good, and savings. The representative agent s preferenes are modeled aording to a CES expenditure funtion. The agent is assumed to exhiit onstant marginal propensity to save, so that savings make up a onstant fration of aggregate expenditure. The government setor is modeled as a passive entity whih demands ommodities and transforms them into a government good, whih in turn serves as an input to oth onsumption and investment. Aggregate investment and government output are produed aording to CES transformation funtions of the goods produed y the industries in the eonomy. The demand for investment goods is speified aording to a alaned growth path rule. Prodution in industries is represented y the multi-level CES ost funtions shown shematially in Figure, whih are adaptations of Bovenerg and Goulder s (996) struture. Eah node of the tree in the diagram represents the output of an individual CES funtion, and the ranhes denote its inputs. Thus, in the non-resoure ased prodution setors shown in panel A, output (Y j ) is a CES funtion of a omposite of laor and apital inputs (KL j ) and a omposite of energy and material inputs (EM j ). KL j represents the value added y primary fators ontriution to prodution, and is a CES funtion of inputs of laor, v Lj, and apital, v Kj. EM j represents the value of intermediate inputs ontriution to prodution, and is a CES funtion of two further omposites: E j, whih is itself a CES funtion of energy inputs, x ej, and M j, whih is a CES funtion of non-energy material inputs, x mj. 35

36 The prodution struture of resoure-ased industries is shown in panel B. In line with its importane to prodution in these industries, the natural resoure is modeled as a setor-speifi fixed fator whose input enters at the top level of the hierarhial prodution funtion. Output is thus a CES funtion of the resoure input, v Rj, and the omposite of the inputs of apital, laor, energy and materials (KLEM j ) to that setor. In oth resoure-ased and non-resoure-ased industries, input sustitutaility at the various levels of the nesting struture is ontrolled y the values of the orresponding elastiities: σ KLEM, σ KL, σ EM, σ E, σ M and σ R. The prodution funtion for eletri power emodies harateristis of oth primary and non-primary setors desried aove. The top-down model therefore represents the eletriity setor as an amalgam of the prodution funtions in panels A and B. Conventional fossil eletriity prodution omines laor, apital and materials with inputs of oal, oil and natural gas aording to the prodution struture in panel A. Nulear and renewale eletriity are generated y omining laor, apital and intermediate materials with a omposite of non-fossil fixed-fator energy resoures suh as uranium deposits, wind energy and hydrostati head using a prodution funtion similar to that in panel B, ut without the fossil fuel omposite, E. The resulting prodution struture is shown in panel C, where total output is a CES funtion of the outputs of the fossil (F) and non-fossil (NF) eletriity prodution su-setors. The elastiity of sustitution etween y F and y NF is σ F-NF >>, refleting the fat that they are near-perfet sustitutes. 36

37 A. Model Formulation, Numerial Caliration and Solution The eonomy is formulated in the omplementarity format of general equilirium (Sarf 973; Mathiesen 985a, ). Profit maximization y industries and utility maximization y the representative agent give rise to vetors of demands for ommodities and fators. These demands are funtions of goods and fator pries, industries ativity levels and the inome level of the representative agent. Comining the demands with the general equilirium onditions of market learane, zero-profit and inome alane yields a square system of nonlinear inequalities that forms the aggregate exess demand orrespondene of the eonomy (Sue Wing 4). The CGE model solves this system as a mixed omplementarity prolem (MCP) using numerial tehniques. The mathematial relations whih define the exess demand orrespondene are numerially alirated on a soial aounting matrix (SAM) for U.S. eonomy in the year 4, using values for the elastiities of sustitution (ased on Bovenerg and Goulder 996) and fator supply summarized in Tale. The asi SAM is onstruted using 4 Bureau of Laor Statistis data on input-output transations, BEA data on the omponents of GDP y industry, and EIA data on the disposition of energy use. The resulting enhmark tale was then aggregated aording to the industry groupings in Tale A.. The eonomi aounts do not reord the ontriutions to the various setors of the eonomy of key natural resoures that are germane to the limate prolem. Sue Wing () employs information from a range of additional soures to approximate these values as shares of the input of apital to the agriulture, oil and gas, mining, oal, and eletri power, and rest-of-eonomy industries. Applying these shares allows the value of 37

38 natural resoure inputs to e disaggregated from the fator supply matrix, with the value of apital eing deremented aordingly. The eletri power setor in the SAM is disaggregated into fossil and non-fossil eletriity prodution (y F and y NF, respetively) using the share of primary eletriity (i.e., nulear and renewales) in total net generation for the year, given in DOE/EIA (4). The orresponding share of the eletri setor s laor, apital and non-fuel intermediate inputs is alloated to the etween non-fossil su-setor, as is the entire endowment of the eletri setor s natural resoure. The remainder of the laor, apital and intermediate materials, along with all of the fuel inputs to eletriity, are alloated to the fossil su-setor. The final SAM, shown in Figure A-, along with the parameters in Tale A-, speify the numerial aliration point for the stati su-model. The latter is formulated as an MCP and numerially alirated using the MPSGE susystem (Rutherford 999) for GAMS (Brooke et al 998) efore eing solved using the PATH solver (Dirkse and Ferris 995). A.3 Dynami Projetions and Poliy Analysis Projetions of future output energy use and emissions of CO are onstruted y simulating the growth of the eonomy in 5. To do this we update the eonomy s endowments of laor and apital and its supply of net imports, and the growth of energysaving tehnial progress. To keep the analysis simple we assume that the model s ase-year endowments of laor, apital and setor-speifi natural resoures grow at a ommon, exogenous rate. 38

39 This is implemented y means of a saling parameter whose value is speified to inrease from unity in the ase year at a rate equal to the long-run average annual growth of GDP, 3 perent in the referene ase, and varied under unertainty. Single-region open-eonomy simulations require the modeler to make assumptions aout the harateristis of international trade and the urrent aount over the simulation horizon. Sine trade is not our primary fous, we simply redue the eonomy s ase-year urrent aount defiit from the enhmark level at the onstant rate of one perent per year. We aount for energy use and emissions y saling the exajoules of energy used and megatons of CO emitted in the ase year aording to the growth in the orresponding quantity indies of Armington energy demand. We do this y onstruting energy-output fators (χ E ) and emissions-output fators (χ C ), eah of whih assumes a fixed relationship etween the enhmark values of the oal, refined oil and natural gas use in the SAM and the delivered energy and the aron emission ontent of these goods in the enhmark year. The resulting oeffiients, whose values are shown in Tale A-, are applied to the quantities of the orresponding Armington energy goods solved for y the model at eah time-step. Finally, to projet the key future delines in the energy- and emissions-gdp ratios, we redue the oeffiients on energy ommodities in the model's ost and expenditure funtions. We do this through the use of an augmentation fator whose value delines at the rates of growth of the AEEI assumed in the text. Fossil-fuel energy supply and aron emissions in the ase year were divided y ommodity use in the SAM, whih we alulated as gross output net exports. In the year, U.S. primary energy demands for oal, petroleum and natural gas and eletriity were 3.9, 4.5, 5., and 4.8 exajoules, respetively (DOE/EIA 4). The orresponding enhmark emissions of CO from the first three fossil fuels were, 439 and 44 MT, respetively (DOE/EIA 3). Aggregate uses of these energy ommodities in the SAM are.8, 85.6, 7. and 6. illion dollars. 39

40 Tale A.. Setors in the CGE Model CGE model setors Agriulture Coal Crude oil & gas Natural gas Petroleum Eletriity Energy-intensive industries Manufaturing Transportation Servies Rest of eonomy Constituent industries (approximate -digit SIC) Agriulture Coal mining Crude oil & gas Natural gas Petroleum Eletriity Paper and allied; Chemials; Ruer & plastis; Stone, lay & Glass; Primary metals Food & allied; Toao; Textile mill produts; Apparel; Lumer & wood; Furniture & fixtures; Printing, pulishing & allied; Leather; Fariated metal; Non-eletrial mahinery; Eletrial mahinery; Motor vehiles; Transportation equipment & ordnane; Instruments; Mis. manufaturing Transportation Communiations; Trade; Finane, insurane & real estate; Government enterprises Metal mining; Non-metal mining; Constrution Setor Tale A.. Sustitution and Supply Elastiities σ KL a σ E σ A σ R d η R e χ E f χ C g All Setors Agriulture σ KLEM h.7 Crude Oil & Gas σ EM i.7 Coal σ M j.6 Refined Oil σ T k. Natural Gas Eletriity Eletriity Energy Intensive Mfg σ F-NF l Transportation.8.4. Manufaturing Servies.8.8. Rest of the Eonomy a Elastiity of sustitution etween apital and laor; Inter-fuel elastiity of sustitution; Armington elastiity of sustitution; d Elastiity of sustitution etween KLEM omposite and natural resoures; e Elastiity of natural resoure supply with respet to output prie; f Energy-output fator (GJ/$); g CO emission fator (Tons/$); h Elastiity of sustitution etween value added and energy-materials omposite; i Elastiity of sustitution etween energy and material omposites; j Elastiity of sustitution among intermediate materials; k Elastiity of output transformation etween domesti and exported ommodity types; l Elastiity of sustitution etween fossil and non-fossil eletri output. 4