Technological Change and Timing Reductions in Greenhouse Gas Emissions

Transcription

1 Technological Change and Timing Reductions in Greenhouse Gas Emissions Rolf Färe Department of Economics Oregon State University Corvallis, OR Shawna Grosskopf Department of Economics Oregon State University Corvallis, OR Dimitri Margaritis Department of Finance AUT Auckland New Zealand William L. Weber Department of Economics and Finance Southeast Missouri State University Cape Girardeau, MO 6371 March 21, 211

2 2 Abstract In 27 Nicholas Stern s Review (27) estimated that global GDP would shrink by 5-2% due to climate change which brought forth calls to reduce emissions by 3-7% in the next twenty years. Stern s results were contested by Weizman (27) who argued for more modest reductions in the near term, and Nordhaus (27) who questioned the low discount rate and coefficient of relative risk aversion employed in the Stern Review, which caused him to argue that `the central question about global-warming policy how much how, how fast, and how costly remain open. We present a simulation model developed by Fare, Grosskopf and Margaritis (29) on intertemporal resource allocation that allows us to shine some light on these questions. The empirical specification here constrains the amount of undesirable output a country can produce over a given period by choosing the magnitude and timing of those reductions. We examine the production technology of 28 OECD countries over , in which countries produce real GDP and CO 2 using capital and labor and simulate the magnitude and timing necessary to be in compliance with the Kyoto Protocol. This tells us `how fast and `how much. Comparison of observed GDP and simulated GDP with the emissions constraints tells us `how costly. We find these costs to be relatively low if countries are allowed reallocate production decision across time, and that emissions should be cut gradually at the beginning of the period, with larger cuts starting in 2.

3 3 Introduction In 1988 the United Nations created the Intergovernmental Panel on Climate Change (IPCC) to track and advise the UN on the latest research on climate change. Four years later the United States and the European community responded to the problem of global climate change with the United Nations Framework Convention on Climate Change (UNFCCC). The UNFCCC agreed to report greenhouse gas emissions and was amended in 1997 by the Kyoto Protocol, which set limitations on greenhouse gas emissions and proposed that industrialized nations collectively reduce greenhouse emissions by 5.2% from their 199 levels by 28 to 212. (Aldy and Stavins 28) Despite concern regarding the effects of anthropogenic greenhouse gas emissions on climate change the US increased its CO 2 equivalent emissions by 17% during 1992 to 27 (Environmental Protection Agency 29) while by 24, European Union member states had reduced emissions by only.9% of their required 8% average reduction required by the Kyoto Protocol (European Environment Agency 26). In 27 Nicholas Stern (27) presented economic estimates that global GDP would shrink between 5% and 2% due to the impacts of climate change unless emissions were reduced. These estimates brought forth a call for immediate action to reduce greenhouse emissions by 3% to 7% in the next twenty years. In contrast, most economic models argue for more modest reductions in emissions in the near future, but with a gradual ramping up of reductions over time (Weitzman 27). Nordhaus (27) argued that the estimates presented in The Stern Review were at odds with standard economic estimates, mainly because The Stern Review used a discount rate and coefficient of relative risk aversion among generations that are too low and inconsistent with actual market data. In summary, Nordhaus (27) argued that

4 4 the central questions about global-warming policy-how much, how fast, and how costlyremain open. In this paper we present a simulation model that allows us to shine some light on the central questions proposed by Nordhaus. Our method specifies a piece-wise linear production technology where undesirable outputs, such as CO 2 emissions, are jointly produced with desirable outputs. Such production technologies have been studied and formalized by Färe, Grosskopf, Noh, and Weber (25). In addition, we build on the recent work of Färe, Grosskopf, and Margaritis (29) who investigated the problem of intertemporal resource allocation decisions. In their model, DMUs (decision-making units) which have a limited resource to allocate over a finite time period must decide when to begin using the resource and how intensively to use the resource. We modify their time substitution problem to the case where DMUs are constrained in the amount of an undesirable output that can be produced over some period. In this case, the DMU seeks to maximize the sum of the quantities of the desirable output that can be produced over some period by choosing the magnitude and the timing of the reductions in the undesirable output. In an empirical application we examine the production technology of 28 OECD countries during the period These countries produce real GDP and the undesirable output of CO 2 equivalent emissions of greenhouse gases using capital and labor. Given the production technology, we simulate the magnitude and timing of the reduction in emissions necessary to be in compliance with the Kyoto Protocol and address Nordhaus questions about how much and how fast reductions in emissions should occur. Comparing each country s optimal amount of real GDP that can be produced in each period with the actual amount of real

5 5 GDP, we simulate the costs of compliance with the Kyoto Protocol and address the other Nordhaus question regarding how costly compliance will be. 2. Growth, Technology, and the Environment The environmental Kuznets curve hypothesis (EKC) proposes that there is an inverted U-relation between per capita emissions of a pollutant and per capita income. Such a relation implies that emissions will turn down after some threshold level of income has been surpassed. Copeland and Taylor (24) suggest four explanations for the EKC. First, the source of growth theory assumes that labor and capital are used to produce a clean good and a dirty good. If the dirty industry is capital intensive and the clean industry is labor (human capital) intensive, then if growth occurs primarily via physical capital accumulation in the early stages of development and via human capital accumulation in the later stages, pollution will rise and then fall as income grows. Second, the income effects explanation assumes that environmental quality is a normal good, but at low incomes pollution increases with growth because citizens place a higher relative value on increased consumption of material goods. However, as income grows, the income elasticity of demand for environmental quality increases and citizens become willing to trade consumption of material goods for higher environmental quality. Third, if there are the threshold effects for regulation, then at low levels of economic activity pollution might be unregulated or regulation might have little impact on the cost of pollution abatement activities by firms so emissions rise as income grows. However, after some threshold has been surpassed, pollution policies are either implemented or those already in effect start to impact costs, leading to declines in pollution as income continues to grow. If the threshold effect theory of the EKC holds then there should be a period of little or no regulatory policy followed by increasingly tougher policies and pollution

6 6 abatement costs over time. Fourth, if there are increasing returns to abatement activities, then as best practice abatement technologies become widely available firms become more efficient at reducing pollution, even if pollution taxes do not change. Azomahou, Laisney, and Van (26) use a panel of 1 countries for the period 196 to 1996 and examine the EKC for CO 2 and GDP per capita. Using nonparametric regression and accounting for the potential endogeneity of real GDP they find no shift in the CO 2 /GDP relation over time and no downturn in per capita CO 2 emissions as per capita GDP increases. Their work supports previous researchers such as Holtz-Eakin and Selden (1995) and Heil and Selden (21) who found a monotone increasing relation between CO 2 and GDP, but is in contrast to Schmalansee, Stoker, and Judson (1998) who found evidence of an EKC for CO 2 but did not control for the potential endogeneity of real GDP in their estimated EKC equations. Since the findings of Azomahou et al. indicate that economic growth by itself will be insufficient to reduce CO 2 emissions, other policies will have to be pursued. Among these policies are Pigouvian taxes on the carbon content of energy and policies that promote new technologies that reduce carbon emissions. Unfortunately, Barrett (29) reports that energy related research and development expenditures by countries signing the Kyoto Protocol have fallen more than 3% since 198. Here, Jaffe, Newell, and Stavins (25, 26) argue that policy-makers face a double-edged sword since the market failure associated with the global public good of climate is compounded by the market failure associated with research and development. For private companies to have the incentive to invest in R&D activities that reduce greenhouse gas emissions appropriate public policies need to be in place to foster certainty about the expected path of future emissions. However, to the extent that greenhouse gas emissions and climate change are a global public good, some countries may choose to free-

7 7 ride on the contribution of others and not implement emissions reducing policies. The absence of such policies then inhibits firms incentives to invest in R&D. Recent work by Kuosmanen, Bijsterbosch, and Dellink (29) examines the timing of greenhouse gas abatement and the ancillary benefits that arise from reductions in pollutants that cause acidification, eutrophication, smog, and particulate matter. These authors use a DEA (data envelopment analysis) model and estimate shadow prices for the ancillary pollutants under ten different scenarios for the path of decline in greenhouse gas emissions for the Netherlands. They find that policies that reduce emissions in early periods are more cost efficient and yield greater ancillary benefits than policies that reduce emissions in later periods. 3. Method. We follow the work of Färe, Grosskopf, Noh, and Weber (25) in modeling a technology where undesirable outputs are jointly produced as by-products of desirable outputs. Let M y R + represent the desirable output vector, vector, and J b R + represent the undesirable output N x R + represent the input vector. Decision-making units are indexed by k = 1,..., K and time is represented by the index t = 1,..., T. The technology is represented by the output possibility set P( x) = {( y, b) : x can produce ( y, b)}. (1) The output possibility set is assumed to satisfy the assumptions of no free lunch, null jointness of desirable and undesirable outputs, weak disposability of undesirable outputs, and strong disposability of desirable outputs and inputs. These properties are written as

8 8 i. P() = (,) ii. if ( y, b) P( x) and b = then y = iii. if ( y, b) P( x) then for θ 1, ( θ y, θb) P( x) iv. if ( y, b) P( x) then for y ' y, ( y ', b) P( x) v. P( x) P( x') for x' x. (2) For DMU o for period t, the DEA (data envelopment analysis) output possibility set (1) satisfying the assumptions of (2) is given as K t t t t t o m k km k = 1 P ( x ) = {( y, b) : y z y, m = 1,..., M, K t t t on k kn k = 1 x z x, n = 1,..., N, K t t t j k kj k = 1 b = z b, j = 1,..., J, t z, k = 1,..., K, t = 1,..., T}. k (3) To model the idea of time substitution of the undesirable output we assume that the first period in which undesirable output is produced is at τ t. The number of periods in which production of the undesirable output is allowed is denoted production takes place during the interval { τ, τ + T }. T T τ. Thus, Suppose the environmental agency imposes a constraint on the amounts of the undesirable outputs that DMU o can produce during the entire period such that T t boj bj, j = 1,..., J, (4) t = 1 where b j is the regulated quantity ceiling on the j th undesirable output. The idea of time substitution is to determine when to begin ( τ ) and end ( τ +T ) production of the undesirable outputs so as to maximize the production of the desirable outputs.

9 9 To begin to solve the problem of time substitution we consider a technology where a single desirable output is produced. The optimization problem we solve is max τ τ τ z, τ, T, b, y + T = τ subject to K K τ τ τ τ τ τ k k on k kn k = 1 k = 1 y z y, x z x, n = 1,..., N, K τ + T τ τ τ τ j k kj j j k = 1 τ b = z b, j = 1,..., J, b b, j = 1,..., J τ k τ τ y τ z k = K + T t = T, 1,...,, ( τ, τ ) ( 1,..., )} (5) In Figure 1 we illustrate our method for allocating emissions cuts for three countries that define the frontier of P(x) in two periods. In t=1 the three countries A, B, and C use the same inputs, x, but produce different amounts of the desirable and undesirable output given by 1 1 ( A, A) (2,5) b y =, 1 1 ( B, B) (5,9) b y =, and 1 1 ( C, C ) (6,1) b y =. We assume that technological progress occurs so that in t=2 the three countries produce 2 2 ( A, A) (2,1) b y =, 2 2 ( B, B) (3,13) b y =, and 2 2 ( C, C ) (7,16) b y =. Suppose the regulatory authorities require emissions cuts for A equal to 1, emissions cuts for B equal to 2, and emissions cuts for C equal to 4. Thus, the regulatory constraint for A is b + b 3; for B the regulatory constraint is 1 2 A A b + b 6 ; and for C the 1 2 B B regulatory constraint is b + b 9. Time substitution allows the three countries to choose 1 2 C C when to cut emissions so as to maximize the sum of the desirable output in the two periods. Some countries might choose to begin cuts immediately, while other countries might choose to delay cuts until later. Still other countries might cut emissions more deeply than required in an early period if they can more than make up the lost desirable output from early cuts by expanding emissions and the desirable output in a later period. For country A, the optimal solution to the problem

10 max y y s. t. ( b, y ) P ( x), ( b, y ) P ( x), b b (6) is 1* 1* ( A, A ) (,) b y = and 2* 2* ( A, A ) (3,13) b y =. Here, country A cuts more than required in t=1 and foregoes production until t=2, when production is increased. For country B, with regulatory constraint b + b 6, the optimal solution is 1 2 B B 1* 1* ( B, B ) (3,6.3) b y = and 2* 2* ( B, B ) (3,13) b y = and all emissions cuts occur in t=1. Finally, for country C, with regulatory constraint b + b 9, the 1 2 C C optimal solution is 1* 1* ( c, C ) (6,1) b y = and 2* 2* ( C, C ) (3,13) b y = and all emissions cuts are delayed until t=2. This example illustrates that countries facing the same technology but producing different intensities of the desirable and undesirable output, will choose to make cuts in different periods so as to maximize the sum of the desirable output. 3. Data and Estimates 3.1 Data To implement the model described in the previous section we use panel data for 28 OECD countries during Countries transform labor and capital into a desirable output of real GDP and an undesirable output of carbon dioxide equivalent emissions. Data on real GDP and labor are taken from the Heston, Summers, and Aten (29) (Penn World Table Version 6.3). The Penn World Table also reports each country s annual real investment spending. We follow Marquetti (28) and use the perpetual inventory method to construct capital stock figures from the annual flows of real investment spending. Carbon dioxide equivalent emissions are taken from Boden, Marland, and Andres (29) of the Carbon Dioxide Information Analysis Center (CDIAC). Table 1 reports descriptive statistics and Figure 2 graphs annual mean CO 2 emissions and real GDP for the 28 countries. On average, the 28 countries annually generate 119.9

11 11 million metric tons of CO 2 equivalent emissions and 1 trillion dollars of real GDP using a labor force of approximately 18.6 million workers and a real capital stock of 2.78 trillion dollars. Average annual real GDP growth is 2.7% accompanied by.8% average annual growth in CO 2 emissions. The US has the largest absolute flow of CO 2 emissions with emissions growing at an annual rate of 1.1% as real GDP grows at a 3.4% annual rate. The rate of emissions growth (.8%) for our sample of 28 OECD countries is less than the 1.8% forecasted growth rate of global emissions of Holtz-Eakin and Selden (1995) primarily because developing countries are excluded from our sample and those countries have a higher marginal propensity to emit. Although not reported, the five countries with the highest ratio of real GDP to total emissions are Switzerland, Sweden, Norway, Iceland, and France, and the country with the lowest ratio is Poland. On average, real GDP per metric ton of CO 2 is $1,551 and ranges from a low of $2,854 in Poland to a high of $24,81 in Switzerland. 3.2 Estimates We consider a policy scenario where each country is restricted to emitting only 95% of their total actual emissions. For instance, during 1991 to 26 the US emitted 23.8 billion metric tons of CO 2 equivalent emissions so they are restricted to producing only 22.6 billion tons and must cut emissions by 1.2 billion tons. Since some countries might be inefficient producers we project their desirable output to the production possibility frontier before estimating the time substitution model. Countries that are inefficient producers might be able to reduce CO 2 emissions at no cost simply by reducing inefficiency. However, to the extent that inefficiency is persistent because of institutional or cultural choices made by policymakers or citizens, attributing CO 2 emissions cuts to reductions in inefficiency is likely to give an underestimate of the true cost of cutting emissions. For each country we use the output

12 12 distance function to project real GDP (y) to the production possibility frontier, holding CO 2 emissions (b) constant. The output distance function is defined on the production possibility set as y Do( x, y, b) = min{ λ :, b P( x)}. λ (7) Given k=1,,k countries, the reciprocal of the output distance function for country o is estimated using DEA as K K 1 1 1/ Do ( xo, yo, bo ) = max{ λ : zk yk λ yo, zkbk = bo, λ, z k = 1 k = 1 K k = 1 z x x, n = 1,..., N, z, k = 1,..., K}. k kn no k (8) Table 2 reports mean annual output efficiency and the number of countries that produce on the frontier in each period. Between seven and nine countries produce on the frontier with Switzerland, Great Britain, Luxembourg, Norway, Poland, and the US on the frontier in every year and Sweden on the frontier in every year except Since technological change is likely to be an important determinant of when and how much CO 2 emissions should be reduced we estimated the Malmquist productivity index and the technical change component of the Malmquist index for each country. The Malmquist productivity index takes the form D ( x, y, b ) D ( x, y, b ) D ( x, y, b ) (,, ) (,, ) (,, ) t + 1 t t o t + 1 t + 1 t + 1 o t + 1 t + 1 t + 1 t t t t t t t + 1 t + 1 t + 1 = t t + 1 t + 1 Do xt yt bt Do xt + 1 yt + 1 bt + 1 D xt yt bt M ( x, y, b, x, y, b ) where the technical change index (TECH) measures the shift in the P(x) frontier from period t to period t+1 and is given as.5 (9) TECH t t Do ( xt 1, yt 1, bt 1) Do ( xt, yt, b ) t = t + 1 t + 1 Do ( xt + 1, yt + 1, bt + 1) Do ( xt, yt, bt ).5. (1)

13 13 Values of TECH>(<)1 indicate technical progress (regress). The last column in Table 2 reports mean technical change between each pair of years, beginning with 1991 to Technical change for the twenty-eight countries ranges from an average of 2.25% in 25 to 26 to a low of -.29% in 24 to 25. For comparison, Jeon and Sickles (24) use a bootstrapped Malmquist index for 17 OECD countries during the period and find marginally higher productivity growth rates when CO 2 emissions are accounted for, with average annual technical progress of 1.5% adding more to total factor productivity growth than the.15% gain in efficiency. `We solve the time substitution problem (5) for each country for all possible starting periods, τ, and intervals, T. Since τ can take 15 values coinciding with 1991 to 25, and T can take values from 1 to 15, coinciding with production ending in 1992 to 26, there are ( )=12 linear programming problems to solve for each country. The results indicate that each country should produce from the beginning period ( τ =1991) and continue through 26 (T =15) to meet the simulated 5% reduction in emissions. In contrast to our results, in a simulation of time substitution of inputs, Färe, Grosskopf, and Margaritis (29) show that production sometimes does not occur in all periods as inputs are used exclusively in some periods and not in other periods. Our findings can be explained by referencing Figure 1. A country that cuts CO 2 to zero in one year is able to expand CO 2 and real GDP in another year. For 23 out of 28 countries actual emissions in every year are greater than the total required emissions cuts that must occur. For instance, the US has to cut emissions by 1.2 billion tons (.5 x 23.8 billion), but the US emitted no fewer than 1.3 billion in a single year. Our results indicate that for the US and other similar countries it is as if they are producing at point like A in t=1 and at B in t=2, producing 2+3=5 emissions with required cuts equal to 1. If emissions

14 14 are cut to zero in t=1, emissions could be expanded to 4 in t=2, or emissions could be cut to zero in t=2 and expanded to 4 in t=1. However, in both cases, the lost real GDP from cutting emissions to zero is greater than any gains to real GDP from expanding emissions in a different year. For five countries-greece, Norway, Korea, Spain, and Turkey-the simulated 5% emissions cuts are greater than actual emissions in 1991 for Greece, 1992 for Norway, 1993 for Spain, 1991 to 1993 for Korea, and 1991 to 1992 for Turkey. However, with the exception of Korea, the ratio of optimal real GDP to optimal CO 2 emissions is greater in those years than it is in other years, so emissions cuts would be relatively costly and the solution indicates that it is optimal to produce in those years and defer cuts to other periods. For Korea, emissions are cut by 22% in 1991 with a 1% loss in real GDP. Further cuts in emissions in that period would cause real GDP to shrink even more than it would in other periods. Figure 3 depicts the annual means for actual CO 2 emissions and optimal CO 2 emissions that are found as part of the optimal solution to the time substitution problem. Mean optimal emissions under a 5% emission cut are only 88% of actual emissions in 1991, but rise to 97% of actual emissions by 1995 before falling again in In 1999, mean optimal emissions are 14% of actual emissions, but then decrease and finish the period in 26 at only 77% of actual mean emissions. Figure 4 depicts the mean of optimal real GDP * ( t ) y for the 28 countries and mean actual real GDP inflated by the reciprocal of the output distance function: * yt. t ( y / D ( x, y, b )) t o t t t Without restrictions on emissions, frontier real GDP grows at an average annual rate of 3.5%. Restricting CO 2 emissions to 95% of actual emissions, but allowing time substitution, the average annual rate of growth of real GDP is 2.7%. The difference in the growth rates is

15 15 greatest from 1998 to 1999, when frontier real GDP grows by 7.3% and real GDP found as the solution to the time substitution problems for the 28 countries grows by 3.6%. 1 For each country the sum of optimal incomes, T t =τ y * t, is found as the objective function in (5) for an optimal choice of τ and T. Table 3 lists the countries and the ratio of the sum of t optimal incomes to actual income inflated by the output distance function, yt / Do ( xt, yt, bt ). This ratio gives an estimate of the lost real GDP due to the simulated 95% emissions restriction. Poland has the lowest ratio,.921, implying a cost of (1.921) 1% = 7.9% of lost real GDP to comply with the 95% emissions restriction. In contrast, Switzerland has a ratio of 1.46 implying that if real GDP and emissions were optimally reallocated between periods, the sum of real GDP over the sixteen years could be 4.6% higher. Two explanations are offered for the increase in Switzerland s real GDP. First, it could have been producing at a point like C in Figure 5, so that cutting emissions could yield higher levels of real GDP. Second, time substitution might have allowed Switzerland to reduce emissions in a period when the cost was low in terms of lost real GDP and then expand real GDP in a period when the cost of the expansion was small in terms of increased emissions. In fact, the solution for Switzerland indicates that it should make all of its cuts in 1992 with the path of optimal emissions equivalent to actual emissions in every year thereafter. For 17 out of the 28 countries, an optimal reallocation of production across time could experience an increase in real GDP. The second column of Table 3 reports the ratio of the sum of optimal restricted emissions to actual emissions. The emissions restriction is binding for only 21 out of 28 1 Each country s optimal growth rate can be used to estimate the social rate of time preference given suitable choices for the coefficient of relative risk aversion and the rate of individual time preference. T t =τ

16 16 countries. For instance, while the US has a 1.4% cost in terms of lost real GDP, the ratio of optimal to actual emissions is only 85.1%. This result would be consistent with optimal US production at a point like U in Figure 5, where any further increase in emissions is associated with a decline in real GDP. In columns 3 and 4 of Table 3 and in Figures 6 and 7 we provide some information to the Nordhaus question about how fast emissions should be cut. Table 3 reports the year for each country when at least 5% of required emissions cuts are made and the percent of required emissions cuts that are made by the year 2. Figure 6 graphs the path of emissions cuts for all 28 countries and illustrates that 5% of the total cumulative emissions cuts required by the 28 countries do not occur until sometime in 21. Figure 7 graphs the path of optimal emissions and actual emissions for each country. From Table 3 we note that the US does not reach 5% of their required cumulative cuts in emissions until 23 and Great Britain does not reach this level until 26. In contrast, Figure 7 shows that Australia and Denmark cut emissions early in the period and reach 5% of their required cuts in Furthermore, by 2, some countries, such as Belgium, Denmark, France, Iceland, and Japan have made more than 1% of their required emissions cuts which allows them to increase emissions in later years. However, other countries, such as Greece, Korea, Mexico, and New Zealand increase emissions above their actual level by 2, but then cut emissions during 21 to 26. If trading of carbon permits is to be part of the policy apparatus to curb global emissions then the solution to our model provides information on the optimal time to buy and sell those permits. Countries making cuts early in the period, such as Austria, Belgium, and Denmark, will have permits to sell to countries such as Greece, Korea, and Mexico who will

17 17 find it optimal to buy permits in the early periods and wait to cut emissions until it is less costly in terms of lost real GDP. Policy makers might face political constraints regarding annual losses to real GDP that are acceptable due to emissions cuts. (Bosetti and Frankel 29) In the last two columns of Table 3 we report the maximum lost real GDP as a percent of frontier real GDP for each country and the year in which that loss occurs. In 1991, Poland experiences the greatest lost real GDP from emissions reductions, 37.6%. Eight other countries experience one year losses greater than 1%, but in the US, the largest loss is only 4.25% in 26. To account for political losses an additional constraint that limits optimal real GDP to be no less than say 9% or 95% of actual real GDP in a particular year could be added to the model. Of course, such a constraint would raise the overall cost of cutting emissions. 4. Conclusions In this paper we presented a model that allows production decisions to be substituted across time so as to maximize a desirable output while simultaneously adhering to a constraint that limits the production of an undesirable output. We applied our method to investigate the costs of carbon dioxide emissions restrictions for 28 OECD countries that produced during 1991 to 26. The findings indicate that the costs of compliance in terms of lost real GDP are relatively low if countries are able to reallocate production decisions across time. For the largest greenhouse gas emitter-the US-the costs of meeting a 5% reduction in emissions would be 1.4% of the sum of real GDP over the period 1991 to 26. In a recent paper, Tol (29) summarizes numerous studies on the welfare impacts of increases in temperature. The impacts range from a 2.3% gain in GDP if temperature warms by 1 o C to a 4.8% loss if temperature warms by 3 o C. Our simulation estimates indicate that a down payment on reducing emissions

18 18 to 95% of their 1991 to 26 level could be achieved for most countries at a smaller cost than the average output loss of.7% (s=1.2%) reported by Tol. In contrast to The Stern Review, which advocates immediate reductions in greenhouse gas emissions, our simulation model finds that for real GDP to be maximized across the period emissions should be cut gradually, with smaller cuts as a percent of actual emissions during 1991 to 1998 and larger cuts during the period 2 to 26. Our results indicate that 5% of total simulated emissions cuts for the 28 countries would not come until 2 to 21. We caution the reader that although our model indicates that emissions cuts can be made at relatively low cost, the countries in our sample have shown little ability to cut emissions.

19 19 Figure 1. Time Substitution Example y 2 A t=1 16 y C t=2 13 B C 1 A B P 2 (x) P 1 (x) b b

20 2 Figure 2. Annual Mean CO 2 Emissions and Real GDP 1.4E E+12 1E+12 8E+11 Real GDP 6E+11 4E+11 2E CO2 Emissions (1s of metric tons)

21 21 Figure 3. Actual Emissions and CO2 Emissions Restricted to 95% Actual Emissions 95% CO2 Emissions

22 22 Figure 4. Optimal Real GDP with 5% Emissions Cuts and Frontier Real GDP 1.6E E E+12 1E+12 8E+11 6E+11 4E+11 2E Optimal Real GDP Frontier Real GDP

23 23 Figure 5. The Production Possibility Set, P(x) y=real GDP U C P(x) b=co 2

24 24 Figure 6. Proportion of Cumulative Cuts Made by 28 OECD Countries % of total cuts made

25 25 Figure 7. Actual CO 2 and Optimal CO 2 with 5% Emissions Cuts (millions of metric tons) Australia Austria Belgium Canada Switzerland Denmark Spain Finland

26 26 France Great Britain Germany Greece Hungary Ireland Iceland Italy

27 27 Japan Korea, 5% cut Luxembourg Mexico Netherlands Norway New Zealand Poland

28 28 Portugal Sweden Turkey USA

29 29 Table 1. Descriptive Statistics 1 Mean Std. dev. Min. Max. CO 2 =b Realgdp=y 1.1E E E E+13 Labor=x E+8 Capital=x E E E E CO 2 is measured in 1s of metric tons, realgdp and capital have a base year of 2 and are measured at purchasing power parity, and labor is measured as the number of employed workers. Table 2. Annual Efficiency, D( x, y, b ) and Technical Change D( x, y, b ) mean Std. dev. Min. Max # of frontier TECH countries % % % % % % % % % % % % % % %

30 3 Table 3. Optimal Time Substitution Results. With Emissions Restricted To 95% of Actual Emissions 1 16 t= 1 16 t= 1 y * t t ( y / D ( x, y, b )) t t t t 16 t= 1 t t= 1 b * t b t Year by which 5% or more of Required Cuts are Made Percent of Required Cuts Made by 2 Max. Annual Lost Real GDP Year of Max. Annual Lost Real GDP Australia % 17.9% 1998 Austria % 12.22% 2 Belgium % 4.35% 25 Canada % 9.65% 23 Switzerland %.%. Denmark % 6.83% 22 Spain % 5.18% 25 Finland % 8.5% 1994 France % 1.6% 25 Great Britain %.%. Germany % 6.39% 1994 Greece % 7.18% 1995 Hungary % 1.25% 26 Ireland % 4.68% 1994 Iceland % 9.53% 24 Italy % 13.72% 25 Japan % 14.56% 25 Korea % 1.4% 1991 Luxembourg %.%. Mexico % 3.77% 1994 Netherlands % 6.34% 1994 Norway %.%. New Zealand % 13.51% 1993 Poland % 37.4% 1991 Portugal % 1.16% 1997 Sweden %.%. Turkey % 2.54% 22 USA % 4.25% Actual real GDP in year t= y t, optimal real GDP in year t = y * t, optimal emissions in year t given a 95% emissions restriction= b * t, and actual emissions in year t= b t.

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