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# Are Energy Efficiency Standards Justified?

Ian W.H. Parry, David Evans, and Wallace E. OatesDISCUSSION PAPER© 2010 Resources for the Future. All rights reserved. No portion of this paper may be reproduced without permission of the authors. Discussion papers are research materials circulated by their authors for purposes of information and discussion. They have not necessarily undergone formal peer review. 

## Are Energy Efficiency Standards Justified? Ian W.H. Parry, David Evans, and Wallace E. Oates

Abstract This paper develops and parame terizes an overarching analytical framework to estimate the welfare effects of energy efficiency standards app lied to automobiles and electricity-using durables. We also compare standards with sectoral and economywide pricing policies. The model captures a wide range of externalities and preexisting energy policies, a nd it allows for possible “misperceptions”—market failures that cause underinvestme nt in energy efficiency. Automobile fuel economy standards are not part of the first-best policy to reduce gasoline: fuel taxes are always superior because th ey reduce the externalities related to vehicle miles traveled. For the power sector, potential welfare gains from supplementing pricing instruments with efficiency standards are small at best. If pricing instruments are not feasi ble, a large misperceptions failure is required to justify efficiency standards, and even in this case th e optimal reductions in fuel and electricity use are relatively modest. Reducing economywide carbon diox ide emissions through regulatory packages (combining efficiency and emissions standards) involves much higher costs than pricing instruments.

Key Words: standards, energy taxes, market fa ilure, climate, power sector, gasoline
JEL Classification Numbers: Q48, Q58, H21, R48Contents

1. Introduction ............................................................................................................... .......... 1 2. Analytical Framework ....................................................................................................... . 4 A. Model Structure ............................................................................................................ .. 4 B. Welfare Formulas ........................................................................................................... 9
3. Parameter Values ........................................................................................................... ... 15 A. Basic Transportation Data ............................................................................................ 15 B. Basic Electricity Data ................................................................................................... 1 5 C. Externalities .............................................................................................................. .... 16 D. Misperceptions ............................................................................................................. 17 E. Other Parameters .......................................................................................................... 17 4. Quantitative Results........................................................................................................ .. 18 A. Welfare Comparison of Efficien cy Standards and Energy Taxes ................................ 18 B. Market Failures Required to Justify Diffe rent Levels of Efficiency Standards ........... 20 C. Role of Efficiency Standards in CO 2 Mitigation .......................................................... 21
5. Conclusion ................................................................................................................. ........ 22
References .................................................................................................................... .......... 23 Appendix A. Analytical Derivations .................................................................................... 27 Appendix B. Additional Docume ntation for Parameters .................................................. 34Resources for the Future Parry, Evans, and Oates

1 

## Are Energy Efficiency Standards Justified? Ian W.H. Parry, David Evans, and Wallace E. Oates ∗

1. Introduction In recent years, the political pendulum has swung back toward a far more interventionist role for government in U.S. energy markets. A ma jor manifestation of this movement has been the proliferation of act ual and proposed energy efficiency st andards. Most prominent are the recent rulings on new light-duty vehicles requiri ng manufacturers to increase theirs fleets’ average fuel economy from 25 miles per gallon to about 35 mpg by 2016. In addition, household appliances are subject to numerous standards, incandescent light bulbs are being phased out, and federal energy efficiency standa rds are proposed for residentia l and commercial buildings. What kinds of market failure could justif y energy efficiency standards? An obvious possibility is pollution exte rnalities, especially emi ssions of carbon dioxide (CO 2 ). Generally speaking, however, efficiency standards are an infe rior instrument to energy or emissions taxes. Unlike the pricing approach, efficiency standard s do not reduce the intens ity of use of energy durables; in fact, they tend to increase thei r use through the “rebound effect” (Khazzoom 1980). Nor do they reduce pollution emissions per uni t of energy or produce least-cost outcomes through equating marginal abatement co sts across different sectors. A second class of potential market failures is associated with the so-called energy paradox, the observed reluctance of energy users to adopt apparently cost-effective, efficient technologies (Jaffe and Stavins 1994; Gillinghamet al. 2009; Tietenberg 2009), even energysaving technologies with implicit rates of retu rn in excess of 25 percent (Allcott and Wozny 2009, Hausman 1979, Sanstad et al. 2006, Train 1985). Some analysts c ite this as evidence that consumers misperceive energy efficiency benefi ts perhaps because of “missing” information. Others point out that there might be “hidden cost s” not accounted for in th ese studies, such as product attributes (e.g., people may object to the quality of fluores cent lighting), various search

∗ Ian W.H. Parry, corresponding author, Allen V. Kneese Se nior Fellow at Resources for the Future (parry@rff.org); David Evans, U.S. Environmental Protec tion Agency; Wallace E. Oates, University of Maryland. We are grateful to Karen Palmer and seminar participants at Cornell University , the University of Maryland, the University of Arizona, the Society for Cost-Benefit Analysis , and the ASSA meetings for helpfu l comments and suggestions. Zachary Ficklin provided valuable research a ssistance. We also thank the U.S. Environmental Protection Agency (EPA) for financial support. This study has not been subject to EPA peer review, and the views expressed here should not be attributed to the EPA.Resources for the Future Parry, Evans, and Oates

2 costs, high borrowing costs, and aversion toward “irreversible investme nts” with uncertain returns (Hassett and Metcalf 1993). 1 At the same time, certain information programs (like the voluntary EPA Green Lights progr am and various EnergyStar programs) appear to have increased energy-efficiency invest ments (e.g., Howarth et al. 2000). The general issue is important because the source of the failures has direct policy implications. For externalities, the prefe rred approach is pric ing measures, but for misperceptions, information programs can play an important role. In either case, efficiency standards appear to be a s econd-best measure whose justif ication presumably depends on practical constraints on the ec onomically preferred policy. The actual and prospective adoption of energy efficiency standards raises a number of interrelated policy issues. First, what are their overall welfare effects and how do they compare with welfare effects from other policy options? Second, what combinations of market failures, particularly related to CO 2 damages and the extent of misperceptions market failures, justify efficiency standards of given stringencies? And th ird, to what extent can efficiency standards, when combined with other regulatory approaches, achieve the cost-effectiveness of CO 2 pricing instruments, should the latter prove di fficult to implement in practice? Our paper provides an analytical framewor k for understanding these questions and for gaining some sense of the empirical magnitude of welfare effects, for policies affecting energy efficiency in the transport and power sectors. Fr om the model we derive a series of empirically useful formulas that show how the welfare e ffects of regulatory and pricing policies depend on interactions with externalities, informational market failures , and preexisting energy policies. Although a richer framework than ours might incorporate capital dynamics, greater product disaggregation, and producer he terogeneity, a good deal may still be learned from the parsimonious model developed here, which captu res the most important features for our purposes. In general, prior literature provides insight on some components of our welfare analysis but does not construct the overarching framewor k needed for the policy questions posed here. For example, previous studies have been largel y sector specific and therefore do not compare the welfare effects of standards versus economywid e pricing, nor do they compare and contrast

1 Another possibility is that, rather than utility maximization, consumer behavior is based on simplified decision processes, like “rules of thumb,” because of cognitive cons traints on processing information. There is, however, little empirical work relating these kinds of behavioral fa ilures directly to decisionmaking on energy efficiency.Resources for the Future Parry, Evans, and Oates

3 standards across the trans port and power sectors, or explore to what extent regulatory packages can mimic emissions pricing. There has also b een little attempt to si multaneously integrate externalities and informational market failures. And the conditions required to justify standards of different stringencies, with and without constraints on emissi ons pricing policies, have not been explicitly modeled. 2 One study that also, like ours, provides an overarching framework is Krupnick et al. (2010), who estimate the cost-effectiveness of a wide range of policies, including efficiency standards, to reduce CO 2 and oil use. Their analysis is ba sed on simulating a variant of the Department of Energy’s National Energy Modeling System (NEMS) out to 2030; ours is a much simpler, static analytical framework. Nonetheles s, there is useful complementarity between the two studies, and some of our resu lts on policy costs (gross of extern alities) are broa dly consistent with those from the far more sophi sticated variation of NEMS.
We summarize some of our findings as follows. First, efficiency standards are not part of the optimal policy (or policy combination) to address market failures for automobiles, ev en under our upper-bound cas e for misperceptions market failures. Fuel taxes have a much lower ne t cost because of (unpri ced) externality benefits associated with reduced vehicle use (reduced traffic congestion and so on). The welfare gains forgone under efficiency standards from failing to exploit this response outweigh any potential advantage at targeting mispercep tions failures more directly. Even if fuel taxes are fixed, efficiency standards are warranted only under stri ngent conditions. For example, using standards to cut fuel use by 5 percent under a standard value for CO 2 damages is warranted only if consumers fail to internalize 44 percent of the sa vings from higher fuel economy. In fact, recent rulings that rapidly ramp up the corporate average fuel ec onomy (CAFE) standards are not supported on welfare grounds, even under our bounding cases for market failures. Second, in the power sector, where there are no large ancillary externalities related to product use, even under our upper-bound case for misp erceptions market failures, supplementing electricity taxation with an effi ciency standard can increase welf are by only a relatively small amount. And if taxes are infeasib le, the market failures needed to justify reducing economywide

2 For a selection of prior literature, see Goldberg (1998), Austin and Dinan (2005), Kleit (2004), Fischer et al. (2007), Goulder et al. (2009), and Small (2009) on automobile fuel economy standards and Sanstad and Auffhammer (2010) on efficiency standards for the power sector.Resources for the Future Parry, Evans, and Oates

4 electricity use under standards alone soon become implausibly large beyond reductions of a few percentage points. Third, regulatory approaches, even when us ed in least-cost combinations, are poor substitutes for pricing approaches. When larg e misperceptions failures justify a role for efficiency standards, and when these standards are used in combination with CO 2 emissions standards for the power sector, the costs of this regulatory co mbination are around $15 billion more per year than for an emissions pricing pol icy (given the goals for reducing energy-related CO 2 emissions envisioned in recent climate bills). The rest of the paper is organized as follows . The next section deve lops the analytical model and derives key formulas. Section 3 discu sses the baseline data. Section 4 presents the main quantitative findings. Section 5 su mmarizes and discusses model limitations.
2. Analytical Framework We develop a static, genera l equilibrium model with CO 2 emissions produced from vehicle fuel combustion, power ge neration, and other sectors. The model captures the possibility of suboptimal investment in energy efficiency for vehicles and electr icity durables; broader externalities (which are especially important for automobiles); energy efficiency regulations that apply comprehensively to automobiles and par tially to electricity durables (representing a combination of appliance standards, building codes, etc.); possible taxes on energy and CO 2 ; and possible regulations on the power generation mix. Our analysis implicitly assumes that any regulations—efficiency or emissions standards—ar e “smart” in terms of providing credit-trading provisions that equate marginal comp liance costs across different firms.

A. Model Structure (i) Household utility At the start of the period , households purchase three dur able goods for use over the period, indexed by i : an automobile ( A ); an electricity-intensive durable good ( R ) representing an aggregation of final and intermedia te products that are, or could potentially be , subject to binding energy efficiency regulations (e.g., appliances, bu ildings, lighting); and an electricity-intensive durable good ( N

) representing an aggregation of all electricity-using goods that might be difficultResources for the Future Parry, Evans, and Oates

5 to regulate. Although R is an aggregate of many heterogene ous products, we indicate below how results would change if efficiency regulations were applied to narro wer product categories. 3 The representative agen t’s utility function is (1a) ) , , , , , , , ( E A N R A Z Z C Y I v v v u u = (1b) )) ( , , ( i i i i i i e m S v v μ = In (1b), v i (.) is subutility from use of durable good i , S i is purchases (at the start of the period), or the stock, of durable good i , and m i is the intensity with which this good is used— miles driven per auto or hours of operati on for electricity-using goods over the period. 4 e i is energy consumption per unit of use of durable good i—that is, fuel use per mile of driving or electricity use per unit of time; the inverse of e i is thus energy efficiency. The role of e i in the utility function is to allow for possible hidden costs from reductions in energy intensity. For example, fuel-saving technologies have hidden co sts if they imply reduced vehicle power, and fluorescent bulbs may have hidden costs if househol ds prefer the brighter , instantaneous lighting from incandescent bulbs. Thus, μ i represents a broad index of attributes from product i , where μ

i (.) is weakly concave with 0 ≤ ′ i μ . The e i may be determined by household choices (implicitly through their choice of models with and without advanced energy-saving technologies); alternatively, e A and e R may be set by the government, if en ergy intensity standards are binding. 5 In (1a), C is carbon dioxide emissions; Z A is an index of externalities related to automobile use, including local pollution, congesti on, and accidents; Z E

is local pollution from electricity generation. Here we have omitted exte rnalities from oil dependence because they are difficult to define, let alone quantify—including th em would be equivalent to attaching a higher value to CO 2 reductions from the transpor t sector (see below). Finally, I is an aggregate of industrial consumer products, and Y is an aggregate of nonindustrial consumer goods and services that do not use electricit y. The former sector captures CO 2 emissions outside the power and (light-duty) transport sectors, and the latter repr esents “clean” consumption.

3 Explicitly distinguishing the use of electricity durables at the industrial, commercial, and residential level would not affect our results.
4 m i and S i enter v i separately, rather than as a product, to avoid the corner solution where only one good of type i is purchased in the entire economy.
5 Historically, standards for autos have been defined in te rms of fuel economy rather th an fuel intensity. However, they are now inte grated with CO 2 (and hence energy) standards per mile.Resources for the Future Parry, Evans, and Oates

6 All variables are economywide aggregates, e xpressed in per capita terms (variables are therefore continuous even though the quantity of durables is discrete at the individual level). A bar denotes a variable perceive d as exogenous by individuals. u (.), overall utility, is increasing and quasi-concave in its firs t five arguments and declining in the last three; v i (.) is increasing and quasi-concave in its arguments. (ii) Perceived energy costs The (actual) lifetime energy cost for durable good i , denoted L i , is (2) i i E E i e m t q L ) ( + = , i = R , N , A A G G A e m t q L ) ( + = where discounting over the lifecycle is implicit. q E and q G are the producer prices of electricity and gasoline, respectively, and t E

and t G are specific taxes on these goods (residential electricity use is currently taxed at the state level but gaso line is taxed at both fede ral and state levels). Lifetime costs equal product use, times energy consumption per unit of use, times the taxinclusive consumer price. The lifetime cost, as perceived by agents when the good is purchased, is (1

− ρ

i ) L i , where 1 0 ≤

≤ i

ρ reflects the extent to which agents misperceiv e, or otherwise fail to internalize, future energy costs relative to actual costs. Such unde rvaluation could result fr om misperceptions over future energy efficiency, limitations on their cogn itive ability to absorb and process information on energy efficiency, or systematic errors in fore casting energy prices or use of energy durables. Implicitly, government programs, such as require d fuel economy stickers on salesroom cars or certified labeling of appliance efficiency through EnergyStar, imply a lower value of ρ i . (iii) Externalities Externalities are defined by (3a) 

### I z E z G z C I C E C G C 

### + + = , A A A A S m z Z = , E z Z E

E = (3b) A A A S

m e G = , i i i i S m e E = , G i ≠ , N R E E E + =
G

is gasoline consumption (the fuel consump tion rate times miles per vehicle times the vehicle stock). Similarly, E i is electricity use from product i , and E is total electricity use. In (3a), G C 

### z , E C 

### z and I C 

### z denote the CO 2 intensity of gasoline, electricity, and industrial production, respectively. G C 

### z and I C 

### z are given, but E C 

### z is chosen by firms, implicitly through their chosen mix of power generation fuels. z A is an index of conges tion, accident, and local pollution externalities per mile of automobile tr avel; local emissions vary with mileage rather than fuel use, given that all vehicles must satisfy the same emissions per mile standardsResources for the Future Parry, Evans, and Oates

7 regardless of their fuel economy, which decouple s emissions from fuel economy (Parry and Small 2005). z E

is an index of local emissions, whic h vary in proportion to power generation (this potentially includes NO X

, mercury, and SO 2 , depending on how these emissions are regulated). (iv) Production All firms are competitive and produce under consta nt returns; thus, producer prices equal unit production costs. For our purposes, this assumption seems reasonable for automobiles. 6 For the power sector, the issue is mo re complex, and we return to it at the end of the paper. Product and energy prices are determined by (4a) ) ( i i i e k p = , I I p p = , Y Y p p = (4b) G C C G G 

### z t q q + = (4c) E C C E C E E 

### z t z k q + = ) ( (4d) C E C E 

### t z k =

′ )

(
where C 

### t is a uniform, economywide “price” on CO 2 emissions, assumed not to exceed its Pigouvian level. For now, this represents an emi ssions tax, but later we also consider cap-andtrade systems. In (4a), p i is the consumer price and k i (.) the unit production cost for durable good i , respectively. k i (.) is increasing with respect to reductions in e i , reflecting the incorporation of (costly) energy-saving technol ogies into the product. I p and Y p denote the (fixed) unit production costs of the industrial good and the clean good, respectively. In (4b), the producer price of gasoline equals the (fixed) unit production cost G q plus the pass-through of the CO 2 price. In (4c), k E

(.) is the unit production cost for pow er generation, which is increasing and convex with respect to reductions in E C 

### z , reflecting costs of substitu ting coal with cleaner fuels (or possibly, down the road, in stallation of carbon capture an d storage technologies). The producer price of electricity equals th is cost plus the pass-through of the CO 2 price. In (4d), we assume that power companies abate CO 2 emissions from fuel switching until the incremental cost equals the (avoided) tax payment.

6 Although in practice there are signif icant differences between the price of new autos and their unit production cost, this appears to make little quantitative difference to the overall efficiency costs of fuel economy regulations and fuel taxes, given their modest effect on new vehicle demand (e.g., Austin and Dinan 2005).Resources for the Future Parry, Evans, and Oates

8 Firms play a passive role, meeting househol d demand for products, fuel, electricity, and energy efficiency (if it is not fixed by regulation). (v) Government The government sets maximum energy efficiency standards for automobiles, A e , and regulated electricity durables, R e . We also consider a polic y combination involving these standards and an emissions standa rd imposed on the power sector, E C z
. The government budget constraint, equating spending and revenue from gasoline, electricity, and emissions pricing, is (5) 

### C t E t G t GOV C E G 

### + + =
where GOV is a lump-sum government tr ansfer to households to captu re the recycling of revenue to the economy. (vi) Household optimization Households optimize in two steps. First, they make upfront choices over product purchases and energy efficiency, based on percei ved lifecycle costs and planned use of durables and consumption goods, subject to a perceived, fixed-income budget constraint. Second, during the course of the period, they may reoptimize over product usage if energy costs differ from initial perceptions. 7 As shown in Appendix A, this optimization implies that the private benefit from one additional durable good equals its price plus perceived lifetime energy cost; the private benefit from incremental usage of the durable good equals its (tax-inc lusive) energy cost; and energy intensity is reduced until the resulting incr ease in cost of the durable equals the marginal saving in perceived lifetime energy costs less the value of any reduction in other product attributes.
All demands are taken to be constant elas ticity functions of the relevant own-price— product prices plus perceived lifetime energy co sts for durables, and energy prices for product usage and energy intensity (see Appendix A) . In addition, we make the (reasonable) approximation that the demand for travel, indu strial goods, and regulat ed and unregulated electricity durables are independe nt; this rules out, for example, the possibility that reduced emissions from sector-specific policies in the tran sport sector are partly offset by extra emissions

7 This is reasonable because vehicle or appliance usage is an ongoing decision, unlike the one-off consumer durable purchase decision, which requires forecasting energy use and prices over a long period of time.Resources for the Future Parry, Evans, and Oates

9 in the industrial and power sectors. 8 From the demand functions we can decompose the following relations (Appendix A): (6) G m G 

### η A S G 

### η + A e G 

### η + G η = , + i m E η i S E η i e E η + i E 

### η = , i ≠ A

A m G η , A S G η and A e G η are the elasticity of miles per vehicle, vehicle demand, and gasoline intensity with respect to gasoline pri ces, and the sum of these elasticities, G η , is the overall gasoline price elasticity. i m E η , i S E η and i e E η are the elasticity of usag e of electricity durable i , the demand for that good, and its elec tricity intensity, with respec t to electricity prices, and
i E η is the elasticity of electric ity consumption for good i with respect to the electricity price. (All elasticities are negative.)

B. Welfare Formulas We now discuss formulas (derived in Appendi x A) for the marginal welfare effects of policy-induced reductions in gasoline, electricity, and CO 2 emissions. We focus on marginal costs (denoted MC ), defined net of welfare benefits from correcting market failures—thus, policies improve welfare up to the point where MC is zero. Marginal costs are obtained by totally differentiating the household’s in direct utility function with respect to a po licy variable, accounting for changes in pollution, other extern alities, and (balanced budget) government transfers, and dividing by the induced change in gasoline, electricity, or CO 2 . We also briefly discuss how results change when CO 2 is fixed by a cap, when e fficiency standards should complement pricing instruments, the relation between information dissemination programs and efficiency standards, and the welfare potential of policies combining efficiency standards with emissions rate standards. (i) Reducing gasoline use Gasoline tax . The marginal cost of a tax- induced reduction in gasoline ( G t G 

### MC ), expressed per gallon, can be decomposed as follows:
(7a)



### − − − = A C C C G t G 

### z t EXT t MC G 

### ) (

G S G m G

A A A A

e EXT η η η +

⋅ G S G e G G G A A A t q η η η ρ +

⋅ + ⋅ − ) (

8 For example, in Small (2009) the effects of transportation policies on the power sector are negligible. Down the road, the power and transportation sectors could become more integrated if there is substantial penetration of plug-in electric vehicles and greater competition between the two sectors for biomass-based fuels. For the most part, electricity durables that are unregulated (e.g., TV sets) ar e not close substitutes for regulated electricity durables (e.g., refrigerators, buildings).Resources for the Future Parry, Evans, and Oates

10 where
(7b) G G G G q G t q t G

− Δ

− + = η / 1 0 ) ˆ 1 )( ( , 0 0
ˆ G G G G − = Δ
(7c) 

### λ /
C Z C 

### u EXT

− = , 

### λ /
A Z A A 

### u z EXT
⋅ − = (7d) 

### 0 = A e G 

### η if A e is binding

G ˆ Δ denotes the proportionate re duction in gasoline (and sim ilarly for other variables with ^ below), and superscript 0 denotes an initial value prior to policy change. λ is the marginal utility of income. As indicated in (7c), C 

### EXT is the (monetized) disutility, or external cost, per additional unit of CO 2 emissions, and A EXT is the external cost from congestion, accidents, and local pollution, per extra auto mile. We assume C 

### EXT and A EXT are constant (which is reasonable over the range of fuel reduc tions considered below). The first component of the marginal cost in (7a) is the prevaili ng fuel tax or wedge between forgone consumer benefits and savings in supply costs per gallon reduction in gasoline. In (7b) the tax rate rises with respect to the proportionate reduc tion in gasoline. Thus, this first component determines the slope of the ma rginal cost as well as contributing 0 G t to its intercept, given preexisting gasoline taxes. All other components in (7a) se rve to shift down the marginal cost curve and redu ce its intercept. The second component nets out the margin al external benefit from reducing CO 2 emissions per gallon, less any amount of th is externality inte rnalized through a CO 2 tax. The third component nets out the marginal exte rnal benefit from reduced auto mileage. It equals A EXT , divided by e A to express externalities in costs per gallon, where e A falls with higher taxes as manufacturers incorporate fuel-saving te chnologies into vehicles. This component is multiplied by the fraction of the gasoline demand elasticity that is due to reduced overall mileage (through reduced intensity of vehicle use and reduced demand for vehicles) as opposed to improved fuel economy. The smaller the fraction of the marginal reduction in gasoline use that comes from reduced driving, the smaller the mileage-related ex ternality benefits per gallon reduction in fuel use (Parry and Small 2005). The final component nets out the potential we lfare gain from offsetting misperceptions market failures. It equals the noninternalized fraction of fuel economy benefits, times the consumer value per gallon of gasoline savings, ti mes the fraction of the gasoline reduction that comes from improved fuel economy, and also redu ced vehicle purchases (recall that vehicleResources for the Future Parry, Evans, and Oates

11 demand is excessive when 1 < A ρ ). Thus, different assumpti ons about the share of the incremental gasoline reduction that comes from improved fuel economy, as opposed to reduced mileage per vehicle, will alter the relative magnitude of the la st two cost components in (7a), but in opposite directions. Finally, from (7d), preexisti ng and binding fuel economy sta ndards alter the tax-induced welfare cost indirectly by eliminating the reduc tion in fuel intensity. This (greatly) reduces the magnitude of the last welfare component. Howeve r, it also implies that mileage now falls in proportion to gasoline use, which (greatly) increases mileage-related externality benefits per gallon reduction in gasoline. As discussed in Small (2009), A e G 

### η may still be nonzero, even with binding fuel economy standards (e.g., households with two vehicles may drive the more efficient one more intensively in response to higher fuel prices); hence our anal ysis with and without binding standards prov ides bounding cases. Energy efficiency standard . The marginal cost from tightening a (binding) fuel per mile standard ( A e G 

### MC ) is (Appendix A)
(8a) 

### +

− − = A C C C G e G 

### z t EXT MC A 

### ) ( δ

A A

A A r r
e EXT

− ⋅ 1 A G G A 

### r t q

− ⋅ + ⋅ − 1 1 ) ( ρ

(8b) G r G G G q G t q A A e G

− Δ

− + = − ) 1 ( 1 ) ˆ 1 )( ( η δ
(8c)

A A A

A A A A e d S m d S m e r ) (

⋅ − = A m G 

### η

− ≅

r

A denotes the rebound effect. As defined in (8c) , this is the fraction of the initial fuel savings from an incremental reduction in fuel intensity ( A A S m ) that is offset by the increase in mileage in response to lower fuel costs per mile ( A A A A e d S m d e / ) (

⋅ − ). Here (following Small and Van Dender 2006), we approximate by assuming that changes in fuel economy do not affect vehicle demand. The rebound effect is therefore equivalent to A m G η

− because proportionate reductions in fuel consumption and fuel prices have an equivalent effect on per mile fuel costs and vehicle use.

G δ is the shadow price on gasoline. As show n in Appendix A, it corresponds to the gap between the increase in vehicle costs and possibl e loss of vehicle attri butes, net of the actual savings in lifetime fuel costs, expressed per gallon of fuel savings. Its initial value (when 0 ˆ = G ) is the preexisting fuel tax (whi ch distorts equally all margin s of behavior affecting fuel consumption). However, this shadow cost rises more rapidly with respect to G ˆ than the gasoline tax does in (7b) because the policy places almost the entire burden of fuel savings on improvedResources for the Future Parry, Evans, and Oates

12 efficiency and does not exploit savings from reduced mileage per vehicle. In other words A e G MC is more steeply sloped than G t G MC . In fact, because of the rebound effect, an even larger improvement in fuel economy is required to achieve a given G ˆ (i.e., the rebound effect increases the rate at which G δ rises). The second component in (8a), reflecting net CO 2 benefits per gallon, is the same as in (7a). However, the third component in (8a) is a positive (rather than negative) cost because mileage-related externalities incr ease with the rebound effect; thus , this component shifts up the marginal cost curve. On the othe r hand, to the extent that lifecycle costs are not in ternalized, the last component is a larger gain than under the tax. This is becau se all, rather than a fraction, of the gasoline reduction comes from improved fuel economy (or reduced vehicle demand). These gains are magnified (moderately) to the extent th at the fuel economy increase must be higher, because of the rebound effect, to achiev e a given reduction in fuel use. (ii) Reducing electricity use The marginal cost of reducing electricity th rough higher electricity taxes, expressed per kWh, is given by
(9a)



### − − − = E C C C E t E 

### z t EXT t MC E 

### ) ( E 

### EXT

E S E e E

U R i E E i i i t q η η η ρ +

⋅ + ⋅ − 

## ∑

= , ) (

where (9b) E E E E 

### q E t q t E



### − Δ

− + = η / 1 0 

### ) ˆ 1 )( ( (9c) 

### λ /
E Z E E 

### u z EXT
⋅ − = (9d) 

### 0 R e E 

### η = if R e is binding

E EXT is the external cost from non-CO 2 pollution, per extra kW h (assumed constant). The components of (9a) are essentially anal ogous to those for the gasoline tax in (7a), with two exceptions. On e is that that non-CO 2 externalities are proporti onal to all changes in electricity consumption (rather th an just those from changes in product use). The other is that noninternalized lifecycle costs ar e weighted averages across th e two electricity durables. The marginal cost of the efficiency standard ( R e E MC ) is similar to that for the auto efficiency standard in (8a and b) (see Appendix A for the formul a). The big difference is that there is no exacerbation of non-CO 2 externalities from the re bound effect. The final welfare component for the efficiency standard is analogous to that in (8a), with parameters applying only to the regulated durable.Resources for the Future Parry, Evans, and Oates

13 (iii) Deriving iso-market failures curves required to justify efficiency standards For any given level of (prevailing or pros pective) energy or emissions taxation, an efficiency standard that furt her reduces gasoline by amount G ˆ , or electricity by E ˆ , is fully efficient if the marginal cost curves, G e G MC and R e E MC , have negative intercepts and are exactly zero when evaluated at these reductions. From these conditions, it is straightforward to obtain “iso-market failure” curves that indicate combinations of CO 2 (or energy security) externalities and misperceptions failures that ar e required to justify efficiency standards of given stringencies. (iv) Reducing (nationwide) CO2 emissions The marginal costs of energy taxes and efficien cy standards are easily expressed in costs per ton of (economywide) CO 2 reduced, by dividing the above expressions by CO 2 per gallon or CO 2 per kWh of electricity, as follows (see Appendix A):
(10) A C t

G t C z MC MC G G = , A C e

G e C z MC MC G G = , E C t

E t C z MC MC E E = , E C e

E e C z MC MC R R =
The marginal cost per ton of reduced CO 2 under the emissions tax, denoted C t C 

### MC , can be expressed thus (see Appendix A): (11a) C t C 

### MC G t C G MC

⋅ = α E t C E MC

⋅ + α C I E C z 

### t EXT t E



### ⋅ +

− ⋅ + α

α ) ( (11b) C C t C η β ˆ

⋅ = Equation (11b) shows our assumed func tional relation betw een economywide CO 2 emissions and the CO 2 tax, where β and C η are parameters. In (11a) G α , E α , E z 

### α , and I α are the share of the margin al, tax-induced reduction in nationwide CO 2 emissions from reduced gasoline us e, reduced electricity consumption, reductions in CO 2 per unit of electricity, and reductions from the industrial sector, respectively (see Appendix A for definitions of thes e terms). The marginal cost of the CO 2 tax is the envelope of the marginal costs of reducing emissions through these four behavioral responses. For industrial reductions, the margin al cost is simply the CO 2 tax rate, since there are no broader market failures for this margin of behavior, bu t for reductions from reduced emissions intensity in the power sector, local pollution effects are netted out from the CO 2 tax. (v) The distinction between cap-and-trade and emissions taxes We show, in Appendix A, that the marginal cost formulas G t G 

### MC , G e G 

### MC , E t E MC , and

R e E MC change in one regard when CO 2 emissions are fixed by a bi nding cap-and-trade system rather than taxed. The term C C t EXT

− in the second component of the marginal cost formulas isResources for the Future Parry, Evans, and Oates

14 replaced by C t C 

### MC . In this case, each unit reduction in CO 2 due to the new policy is offset by a unit increase in emissions in the economy as a whole (via a reduction in the CO 2 allowance price), resulting in a cost savings of C t C 

### MC . Thus, if the emissions price imposed by climate policy is greater than 50 percen t of the external cost of CO 2 emissions, there is a greater gain from reducing emissions through other policies when the carbon instrument is cap-and-trade rather than an emissions tax. (vi) Potential value of en ergy information programs As shown in Appendix A, the marginal cost of information programs, per unit reduction in gasoline, electricity, or CO 2 emissions, is analogous to the marg inal cost of the relevant energy efficiency standards (hence we do not illustrate separate results for information programs). Information programs increase energy efficiency, ju st like standards, though this is achieved indirectly through raising the per ceived private benefits from hi gher efficiency. The effects of these programs may be limited if ρ is already close to zero. However, information programs avoid the risk of excessively increasing en ergy efficiency, in the sense of pushing the incremental costs of energy efficiency improveme nts beyond the point at which they are justified by discounted energy savings. (vii) Regulatory alternatives to CO 2 pricing Although not a central focus of our paper, a CO 2 /kWh emissions standard can be a relatively low cost approach for e xploiting the large potential for CO 2 emissions reductions in the power sector. Our interest here lies in the extent to which combining this policy with efficiency standards can mimic the effects of a CO 2 pricing policy, which is especially timely given the practical obstacles to pricing policies. As shown in Appendix A, the marginal cost of the emissions standard is approximately equivalent to the CO 2 tax that would produce the same overall emissions reduction as the emissions standard, divided by the sh are of reductions under this CO 2 tax that would come from reduced emissions intensity in the power sect or. The emissions standard does also reduce electricity demand because abatement costs are pa ssed forward into electricity prices. However, this effect is relatively small, given that the em issions standard does not cr eate the equivalent of carbon tax payments, or allowances rents, that are reflected in higher electricity prices under market-based policies.
All of the above formulas were simulated in a spreadsheet, us ing functional form assumptions noted above and parameter values de scribed below. In addition, we also mentionResources for the Future Parry, Evans, and Oates

15 some results for policy combinations that were obtained iteratively in the spreadsheet (rather than from explicit analytical formulas).

3. Parameter Values Here we comment briefly on data assumpti ons for our simulations, as summarized in Table 1, which is representative of year 2008 or thereabouts. Parameters for the transportation sector are taken from prior literature; for the pow er sector we construct estimates by aggregating products within regulated a nd unregulated sectors.
A. Basic Transportation Data We assume the average fuel economy of the ( on-road) light-duty vehicle fleet is 23 miles per gallon, or alternatively, fuel intensity is 43.5 gallons per 1,000 miles (BTS 2009, Table 4.23). From Parry and Small (2005), we take the combin ed federal and (average ) state gasoline tax to be $0.40/gallon And, based on the average price between 2003 and 2008, we assume a pretax gasoline price of $2.15/gallon. 9 Initial fuel use is taken to be 130 billion gallons (BTS 2009, Table 4.5). Based on the widely cited study by Small a nd Van Dender (2006), we assume that the (long-run) own-price elasticity of gasoline is –0.4, with half of the response due to changes in fuel economy and half due to changes in vehicle miles. Thus, the gasoline demand elasticity is – 0.2 in the presence of fully binding fuel economy st andards. We further assume that the mileage response is split equally between changes in the ve hicle stock and miles per vehicle. This implies a rebound effect of 10 percent (for a given vehicle stock), which is approximately consistent with Small and Van Dender (2006).
B. Basic Electricity Data Electricity consumption in th e residential, industrial, a nd commercial sectors was 4,176 billion kWh in 2007, according to the Energy In formation Administration (EIA 2009). Based on classifying products, and aggregating over each pr oduct’s electricity use, in EIA surveys, we assume that 60 percent of this consumption is from durables that are, or ar e potentially, subject to efficiency standards. The main groups in the re gulated category include most major appliances, lighting, buildings, and heating a nd cooling equipment, while the unregulated category includes

9 See http://tonto.eia.doe.gov/dnav/pet/hist/mg_tco_usA.htm

.Resources for the Future Parry, Evans, and Oates

16 smaller appliances, audio and entertainment equi pment, industrial processes such as assembly lines. We suspect that a large share of industrial electricity consumption is unlikely to be subject to efficiency standards given th e heterogeneity of the electrici ty-consuming capital stock across industries and facilities. Furtherm ore, in the analysis below, we make the favorable assumption that the set of efficiency standa rds reduce consumption at least co st. That is, the marginal cost per kWh of consumption reduced of each indi vidual product standard is the same. Energy intensity for the two electric ity sectors is simply usage divided by 8760 hours per year. The average (pretax) electricity price over all end users was 8.2 cents/kWh in 2007, and state taxes averaged 0.9 cents/kWh (EIA 2010). We assume that the own-pri ce elasticity of demand for electricity is –0.4 for both regulated and unregulated sectors, based on a lo ng-run estimate by Myers et al. (2009), which is broadly consistent with other evidence (Sanst ad and McMahon 2008). We further assume that the use per product, product demand, and electr icity intensity elasticities are –0.13, –0.07, and – 0.2, respectively, for both sectors. 10

C. Externalities As regards CO 2 emissions intensities, a gallon of gasoline combustion produces 0.009 ton of CO 2 , and given the prevailing fuel mix, the average emissions inte nsity of power generation is 0.0005 ton of CO 2 per kWh (EIA 2009). 11 We consider a benchmark value of $20/ton for CO 2 damages and a range of up to $100/ton for se nsitivity analysis (see Appendix B for the justification). The benchmark value implies CO 2 damages of 18 cents/gallon and 1 cent/kWh. As regards oil dependence, Brown and Hunti ngton (2009) put the external costs due to macroeconomic disruptions from world oil price volatility at equivalent to about 10 cents per gallon. Perhaps more important, dependence on an oil market influenced by hostile regimes might constrain U.S. foreign policy or threaten national security, though these geopolitical costs are not easily quantified. Therefor e, we simply infer the implicit costs per gallon that would be required to justify automobile efficiency standards of different stringencies.

10 The first figure is Myers et al. (200 9)’s electricity demand elasticity over the very short run, when there is very limited scope for altering product demand or energy efficiency.
11 The latter reflects an average rate over different fuels. In practice, natural gas is often the marginal fuel, but its emissions intensity of 0.00045 tons/kWh for state-of-t he-art plants is close to the average (EIA 2009).Resources for the Future Parry, Evans, and Oates

17 From Small and Verhoef (2007), we assume local pollution damages of $0.01/auto-mile. For marginal congestion costs, we update Pa rry and Small (2005)’s figure by 30 percent to $0.045/mile. 12 For marginal accident externalities, we increase Parry and Small (2005)’s estimate to $0.035/mile, based on the value of a statistical life now assumed by the U.S. Department of Transportation, $5.8 million. Thus other extern alities amount to $0.09/mile for autos. For electricity generation there are no extern alities analogous to th e energy security and product usage externalitie s applicable to autos. 13 And local pollution benefits are modest, 0.13 cents/kWh, because the bulk of high-damage em issions are capped under the sulfur trading program (see Appendix B).
D. Misperceptions Appendix B describes empirical literature on implicit discount rate s and possible reasons why they exceed market rates. We consider two bounding cases, one in which there is no misperceptions market failure ( ρ i = 0); that is, any differenc es between implicit and social discount rates are entirely explai ned by hidden costs. In the other, the entire difference is due to misperceptions over energy efficiency benef its. For electricity durables, we assume ρ i ( i = R , N ) = 0.62 for this case, based on typical estimates of implicit discount rates; for automobiles, we adopt a bounding case of ρ A = 0.65, based on a common assumption that consumers consider fuel savings from higher efficiency over only the first three years of a vehicle’s life (see Appendix B).

E. Other Parameters
We choose the α s in equation (11) to imply that fo r a 10 percent redu ction in energyrelated, economywide CO 2 emissions under a CO 2 tax, 60 percent of these reductions would come from reduced emissions inte nsity in the power sector, 20 pe rcent from reduced electricity demand, and 10 percent each from automobiles and from industrial and other sources. These assumptions are approximately consistent with U.S. EPA (2010), EIA (2008), and the relative responsiveness in the po wer and transport sectors implied by our own assumptions. Note that CO 2 emissions from the power sector (which initially account for 40 percent of nationwide

12 This accounts for recent growth in th e value of travel time and congestion (b ased on data in CEA 2009, Table B 47, and Schrank and Lomax 2009, Table 4). 13 Power generation fuels are domestically supplied. And although there is sporadic congestion on the grid, the damage risk, averaged across annual, nationwide generation, is likely very small.Resources for the Future Parry, Evans, and Oates

18 emissions) are approximately twice as large as those for autos (Table 1). Finally, based approximately on U.S. EPA (2010) and EIA (2008) we set C η = 1.2 (implying a moderately convex function), and we choose β such that the CO 2 tax associated with an emissions reduction of 10 percent is $30 per ton.

4. Quantitative Results This section compares the welfare effect of efficiency standards and energy taxes for the transport and power sectors a nd identifies conditions under wh ich efficiency standards are warranted. The marginal costs of reducing economywide CO 2 emissions under all policies are also compared.
A. Welfare Comparison of Effici ency Standards and Energy Taxes (i) Reducing Gasoline Figure 1 shows the marginal cost of reduci ng gasoline under fuel taxes and efficiency standards with either no misp erceptions failures (panel (a)) or our bounding case for the magnitude of misperceptions failures (panel (b)) . These estimates incorporate preexisting fuel taxes but assume that under higher fuel taxes, efficiency standards are not binding. We note the following points. First, the marginal cost curves under the sta ndards are more than twice as steep as those under the gasoline tax. This is because the fuel st andard puts the entire burden of fuel reductions on improvements in fuel economy, whereas the gaso line tax also exploits fuel savings from reduced vehicle miles traveled. Second, with no misperceptions failures, the intercept of the marg inal cost under the standard is well above that for the tax. For both policie s, the preexisting gaso line tax contributes 40 cents/gallon to the intercept, t hough this is partly offset by CO 2 externality benefits of 18 cents per gallon in the benchmark case. Under the gasoline tax there is an additio nal welfare gain of $1.04/gallon due to the reduction in congestion and other mileage-related ex ternalities. Overall, the marginal cost curve under the gasoline tax in panel (a) has a negative intercept of 81 cents/ga llon. The marginal cost is negative up to a fuel reduction of 11 percen t, corresponding to the fuel reduction under the optimal gasoline tax, which is $1.26/gallon. Impl ementing this optimal tax would yield annual welfare gains of $5.8 billion. In contrast, mileag e increases moderately under the fuel economy standard, and the resulting increa se in congestion and other exte rnalities further shifts up the marginal cost, so it has an ove rall intercept of 43 cents/gallon. In fact, in this scenario theResources for the Future Parry, Evans, and Oates

19 standard would impose potentially large (total) welfare losses—for example, $5.9 billion a year for a 5 percent fuel reduction. The third main point is that even with our bounding case for misperceptions failures, the marginal cost under the standard does not fall belo w that for the tax. Again, a fuel tax–efficiency standard combination is inferior to the fuel tax alone. This resu lt is independent of climate and oil security externalities because they affect the intercept of both marginal cost curves by the same amount. The marginal cost under the gasoline tax is shifted down substantially further: now the intercept is –$1.64 per gallon, the optimal fuel tax rises to $3. 08/gallon, and the fuel reduction under the optimized tax is 25 percent. The downwar d shift in the marginal cost curve is much larger under the standard because all, rather than a fraction, of the reduction in fuel use comes from improved fuel economy. However, even un der this bounding case, the intercept of the marginal cost under the efficiency standard doe s not (quite) fall below that for the tax. If there are constraints on fuel taxes, fu el economy standards can still be warranted, but only with big misperceptions mark et failures. In our bounding case for these failures, a standard that cut fuel use by 8.9 percent would be optimal, though potential we lfare gains are only about a third of those for the fuel tax. (ii) Reducing Electricity Figure 2 shows the marginal cost of reduci ng electricity under taxes and efficiency standards, again with no mi sperceptions failure (panel (a)) and our bounding case for the magnitude of the misperceptions failure (p anel (b)). We note th e following points. First, the marginal cost curve under the sta ndard is much steeper than that under the electricity tax. This again reflects the failure of the standard to exploit reductions in product usage. However in addition, unlike the electricity ta x, the standard fails to exploit any electricity savings in the unregulated sector (w hich accounts for 40 percent of use). Second, with no misperceptions failures, the el ectricity tax is welfare improving up to a reduction in electricity use of 5.5 percent. Impl ementing the optimal tax increase (1.4 cents per kWh) would generate modest welfare gains of $1.6 billion. Potential we lfare gains under the efficiency standard are positive (unlike the corresponding case for autos) but very modest, at $0.3 billion (the optimized standa rd would reduce overall electric ity use by just 1.3 percent). For these policies, local pollution benefits are approximately ca ncelled out by prior (state-level) electricity taxes. Both curves have negative interc epts of –1.3 cents/kWh, reflecting the carbon externality.Resources for the Future Parry, Evans, and Oates

20 Third, accounting for the misperceptions failure, efficiency standards can be superior to electricity taxes, but only for m odest reductions in electricity us e, of 3 percent or less. The marginal cost in Figure 2(b) under the standard has a lower intercept ( –8.4 cents/kWh) compared with the electricity tax (–5.2 cents/kWh). However, because of its much steeper slope, marginal costs under the standard quickly rise above those under the tax. If standards alone were optimized, total electricity use would be reduced by 5.5 percent (electricity use in the regulated sector would fall by 9.2 percent), but if the tax alone were op timized, electricity would be reduced by 24 percent. In principle, for any gi ven reduction in electricity use, it would be optimal to supplement the electricity tax with an efficiency standard to skew reductions toward efficiency improvements (away from reductions in product use). But ev en in this upper-bound case for misperceptions, in general the potential welfare gains from this combination policy are only moderately larger than those from the elec tricity tax. For example, cutting electricity use by 10 percent under the tax yields welfare gains of $19.8 bill ion, while achieving the same reduction under the combination yiel ds welfare gains of $21.1 billion.
B. Market Failures Required to Justify Different Levels of Efficiency Standards Figure 3 summarizes, in a different way, the results so far for the efficiency standards. It shows “iso-market failure” curves —that is, combinations of CO 2 damages and misperceptions failures under which it is optimal to reduce fuel or electricity use by different amounts, given current energy taxes. For automobiles, there is still a high threshol d for standards to improve welfare, even if current fuel taxes are fixed. For example, if th ere is no misperceptions market failure, even if CO 2 damages were $100 per ton, cutting fuel use by 2.5 percent under standards is not warranted. Alternatively, reduci ng gasoline use by 5 percent or more by raising fuel economy standards is efficient only if cons umers fail to internalize at least 44 percent of the value of fuel savings (under our benchmark value for CO 2 damages). The recent tight ening of CAFE standards actually represents a far more a ggressive policy than this: new passenger vehicle fuel economy is set to rise from 25 mpg to about 35 mpg by 2016, implying a long-run gasoline reduction of about 25 percent (after allowing for the rebound effect). Most likely, there would be some improvement without regulation as new fuel-saving technologies are incorpor ated and fuel prices rise. Nonetheless, our anal ysis suggests that it is difficult to justify such a rapid ramp-up in the CAFE standards on welfare grounds (i.e., the iso-mark et failure cost curve for this scale of fuel reduction is outside our upper-bound cases for market failures). For the power sector, there is a lower threshold for efficiency standards to be optimal, but only for small (2.5 percent) reductions in energy use. For more substantial reductions, efficiencyResources for the Future Parry, Evans, and Oates

21 standards for the power sector are even more diff icult to justify, on market failure grounds, than for automobiles. In Figure 3, this is indicated by the higher position of the iso-market failure curve in panel b for the 5 percent electricity re duction compared with th e corresponding curve in panel a, in part because only 60 percent of cons umption is subject to th ese standards. And a 7.5 percent reduction in electricity use under standards is warranted only under the most extreme of our scenarios for market failures.
C. Role of Efficiency Standards in CO 2

Mitigation Figure 4 shows marginal cost curves for reducing economywide CO 2 emissions under alternative policies, where again panels a and b correspond to our two bounding cases for misperceptions failures. In contrast to Figures 1 and 2, we do not net out CO 2 externality benefits from these costs. Again, these figures underscore our previous point that efficiency standards, and regulatory approaches more generally, ar e poor substitutes fo r pricing policies. With no misperceptions failures, the costs of ei ther efficiency standa rd are huge, relative to those of the CO 2 tax, for nonmarginal emissions reducti ons. An emissions standard for the power sector is dramatically more effective a nd cost-effective than efficiency standards. But even this regulatory policy does not perform that well relative to the CO 2 tax. For example, for a CO 2 reduction of 10 percent (which, roughly sp eaking, was projected for 2020 under recent federal cap-and-trade proposals), this polic y costs $12.9 billion. In contrast, the CO 2 tax costs only $2.3 billion for the same emissions reduction , given that it exploits more margins for abatement and it reduces driving-related extern alities. In fact, to target these broader externalities, an optimal policy in this case would combine a fuel tax increase with a CO 2 tax. With (our bounding case for) misperceptions failures, marginal costs under both efficiency standards and the gaso line and electricity taxes lie below marginal costs under the CO 2 emissions tax for some range of reductions. Howeve r, for both the efficiency standards, marginal costs rise rapidly, becoming positive at economywid e emissions reductions of 2 percent or less. In contrast, marginal costs under the electricity tax and CO 2 tax are negative up to emissions reductions of about 8 and 15 percent, respectivel y. In fact, for the 10 pe rcent reduction in CO 2 , total costs under the CO 2 tax are now negative, –$10.8 billion. Even the least-cost regulatory approach involving both efficiency standards and the emissions st andard has costs of plus $3.8 billion (costs for this combination are not show n in Figure 4), or $14.6 billion more than the CO 2 tax.Resources for the Future Parry, Evans, and Oates

22 5. Conclusion Our analysis suggests that effi ciency standards applied to th e transport and power sectors are difficult to justify, certainl y as a complement to pricing in struments, and even if pricing instruments are infeasible for the time be ing. Although there is much dispute about the magnitude of possible market failures associat ed with misperceptions over energy efficiency benefits, even under upper-bound assumptions for th ese market failures, only modest reductions in energy use or emissions are warranted under sta ndards, and potential we lfare gains are a minor or tiny fraction of those under pricing policies. Of course, our analytical framework provides only a first-level assessment of welfare effects. Digging deeper, we see a number of caveats. For example, our model assumes “smart” regulation that (implicitly) equates marginal compliance costs across producers within a sect or. Moving forward, this may be a reasonable approximation for automobiles, given the recent extension of credit-trading provisions in the CAFE program. It is more questionable for the po wer sector, given the practical complexities of monitoring credit trading among heterogeneous pr oducer groups (e.g., real es tate developers and refrigerator manufacturers). At any rate, allowi ng the possibility of imperfect regulation would only strengthen our main findings. The same would apply to incorporating dynamics into our analysis. Distinguishing capital of different vintages would allow us to expl ore transitory ineffici encies from new product standards resulting from the une ven treatment of new and pree xisting capital (though it would add considerable analytical complexity). We assume marginal-cost pricing. In practice, prices deviate from marginal costs because of cost-of-service regulation of power generation in many states and limited use of time-of-day pricing. However, it is difficult to make general statements about the economywide implications of these deviations (even with re gard to their sign, let alone their magnitude), given that they are highly specific to region and time of day. Finally, our welfare analysis is incomplete in that it excludes interactions between energy and environmental policies and the distortions in the economy created by the broader fiscal system, particularly distortions in factor markets. Literature on this issue suggests that the tax revenue or allowance rent created by correctiv e taxes or cap-and-trade systems is potentially problematic (e.g., Goulder et al. 1999) . This revenue or rent needs to be used in ways to increase economic efficiency, particularly by cutting other distortionary taxe s, to offset efficiency losses in factor markets caused by higher energy prices and the consequently higher general price level and lower real factor returns. Sta ndards, in contrast, have an advant age in this regard: they have aResources for the Future Parry, Evans, and Oates

23 weaker effect on the general price level (i.e ., they do not involve the pass-through of tax revenues or allowance rents).

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24 ———. 2010. Electric Power Annual . U.S. Department of Energy, Washington, DC. Fischer, Carolyn, Winston Harrington, and Ia n W.H. Parry. 2007. “Should Corporate Average Fuel Economy Standards Be Tightened?” Energy Journal 28: 1–29. Gately, D. 1980. “Individual Discount Rates and th e Purchase and Utilization of Energy-Using Durables: Comment.” Bell Journal of Economics 11: 373–74. Gillingham, Kenneth N.G., Richard G. Newell, and Karen L. Palmer. 2009. “Energy Efficiency Economics and Policy.” Annual Review of Resource Economics 1: 597–620. Goldberg, Pinelopi. 1998. “The Effects of the Co rporate Average Fuel Economy Standards in the Automobile Industry.” Journal of Indus trial Economics 46: 1–33. Goulder, Lawrence H., Ian W.H. Parry, Roberton C. Williams, and Dallas Burtraw. 1999. “The Cost-Effectiveness of Alternative Instrument s for Environmental Protection in a SecondBest Setting.” Journal of Public Economics 72: 329–60. Goulder, Lawrence H., Mark Jacobsen, a nd Arthur van Benthe m. 2009. “Unintended Consequences from Nested State & Federa l Regulations: The Case of the Pavley Greenhouse-Gas-per-Mile Limits.” Working pa per, Department of Economics, Stanford University. Greene, David L. 2010. How Consumers Value Fuel Ec onomy: A Literature Review . EPA-420- R-10-008. U.S. Environmental Prot ection Agency, Washington, DC. Hassett, Kevin A., and Gilbert E. Metcalf. 1993. “Energy Conservation Investment: Do Consumers Discount the Future Correctly?” Energy Policy 21: 710–16. ———. 1995. “Energy Tax Credits and Residential Conservation Investment: Evidence from Panel Data.” Journal of Public Economics 57: 201–17. Hausman, Jerry A. 1979. “Individual Discount Rates and the Purchase and Utilization of EnergyUsing Durables.” Bell Journal of Economics 10: 33–54. Heal, Geoffrey. 2009. “Climate Economics: A Meta -Review and Some Suggestions for Future Research.” Review of Environmental Economics and Policy 3: 4–21. Howarth, Richard B., Brent M. Haddad, and Bruce Paton. 2000. “The Economics of Energy Efficiency: Insights from Vol untary Participation Programs.” Energy Policy 28: 477–86. Jaffe, Adam B., and Robert N. Stavins. 1994. “T he Energy-Efficiency Gap: What Does It Mean?” Energy Policy 22: 804–10.Resources for the Future Parry, Evans, and Oates

25 Khazzoom, Daniel J. 1980. “Economic Implicati ons of Mandated Efficiency Standards for Household Appliances.” Energy Journal 1: 21–40. Kleit, Andrew N. 2004. “Impacts of Long-Range Increases in the Corporate Average Fuel Economy (CAFE) Standard.” Economic Inquiry 42: 279–94. Krupnick, Alan J., Ian W.H. Pa rry, Margaret Walls, Tony Know les, and Kristin Hayes. 2010. Toward a New National Energy Policy: Assessing the Options . Resources for the Future and National Energy Policy In stitute, Washington, DC. Little, Arthur D. Inc. 1984. “Measuring the Imp act of Residential Cons ervation Programs: An Econometric Analysis of Utility Data.” Volume III, Final Report for RP1587, Electric Power Research Institute. Myers, Erica, Karen L. Palmer, and Anthony Paul . 2009. “A Partial Adjustment Models of U.S. Electricity Demand by Region, Season and Sect or.” Discussion Paper 08-50, Resources for the Future, Washington, DC. National Research Council (NRC). 2002. Effectiveness and Impact of Corporate Average Fuel Economy (CAFE) Standards . National Academy Press, Washington, DC.
———. 2009. Hidden Costs of Energy: Unpriced Cons equences of Energy Production and Use. Washington, DC, National Academy Press. Nordhaus, William D. 2007. “The Stern Review on the Economics of Climate Change.” Journal of Economic Literature . XLV: 686–702.
———. 2008. A Question of Balance: Weighing the Options on Global Warming Policies. Yale University Press, New Haven, CT. ———. 2009. “An Analysis of Weitzman’s Dismal Th eorem.” Working paper, Yale University. Parry, Ian W.H., and Kenneth A. Small. 2005. “Does Britain or the United States Have the Right Gasoline Tax?” American Economic Review 95: 1276–89. Ruderman, Henry, Mark D. Levine, and James E. McMahon. 1987. “The Behavior of the Market for Energy Efficiency in Residential A ppliances including Heating and Cooling Equipment.” Energy Journal 8: 101–24

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26 Sanstad, Alan H., and Maximilian Auffhammer. 2010. “Energy Efficiency in the Residential and Commercial Sectors.” Agricultural and Res ource Economics Department, University of California, Berkeley. Sanstad, Alan H., and James E. McMahon. 2008. “A spects of Consumers’ and Firms’ Energy Decision-Making: A Review and Recommenda tions for the National Energy Modeling System (NEMS).” Papers from the Works hop on Energy Market Decisionmaking for the New NEM. Energy Information Admi nistration: Washington, DC. Sanstad, Alan H., W. Michael Hanemann, and Maximillian Auffhammer. 2006. “End-use Energy Efficiency in a ’Post-Carbon’ California Economy: Policy Issues and Research Frontiers.” California Climate Change Center at UC-Berkeley, Berkeley, CA. Schrank, David, and Timothy Lomax. 2009. The 2009 Urban Mobility Report . Texas Transportation Institute, Texas A&M University, College Station. Small, Kenneth A. 2009. “Energy Policies for Pa ssenger Transportation: A Comparison of Costs and Effectiveness.” Working paper, University of California, Irvine. Small, Kenneth A., and Kurt Van Dender. 2006. “F uel Efficiency and Motor Vehicle Travel: The Declining Rebound Effect.” Energy Journal 28: 25–52. Small, Kenneth A., and Erik Verhoef. 2007. The Economics of Urban Transportation. Routledge, New York. Stern, Nicholas. 2007. The Economics of Climate Change . Cambridge University Press, Cambridge. Tietenberg, Tom. 2009. “Reflections —Energy Efficiency Policy: Pipe Dream or Pipeline into the Future?” Review of Environmen tal Economics and Policy 3: 304–20. Train, Kenneth. 1985. “Discount Rates in Consumer s’ Energy-Related Decisions: A Review of the Literature.” Energy 10: 243–53. U.S. Environmental Protection Agency (EPA). 2010. EPA Analysis of the American Power Act in the 111th Congress . Washington, DC. U.S. Interagency Working Group on So cial Cost of Carbon (IAWG). 2010. Technical Support Document: Social Cost of Carbon for Regulat ory Impact Analysis under Executive Order 12866 . U.S. Government, Washington, DC. Weitzman, Martin L. 2009. “On Modeling and Interpreting the Economics of Catastrophic Climate Change.” Review of Economics and Statistics 91: 1–19.Resources for the Future Parry, Evans, and Oates

27 Appendix A. Analyti cal Derivations
Household first-order conditions Households solve a two-step optimization procedure using equations (1), (2), and (4). First, they choose the quantity of durable goods S i , energy consumption rates e i , planned use of durables m i , and planned consumption of I and Y , to maximize utility as follows: (A1) 

### = φ

} , , , , )), ( , , ( E A N N N N N Z Z C Y I e m S v μ

i A i i i E E i i i S e m t q e k GOV INC 

# ∑

≠ +

− +

− + + ) ) )( 1 ( ) ( ( { ρ λ
} ) ) )( 1 ( ) ( ( Y p I p S e m t q e k Y I A A A G G A A A − − +

− +

− ρ

where λ is the marginal utility of income and φ (.) is the (perceived) indirect utility function. The budget constraint here equates disposable income , which includes fixed private income of INC , with purchases of durable goods, expected lifetime energy spending, and planned consumption of other goods. In the second stage, during the course of the period, agents ma y reoptimize over product usage (and by implication, consumption of Y ) if energy costs differ from initial perceptions. This optimization yields
(A2a) i i i S 

### L p u i 

### ) 1 ( / ρ

λ

− + =
(A2b) A G G A m 

### e t q S u A 

### ) ( ) / ( + = λ
, i E E i m 

### e t q S u i 

### ) ( ) / ( + = λ
, i ≠ A
(A2c) i e i i i i S u e L k
i / ) / 1 ( / ) 1 ( λ ρ

− ∂ ∂

⋅ − = ′

−
(A2d) Y Y 

### p u = λ / , I I 

### p u = λ /
If, through regulation, the energy intensity for product i is reduced below the level that would be implied by equation (A2c), then this condition becomes
(A2e) λ μ ρ δ μ / / ) 1 ( ~ i i i i G i i u e L k ′

− ∂ ∂

⋅ − = − ′

−

where G δ ~ is the shadow value of the constraint, expressed per unit of gasoline intensity. The interpretation for equations (A2a–A2e ) is provided in the main text. Note that the use of energy durables N )), ( , , ( )), ( , , ( {

, , , , R R R R R A A A A A

i i i e m S v e m S v u Y I e m S Max μ μResources for the Future Parry, Evans, and Oates

28 in (A2b) may differ from planned use, if agents misp erceive future energy prices. This discrepancy is taken into account in our choice of values for ρ i . Demand functions and equation (6) From the household’s first-order conditions and budget constraint, we obtain demand functions for products, product usage, and energy efficiency. All demands can be expressed as functions of energy prices. Even though product demands in (A2a ) depend on product prices, these depend on energy efficiency, which in turn is a function of energy pr ices. Demand functions are assumed to have constant elasticities with respect to their own prices. And as discussed in the text, we approximate by assuming that demands for the three energy durables are take n as being decoupled, and so, for example, higher gasoline prices do not have a (significant) effect on the demand for electricity durables like household appliances. This implies

(B1a) A S G

G G G G

A A t q t q S S η ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

+ +

= 0 0 , A m G

G G G G

A A t q t q
m m η ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

+ +

= 0 0 , A e G

G G G G

A A t q t q
e e η ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

+ +

= 0 0

(B1b) i S E

E E E E

i i t q t q S S η ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

+ +

= 0 0 , i m E

E E E E

i i t q t q
m m η ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

+ +

= 0 0 , i e E

E E E E

i i t q t q
e e η ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

+ +

= 0 0 , i ≠ A

In these equations, superscript 0 denot es an initial value, and parameters A S G η and so on are elasticities (hidden costs are implicit in the expressi ons below). Using these equa tions and (3a), we can also obtain

(B2a) G

G G G G t q t q G G η ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

+ +

= 0 0

(B2b) i E

E E E E

i i t q t q E E η ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

+ +
= 0 0 , i ≠ A , E

E E E E t q t q E E η ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

+ +
= 0 0

where = G η G m G 

### η A S G 

### η + A e G 

### η + is the gasoline demand elasticity, 

### = i E 

### η + i m E η i S E η i e E η + , i ≠ A is the

demand elasticity for electricity used by durable good i, and E E i i E E i / 

# ∑ = η η is the demand elasticity for total electricity use. Elasticities are defined byResources for the Future Parry, Evans, and Oates

29 (B3a)
A G G

G A S G S t q t S A + ∂ ∂

= η , A G G

G A m G m t q t m A + ∂ ∂

= η , A G G

G A e G e t q t e A + ∂ ∂

= η , G t q t G G G

G G + ∂ ∂

= η

(B3b)

i E E

E i S E S t q t S
i + ∂ ∂

= η , i E E

E i m E m t q t m i + ∂ ∂

= η , i E E

E i e E e t q t e i + ∂ ∂

= η , i E E

E i E E t q t E

i + ∂ ∂

= η

and so on. From differentiating equati on (3b) with respect to gasoline and electricity prices, and using (B1) and (B3), we can obtain the decomposition of elasticities in (6).
Equation (7a): Marginal welf are effect of gasoline tax The actual (as opposed to perceived) indirect utility is defined by the household’s utility maximization problem with future costs correctly me asured (deviations from this optimization, due to consumer misperceptions, will therefore reduce actual u tility). Totally differentiating (A1) with respect to

t G , with 1 = i ρ and electricity and industrial variables constant (because they are assumed independent of transportation prices) gives, after substituting for gaso line and lifetime gasoline costs, and using (4a) to replace the vehicle price p A ,
(C1) 

# { }

G A A A S G dt dS L p u dt d

A ) ( +

− = λ φ 

# { } + +

− +
G A A A G G m dt dm S e t q u A ) ( λ 

# { }

G A A A A A G G e dt de S k S m t q u A ′

− +

− λ

λ )

( 

## { }

G Y Y dt dY p u λ

− +
G G A Z G C dt dGOV dt dZ u dt dC u A λ + + + G λ

−

Note that 0 / = G A dt de if the fuel economy standard is binding.
Substituting the household’s first-order conditions (A2) into (C1), the second and fourth terms cancel, and the sum of the first and third terms is

(C2) ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ + +

− G A A A G A A A G G A dt de S m dt dS m e t q ) ( λρ

From differentiating the first expression in (3a) with respect to t G , holding E and I fixed gives

(C3)
G G C G dt dG z dt dC

=

Differentiating the second expression in (3a) with respect to t G givesResources for the Future Parry, Evans, and Oates

30 (C4)
G A A A G A dt S m d z dt dZ ) (

=

And using the definition of elasticities in (B3a),

(C5) = ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ +
G A A A G A A A G dt de S m dt dS m e dt dG / 1

G S G e G A A η η η +

, G A S G m G

G G A A e dt dG dt S m d A A η η η +

= / /

) (

Finally, from totally differentiating the govern ment budget constraint (5) with respect to t G , we obtain

(C6)
G C G G G dt dC t dt dG t G dt dGOV + + =

Dividing (C1) by G dt dG /

− to express the utility effect per gallon reduction in gasoline, and by
λ to express utility in monetary units, and substitu ting (C2)-(C6), along with (7c), gives the welfare decomposition in equation (7a).
Deriving equation (7b): Relation between tax rate and gasoline reduction This is easily obtained from the gasoline demand function in (B2a). First invert, and then
substitute for 0 / G G using 0 

### / 1 ˆ G G G

− = Δ

. Deriving equation (8a): Marginal welf are effect of fuel economy standard Setting G G e e = (i.e., the fuel economy standard is bindi ng) and totally differentiating (A1) with
respect to G e , with 1 = i ρ , electricity and industrial variables constant, and 0 / = G A e d dS (see text), gives

(D1) = G e d d

φ 

# { } + +

− G A A A G G m e d dm S e t q u A ) ( λ 

# { } A A A A G G e S k S m t q u A ′

− +

− λ

λ )

( 

## { }

G Y Y e d dY p u λ

− +

G G A Z G C e d dGOV

e d dZ u e d dC u A λ + + +

Following the derivation of (C2) above, using (A 2e) instead of (A2d), the first three terms
amount to
(D2) A A G G A S m t q ) ( +

− λ ρ G δ ~

− And analogous to (C3) and (C4) above,Resources for the Future Parry, Evans, and Oates

31 (D3)
G G C G e d dG z e d dC

=

(D4)
G A A A G A e d S m d z e d dZ ) (

=

Using the definition of the rebound effect in (8c),

(D5)
G A A A A A G e d S m d e S m e d dG ) ( + = 

### ) 1 ( A A A 

### r

S m
− = , A A

A A A A A r r
e e d dG e d S m d

− − = 1 1 / /

) (

And from differentiating the government budget constraint,

(D6)
G C G G G e d dC t e d dG t e d dGOV + = 0

where 0 G t is the preexisting gasoline tax. Substituting (D2 )-(D6) into (D1), and using the definition of external costs in (7c), we obtain (8a), where ) / /( ~ 0 G G G G e d dG t δ δ + =
. Deriving equation (8b): relation shadow price and fuel reduction

G δ can be viewed as a virtual tax that reduces gasoline use by improving fuel economy, adjusted for the offsetting fuel increase from the rebound effect. That is, the relevant elasticity for this shadow price is ) 1 ( A e G r A

− η rather than G η for an increase in the gasoline ta x (affecting all margins for fuel reduction opportunities). Thus, under the fuel econom y standard, the gasoline demand function in (B2a) can be written,

(E1) ) 1 (

0 0 A r A e G

G G G G t q q G G − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

+ +

= η δ

Inverting using 0 

### / 1 ˆ G G G

− = Δ gives (8b).
Deriving equation (9a): Marginal we lfare effect of electricity tax Following the analogous derivation to derivations (C1)-(C6), but this time for raising the electricity tax, yields

(F1) 

# { } ∑

≠ +

− = A i E E i i S E dt dS L p u dt d i
i ) ( λ φ 

# { } + +

− + 

# ∑

≠ A i E i i i E E m dt dm S e t q u i ) ( λResources for the Future Parry, Evans, and Oates

32 

# { } ∑ ′

− +

− i E i i i i i E E e dt de S k S m t q u i λ λ )

( 

## { }

E Y Y dt dY p u λ

− +
E E E Z E C dt dGOV dt dZ u dt dC u E λ + + + E λ

−

(F2) ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ + +

− 

## ∑

≠ E i i i E i i i A i E E i dt de S m dt dS m e t q ) ( ρ λ

(F3) 

# ∑ = i E i E C E dt dE z dt dC

(F4) 

# ∑

≠ = A i E i i E E E dt S m d z dt dZ ) (

(F5) = ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ +
E i i i E i i i E i dt de S m dt dS m e dt dE / 1

i i i

E S E e E

η η η +

,

i i i

E i S E m E

E i E

i i e dt dE dt S m d η η η +

= / /

) (

(F6)

E C i E i E E dt dC t dt dE t E dt dGOV + + = 

# ∑

Dividing (F1) by 

# ∑

− i E i dt dE / to express the utility effect per unit reduction in electricity, and
by λ to express utility in monetary units, and substituting (F2)-(F6), along with (9c), gives the welfare decomposition in equation (9a).
Deriving equation (9b): Relation betw een tax rate and electricity reduction Again, this is easily obtained from the electric ity demand function in (B2b) after inverting and substituting 0 / E E with 0 

### / 1 ˆ E E E

− = Δ

. Deriving the marginal welfare effect of ef ficiency standard for the power sector Following the analogous derivation to derivations (D1)-(D6), but this time for the efficiency standard (and ignoring cross-price effects among energy durables), we obtain

(G1) = R e d d

φ 

# { } + +

− +
R R R R E E m e d dm S e t q u R ) ( λ 

# { } R R R R E E e S k S m t q u A ′

− +

− λ

λ )

( 

## { }

R Y Y e d dY p u λ

− +
R R E Z R C e d dGOV

e d dZ u e d dC u E λ + + +

(G2) R R E E R 

### S m t q ) ( +

− λρ R δ ~

−Resources for the Future Parry, Evans, and Oates

33 (G3)

R R E C R e d dE z e d dC

=

(G4)

R R R E R E e d S m d z e d dZ ) (

=

(G5)

R R R R R R R R e d S m d e S m e d dE ) ( + = 

### ) 1 ( R R R 

### r

S m
− = , R R

R R R R

R R r r
e e d dE e d S m d

− − = 1 1 / /

) (

(G6)

R C R R E R e d dC t e d dE t e d dGOV + = 0

Substituting (G2)-(G6) into (G1), we obtain

(G7)



### − − − = E C C C R e E 

### z t EXT MC R 

### ) ( δ E 

### EXT

E E E E 

### r t q

− ⋅ + ⋅ − 1 1 ) ( ρ

where ) / /( ~ 0 R R R E R e d dE t δ δ + =
. Deriving equation (11a): Marg inal welfare effect of a CO 2 tax The marginal welfare cost of an increase in the CO 2 tax can be decomposed as follows:

(H1) 1 1 / / 1 − ⎭ ⎬ ⎫ ⎩ ⎨ ⎧

⋅ ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ∂ ∂ + ∂ ∂ + ∂ ∂ + ∂ ∂

= C C I

I C E C E C C E

E C G

G C C dt dZ dt dp p dt dz

z dt dt t dt dt t dt dZ dt d φ φ φ φ λ φ λ
The first component is the gasoline tax equivalent of the increase in the CO 2 tax. That is, the CO 2 tax effectively raises the gasoline tax per gallon by G C C G z dt dt = / . And an incremental increase in the gasoline tax has a welfare cost per gallon of ) / /( ) / ) / (( G G t G dt dG t MC G λ φ ∂ ∂ = . Making these substitutions in (H1), and using (10), gives th e first component of equation (11a), where

(H2)
C C G G A C G dt dZ dt dt dt dG z / ) / )( / (

= α

This expression is the share of the reduction in economywide CO 2 reductions that comes from reduced gasoline use. The second component in (H1) is the electricity tax equivalent of the increase in the CO 2 tax. That is, the CO 2 tax has the equivalent effect on electricity output as an increase in the electricity tax of

E C C E z dt dt = / . And an incremental increase in the electr icity tax has a welfare cost per kWh ofResources for the Future Parry, Evans, and Oates

34 ) / /( ) / ) / (( E E t E dt dE t MC E λ φ ∂ ∂ = . Making these substitutions in (H1), and using (10), gives the second component of equation (11a), where

(H3)
C C E E E C E dt dZ dt dt dt dE z / ) / )( / (

= α

This expression is the share of the reduction in economywide CO 2 reductions that comes from reduced electricity use. The third component in (H1) is the equivalent effect of the CO 2 tax in terms of reducing emissions per unit of electricity, holding electricity ou tput constant. From (4d) the added abatement cost per unit reduction in the emissions rate is C E t k =

′ , though there is a gain from reducing local pollution of
EXT E

per unit reduction in emissions. Thus, the welfare cost per unit of emissions reduction is the third component in equation (11a), where

(H4)
C C E C z dt dZ dt

dz E E / /

⋅ = α

Finally, aside from CO 2 , there are no market failures associated with production and use of the industrial good, and therefore the welfare cost per un it of emissions reduction from this sector is simply
t C . (This can be verified by differentiating the utility function with respect to the tax-induced increase in the unit price of this good, I C z , taking account of the increase in government transfers ) / ( C I C dt dI I z + ).
The share of the emissions reductions from the industrial sector is

(H5)
C C I C I dt dZ dt

dz I / /

⋅ = α

Appendix B. Additional Docu mentation for Parameters
CO 2 Damages Some studies (e.g., Nordhaus 2008) value CO 2 damages at about $10/ton, while others value it at about $80/ton (e.g., Stern 2007). One reason for th e different estimates is that because of long atmospheric residence times and the gradual adjustment of the climate system, today’s emissions have very long range consequences, and their discounted damages are therefore highly sensitive to assumed discount rates. Some analysts (e.g., Heal 2009) argue against discounting the utility of future generations on ethical grounds, to avoid discriminating against peopl e just because they are born in the future; othersResources for the Future Parry, Evans, and Oates

35 (e.g., Nordhaus 2007) view market discounting as essentia l for meaningful policy analysis and to avoid perverse policy implications in other contexts.
The second reason for different CO 2 damage assessments has to do with the treatment of extreme catastrophic risks, such as the possibility that an uns table feedback mechanism in the climate system might lead to a truly catastrophic warming. In partic ular, it is possible that the marginal damages from CO 2 emissions are arbitrarily large if the probability distribution over future climate damages has “fat tails”—that is, the probability of increasingly catast rophic outcomes falls more slowly than marginal utility rises (with diminished consumption) in tho se outcomes (Weitzman 2009). Others (e.g., Nordhaus 2009) have critiqued the fat-tails hypothesis on the gro unds that we can head off a future catastrophic outcome by radical mitigation measures, and possibl y geoengineering, in response to future learning about the seriousness of climate change. A recent Inter-Agency Working Group (U.S. IA WG 2010) recommended us ing a value of $21.4 per ton of CO 2 for 2010, with additional values of $4.70, $35.10, and $64.90 per ton for sensitivity analysis. We begin with a benchmark value of $20 per ton and use a range of $1 0 to $100 for sensitivity analysis.
Local pollution from electricity generation In our analysis, local pollutants consist of sulfur dioxide, nitrogen oxides, fine particulate matter (with a diameter less than 2.5 micrograms), and coarse particulate matter (with a diameter between 2.5 and 10 micrograms) from natural gas and coal comb ustion. We use the generation-weighted national estimates of damages per kWh reported in a stud y by the National Research Council (NRC 2009). We then weight these per kWh damages by the share of total 2007 production as reported in EIA (2009), assuming that other methods of generation are not a si gnificant source of local air pollutants (oil-fired and waste-fired generation are less than 2.1 percent of total generation). Our estimate of the average local pollution damage is 1.7 cents per kWh. Howeve r, baseload coal-fired generation accounts for a disproportionately large share of these damages, but th e marginal fuel (typically natural gas) accounts for a disproportionately large share of reductions in electri city use. To make some adjustment for this, we assume a local pollution benefit from electricity reductions of 1.3 cents per kWh.Resources for the Future Parry, Evans, and Oates

36 Energy efficiency misperceptions There is evidence, from studies examining consumer purchases of a wide range of domestic appliances and other energy-related investments, that consumers have very high implicit discount rates for energy efficiency. 14 However, whether these high implicit discount rates reflect market failures or hidden costs is very unsettled. Market failure explanations may reflect the basi c problem of the costly acquisition and processing of information. Many consumers may not know what the relevant cost savings are. Furthermore, consumers may believe that the prosp ective cost savings are exaggerated. 15 On the other hand, high implicit discount rates may instead reflect hidden co sts, like reductions in other product attributes as a result of higher energy efficiency. Moreover, rationa l consumers may hold back on what may be largely “irreversible investments” with uncertain returns (Hassett and Metcalf 1993) because of risk aversion or liquidity constraints. If high implicit discount rates reflect real inform ation problems, consumers are largely unaware of the potential costs savings from energy-efficient t echnologies, and this corresponds to a positive value for ρ i . In contrast, if these high rates reflect hidden or other costs, this corresponds to a positive value for

i i u μ

μ ′ , which does not enter the welfare formulas becau se it is an internalized cost. We therefore consider two bounding cases meant to span the range of possibilities: one where the difference between implicit and social discount rates reflects a misperceptions market failure (i.e., ρ i > 0) and another where it is explained entirely by hidden costs (i.e., ρ i = 0). For electricity durables, we use a bounding case of ρ i ( i = R , N ) = 0.62. This is equivalent to discounting electricity savings at 25 percent, compared with a social discount rate of 5 percent, for a product with a 20-year life, where excessive disc ounting is due entirely to market failures.

14 Hausman (1979), examining household purchases of ro om air-conditioners, found implicit discount rates of around 20 percent. Later studies found comparable, and in some instances, much higher rates. Dubin and McFadden (1984), for example, in a study of space-heating and water-heating investments, also found implicit discount rates of around 20 percent, but Gately (1980) found much higher discount rates, 45 to 300 percent, in his study of consumer purchases of refrigerators. Likewise, Ruderman et al. (1987) calculated implicit discount rates ranging all the way from 20 to 800 percent on residential purchases of heatin g and cooling equipment and appliances. Little (1984) and Berkovec et al. (1983) report implicit discount rates of 32 percent for thermal shell investments and 25 percent for space-heating systems. 15 For example, Hassett and Metcalf (1995) found, after accountin g for all the costs, that the realized return to attic insulation (9.7 percent) was well below that promised by engineers and manufacturers.Resources for the Future Parry, Evans, and Oates

37 For automobiles, empirical literature on implicit discount rates is more mixed. 16 We follow one scenario explored by NRC (2002) in which consumer s value fuel economy improvements by considering (undiscounted) fuel savings over the first three year s of a vehicle life. Using NRC’s assumptions for vehicle life and declining vehicle usage with age, with a social discount rate of 5 percent, this implies ρ A = 0.65 if there are no hidden costs.

16 One study, by Dreyfus and Viscusi (1995), finds a discount rate of 11 to 17 percent, though the average new car loan interest rate was 12.6 percent in their sample, sugges ting that car buyers may have been constrained by liquidity rather than myopic. Another study, by Allcott and Wozny (2009), however, suggest consumers may consider fuel savings from efficiency improvements over only three years. This finding is consistent with EIA’s National Energy Modeling System, in which new auto buyers are assumed to use payback periods of three years. On the other hand, Sallee and West (2010) estimate implicit discount rates clos e to market rates, based on a study of the used-auto market. For more discussion of the literature, see Greene (2010).Resources for the Future Parry, Evans, and Oates

38 Table 1. Baseline Data, 2008

Autos Regulated Non

‐ regulated

Basic data for energy ‐ using products Energy intensity, gal./1000 miles or kWh/hour 43.5 0.73 0.48 Initial energy tax, $/gal., $/kWh 0.4 0.009 0.009 Initial pre ‐ tax energy price, $/gal., $/kWh 2.15 0.082 0.082 Initial quantity of fuel/energy, bn gallons, billion kWh 130 2,506 1,670

Price elasticities (standards non ‐ binding) elasticity with repsect to own price of energy ‐ 0.40

‐ 0.40

‐ 0.40 fraction of elasticity from: reduced usage per product 0.25 0.33 0.33 reduced demand for product 0.25 0.17 0.17 reduced energy intensity per unit of use 0.50 0.51 0.51

External costs CO 2 intensity, tons/gal., tons/kWh 0.009 0.0005 0.0005 CO 2 damages, $/gal., $/kWh 0.18 0.01 0.01 Other external costs, $/mile, $/kWh 0.09 0.01 0.01

0.65 0.62 0.62

Source. See text and Appendix B. Table 1. Baseline Data

Electricity Durables (for 2008)

Non
‐ internalized fraction of lifecycle energy costs in misperceptions scenarioResources for the Future Parry, Evans, and Oates39Figure 1. Marginal Cost of Policies to Reduce Gasolinea.NoMisperceptionsFailure‐2.0‐1.5‐1.0‐0.50.00.51.01.52.00 5 10 15 20 25 30%reductioningasoline

Marginal cost, $/gallonGasolinetaxEfficiencys tanda rdb.MisperceptionsFailure‐2.0‐1.5‐1.0‐0.50.00.51.01.52.00 5 10 15 20 25 30%reductioningasoline

Marginal cost, $/gallonGasolinetaxEfficiencys tanda rdResources for the Future Parry, Evans, and Oates40Figure 2. Marginal Cost of Policies to Reduce Electricitya.NoMisperceptionsFailure‐0.10‐0.08‐0.06‐0.04‐0.020.000.020.040.060.080.100 10 20 30%reductioninelectricity

Marginal cost, $/kWhElectricitytaxEfficiencystandardb.MisperceptionsFailure‐0.10‐0.08‐0.06‐0.04‐0.020.000.020.040.060.080.100 10 20 30%reductioninelectricity

Marginal cost, $/kWhElectricitytaxEfficiencystandardResources for the Future Parry, Evans, and Oates41Figure 3. Market Failures Required to Justify Efficiency Standards of Different StringenciesNote. For the power sector, reducing electricity use by 7.5 percent is optimal only for extreme scenarios for market failures.a.FuelIntensityStandard0.00.10.20.30.40.50.60.70 20 40 60 80 100CO2damage,$/ton

Misperceptions fraction, ρopt.fuelreduction,2.5%opt.fuelreduction5%opt.fuelreduction7.5%b.EnergyEfficiencyStandard0.00.10.20.30.40.50.60.70 20 40 60 80 100CO2damage,$/ton

Misperceptions fraction, ρopt.elec.reduction2.5%opt.elec.reduction5%opt.elec.reduction7.5%Resources for the Future Parry, Evans, and Oates42Figure 4. Marginal Cost of Policies to Reduce CO2EmissionsNote.Costs are defined gross of CO2externality benefits.‐100‐80‐60‐40‐200204060801000 5 10 15

Marginal cost, $/ton of CO2%reductionineconomywideCO2a.NoMisperceptionsFailureGasolinetaxStandard‐‐autoselectricitytaxStandard‐‐electricityCO2taxEmissionsstandard‐100‐80‐60‐40‐200204060801000 5 10 15

Marginal cost, $/ton of CO2%reductionineconomywideCO2b.MisperceptionsFailureGasolinetaxStandard‐‐autoselectricitytaxStandard‐‐electricityCO2taxEmissionsstandard