Combining price and quantity controls to mitigate global climate change

Transcription

1 Journal of Public Economics 85 (2002) locate/ econbase Combining price and quantity controls to mitigate global climate change William A. Pizer* Resources for the Future, 1616 P Street NW, Washington, DC 20036, USA Received 14 July 1999; received in revised form 18 December 2000; accepted 21 March 2001 Abstract Uncertainty about compliance costs causes otherwise equivalent price and quantity controls to behave differently and leads to divergent welfare consequences. Although most of the debate on global climate change policy has focused on quantity controls due to their political appeal, this paper argues that price controls are more efficient. Simulations based on a stochastic computable general equilibrium model indicate that the expected welfare gain from the optimal price policy is five times higher than the expected gain from the optimal quantity policy. An alternative hybrid policy combines both the political appeal of quantity controls with the efficiency of prices, using an initial distribution of tradeable permits to set a quantitative target, but allowing additional permits to be purchased at a fixed trigger price. Even sub-optimal hybrid policies offer dramatic efficiency improvements over otherwise standard quantity controls. For example, a $50 trigger price per ton of carbon converts the $3 trillion expected loss associated with a simple 1990 emission target to a $150 billion gain. These results suggest that a hybrid policy is an attractive alternative to either a pure price or quantity system Elsevier Science B.V. All rights reserved. Keywords: Climate change; Decision-making under uncertainty; Price and quantity controls; General equilibrium modeling JEL classification: Q28; D81; C68 *Tel.: ; fax: address: pizer@rff.org (W.A. Pizer) / 02/ $ see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S (01)

2 410 W.A. Pizer / Journal of Public Economics 85 (2002) Introduction Seminal work by Weitzman (1974) drew attention to the fact that, in regulated markets, uncertainty about costs leads to a potentially important efficiency distinction between otherwise equivalent price and quantity controls. Despite this well-known observation and its relevance for climate change policy, most of the debate concerning the use of taxes and emission permits to control greenhouse 1 gases (GHGs) has centered on political, legal and revenue concerns. This paper responds to this important omission by examining the efficiency properties of 2 permit and tax policies to mitigate global climate change. The basic distinction among policy instruments arises because taxes fix the marginal cost of abatement at a specified tax level (assuming optimal firm behavior). With uncertainty about costs, this generates a range of possible abatement levels and emission outcomes. In contrast, a permit system precisely limits emissions but leads to a range of potential cost outcomes. When coupled with a model of the benefits associated with emission reduction, this divergence in emission and cost outcomes creates a distinction in the expected welfare associated with each policy. In the case of climate change, part of the cost uncertainty arises due to uncertainty about the level of future baseline emissions. The Intergovernmental Panel on Climate Change (1992; hereafter IPCC) gives a range of CO2 emission 3 levels in 2010 of between 9.2 and 13.1 gigatons carbon (GtC). This requires a uniform 1 15% adjustment to IPCC forecasts of carbon emissions. See p. 71 in Nordhaus (1994b). The cost of attaining a particular target, say the 1990 emission level of 8.5 GtC, will obviously fluctuate depending on the level of future uncontrolled emissions. In addition to the baseline, however, there is considerable uncertainty about the cost of reducing emissions below the baseline. A study by Nordhaus (1993) reports that a $30/ton carbon (tc) tax might reduce emissions anywhere from 10 to 40%. While some models predict that a $300/ tc would virtually eliminate 4 emissions, other models require a tax in excess of $400/tC. This wide range of 1 See Wiener (1998), McKibbin and Wilcoxen (1997) and Goulder et al. (1997). 2 Earlier work by the author (Pizer, 1999) focused on the effect of uncertainty on the level of control, measured by a control rate or emission tax. That paper compared price and control rate policies, but did not consider fixed emission limits. Recent work by Newell and Pizer (1998) and Hoel and Karp (1998) considers the theory of price and quantity regulation applied to pollution such as greenhouse gas emissions that accumulate in the environment. 3 The actual range is GtC. However, we include the carbon equivalent of CFC emissions in our discussions of controllable greenhouse gas/ carbon emissions in order to parallel the treatment in Nordhaus (1994b) and Pizer (1999). 4 A recent report by the Energy Information Administration (1998) indicates similar marginal costs ranging from $50 to $400/ tc to achieve comparable reductions in emissions based on different models. Weyand and Hill (1999) suggest even higher costs.

3 W.A. Pizer / Journal of Public Economics 85 (2002) reduction estimates only compounds the uncertainty about baselines to generate extreme uncertainty about the cost of a particular emission target years in the future. Motivated by the policy implications of these large uncertainties, this paper uses a modified version of the Nordhaus (1994b) DICE model in order to analyze alternative policies under uncertainty. In particular, the model incorporates uncertainty about a wide range of model parameters developed in both Nordhaus (1994b) and Pizer (1996). The simulations are then sped up using a technique presented in Pizer (1999) that greatly facilitates computation. Details concerning costs and benefits are discussed in the next section while additional detail can be found in Pizer (1999) and Nordhaus (1994b). Two sets of simulations are emphasized. The first set focuses on the choice of policy in the year 2010 only. By examining estimated marginal cost and benefit schedules in this single period, we can directly apply Weitzman s original intuition. Such an analysis reveals the consequences of very short-term policy decisions, showing that the optimal price policy (a tax of $7.50/ tc) yields expected social benefits of $2.5 billion in net present value versus the optimal quantity policy (a 13 GtC permit scheme) yielding only $0.3 billion. The single-period experiments are followed by simulations of the optimal price and quantity policies over a 100-year horizon. These longer-term policy simulations indicate that an optimal permit path would similarly begin with a 13 GtC target in 2010, but rise gradually over time to about 45 GtC by 2100 in order to accomodate economic growth. This policy generates $69 billion in expected net benefits versus a no policy, business-as-usual alternative. Meanwhile, the optimal tax policy starts at $7/tC in 2010 and rises to about $55/tC by In contrast, this policy generates $337 billion in expected net benefits five times the gain of the optimal permit policy. Since these results are driven by untestable assumptions about the consequences of climate change, an obvious question is whether they are sensitive to increasingly non-linear climate effects. Indeed, the presence of a significant threshold can reverse the preference for taxes. Specifically, when damages rise from 1% to 9% as the mean global temperature rises from 3 to 4 degrees above historic levels, this is sufficient to encourage the use of quantity-based regulations over a 50-year policy horizon. Finally, a combined hybrid policy is proposed as an alternative to both the pure tax and permit approaches Roberts and Spence (1976); Weitzman (1978); and McKibbin and Wilcoxen (1997). Such a mechanism would involve an initial distribution of tradeable permits, with additional permits available from the government at a specified trigger price. This system turns out to be only slightly more efficient than a pure tax system. However, it achieves this efficiency while preserving the political appeal of permits: the ability to flexibly distribute the rents associated with emission rights. More importantly for current policy discussions, sub-optimal hybrid policies based on an aggressive target and high trigger price

4 412 W.A. Pizer / Journal of Public Economics 85 (2002) lead to better welfare outcomes than a pure quantity-based policy with the same target. Both the improved flexibility and better welfare outcomes make the hybrid policy an attractive alternative to either permits or taxes alone. 2. Background 2.1. Weitzman Roberts Spence The analysis presented in Weitzman (1974) concerns the choice of a policy instrument to regulate a market where either political considerations or market failure require government intervention. A price (tax) or quantity (permit) instrument is at the government s disposal and the question posed by Weitzman is which of the two leads to the best welfare outcome, measured as net social 5 surplus. Importantly, the policy must be fixed before any uncertainty is resolved 6 and cannot be revised. Weitzman s basic result was that price instruments would be favored when the marginal benefit schedule was relatively flat and quantity instruments would be favored when the marginal cost schedule was relatively flat. In particular, he derived an expression for the relative welfare advantage of prices over quantities: 2 s D 5 ] 2(c 22 b 2) (1) 2c 2 2 where s is the variance of the shocks to the marginal cost schedule, c2 is the slope of the marginal cost schedule and b2 is the slope of the marginal benefit 7 schedule. Based on this expression, the price instrument is preferred when benefits are relatively flat (D. 0 when b 2, c 2) and the quantity instrument is preferred when benefits are relatively steep (D, 0 when b 2. c 2). More recently, Hoel and Karp (1998) and Newell and Pizer (1998) have demonstrated that Eqs. (1) continues to hold when benefits are related to the stock of accumulated output, rather than the annual flow, after adjusting b2 to account for discounting, decay, growth, and the potential correlation of cost shocks over time. Not long after Weitzman s original article, several authors proposed a hybrid policy in place of pure price or quantity controls (Weitzman, 1978; Roberts and 5 Here and throughout it is assumed that the quantity instrument is an efficient quantity instrument; e.g. a tradeable permit system with negligible transaction costs. 6 Laffont (1977) provides a careful description of the information structure assumed in policy choice problems formulated in the Weitzman tradition. 7 The parameter b2 is actually minus the slope since the schedule of total benefits is usually concave. This result is derived for the case of linear marginal costs and benefits, where uncertainty enters as small shifts to each curve (therefore the slopes b2 and c2 are known with certainty). The uncertainty about costs is assumed to be independent of any uncertainty about benefits. See Stavins (1996).

5 W.A. Pizer / Journal of Public Economics 85 (2002) Spence, 1976). A hybrid policy gives producers the choice of either obtaining a permit in the marketplace or purchasing a permit from the government at a 8 specified trigger price. Such a policy operates like a permit scheme with uncertain costs and fixed emissions as long as the marginal cost, reflected by the permit price, remains below the trigger. When the trigger price is reached, however, control costs are capped and emissions become uncertain, as in a tax scheme. By setting the trigger price high enough or the number of permits low enough, the hybrid policy can mimic either a pure quantity or pure price mechanism, respectively. Since it encompasses both tax and permit mechanisms as special 9 cases, the hybrid policy will always perform at least as well as either pure policy. Policymakers and economists often focus on many considerations other than the partial equilibrium welfare concerns highlighted by the Weitzman Roberts Spence analysis (Stavins, 1989; Goulder et al., 1997; and Parry and Williams, 1999). In the United States, experience with quantity-based permit systems for both national SOx and regional NOx pollution control has created political support for market-based quantity controls especially when valuable permits are provided gratis to those bearing the most concentrated cost burden. At the same time, popular opposition to taxes of any kind makes the prospect for pure 10 price-based regulations rather grim. Yet, a hybrid system with welfare properties nearly identical to (or better than) a pure price-based mechanism retains virtually 11 all the politically desirable characteristics of a permit system. Since this paper indicates that price-based or hybrid mechanisms produce five-times the welfare gain associated with quantity controls, it suggests an opportunity for significant and feasible policy improvement Costs of climate change mitigation In order to compare price- and quantity-based policies to mitigate climate change, we need a dynamic model of mitigation costs, benefits, and uncertainty. To this end, we make use of the model developed in Pizer (1999), which involves a stochastic extension to the deterministic climate economy model presented in Nordhaus (1994b). Based on the previous discussion of Weitzman Roberts Spence, we focus our attention on the model s characterization of costs, benefits and uncertainty, leaving the more interested reader to consult earlier work. The global cost of climate change mitigation is typically measured as the 8 A hybrid policy may also involve a price floor at which the government offers to buy back permits. However, this type of subsidy program creates dynamic inefficiencies. See Chapter 14 of Baumol and Oates (1988). 9 Such policies have been proposed in the climate change arena by McKibbin and Wilcoxen (1997), McKibbin (2000) and Kopp et al. (2000). 10 See Pearce (1991) for a discussion of the pros and cons of carbon taxes. 11 The one feature it does not share is an absolute cap on emissions. This is, however, somewhat illusory since even an absolute cap can be relaxed in the face of future political pressure.

6 414 W.A. Pizer / Journal of Public Economics 85 (2002) reduction in consumable output associated with a particular emission level of greenhouse gases. This cost calculation is conveniently viewed in two steps: (1) calculation of the required emission reduction, expressed as a fraction of gross emissions; and (2) calculation of the fractional reduction in global output required 12 to achieve that fractional emission reduction. The first part of the calculation is determined by growth forecasts of population, productivity, and the carbon intensity of production (because carbon dioxide is the primary anthropogenic greenhouse gas). None of these trends are known with certainty and are therefore assigned probability distributions based on Nordhaus (1994b), Nordhaus and Popp (1997), and Pizer (1996). Fig. 1 shows the resulting distribution of CO2 emission forecasts used in this paper, along with the 1992 IPCC future emission scenarios for comparison. The Fig. 1. Simulated CO2 emission distribution vs. IPCC scenarios. Lines indicate the distribution of CO2 emission paths generated by the model. Circles (s) indicate 1992 IPCC CO2 emission scenarios (p. 12 IPCC 1992; pp , Pepper et al., 1992) adjusted to include controllable CFC s (see p. 71 Nordhaus (1994b)): letters in right margin refer to individual IPCC scenarios. 12 There is a third step converting the fractional loss of global output into an actual dollar loss. However, we really care about utility, not the level of output or consumption. Assuming roughly logarithmic utility (so du 5 (1/c)dc), fractional losses are a reasonable focal point since changes in utility are more closely related to fractional (versus level) changes in consumption.

7 W.A. Pizer / Journal of Public Economics 85 (2002) IPCC forecasts tend to fall between the 5th and 75th quantiles of our simulations. This is consistent with more recent analysis suggesting a wider range of 13 possibilities than those contained in the 1992 scenarios (IPCC, 2000). The second part of the cost calculation relating fractional reductions in greenhouse gases to fractional reductions in world output is based on a survey of studies first summarized in Nordhaus (1993). These studies compute costs by various means, including engineering assessments, econometric estimation, and mathematical programming. The relationship and range of estimates are approximated in Nordhaus (1994b) by a power rule, fractional reduction in global output b 1(fractional reduction in GHG emissions) (2) Nordhaus (1994b) considers a range of values for b 1: 0.027, 0.034, 0.069, and 0.133, with the best guess being These values imply that a 20% reduction global emissions would require 0.026%, 0.033%, 0.066%, 0.077% and 0.128% reductions in global output, respectively. Here and in Pizer (1999), these values are assumed to occur with equal probability, independent of other uncertainty in the model (including the emission levels shown in Fig. 1). There are two subtle assumptions embedded in Eqs. (2) that bear mentioning. First, the relation assumes that marginal costs are increasingly steep as additional reductions are undertaken, and second, the choice of emission level is an annual decision involving an annual cost function. Both of these points are important in this analysis because they affect the slope of marginal costs, in turn affecting the difference in expected welfare between taxes and permits. The assumption of increasing marginal costs would seem innocuous based on the fact that one input the uncontrolled emission level is fixed. However, it has been argued that once non-marginal changes in production technologies are considered, costs could fall (Lovins, 1996). This relates to the second point: Over time the stock of both human and physical capital could evolve in a less carbon intensive direction, making emission choice a multi-period rather than single- 14 period decision. Both effects suggest a preference for price controls when regulation is focused on the near term, possibly switching to a preference for quantity controls when regulation is flexibly applied over a long horizon (e.g., with 15 banking and borrowing). 13 The 1992 scenarios were specifically criticized for ignoring the possibility that developing country income converges to developed country income (per capita), which would lead to higher uncontrolled emission forecasts. 14 This touches on the issue of endogenous technological change; see Grubler and Messner (1998); and Goulder and Mathai (2000). 15 If emissions can eventually be reduced at substantially lower costs, it suggests that the long-run marginal cost curve is flatter than the short-run marginal cost curve, favoring quantity controls applied over a sufficiently long horizon; see Eqs. (1).

8 416 W.A. Pizer / Journal of Public Economics 85 (2002) Benefits of climate change mitigation In contrast to mitigation costs, which are rooted in the economically familiar areas of aggregate energy use and fuel substitution, mitigation benefits are determined by long-term climate changes and the economic impacts associated with those changes. With only limited historical experience concerning climatic changes and especially their economic consequences, this is understandably the 16 most subjective and uncertain area of climate economy modeling. Nordhaus (1994a) found that scientists opinions on the possible damages from climate change range from 0% up to a 50% loss of global output. A simple model of climate dynamics coupled with a damage function based on the square of the change in global mean temperature drives our mitigation benefits. Economic activity determines a baseline, uncontrolled emission level for carbon dioxide. Mitigation activities reduce current emissions below the baseline. Each ton of unmitigated carbon dioxide generates a rise in the global mean temperature that peaks about 40 years after it is emitted, then dissipates slowly with a half-life of about 60 years. The initial 40-year delay arises because the global mean temperature equilibrates gradually in response to higher levels of accumulated carbon dioxide as the earth s atmosphere traps more solar radiation. The subsequent decline follows the gradual decay of carbon dioxide and other greenhouse gases in the atmosphere. A one-time 100 million ton increase in emissions (roughly 1% of annual global emissions in 1990) generates a peak temperature rise of about 2/ 10,000 of one degree Celsius using best-guess parameter values. Uncertainty in the climate model could double or halve this 18 estimated temperature increase. The economic consequences of climate change depend on these increases in global mean temperature. Following Nordhaus (1994b) and Pizer (1999), we specify a quadratic damage function with 2 fractional reduction in output due to climate damages 5 D? (T/3) (3) 0 where T is the change in temperature relative to a pre-industrialization baseline Current atmospheric CO2 concentrations of 368 ppm are higher than in any period over the past 400,000 years, which ranged ppm (Petit et al., 1999). Some work has used cross-sectional variation in climate to estimate economic consequences of climate changes such as temperature and precipitation (Mendelsohn et al., 1994). While instructive, these analyses ignore the difference between regional and global climate changes analogous to the difference between partial and general equilibrium as well as changes in storm patterns and extreme weather behavior. 17 As temperatures rise the earth radiates more heat into space, counteracting the increased retention of solar radiation due to higher levels of greenhouse gases. Eventually the earth reaches a new greenhouse gas/ temperature equilibrium. 18 There is uncertainty about both the amount of emitted CO2 that is rapidly absorbed by oceans (atmospheric retention rate) as well as the temperature change resulting from changes in atmospheric CO (climate sensitivity). 2

9 W.A. Pizer / Journal of Public Economics 85 (2002) (circa 1860) and D0 is a parameter describing the global output reduction associated with a 38 temperature increase. Nordhaus (1994b) focuses on a bestguess value of for D0 with a sensitivity analysis including values of zero, 0.004, 0.013, and Pizer (1999) assumes these five values occur with equal probability and independently of other uncertainty in the model. The main weakness of this model of mitigation benefits is its failure to capture possibly abrupt temperature changes and/ or economic consequences related to both the level and rate of change in greenhouse gas concentrations. The thermohaline circulation of the North Atlantic Ocean, for example, warms Northern Europe by as much as 10 degrees Celsius and could collapse as a result of increased greenhouse gas emissions (Broecker, 1997; Stocker and Andreas, 1997). Such a collapse would lead to more dramatic consequences than those predicted by this model. In Section 4 we consider relaxing the quadratic functional form in Eqs. (3) to address this possibility of more abrupt climate effects Economic behavior These models of costs and benefits are dynamically linked via a simple one-sector stochastic growth model (Pizer, 1999). A representative agent chooses between consumption and savings each period based on the expected return to capital, which itself depends on population, the capital stock, and productivity. Productivity includes the negative consequences of both mitigation costs and climate damages. In this way, current mitigation costs and climate damages influence both current and, through investment, future consumption and output. Of course, mitigation activities also reduce greenhouse gas emissions and future climate damages. We compute the optimal savings level each period based on a linearized steady-state decision rule (Campbell, 1994). This allows us to simulate the economic and climate outcomes quite rapidly for a single random draw of model parameters and stochastic shocks over a 250-year horizon. We then use eight thousand random draws to approximate the range of uncertain outcomes. Mitigation costs and controlled (actual) emissions are computed separately in each period and for each state of nature based on the specified carbon tax or permit policy. The uncontrolled emission level and global output gross of climate mitigation are both determined by state variables at the beginning of each period. Under a permit policy, Eqs. (2) can be used to directly compute mitigation costs, where fractional reductions equal one minus the ratio of permits to uncontrolled emissions. In the case of a tax policy, Eqs. (2) can be differentiated to yield a marginal cost expression that, when set equal to the tax rate, can be solved for the fractional emission reduction. This reduction can then be substituted into the original relation to yield mitigation costs. With separate calculations in each state of nature, this procedure highlights how tax policies fix marginal costs and lead to

10 418 W.A. Pizer / Journal of Public Economics 85 (2002) uncertain emissions while permit policies fix emissions and lead to uncertain marginal costs. The welfare effects of a particular policy are computed in terms of discounted utility for each state of nature. Discounted utility is then valued in a particular base year using the marginal utility of consumption in that year. Dollars in the base year can be averaged across states of nature to yield expected welfare. Additional details concerning the model specification, simulation, and welfare calculations can be found in Pizer (1999). 3. Simulation results Given the long-term nature of climate change, a policy to reduce greenhouse gas emissions inevitably involves decisions spanning many decades. In the first part of this Section, however, we consider the expected welfare consequences of choosing price or quantity controls for GHG emissions in a single year, By focusing on a single year in the near future, we can address the difference between alternate price/ quantity controls now, without becoming mired in the question of longerterm policy. In addition, focusing on a single year allows us to easily visualize the policy in quantity/ price space. While the policy is implemented in a single period, the measurement of costs and benefits includes consequences over a 250-year horizon. The second part of this section considers price and quantity policies spanning many periods. The policies are open-loop: There are no revisions to future policies as we learn about uncertain outcomes. Although such feedback is both desirable and more realistic, it would require a simplification of either the model or the 19 specification of uncertainty. With our motivating interest in instrument choice under uncertainty and not learning this is an undesirable trade-off. Based on the idea that policies are often fixed for long periods of time, we use these open-loop policies to provide an alternate bound on the welfare difference associated with the choice between price and quantity controls. A policy optimization over many periods also allows us to see whether the choice of policy in the future influences the optimal near-term policy choice. The remainder of the paper then considers the sensitivity of these results to key damage damage assumptions as well as hybrid policies that combine price and quantity controls Marginal costs and benefits We begin by computing schedules of mitigation costs and benefits in The benefits schedule is computed using 100 distinct simulations that fix emissions at 19 See Kelly and Kolstad (1999) who consider closed-loop policies in a similar model focused on learning.

11 W.A. Pizer / Journal of Public Economics 85 (2002) intervals of 0.1 GtC over the range 5 15 GtC in the year 2010, leaving emission levels in other periods unchanged. By turning off the mitigation costs associated with the fixed emission level and comparing welfare to the base case where 2010 emissions are left unchanged, we can compute the gross benefit of a particular emission level (e.g., gross of costs). The cost schedule is computed by repeating these simulations with mitigation costs turned on. This produces estimates of the net benefits. By subtracting these net benefits from the aforementioned gross benefits, we produce estimates of cost. Both schedules can be converted to marginal ($/tc) measures by dividing the change in benefits and costs associated with an incremental 0.1 GtC reduction, measured in $billions, by 0.1 GtC. These two calculations result in a distribution of marginal benefits and marginal costs at each simulated emission level. Fig. 2 summarizes these distributions by showing both the mean marginal cost and marginal benefit at each level of emissions along with the 5% and 95% quantiles based on 8,000 states of nature (note that the 5% marginal benefit quantile overlaps the x-axis). Keeping in mind that 1990 GHG emissions were around 8.5 GtC, this figure indicates that achieving 1990 emission levels in 2010 would involve a marginal cost of between zero and Fig. 2. Distribution of marginal costs and benefits in (The 5% quantile of marginal benefits overlaps the x-axis.).

12 420 W.A. Pizer / Journal of Public Economics 85 (2002) in excess of $30/tC far more than even the 95% quantile of marginal benefits. This large variation occurs for two reasons: Marginal costs are assumed to rise steeply given the specified cost function in Eqs. (2), and baseline emissions in 2010 are not known with certainty as highlighted in Fig. 1. Realizations of marginal costs in this figure are essentially a collection of fairly steep curves whose horizontal intercept is unknown. This figure indicates that marginal benefits, in contrast, are relatively constant though unknown. Considering the description of climate damages in the previous section, this may not come as a surprise. First, climate damage is presumed to be a gradual phenomenon with little consequence for small temperature changes, reflected in the quadratic damage function given in Eqs. (3) coupled with small values of D. Second, damages depend on the accumulated stock of GHGs in the 0 21 atmosphere and not the annual flow. Emissions in any single year, such as the 8.5 GtC emitted in 1990, represent a small fraction of the extra 190 GtC accumulated since the beginning of industrialization. This damage relation contrasts with traditional pollutants, such as particulates, SO x, NO x, etc., whose damages depend on the annual emission level because they dissipate rapidly in the environment. The scale of Fig. 2 masks the fact that marginal mitigation benefits/emission damages actually fall from $7.45 to $7.37 as emissions rise from 5 to 15 GtC. This is surprising because we generally assume convex damages: As we pollute the environment, there ought to be increasingly dire consequences from each additional ton. In the case of climate change, however, a key physical relationship connects the logarithm of atmospheric greenhouse gas concentrations to the 22 change in temperature. That is, there is some fixed (but unknown) temperature change associated with each doubling of the level of carbon dioxide and other GHGs in the atmosphere thus as we emit more, the marginal temperature change is actually less. This feature coupled with quadratic damages due to temperature change guarantees a very flat and slightly concave benefit/ damage relation. We revisit this assumption in Section Comparative advantage of prices over quantities Under the assumptions made by Weitzman, the optimal permit level is simply the emission level where expected marginal benefits equal expected marginal costs and the optimal tax level is similarly the expected marginal benefit at that intersection. Thus P* 5 $7.50 and Q* 5 12 GtC indicate the optimal tax and permit policies in 2010 for controlling GHG emissions based on a Weitzman analysis. Calculating the slopes at the intersection, B050 and C055.4 $/(tc? 20 The actual 95% marginal cost quantile at 8.5 GtC is $180/tC. 21 More specifically, temperature change depends on the GHG stock and damages depend on temperature change. 22 See Eq. (2.9) in Nordhaus (1994b).

13 W.A. Pizer / Journal of Public Economics 85 (2002) GtC), and setting s equal to the variance of marginal costs at the optimum, ($/tc), allows a rough calculation of the welfare gain of taxes over permits using Eqs. (1): ($/tc) D 5 ]]]]]] 2( $/(tC? GtC)) $25billion. 2? (5.4 $/(tc? GtC)) Discounting this to 1995 (the base year of the model) with a 6% discount rate suggests a gain of $10 billion from using taxes instead of permits just in the year This analysis based on Fig. 2 provides important intuition and a rough approximation of the welfare consequences of taxes and permits. However, it ignores important failures of the Weitzman assumptions in the current exercise. 23 Costs are not quadratic and the quantity control is not binding in all cases. In order to overcome these limitations, we now turn to the direct evaluation of social welfare. Numerically maximizing expected welfare over the range of possible price and quantity controls in 2010, we find that the optimal price policy is a $7.50/tC tax, yielding a $2.5 billion gain, and the optimal quantity policy is a 13 GtC emission 24 limit, yielding a $0.3 billion gain. The positive gain associated with price controls is quite robust: Taxes of up to $20/tC (almost three times the optimal level) continue to generate positive expected benefits. In contrast, quantitative targets below 12 GtC have negative expected benefits. A policy set at 8.5 GtC the emission level in 1990 and 20% below the median emission estimate in 2010 yields a expected net loss of $10 billion. The difference between optimal policies based on these direct simulations, $2.2 billion, is considerably less than the estimated value based on Fig. 2, $10 billion. While the Weitzman approach provides good qualitative intuition about the relative advantage of price- and quantity-based policies, the violation of key assumptions 25 clearly limits its quantitative application in this setting Optimal policy paths Up to this point the analysis has focused on the costs and benefits of different policies in a single year. The problem of climate change, however, is spread out over decades if not centuries. Policies to combat climate change may remain in 23 Uncontrolled emissions in 2010 are less than Q* 5 12 GtC in many of the simulated outcomes; see Figs. 1 and When optimizing over quantity controls, we require that emissions be at or below the specified quantity target in all states of nature (emissions will fall below the quantity target if uncontrolled emissions are low). 25 See Yohe (1978) and Watson and Ridker (1984) for further discussion.

14 422 W.A. Pizer / Journal of Public Economics 85 (2002) place for a long time. Further, it is not obvious whether the results comparing different instruments in a single year are appropriate for a multi-period analysis. In particular, policies in future periods may influence the choice of policy in We now consider optimal policy paths for both taxes and permits. To compute optimal policies, these paths are parameterized with six values describing the tax or permit level in 2010 (the first year of implementation), 2020, 2040, 2070, and Policies in intervening years are based on smooth interpolations, except the level in 2160 which is allowed to be discontinuous and is held fixed through the end of the simulation (2245). The length of the simulation as well as the spacing of the policy parameters were chosen to emphasize policy evaluation in the period and especially the early period. Fig. 3 shows the optimized permit and tax policies over In the top panel, we see the optimal quantity limit on global greenhouse gas emissions. Interestingly, the optimal permit level of 13 GtC in 2010 is roughly the same as the optimal permit level determined in the one-period analysis. There are two explanations. First, given the large initial stock of GHGs in 1995 (190 GtC above the pre-industrialization level), emission reductions do not substantially affect the GHG stock for many years. Second, as we noted in the previous section, the marginal benefits are flat over a wide range of stock levels. Thus, future policies are unlikely to affect the value of discounted marginal benefits today both because marginal benefits are flat and, even if they were not flat, significant changes in the stock level will not occur for many years, leading us to discount the value of those changes in present value terms. A second observation is that a proposal to reduce emissions to their 1990 levels (roughly 8.5 GtC) and to then maintain (or further reduce) that level in the future is far below the optimal permit level in these simulations, a point emphasized in Nordhaus original analysis. In particular, the optimal permit level rises in the future to accomodate growth in population and productivity. While it is more useful to focus on the near-term policy implications specifically the fact that they are essentially independent of future manipulations of the GHG stock this second point shows that our historical experience with growth and technology coupled with our current climate damage assumptions is inconsistent with stabilizing long-term GHG emissions. Finally, we note that when the optimal permit policy is implemented it improves welfare on average by $69 billion discounted to 1995 (total discounted benefits minus total discounted costs). This can be compared to annual global output in 1995 of $24 trillion. The bottom panel of Fig. 3 shows the path of carbon taxes that maximize expected welfare. The initial tax of $7.35 is close to, but slightly lower than, the tax computed in the one-period analysis. Unlike the optimal permit policy which 26 Policies are interpolated to 10-year intervals using a cubic spline; annual policies are linearly interpolated from the 10-year values.

15 W.A. Pizer / Journal of Public Economics 85 (2002) Fig. 3. Optimized permit and tax policies over time.

16 424 W.A. Pizer / Journal of Public Economics 85 (2002) relaxes over time in order to accomodate growth, the optimal tax policy becomes more stringent in the future. This occurs because a given tax encourages proportional reductions if the economy doubles and the tax remains the same, emissions will double. Although some increase in emissions is desirable as the economy grows, a proportional increase is not. Therefore the optimal tax must increase in stringency at the same time an optimal permit system must be relaxed. When this optimal tax policy is imposed, it improves welfare on average by $338 billion. Compared to the $69 billion gain under the optimal permit instrument, this represents an expected improvement that is five times higher. 4. Catastrophic damages We have noted that the efficiency gains associated with price-based regulation follow largely from underlying assumptions about climate behavior and the likely economic consequences. Let us now consider how the results change if these assumptions are relaxed. There are at least two rationales for considering this possibility: The climate might behave in a more dramatic, non-linear way than specified by Schneider and Thompson (1981) and subsequently used by Nordhaus (1994b) and Pizer (1999). Alternately, the economic consequences of climate change with which we have little experience might be more convex than 27 suggested by a quadratic damage function. For transparency we focus on the latter possibility, that damages are increasingly convex, and consider the impact of changing the exponent in Eqs. (3). Specifically, we consider a modified damage function of the form fractional reduction in GDP due to damages 5 D 3 (T/3) 0 d 1 (3a) where d1 is allowed to take on values Note that by writing the damage function such that (T/3) is raised to the exponent d 1, the kink in the damage function is fixed at 3 degrees and D0 continues to reflect the damage associated 28 with this amount of warming. It turns out that one additional modification is necessary to conduct the sensitivity analysis. Earlier, it was noted that the choice of policy in 2010 was relatively insensitive to whether or not mitigation policies were implemented in future years. This allowed us to consider isolated price and quantity controls in 2010 without worrying about what occurred in the future. It also allowed us to consider policies over a 50- or 100-year horizon without worrying that the 250-year simulation horizon would be too short to produce sensible results. This 27 For a more general discussion of catastrophic damages, see Gjerde et al. (1999). 28 It is possible to treat the kink as unknown, but this only smooths out the non-linearity. Sensitivity analysis in this direction does not qualitatively alter the price/ quantity comparison.

17 W.A. Pizer / Journal of Public Economics 85 (2002) ability to focus on near-term policies is lost when damages acquire catastrophic proportions. The choice of current policy depends on how well we avoid catastrophes in the future. In the absense of future controls, for example, it becomes desirable to increase emissions now in order to create short-term damages that reduce the capital stock and thereby reduce emissions in the future indirectly a rather perverse result. Even when future controls are included, welfare estimates become sensitive to the simulation horizon and to minute policy changes hundreds of years in the future, obscuring the effect of near-term policies. In order to continue our focus on the near-term distinction between price and quantity controls, we hold future policy constant in a sensible way across all of our policy simulations. Specifically, emissions after 2060 are costlessly reduced to 6 GtC, a level that avoids any catastrophes in the distant future if prudent policies 29 are pursued in the near term. The elimination of mitigation costs after 2060 leads us to a slightly different comparison of prices and quantities under the benchmark assumption of quadratic damages discussed previously: Prices generate a $138 billion expected gain while quantity controls generate only $20 billion. Compared to the analysis in Section 3.3 this raises the relative advantage (price gain 4 30 quantity gain) from a factor of five to a factor of seven. Fig. 4 shows how this difference between prices and quantities varies as the damages become increasingly non-linear (d. 2). In the top panel, indicating the 1 expected welfare difference between prices and quantities, D in Eqs. (1), we see that prices continue to be preferred until the non-linearity becomes quite large. This crossover occurs when d1 7. With this degree of non-linearity, best-guess damages rise from 1% of global output with 3 degrees of warming to 9% with 4 31 degrees of warming. A second observation in the left panel is that initially the comparative advantage of prices over quantities increases in absolute terms as marginal damages become steeper, apparently violating Weitzman s Eqs. (1). That is, as d1 in Eqs. (3a) rises from two to three, the marginal benefit slope b2 in Eqs. (1) presumably rises as well which should reduce D. Such a conclusion is 2 mistaken, however, as both s and c 2 (the variance of cost shocks and slope of marginal costs) in Eqs. (1) may be changing along with the marginal benefit slope as d rises Of course, one could argue that the most important effect of near-term policy should be its influence on future emissions and mitigation costs, not current emissions. However, such an effect is arguably more dependent on the aggressiveness of mitigation policy than the choice of policy instrument. Since this paper is tightly focused on the issue of instrument choice, and since such connections between current and future policy are probably more complex than the current model allows, our emphasis on near-term emission reductions and mitigation costs remains a sensible starting point. 30 This should not come as a surprise since we are now more focused on the near term and the ratio for a single year discussed in Section 3.1 is more than a factor eight ($2.5B 4 $0.3B). 31 d1 21 The actual damage function is 1 2 (1 1 D 0(T/ 3) ) ; see Nordhaus (1994b). The distinction between this expression and Eqs. (3a) is only important at high damage levels.

18 426 W.A. Pizer / Journal of Public Economics 85 (2002) Fig. 4. Effect of non-linear damages on the relative advantage of price mechanisms. In the bottom panel, another pattern arises. When we consider the ratio of welfare gains under prices and quantities, that is, expected welfare with optimal price controls 2 expected welfare without any mitigation ]]]]]]]]]]]]]]]]]]]] expected welfare with optimal quantity controls 2 expected welfare without any mitigation 32 that ratio may be much larger than one but never falls noticeably below one. 32 The smallest value of this ratio is about 0.95 when d In

19 W.A. Pizer / Journal of Public Economics 85 (2002) other words, when d 5 12 the $600 billion dollar advantage associated with 1 quantity controls, shown in the left panel, pales in comparison to the roughly $34 trillion dollar expected welfare gain associated with either policy, generating a ratio near one in the bottom panel. However, when d 5 2 the $118 billion dollar 1 difference is quite large compared to the $20 billion dollar gain associated with the optimal quantity policy. Here, the ratio of the gains associated with a price price policy is almost a factor of seven times larger than the gains associated with a quantity policy. Why is the gain from an optimal quantity policy never more than a few percent higher than the gain from an optimal price policy? Quantity controls are only preferred when marginal damages are quite steep. In this case, the gains from any policy to drastically reduce emissions even an inefficient one will be large. Although price controls will necessarily over-control in some cases in order to guarantee adequate control in others, this inefficiency will be small relative to the gain from reduced damages. In the extreme, sufficiently high prices will induce % abatement and will be equivalent to a quantitative ban on emissions. When we look more closely at the simulations, we see that this is indeed the case. In the absence of any policy, the likelihood that temperatures rise by more than 4 degrees by 2100 exceeds 9%. In the presence of catastrophic damages (d 5 12) optimal price and quantity controls both reduce emissions in such a way 1 that the temperature increase never exceeds 4 degrees roughly the point where the catastrophic consequences begin. Fig. 5 shows the actual policy choices. In terms of quantity controls, the optimal policy involves an emission limit of 10 GtC from 2010 through In terms of price controls, it involves a tax that begins at about $15 per ton in 2010 and rises to more than $500 per ton by These are considerably more aggressive than the policies based on quadratic damages. 5. Hybrid policies As pointed out in Section 2.1, a hybrid permit policy where an initial quantity target is coupled with a trigger price at which additional, above-target, permits are sold will perform at least as well as either a pure tax or permit scheme (which are counted as special cases). We now explore the extent to which this is true for climate change mitigation policies and then consider the welfare consequences of certain suboptimal policies Optimal hybrid policies We return to the case of quadratic climate damages and begin with the choice of 33 An important distinction between the real world and the stylized world of Weitzman (1974) is that real cost shocks are not arbitrarily large; we can impose price policies that for all practical purposes guarantee a certain level of emissions.

20 428 W.A. Pizer / Journal of Public Economics 85 (2002) Fig. 5. Optimal policies with quadratic and catastrophic damages. policy in A hybrid policy in the year 2010 can be represented by an arbitrary point in a two-dimensional plane, where one dimension is the initial quantity target and the other dimension is the trigger price. Picking any point in that plane, we can use our climate economy model to compute the expected welfare gain of the policy represented by that point. Repeating the process over a grid of quantity target/ trigger price combinations, we can create a surface summarizing the welfare gains associated with those policies. Fig. 6 plots this surface for initial permit levels of between zero and 15 GtC and trigger prices of between zero and 25 $/tc. The proper way to read Fig. 6 is to note that for a grid of emission targets (0 15

21 W.A. Pizer / Journal of Public Economics 85 (2002) Fig. 6. Net expected policy benefits of alternative hybrid permit policies in GtC) and trigger prices (0 $25/ tc), the expected welfare gain relative to business as usual (no policy) is plotted on the z-axis in net present value terms. For low permit levels (, 5 GtC; back right edge of figure), the policy is essentially a tax and the surface traces out, from front to back, the welfare gain associated with a pure price policy. Similarly, for high trigger prices ($25/tC; front right edge of figure), the surface roughly traces, from left to right, the welfare gain associated with a pure quantity policy. The global optimum, a 5 GtC target and $7/tC trigger price, yields a welfare gain that is imperceptibly higher than the $2.5 billion gain achieved with a straight 34 tax of $7.50/ tc. More importantly, however, it performs considerably better than even the best pure permit policy. Relative to sub-optimal permit policies such as 34 Such a policy is remarkably close to the proposal suggested by McKibbin and Wilcoxen (1997). They advocated 1990 emission levels as the permit volume coupled with a $10/ton C trigger global controllable GHG emissions were 8.5 GtC.