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Analyzing the economic cost of the Kyoto protocol
Ecological Economics 38 (2001) 59 – 69 www.elsevier.com/locate/ecolecon
ANALYSIS
Analyzing the economic cost of the Kyoto protocol Neha Khanna * Economics and En6ironmental Studies, Binghamton Uni6ersity, LT 1004, PO Box 6000, Binghamton, NY 13902 -6000, USA Received 6 June 2000; received in revised form 7 December 2000; accepted 8 December 2000
Abstract This paper examines the cost of meeting the Kyoto Protocol commitments under alternative assumptions regarding technology and technical change. Real GDP is modeled as a function of the capital, labor, and energy inputs. The analysis is based on data for 23 Annex 1 countries from 1965 to 1999. Two important results emerge. First, the standard assumption of Hicks neutral technical change and time and scale independent output elasticities is not supported by the data. Second, when technical change is allowed to be biased in favor of the energy and capital inputs, and when the output elasticities vary with the level of factor use and over time, the loss in real GDP due to the Kyoto commitments rises substantially. On average, the loss in real GDP is one and a half times higher than obtained under the standard assumptions. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Technical change; Output elasticity; Bias; Annex 1; Translog production function; Cobb– Douglas production function; Linear homogenous
1. Introduction In the past decade, a substantial body of literature has emerged analyzing the economic cost of reducing future carbon dioxide (CO2) emissions. The range of model structures is quite varied. At one end, there are highly aggregate, top-down, regional dynamic models based on optimal control techniques. There are also multi-sector models in the tradition of the regional computable general equilibrium models, which allow for inter* Tel.: +1-607-7772689; fax: +1-607-7772681. E-mail address: [email protected] (N. Khanna).
industry differences and international commodity trade. Yet another model type are the bottom-up style models with a significant level of detail on the energy sector including several fuel types and technology options for energy supply. Not surprisingly, these models yield very different numerical results. Recently, under the 16th Energy Modeling Forum (EMF-16) organized by Stanford University, some of the most prominent among these models were used to estimate the potential costs of the Kyoto Protocol. Under this Protocol, Annex 1 countries, that is developed countries included in Annex 1 to the UN Framework Convention on
0921-8009/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 8 0 0 9 ( 0 0 ) 0 0 2 9 5 - 0
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Climate Change, have agreed to reduce their overall net greenhouse gas emissions to 5% below their 1990 levels by the years 2008– 2012. As in the case of previous such exercises, the great advantage of the EMF study is that it tends to highlight the differences in model results due to different model structures, rather than differences in scenario construction. Despite the generally uniform scenarios under which the models were operated, the carbon tax in 2010 required for USA to meet its Kyoto commitments through domestic emissions reductions alone, ranged from about $75 per metric tonne to more than $400 per metric tonne (as measured in 1990 prices). In the case of Japan and the European Union, this range is even wider. However, there is one aspect in terms of which the model results are remarkably consistent. This relates to the estimated cost of the emissions reductions under Kyoto Protocol as measured by the loss in GDP in 2010. Table 1 summarizes the GDP impact on Annex 1 countries obtained under the no-trading scenario of EMF-16. The overriding conclusion that emerges from this Table is that the economic cost of the Kyoto commitments is small. Table 1 GDP loss under EMF-16’s no-trading scenario (as a percent of 2010 baseline)a Model
SGM GRAPE Oxford MERGE3 MS-MRT G-CUBED ABARE CETA AIM RICE Average
Country US
Japan
CANZ
EU
n.a. n.a. 1.91 1.07 1.90 0.45 2.14 1.98 0.47 0.97 1.34
n.a. 0.18 1.88 0.80 1.73 0.54 0.83 n.a. 0.24 0.81 0.88
n.a. n.a. n.a. 2.07 1.82 0.60 1.59 n.a. 0.57 1.15 1.30
n.a. 0.37 0.76 0.43 0.27 0.71 0.42 n.a. 0.15 0.23 0.42
a Note: these estimates are based on Figures 7 and 9 of Weyant and Hill (1999), since published versions of these models do not provide the data directly. In addition, GDP figures for 1990 were obtained from World Bank (1992). For CANZ, the sum of GDP in Canada, Australia, and New Zealand was used. For the European Union (EU), the 1990 OECD GDP was used. For detailed model results, see the 1999 special issue of the Energy Journal. n.a., Not available.
On average, the loss in 2010 GDP would be less than 1%. Even in the models with the highest estimates, the reduction in GDP is about 2%.1 One factor that could possibly explain this result is the structure of the production function embedded in these models, and the nature of technical change implicit therein. While the models included in this study differ widely in terms of overall structure, they uniformly assume Hicks neutral technical change and time invariant production or output elasticities. In addition, it is also assumed that the output elasticities do not vary with the level of factor use. The current analysis has a dual focus. First, it will be shown that these assumptions are not borne out by the recent empirical history of the Annex 1 countries. Second, and more important, relaxing these assumptions may significantly increase the estimated loss in GDP.
2. The econometric model Since the focus of the paper is the impact of technology assumptions embedded in the aggregate production function on the costs of meeting the Kyoto commitments, the model used here abstracts from all other economic factors that might affect the results. An econometric model based on pooled cross-section and time series data from 1965 to1990 for 23 industrialized Annex 1 countries is used. Countries not included in the sample are Liechtenstein, Monaco, countries of the former Soviet Union and those in Eastern Europe, due to nonavailability of data. Details on data and data sources are provided in the Appendix A. Real GDP in each time period (GDPt ) is modeled as a function of the contemporaneous capital (Kt ), labor (Lt ), and energy (Et ) inputs. The trend variable (~) captures technological change. Output elasticities for each factor input are estimated using a translog production function that is linear homogenous in factor inputs. Interactions between factor use and time are included to allow for biased technical change. This also allows the output elas1
Another important conclusion is that USA is likely to bear the highest relative cost, followed closely by CANZ, an economic region defined by Canada, Australia, and New Zealand.
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ticities to vary directly with time. Further, the interaction terms between the factor inputs implies that the output elasticities are a function of the level of factor use. A fixed effects model is used to account for country-specific effects. The estimating equation is ln(GDPt )=country dummies+ i~~ + i~~~ 2 + iK ln(Kt )+iL ln(Lt ) + iE ln(Et ) + iKL ln(Kt ) ln(Lt )+ iKE ln(Kt )ln(Et ) + iKK ln(Kt )2 +iLL ln(Lt )2 +iEE ln(Et )2 + iK~ ln(Kt )~+iL~ ln(Lt )~ +iE~ ln(Et )~
(1)
subject to the restrictions Hi = h, where Æ iK Ã Ã 2iKK Hi = Ã iKL Ã Ã iKE È iK~ Æ1 Ç Ã0 Ã Ã Ã h= Ã0 Ã Ã0 Ã Ã Ã È0 É
+
iL
+
+ + + +
iKL 2iLL iLE iL~
+ + + +
iE Ç Ã iKE Ã iLE Ã , Ã 2iEE Ã iE~ É
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Table 2 Estimated parameters for the linear homogenous translog modela Variable
Estimated coefficient
S.E.
P-value
~ ~2 ln(Kt ) ln(Lt ) ln(Et ) ln(Kt )ln(Lt ) ln(Kt )ln(Et ) ln(Lt )ln(Et ) (ln Kt )2 (ln Lt )2 (ln Et )2 ~ ln(Kt ) ~ ln(Lt ) ~ ln(Et )
−0.025 0.0001 1.038 −0.0385 0.347 0.338 −0.153 0.0161 −0.092 −0.177 0.068 0.005 −0.013 0.008
0.0081 0.0001 0.175 0.145 0.0862 0.061 0.051 0.031 0.040 0.029 0.023 0.003 0.003 0.002
0.0019 0.5001 0.0001 0.0082 0.0001 0.0001 0.0028 0.5987 0.0223 0.0001 0.0025 0.0902 0.0001 0.0001
a Sum of squares of errors =0.4323; R 2 =0.99; errors corrected for first order autocorrelation; estimated correlation coefficient=−0.794. Note: ~ represents the trend variable.
(2)
The estimated slope coefficients, S.E., P-values, and other regression statistics are shown in Table 2. The estimates are reasonably robust. Only three out of the 14 slope coefficients are insignificant at the 5% level. This is not unreasonable as the equation includes the squares and cross-products of the independent variables.2 Output elasticities for each of the three factor inputs are obtained as the first derivative of the estimating equation with respect to ln(Kt ), ln(Lt ), and ln(Et ). The advantage of using such a production function is that though the output elasticities are constrained to sum to unity, individual elastic2 The inclusion of squares and cross products enhances the problem of multicollinearity. The variance inflation factors for all variables are quite large. However, the overall results are robust. The model was re-estimated using an alternative labor series obtained from the World Bank (1999). The estimated coefficients and output elasticities did not change significantly.
ities are allowed to vary with the level of factor use and time.3 Another advantage is that even though the slope coefficients are restricted to be identical for all countries and over time, the computed output elasticities vary by country and period as they are directly determined by the level of the factor input in each case. Fig. 1 shows these elasticities for the G-7 countries, and also the average elasticities for all countries in the data set. Note the significant differences in the trends observed over the sample period.4 Another policy variable of direct interest is the bias in technical change. It is measured as the 3 For more details on the translog production function, see Christensen et al. (1973), Jorgenson and Fraumeni (1981), Berndt and Wood (1982), Boisvert (1982). The Jorgenson and Fraumeni work provides a lucid interpretation of the individual coefficients under duality theory. 4 The values and trends obtained for the output elasticities fall in the range found in the literature. Kim and Lau (1994) estimated a translog meta production function in capital and labor using data from at least 1966 to 1990 for nine countries including France, Germany, Japan, UK, and USA. The estimates obtained here are very close to the Kim – Lau estimates. McKibbin et al. (1999) also estimate output elasticities. However, they use US data only. Furthermore, in some cases, there is a large difference between the estimated elasticities and the values imposed in their model.
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proportional change in the marginal rate of substitution between any pair of inputs over time (Ferguson, 1979). In the present case, this is equivalent to the relative proportional change over time in pairwise input production elasticities. That is, the bias in technical change between a pair of factor inputs, i and j, Biasi,j, may be calculated as Biasi, j =
ii~ ij~ ] 0 − pi pj 5
(3)
where ii~ (ij~ ) refers to the coefficient on the interaction term between input i ( j ) and the trend variable (~), and pi (pj ) is the output elasticity of input i ( j ). Note that ii~ is also the derivative of pi with respect to the trend variable.5 A positive
Fig. 2. Bias in technical change (G-7 countries).
Fig. 1. Production elasticities (G-7 countries). 5 For a complete derivation of Eq. (3), see Khanna et al. (1997).
(negative) sign on Biasi, j indicates that technical change is factor i ( j ) intensive. The hypothesis of Hicks neutral technical change is tested by examining the joint significance of the coefficients on the interaction terms between the factor inputs and the trend variable. That is, under the null hypothesis, ii~ = 0 for all i {i= K, L, E}, simultaneously. This was rejected at the 1% level of significance. It was found that technical change was either capital or energy intensive, but not labor intensive. Fig. 2 shows the bias in technical change for the G-7 countries. This result has important implications for climate policy. The implementation of the Kyoto Protocol is likely to increase the relative price of energy. In the presence of energy intensive technical change, this would have an adverse impact on the growth in total factor productivity. There is some evidence for this during the oil shocks of the
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1970s and the early 1980s.6 However, the decline in the growth rate is fairly small, with the latter oil shock having a much smaller impact. On the basis of the current model it cannot be predicted, a priori, whether the future impact will be beyond this historical range. However, the issue is raised due to its significance. 3. The economic impact of the Kyoto Protocol How important is the presence of time- and scale-dependent output elasticities and biased technical change when assessing the economic impact of the Kyoto Protocol? To answer this question the loss in GDP is compared under two alternative models. The first model is shown in Eq. (1). Under the alternative model real GDP is as a linear homogenous Cobb – Douglas function of the three factor inputs and the trend variable, under the restriction of Hicks neutral technical change. As before, a fixed effects model is used to account for country-specific effects, and the errors are corrected for first order autocorrelation. The estimated slope coefficients and other regression statistics for this model are shown in Appendix A.7 To facilitate the analysis, the following simplifying assumptions are made to define the ‘Kyoto Scenario’. First, every country in the sample is assumed to meet its commitment in 2010, the midpoint of the 4-year commitment period under the Protocol. Second, the possibility of emissions trade, allowed under the Protocol to supplement domestic reductions, is ignored. The analysis is, thus, comparable to the no-trading scenario of 6 See, for example, Watkins (1992) for the case of Canada, and Berndt and Wood (1987) for the US manufacturing sector. Jorgenson (1984) links electric and non-electric energy to productivity growth. 7 Nordhaus and Boyer (1999b) also use a linear homogenous Cobb– Douglas production function in capital, labor, and carbon-energy. In the current analysis, the null hypothesis of linear homogeneity is rejected in both models. However, in the absence of this restriction, both models yield negative or zero output elasticities for several countries, a result clearly incompatible with economic theory. In contrast, when the restriction is imposed both models yield output elasticities that are comparable with other work. Therefore, this restriction was retained.
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EMF-16. Third, each country is assumed to meet its GHG commitment through a proportional reduction in CO2 emissions. While this is likely, it does not necessarily have to be so. The Protocol includes reductions for CH4, N2O, HCFs, PFCs, and SF6, in addition to CO2. However, CO2 accounts for the bulk of the GHG emissions for the Annex 1 countries. Also, the sources of CO2 are relatively well understood and the main body of the literature has focused on the implications of reducing these emissions. Fourth, and most important, it is assumed that a reduction in CO2 emissions requires a proportional reduction in energy use. This is a pessimistic assumption. A significant fraction of each country’s commitment could be achieved by switching to less carbon intensive fuels such as natural gas. However, since this assumption is maintained under both models, it is unlikely to affect the qualitative results obtained here. In this sense, the assumption is ‘neutral’. Finally, it is assumed that countries reduce their gross emissions whereas the Protocol calls for a reduction of net GHG emissions. The various carbon sinks and their potential for emissions reductions are fairly tentative at this point. As in the case of fuel switching, this assumption is maintained under both models and is unlikely to affect the overall conclusion. The baseline real GDP in 2010 is estimated for each country in the sample on the basis of the projected factor input levels, and the estimated coefficients under both models. National labor force projections are based on WRI (1998).8 DoE (1999) (Table A1) forecasts energy use in 2010 for several Annex 1 countries. The growth rates provided there were used as far as possible.9 For the countries where these predictions were not provided, the average projected growth rate for ‘other Western Europe’ was used. The exceptions were Belgium, Denmark, The Netherlands, and Luxembourg, where energy use has remained more or less constant since the 1970s oil shock. In this case 8 WRI (1998) did not provide the projected labor force growth rate for Luxembourg. The average projected growth rate for Europe was used in this case. 9 DoE (1999) projects energy use in quadrillion BTUs. In the present data set, energy is measured in mtoe. It is assumed that the projected growth rates are independent of the measurement units.
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64 Table 3 Impact of the Kyoto Protocol Countrya
Australia Austria Belgium Canada Denmark Finland France Germany Greece Iceland Ireland Italy Japan Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA Average
CO2 emissions (percent of 1990 baseline)b
108 92 92 94 92 92 92 92 92 110 92 92 94 92 92 100 101 92 92 92 92 92 93 94.43
Energy use (percent reduction from 2010 baseline)c
18.54 27.67 8.00 33.43 8.00 27.67 28.66 19.50 27.67 13.52 27.67 28.38 30.21 8.00 8.00 24.57 20.59 27.67 27.67 27.67 27.67 26.08 29.58 27.92
GDP loss (percent of 2010 baseline) Translog model
Cobb–Douglas model
8.04 9.95 3.48 14.66 2.90 11.19 11.98 7.10 12.11 5.87 13.10 11.62 8.27 3.56 3.46 11.29 8.50 12.35 10.41 11.78 7.93 12.72 15.10 9.45
4.81 7.50 1.99 9.33 1.99 7.50 7.81 5.09 7.50 3.43 7.50 7.72 8.29 1.99 1.99 6.56 5.40 7.50 7.50 7.50 7.50 7.01 8.09 6.15
a
Liechtenstein, Monaco, countries of the former Soviet Union, and East European countries are also included in Annex 1. The Kyoto Protocol requires a reduction in net GHG emissions. This analysis assumes an equivalent reduction in gross CO2 emissions. c This assumes CO2 emissions are reduced via an equivalent reduction in energy use. b
it was assumed that energy use remains constant at the 1990 level. Capital stock projections were not available, so this variable was projected on the basis of the available data. It was assumed that capital stock would grow at the same annual average growth rate observed between 1976 and 1990 for all countries.10
10 Several models were tried. Each gave very good predictions for the sample period. In the post sample period, however, the projected capital stock would decline for many countries under the other models. The percentage loss in GDP under the ‘Kyoto Scenario’ was also not sensitive to these alternative projections.
Table A2 in Appendix A shows the predicted increase in the baseline GDP from 1990 to 2010 under both models. The predicted increase in real GDP is generally within the range observed elsewhere in the case of both models (see Weyant and Hill, 1999, for an overview of other recent work). However, the translog model consistently yields a higher forecast, with the percentage increase from 1990 being 1.4 times higher, on average, as compared with the Cobb–Douglas model. Under the Kyoto Scenario, Annex 1 countries reduce their energy use to about 95%, on average, of their 1990 levels by 2010. On average, this translates to a 28% reduction from the 2010 baseline. The individual Kyoto commitments and the
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resulting reduction in energy consumption for all countries in the data set are shown in Table 3. This Table also shows the potential impact of the Kyoto Protocol commitments on real GDP in 2010. Recent research estimates the loss in GDP due to the Kyoto commitments to be around 1% (see Table 1). In the present analysis, under the standard assumption of Hicks neutral technical change and time as well as scale invariant output elasticities, the loss is about 6%, on average. Given the simple model being used here, this is not unreasonable. As mentioned earlier, other models allow for substitution to less carbon intensive fuels, whereas the current model reduces energy use proportionately to the required CO2 reduction. In addition, we assume a reduction in gross emissions, whereas other models allow for a reduction in net emissions. Furthermore, in some cases, such as Manne and Richels (1999), the sink enhancement is assumed to be costless. In the computable general equilibrium models, such as the Second Generation Model (MacCracken et al., 1999), it is assumed that the revenues obtained through the carbon tax are recycled back to the consumer as a lump-sum transfer. In the presence of such revenue recycling, the estimated loss in GDP is typically lower. Finally, the cost estimated here is a short-run cost. Several other models, including Manne and Richels (1999), Nordhaus and Boyer (1999a,b), Peck and Teisberg (1999), Tol (1999), compute the long-run cost of emissions reduction, which is necessarily lower. Another finding in the literature is that the bulk of the cost of reducing Annex 1 emissions is borne by USA. Nordhaus and Boyer (1999a) estimate that USA would bear approximately two-thirds of the global cost. In the present analysis, the US share is 45 and 55% under the Cobb– Douglas and the translog models, respectively. It is clear, however, that the results are sensitive to the form of the production function and the assumptions regarding the nature of technical change. While the overall ranking of countries in terms of the percentage loss in 2010 GDP is consistent between the two models, and also consistent with other work, the estimated loss is about 1.5 times higher, on average, under the translog model. Given that the predicted baseline
65
GDP in 2010 is also higher under the translog model, this implies a more than proportionately higher absolute loss in real GDP under this model. The comparative results for the individual countries vary according to the projected output elasticities for energy.
4. Conclusions and suggestions for further research This paper uses a simple econometric model to evaluate the sensitivity of the cost of the Kyoto Protocol commitments to standard economic assumptions regarding technology and technical change. While there are a large number of diverse and computationally sophisticated models being used to estimate the economic impact of the Protocol, they are remarkably uniform in their assumptions regarding the production function. The relative simplicity of current model is also its advantage in this context; it allows us to focus on the impact of the technology assumptions embodied in the production function on the economic cost of the Protocol. Two important results emerge. First, the common assumption of Hicks neutral technical change and intertemporally constant output elasticities is not supported by the data for the Annex 1 countries between 1965 and 1990, the countries and time period typically used to calibrate economic models of climate change. Instead, over this period, there are statistically significant trends in the output elasticities for all 23 countries included in the sample. Most important, an upward trend in the output elasticity of the energy input is observed. Furthermore, technical change is biased in favor of the energy and capital inputs and away from the labor input. Second, this finding has a significant impact in terms of the reduction in real GDP due to the Kyoto commitments. Under Hicks neutral technical change and constant output elasticities, the model yields a 6% decline in real GDP in 2010, on average, due to the CO2 reductions implicit in the Protocol. When technical change is allowed to be biased, and output elasticities are allowed to vary over time and with the level of factor use, the
N. Khanna / Ecological Economics 38 (2001) 59–69
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average loss in real GDP rises to about 9.5% in 2010. These results have potentially significant implications for future climate policy. The ratification deadline for the Kyoto Protocol passed on March 15, 1999. As of September 28, 2000, only 30 of the 84 signatory countries had ratified the Protocol. These do not include any Annex 1 countries. Without ratification by USA and at least some other Annex 1 countries, the Protocol cannot come into force. The results obtained in this paper indicate that the near term cost to USA and other Annex 1 countries of meeting their commitments are potentially higher than typically predicted by other work. If this is correct, then the likelihood that the Protocol would come into force in the near future is even lower, ceteris paribus. Perhaps the collapse of the recent Conference of Parties 6 at The Hague is indicative of this pessimistic possibility. The obvious next step would be to examine the impacts of relaxing similar assumptions regarding the nature of aggregate technology and technical change embedded in other, more sophisticated models. A priori, it is difficult to predict the results. However, it is quite possible that at least in the case of models such as RICE, FUND, MERGE3, and CETA, which have very long horizons of as much as 400 years, the cumulative impact over the model horizon would be quite significant.
Acknowledgements This paper has benefited from the comments of several people. I am particularly grateful to four anonymous reviewers for their constructive comments. Yuri Titkov provided excellent research assistance. The author is solely responsible for any remaining errors.
Appendix A (A) Data and data sources. The sample consists of data on real GDP, capital stock, labor force, and commercial energy consumption for 23 countries from 1965 to 1990. Real
GDP and capital stock data were obtained from the Penn World Tables (version 5.6), available at http://pwt.econ.upenn.edu. All monetary units are in 1985 international prices (see Summers and Heston, 1991, for details). Labor force data were calculated by the author using the series on real GDP per worker, real GDP per capita, and population from the same source. The resulting estimates are similar to the World Bank’s and the econometric results obtained do not differ significantly under either series. Commercial energy consumption data from 1965 to 1970/1971 were obtained from UN (1976), and from 1970/1971 to 1990 from World Bank (1995). Cleveland et al. (2000) point out that the rule used for aggregating energy flows can affect the analytical results. According to them, the approach used in the current analysis, which simply adds up the individual energy variables in million tons of oil equivalents (mtoe), ignores the qualitative differences among energy forms. They prefer an economics-based approach, which would account for the different marginal products of various energy types. This approach would require energy price data from 1965 to 1990 for all countries included in the sample. These data were not available. However, since the aggregation rule is maintained throughout the current analysis, the comparative results obtained should remain unaffected. A brief summary of the data is provided in Table A1. Even among the Annex 1 countries, there is a large variability in terms of the size of the economy as measured by real GDP. Clearly, the US dominates in this respect with an average real GDP of more than $3 trillion (1985 international prices) between 1965 and 1990, which is an order of magnitude larger than the real GDP of Iceland during the same period. Similar statements can be made for each of the factor inputs. On average, each of the variables has been growing consistently between 1965 and 1990. The exception is the energy input during the two oil shocks of 1973–1975 and 1979–1983. During these periods, total commercial energy consumption declined or remained approximately constant for almost every country in the data set, resulting in a decline in the average energy use for all Annex 1 countries during both oil shocks.
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(B) Econometric results for the Cobb – Douglas model. The estimates for the linear homogenous Cobb –Douglas model with Hicks neutral technical change are shown below. S.E. are in parenthesis. The errors were corrected for first degree autocorrelation and the estimated correlation coefficient was −0.82 (0.024). Estimates for the individual country dummies and overall intercept are available from the author upon request. ln(GDPt )=country dummies
67
+
0.007× Trend 0.26× ln(Kt ) 0.5×ln(Lt ) + + (0.03) (0.03) (0.001)
+
0.24×ln(Et ) (0.02)
R 2 = 0.99; sum of squares of errors=0.47. (C) Baseline GDP projections for 2010. Table A2 shows the baseline percentage increase in real GDP from 1990 to 2010 under the translog and the Cobb–Douglas models.
Table A1. Average values by country, 1965– 1990. Country
GDP (billions)1
Australia 173.1 Austria 71.4 Belgium 98.0 Canada 309.7 Denmark 56.2 Finland 48.1 France 579.7 Germany 672.4 Greece 49.9 Iceland 2.3 Ireland 20.6 Italy 513.1 Japan 1074.9 Luxembourg 4.2 Netherlands 145.0 New Zealand 32.1 Norway 44.5 Portugal 43.4 Spain 256.8 Sweden 99.0 Switzerland 87.5 UK 564.5 USA 3326.3 AAGR4 3.29 (1965–1990, % per year) 1. 2. 3. 4.
Capital stock (billions)1
Labor force (millions)2
Energy (mtoe)3
194.4 74.8 107.9 319.0 65.9 73.6 599.0 1021.7 61.2 1.5 19.2 496.4 1409.1 5.5 137.4 34.3 77.8 31.2 215.7 109.6 163.1 405.1 2784.2 5.42
6.4 3.4 3.9 10.7 2.6 2.4 23.3 27.4 3.6 0.1 1.2 21.8 70.6 0.2 5.3 1.3 1.9 4.0 12.8 4.0 3.1 26.7 102.8 1.13
63.6 20.6 41.9 162.3 18.3 21.1 171.3 254.1 13.5 0.9 7.7 124.1 307.1 3.6 56.0 8.8 16.6 9.1 58.0 40.1 18.9 203.4 1686.7 2.38
In 1985 international prices. Number of workers. Million tons of oil equivalent (mtoe). Annual average growth rate of mean value across all countries (% per year).
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Table A2. Percentage increase in GDP (1990– 2010) under the translog and Cobb–Douglas models. Country
Translog model
Cobb–Douglas model
Australia Austria Belgium Canada Denmark Finland France Germany Greece Iceland Ireland Italy Japan Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA Average
105.1 74.0 43.6 106.0 38.5 49.4 64.8 48.7 65.9 128.7 66.2 45.1 61.0 34.6 56.7 135.5 62.5 59.9 84.2 83.9 81.6 52.6 104.1 71.9
76.3 61.2 23.9 80.3 28.0 36.5 45.5 34.8 56.0 102.3 45.8 33.5 56.8 12.4 36.0 109.5 38.4 34.5 64.2 58.9 73.4 35.3 65.4 52.6
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N. Khanna / Ecological Economics 38 (2001) 59–69 MacCracken, C.N., Edmonds, J.A., Kim, S.H., Sands, R.D., 1999. The economics of the Kyoto Protocol. The costs of the Kyoto Protocol — a multi-model evaluation (special issue). Energy J. 25 – 72. Manne, A.S., Richels, R., 1999. The Kyoto Protocol: a cost-effective strategy for meeting environmental objectives? The costs of the Kyoto protocol — a multi-model evaluation (special issue). Energy J. 1 –24. McKibbin, W., Ross, M., Shackleton, R., Wilcoxen, P., 1999. Emissions trading, capital flows and the Kyoto Protocol. The costs of the Kyoto Protocol — a multi-model evaluation (special issue). Energy J. 257 – 286. Nordhaus, W.D., Boyer, J.G., 1999a. Requiem for Kyoto: an economic analysis of the Kyoto Protocol. The costs of the Kyoto Protocol — a multi-model evaluation (special issue). Energy J. 93 – 130. Nordhaus, W.D., Boyer, J.G., 1999b. Roll the Dice Again: Economic Models of Global Warming. Yale University. Peck, S.C., Teisberg, T.J., 1999. CO2 emissions control agreements: incentives for regional participation. The costs of the Kyoto Protocol — a multi-model evaluation (special issue). Energy J. 367 –390. Summers, R., Heston, A., 1991. The Penn World Tables (Mark 5): an expanded set of international comparisons, 1950 – 1988. Q. J. Econ. 327 –368.
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Tol, R.S.J., 1999. Kyoto, efficiency, and cost-effectiveness: applications of FUND. The costs of the Kyoto Protocol — a multi-model evaluation (special issue). Energy J. 131 – 156. United Nations (UN), 1976. World Energy Supplies, 1950 – 1974. Statistical Papers, series J, number 19. Department of Economic and Social Affairs, Statistical Office, New York. Watkins, G.C., 1992. The economic analysis of energy demand: perspectives of a practitioner. In: Hawdon, D. (Ed.), Energy Demand: Evidence and Expectations. Surrey University Press, London, pp. 29 – 96. Weyant, J.P., Hill, J.N., 1999. Introduction and overview. The costs of the Kyoto Protocol — a multi-model evaluation (special issue). Energy J. vii – xliv. World Bank, 1992. World Development Report 1992. Oxford University Press, New York. World Bank, 1995. World*Data 1995: Socio-Economic TimeSeries Access and Retrieval System (STARS), version 3.0. Washington, DC. World Bank, 1999. 1999 World Development Indicators. CDROM. Washington, DC. World Resources Institute (WRI), 1998. World Resources 1998 – 1999. Oxford University Press, New York.
ANALYSIS
Analyzing the economic cost of the Kyoto protocol Neha Khanna * Economics and En6ironmental Studies, Binghamton Uni6ersity, LT 1004, PO Box 6000, Binghamton, NY 13902 -6000, USA Received 6 June 2000; received in revised form 7 December 2000; accepted 8 December 2000
Abstract This paper examines the cost of meeting the Kyoto Protocol commitments under alternative assumptions regarding technology and technical change. Real GDP is modeled as a function of the capital, labor, and energy inputs. The analysis is based on data for 23 Annex 1 countries from 1965 to 1999. Two important results emerge. First, the standard assumption of Hicks neutral technical change and time and scale independent output elasticities is not supported by the data. Second, when technical change is allowed to be biased in favor of the energy and capital inputs, and when the output elasticities vary with the level of factor use and over time, the loss in real GDP due to the Kyoto commitments rises substantially. On average, the loss in real GDP is one and a half times higher than obtained under the standard assumptions. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Technical change; Output elasticity; Bias; Annex 1; Translog production function; Cobb– Douglas production function; Linear homogenous
1. Introduction In the past decade, a substantial body of literature has emerged analyzing the economic cost of reducing future carbon dioxide (CO2) emissions. The range of model structures is quite varied. At one end, there are highly aggregate, top-down, regional dynamic models based on optimal control techniques. There are also multi-sector models in the tradition of the regional computable general equilibrium models, which allow for inter* Tel.: +1-607-7772689; fax: +1-607-7772681. E-mail address: [email protected] (N. Khanna).
industry differences and international commodity trade. Yet another model type are the bottom-up style models with a significant level of detail on the energy sector including several fuel types and technology options for energy supply. Not surprisingly, these models yield very different numerical results. Recently, under the 16th Energy Modeling Forum (EMF-16) organized by Stanford University, some of the most prominent among these models were used to estimate the potential costs of the Kyoto Protocol. Under this Protocol, Annex 1 countries, that is developed countries included in Annex 1 to the UN Framework Convention on
0921-8009/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 8 0 0 9 ( 0 0 ) 0 0 2 9 5 - 0
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Climate Change, have agreed to reduce their overall net greenhouse gas emissions to 5% below their 1990 levels by the years 2008– 2012. As in the case of previous such exercises, the great advantage of the EMF study is that it tends to highlight the differences in model results due to different model structures, rather than differences in scenario construction. Despite the generally uniform scenarios under which the models were operated, the carbon tax in 2010 required for USA to meet its Kyoto commitments through domestic emissions reductions alone, ranged from about $75 per metric tonne to more than $400 per metric tonne (as measured in 1990 prices). In the case of Japan and the European Union, this range is even wider. However, there is one aspect in terms of which the model results are remarkably consistent. This relates to the estimated cost of the emissions reductions under Kyoto Protocol as measured by the loss in GDP in 2010. Table 1 summarizes the GDP impact on Annex 1 countries obtained under the no-trading scenario of EMF-16. The overriding conclusion that emerges from this Table is that the economic cost of the Kyoto commitments is small. Table 1 GDP loss under EMF-16’s no-trading scenario (as a percent of 2010 baseline)a Model
SGM GRAPE Oxford MERGE3 MS-MRT G-CUBED ABARE CETA AIM RICE Average
Country US
Japan
CANZ
EU
n.a. n.a. 1.91 1.07 1.90 0.45 2.14 1.98 0.47 0.97 1.34
n.a. 0.18 1.88 0.80 1.73 0.54 0.83 n.a. 0.24 0.81 0.88
n.a. n.a. n.a. 2.07 1.82 0.60 1.59 n.a. 0.57 1.15 1.30
n.a. 0.37 0.76 0.43 0.27 0.71 0.42 n.a. 0.15 0.23 0.42
a Note: these estimates are based on Figures 7 and 9 of Weyant and Hill (1999), since published versions of these models do not provide the data directly. In addition, GDP figures for 1990 were obtained from World Bank (1992). For CANZ, the sum of GDP in Canada, Australia, and New Zealand was used. For the European Union (EU), the 1990 OECD GDP was used. For detailed model results, see the 1999 special issue of the Energy Journal. n.a., Not available.
On average, the loss in 2010 GDP would be less than 1%. Even in the models with the highest estimates, the reduction in GDP is about 2%.1 One factor that could possibly explain this result is the structure of the production function embedded in these models, and the nature of technical change implicit therein. While the models included in this study differ widely in terms of overall structure, they uniformly assume Hicks neutral technical change and time invariant production or output elasticities. In addition, it is also assumed that the output elasticities do not vary with the level of factor use. The current analysis has a dual focus. First, it will be shown that these assumptions are not borne out by the recent empirical history of the Annex 1 countries. Second, and more important, relaxing these assumptions may significantly increase the estimated loss in GDP.
2. The econometric model Since the focus of the paper is the impact of technology assumptions embedded in the aggregate production function on the costs of meeting the Kyoto commitments, the model used here abstracts from all other economic factors that might affect the results. An econometric model based on pooled cross-section and time series data from 1965 to1990 for 23 industrialized Annex 1 countries is used. Countries not included in the sample are Liechtenstein, Monaco, countries of the former Soviet Union and those in Eastern Europe, due to nonavailability of data. Details on data and data sources are provided in the Appendix A. Real GDP in each time period (GDPt ) is modeled as a function of the contemporaneous capital (Kt ), labor (Lt ), and energy (Et ) inputs. The trend variable (~) captures technological change. Output elasticities for each factor input are estimated using a translog production function that is linear homogenous in factor inputs. Interactions between factor use and time are included to allow for biased technical change. This also allows the output elas1
Another important conclusion is that USA is likely to bear the highest relative cost, followed closely by CANZ, an economic region defined by Canada, Australia, and New Zealand.
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ticities to vary directly with time. Further, the interaction terms between the factor inputs implies that the output elasticities are a function of the level of factor use. A fixed effects model is used to account for country-specific effects. The estimating equation is ln(GDPt )=country dummies+ i~~ + i~~~ 2 + iK ln(Kt )+iL ln(Lt ) + iE ln(Et ) + iKL ln(Kt ) ln(Lt )+ iKE ln(Kt )ln(Et ) + iKK ln(Kt )2 +iLL ln(Lt )2 +iEE ln(Et )2 + iK~ ln(Kt )~+iL~ ln(Lt )~ +iE~ ln(Et )~
(1)
subject to the restrictions Hi = h, where Æ iK Ã Ã 2iKK Hi = Ã iKL Ã Ã iKE È iK~ Æ1 Ç Ã0 Ã Ã Ã h= Ã0 Ã Ã0 Ã Ã Ã È0 É
+
iL
+
+ + + +
iKL 2iLL iLE iL~
+ + + +
iE Ç Ã iKE Ã iLE Ã , Ã 2iEE Ã iE~ É
61
Table 2 Estimated parameters for the linear homogenous translog modela Variable
Estimated coefficient
S.E.
P-value
~ ~2 ln(Kt ) ln(Lt ) ln(Et ) ln(Kt )ln(Lt ) ln(Kt )ln(Et ) ln(Lt )ln(Et ) (ln Kt )2 (ln Lt )2 (ln Et )2 ~ ln(Kt ) ~ ln(Lt ) ~ ln(Et )
−0.025 0.0001 1.038 −0.0385 0.347 0.338 −0.153 0.0161 −0.092 −0.177 0.068 0.005 −0.013 0.008
0.0081 0.0001 0.175 0.145 0.0862 0.061 0.051 0.031 0.040 0.029 0.023 0.003 0.003 0.002
0.0019 0.5001 0.0001 0.0082 0.0001 0.0001 0.0028 0.5987 0.0223 0.0001 0.0025 0.0902 0.0001 0.0001
a Sum of squares of errors =0.4323; R 2 =0.99; errors corrected for first order autocorrelation; estimated correlation coefficient=−0.794. Note: ~ represents the trend variable.
(2)
The estimated slope coefficients, S.E., P-values, and other regression statistics are shown in Table 2. The estimates are reasonably robust. Only three out of the 14 slope coefficients are insignificant at the 5% level. This is not unreasonable as the equation includes the squares and cross-products of the independent variables.2 Output elasticities for each of the three factor inputs are obtained as the first derivative of the estimating equation with respect to ln(Kt ), ln(Lt ), and ln(Et ). The advantage of using such a production function is that though the output elasticities are constrained to sum to unity, individual elastic2 The inclusion of squares and cross products enhances the problem of multicollinearity. The variance inflation factors for all variables are quite large. However, the overall results are robust. The model was re-estimated using an alternative labor series obtained from the World Bank (1999). The estimated coefficients and output elasticities did not change significantly.
ities are allowed to vary with the level of factor use and time.3 Another advantage is that even though the slope coefficients are restricted to be identical for all countries and over time, the computed output elasticities vary by country and period as they are directly determined by the level of the factor input in each case. Fig. 1 shows these elasticities for the G-7 countries, and also the average elasticities for all countries in the data set. Note the significant differences in the trends observed over the sample period.4 Another policy variable of direct interest is the bias in technical change. It is measured as the 3 For more details on the translog production function, see Christensen et al. (1973), Jorgenson and Fraumeni (1981), Berndt and Wood (1982), Boisvert (1982). The Jorgenson and Fraumeni work provides a lucid interpretation of the individual coefficients under duality theory. 4 The values and trends obtained for the output elasticities fall in the range found in the literature. Kim and Lau (1994) estimated a translog meta production function in capital and labor using data from at least 1966 to 1990 for nine countries including France, Germany, Japan, UK, and USA. The estimates obtained here are very close to the Kim – Lau estimates. McKibbin et al. (1999) also estimate output elasticities. However, they use US data only. Furthermore, in some cases, there is a large difference between the estimated elasticities and the values imposed in their model.
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proportional change in the marginal rate of substitution between any pair of inputs over time (Ferguson, 1979). In the present case, this is equivalent to the relative proportional change over time in pairwise input production elasticities. That is, the bias in technical change between a pair of factor inputs, i and j, Biasi,j, may be calculated as Biasi, j =
ii~ ij~ ] 0 − pi pj 5
(3)
where ii~ (ij~ ) refers to the coefficient on the interaction term between input i ( j ) and the trend variable (~), and pi (pj ) is the output elasticity of input i ( j ). Note that ii~ is also the derivative of pi with respect to the trend variable.5 A positive
Fig. 2. Bias in technical change (G-7 countries).
Fig. 1. Production elasticities (G-7 countries). 5 For a complete derivation of Eq. (3), see Khanna et al. (1997).
(negative) sign on Biasi, j indicates that technical change is factor i ( j ) intensive. The hypothesis of Hicks neutral technical change is tested by examining the joint significance of the coefficients on the interaction terms between the factor inputs and the trend variable. That is, under the null hypothesis, ii~ = 0 for all i {i= K, L, E}, simultaneously. This was rejected at the 1% level of significance. It was found that technical change was either capital or energy intensive, but not labor intensive. Fig. 2 shows the bias in technical change for the G-7 countries. This result has important implications for climate policy. The implementation of the Kyoto Protocol is likely to increase the relative price of energy. In the presence of energy intensive technical change, this would have an adverse impact on the growth in total factor productivity. There is some evidence for this during the oil shocks of the
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1970s and the early 1980s.6 However, the decline in the growth rate is fairly small, with the latter oil shock having a much smaller impact. On the basis of the current model it cannot be predicted, a priori, whether the future impact will be beyond this historical range. However, the issue is raised due to its significance. 3. The economic impact of the Kyoto Protocol How important is the presence of time- and scale-dependent output elasticities and biased technical change when assessing the economic impact of the Kyoto Protocol? To answer this question the loss in GDP is compared under two alternative models. The first model is shown in Eq. (1). Under the alternative model real GDP is as a linear homogenous Cobb – Douglas function of the three factor inputs and the trend variable, under the restriction of Hicks neutral technical change. As before, a fixed effects model is used to account for country-specific effects, and the errors are corrected for first order autocorrelation. The estimated slope coefficients and other regression statistics for this model are shown in Appendix A.7 To facilitate the analysis, the following simplifying assumptions are made to define the ‘Kyoto Scenario’. First, every country in the sample is assumed to meet its commitment in 2010, the midpoint of the 4-year commitment period under the Protocol. Second, the possibility of emissions trade, allowed under the Protocol to supplement domestic reductions, is ignored. The analysis is, thus, comparable to the no-trading scenario of 6 See, for example, Watkins (1992) for the case of Canada, and Berndt and Wood (1987) for the US manufacturing sector. Jorgenson (1984) links electric and non-electric energy to productivity growth. 7 Nordhaus and Boyer (1999b) also use a linear homogenous Cobb– Douglas production function in capital, labor, and carbon-energy. In the current analysis, the null hypothesis of linear homogeneity is rejected in both models. However, in the absence of this restriction, both models yield negative or zero output elasticities for several countries, a result clearly incompatible with economic theory. In contrast, when the restriction is imposed both models yield output elasticities that are comparable with other work. Therefore, this restriction was retained.
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EMF-16. Third, each country is assumed to meet its GHG commitment through a proportional reduction in CO2 emissions. While this is likely, it does not necessarily have to be so. The Protocol includes reductions for CH4, N2O, HCFs, PFCs, and SF6, in addition to CO2. However, CO2 accounts for the bulk of the GHG emissions for the Annex 1 countries. Also, the sources of CO2 are relatively well understood and the main body of the literature has focused on the implications of reducing these emissions. Fourth, and most important, it is assumed that a reduction in CO2 emissions requires a proportional reduction in energy use. This is a pessimistic assumption. A significant fraction of each country’s commitment could be achieved by switching to less carbon intensive fuels such as natural gas. However, since this assumption is maintained under both models, it is unlikely to affect the qualitative results obtained here. In this sense, the assumption is ‘neutral’. Finally, it is assumed that countries reduce their gross emissions whereas the Protocol calls for a reduction of net GHG emissions. The various carbon sinks and their potential for emissions reductions are fairly tentative at this point. As in the case of fuel switching, this assumption is maintained under both models and is unlikely to affect the overall conclusion. The baseline real GDP in 2010 is estimated for each country in the sample on the basis of the projected factor input levels, and the estimated coefficients under both models. National labor force projections are based on WRI (1998).8 DoE (1999) (Table A1) forecasts energy use in 2010 for several Annex 1 countries. The growth rates provided there were used as far as possible.9 For the countries where these predictions were not provided, the average projected growth rate for ‘other Western Europe’ was used. The exceptions were Belgium, Denmark, The Netherlands, and Luxembourg, where energy use has remained more or less constant since the 1970s oil shock. In this case 8 WRI (1998) did not provide the projected labor force growth rate for Luxembourg. The average projected growth rate for Europe was used in this case. 9 DoE (1999) projects energy use in quadrillion BTUs. In the present data set, energy is measured in mtoe. It is assumed that the projected growth rates are independent of the measurement units.
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64 Table 3 Impact of the Kyoto Protocol Countrya
Australia Austria Belgium Canada Denmark Finland France Germany Greece Iceland Ireland Italy Japan Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA Average
CO2 emissions (percent of 1990 baseline)b
108 92 92 94 92 92 92 92 92 110 92 92 94 92 92 100 101 92 92 92 92 92 93 94.43
Energy use (percent reduction from 2010 baseline)c
18.54 27.67 8.00 33.43 8.00 27.67 28.66 19.50 27.67 13.52 27.67 28.38 30.21 8.00 8.00 24.57 20.59 27.67 27.67 27.67 27.67 26.08 29.58 27.92
GDP loss (percent of 2010 baseline) Translog model
Cobb–Douglas model
8.04 9.95 3.48 14.66 2.90 11.19 11.98 7.10 12.11 5.87 13.10 11.62 8.27 3.56 3.46 11.29 8.50 12.35 10.41 11.78 7.93 12.72 15.10 9.45
4.81 7.50 1.99 9.33 1.99 7.50 7.81 5.09 7.50 3.43 7.50 7.72 8.29 1.99 1.99 6.56 5.40 7.50 7.50 7.50 7.50 7.01 8.09 6.15
a
Liechtenstein, Monaco, countries of the former Soviet Union, and East European countries are also included in Annex 1. The Kyoto Protocol requires a reduction in net GHG emissions. This analysis assumes an equivalent reduction in gross CO2 emissions. c This assumes CO2 emissions are reduced via an equivalent reduction in energy use. b
it was assumed that energy use remains constant at the 1990 level. Capital stock projections were not available, so this variable was projected on the basis of the available data. It was assumed that capital stock would grow at the same annual average growth rate observed between 1976 and 1990 for all countries.10
10 Several models were tried. Each gave very good predictions for the sample period. In the post sample period, however, the projected capital stock would decline for many countries under the other models. The percentage loss in GDP under the ‘Kyoto Scenario’ was also not sensitive to these alternative projections.
Table A2 in Appendix A shows the predicted increase in the baseline GDP from 1990 to 2010 under both models. The predicted increase in real GDP is generally within the range observed elsewhere in the case of both models (see Weyant and Hill, 1999, for an overview of other recent work). However, the translog model consistently yields a higher forecast, with the percentage increase from 1990 being 1.4 times higher, on average, as compared with the Cobb–Douglas model. Under the Kyoto Scenario, Annex 1 countries reduce their energy use to about 95%, on average, of their 1990 levels by 2010. On average, this translates to a 28% reduction from the 2010 baseline. The individual Kyoto commitments and the
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resulting reduction in energy consumption for all countries in the data set are shown in Table 3. This Table also shows the potential impact of the Kyoto Protocol commitments on real GDP in 2010. Recent research estimates the loss in GDP due to the Kyoto commitments to be around 1% (see Table 1). In the present analysis, under the standard assumption of Hicks neutral technical change and time as well as scale invariant output elasticities, the loss is about 6%, on average. Given the simple model being used here, this is not unreasonable. As mentioned earlier, other models allow for substitution to less carbon intensive fuels, whereas the current model reduces energy use proportionately to the required CO2 reduction. In addition, we assume a reduction in gross emissions, whereas other models allow for a reduction in net emissions. Furthermore, in some cases, such as Manne and Richels (1999), the sink enhancement is assumed to be costless. In the computable general equilibrium models, such as the Second Generation Model (MacCracken et al., 1999), it is assumed that the revenues obtained through the carbon tax are recycled back to the consumer as a lump-sum transfer. In the presence of such revenue recycling, the estimated loss in GDP is typically lower. Finally, the cost estimated here is a short-run cost. Several other models, including Manne and Richels (1999), Nordhaus and Boyer (1999a,b), Peck and Teisberg (1999), Tol (1999), compute the long-run cost of emissions reduction, which is necessarily lower. Another finding in the literature is that the bulk of the cost of reducing Annex 1 emissions is borne by USA. Nordhaus and Boyer (1999a) estimate that USA would bear approximately two-thirds of the global cost. In the present analysis, the US share is 45 and 55% under the Cobb– Douglas and the translog models, respectively. It is clear, however, that the results are sensitive to the form of the production function and the assumptions regarding the nature of technical change. While the overall ranking of countries in terms of the percentage loss in 2010 GDP is consistent between the two models, and also consistent with other work, the estimated loss is about 1.5 times higher, on average, under the translog model. Given that the predicted baseline
65
GDP in 2010 is also higher under the translog model, this implies a more than proportionately higher absolute loss in real GDP under this model. The comparative results for the individual countries vary according to the projected output elasticities for energy.
4. Conclusions and suggestions for further research This paper uses a simple econometric model to evaluate the sensitivity of the cost of the Kyoto Protocol commitments to standard economic assumptions regarding technology and technical change. While there are a large number of diverse and computationally sophisticated models being used to estimate the economic impact of the Protocol, they are remarkably uniform in their assumptions regarding the production function. The relative simplicity of current model is also its advantage in this context; it allows us to focus on the impact of the technology assumptions embodied in the production function on the economic cost of the Protocol. Two important results emerge. First, the common assumption of Hicks neutral technical change and intertemporally constant output elasticities is not supported by the data for the Annex 1 countries between 1965 and 1990, the countries and time period typically used to calibrate economic models of climate change. Instead, over this period, there are statistically significant trends in the output elasticities for all 23 countries included in the sample. Most important, an upward trend in the output elasticity of the energy input is observed. Furthermore, technical change is biased in favor of the energy and capital inputs and away from the labor input. Second, this finding has a significant impact in terms of the reduction in real GDP due to the Kyoto commitments. Under Hicks neutral technical change and constant output elasticities, the model yields a 6% decline in real GDP in 2010, on average, due to the CO2 reductions implicit in the Protocol. When technical change is allowed to be biased, and output elasticities are allowed to vary over time and with the level of factor use, the
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average loss in real GDP rises to about 9.5% in 2010. These results have potentially significant implications for future climate policy. The ratification deadline for the Kyoto Protocol passed on March 15, 1999. As of September 28, 2000, only 30 of the 84 signatory countries had ratified the Protocol. These do not include any Annex 1 countries. Without ratification by USA and at least some other Annex 1 countries, the Protocol cannot come into force. The results obtained in this paper indicate that the near term cost to USA and other Annex 1 countries of meeting their commitments are potentially higher than typically predicted by other work. If this is correct, then the likelihood that the Protocol would come into force in the near future is even lower, ceteris paribus. Perhaps the collapse of the recent Conference of Parties 6 at The Hague is indicative of this pessimistic possibility. The obvious next step would be to examine the impacts of relaxing similar assumptions regarding the nature of aggregate technology and technical change embedded in other, more sophisticated models. A priori, it is difficult to predict the results. However, it is quite possible that at least in the case of models such as RICE, FUND, MERGE3, and CETA, which have very long horizons of as much as 400 years, the cumulative impact over the model horizon would be quite significant.
Acknowledgements This paper has benefited from the comments of several people. I am particularly grateful to four anonymous reviewers for their constructive comments. Yuri Titkov provided excellent research assistance. The author is solely responsible for any remaining errors.
Appendix A (A) Data and data sources. The sample consists of data on real GDP, capital stock, labor force, and commercial energy consumption for 23 countries from 1965 to 1990. Real
GDP and capital stock data were obtained from the Penn World Tables (version 5.6), available at http://pwt.econ.upenn.edu. All monetary units are in 1985 international prices (see Summers and Heston, 1991, for details). Labor force data were calculated by the author using the series on real GDP per worker, real GDP per capita, and population from the same source. The resulting estimates are similar to the World Bank’s and the econometric results obtained do not differ significantly under either series. Commercial energy consumption data from 1965 to 1970/1971 were obtained from UN (1976), and from 1970/1971 to 1990 from World Bank (1995). Cleveland et al. (2000) point out that the rule used for aggregating energy flows can affect the analytical results. According to them, the approach used in the current analysis, which simply adds up the individual energy variables in million tons of oil equivalents (mtoe), ignores the qualitative differences among energy forms. They prefer an economics-based approach, which would account for the different marginal products of various energy types. This approach would require energy price data from 1965 to 1990 for all countries included in the sample. These data were not available. However, since the aggregation rule is maintained throughout the current analysis, the comparative results obtained should remain unaffected. A brief summary of the data is provided in Table A1. Even among the Annex 1 countries, there is a large variability in terms of the size of the economy as measured by real GDP. Clearly, the US dominates in this respect with an average real GDP of more than $3 trillion (1985 international prices) between 1965 and 1990, which is an order of magnitude larger than the real GDP of Iceland during the same period. Similar statements can be made for each of the factor inputs. On average, each of the variables has been growing consistently between 1965 and 1990. The exception is the energy input during the two oil shocks of 1973–1975 and 1979–1983. During these periods, total commercial energy consumption declined or remained approximately constant for almost every country in the data set, resulting in a decline in the average energy use for all Annex 1 countries during both oil shocks.
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(B) Econometric results for the Cobb – Douglas model. The estimates for the linear homogenous Cobb –Douglas model with Hicks neutral technical change are shown below. S.E. are in parenthesis. The errors were corrected for first degree autocorrelation and the estimated correlation coefficient was −0.82 (0.024). Estimates for the individual country dummies and overall intercept are available from the author upon request. ln(GDPt )=country dummies
67
+
0.007× Trend 0.26× ln(Kt ) 0.5×ln(Lt ) + + (0.03) (0.03) (0.001)
+
0.24×ln(Et ) (0.02)
R 2 = 0.99; sum of squares of errors=0.47. (C) Baseline GDP projections for 2010. Table A2 shows the baseline percentage increase in real GDP from 1990 to 2010 under the translog and the Cobb–Douglas models.
Table A1. Average values by country, 1965– 1990. Country
GDP (billions)1
Australia 173.1 Austria 71.4 Belgium 98.0 Canada 309.7 Denmark 56.2 Finland 48.1 France 579.7 Germany 672.4 Greece 49.9 Iceland 2.3 Ireland 20.6 Italy 513.1 Japan 1074.9 Luxembourg 4.2 Netherlands 145.0 New Zealand 32.1 Norway 44.5 Portugal 43.4 Spain 256.8 Sweden 99.0 Switzerland 87.5 UK 564.5 USA 3326.3 AAGR4 3.29 (1965–1990, % per year) 1. 2. 3. 4.
Capital stock (billions)1
Labor force (millions)2
Energy (mtoe)3
194.4 74.8 107.9 319.0 65.9 73.6 599.0 1021.7 61.2 1.5 19.2 496.4 1409.1 5.5 137.4 34.3 77.8 31.2 215.7 109.6 163.1 405.1 2784.2 5.42
6.4 3.4 3.9 10.7 2.6 2.4 23.3 27.4 3.6 0.1 1.2 21.8 70.6 0.2 5.3 1.3 1.9 4.0 12.8 4.0 3.1 26.7 102.8 1.13
63.6 20.6 41.9 162.3 18.3 21.1 171.3 254.1 13.5 0.9 7.7 124.1 307.1 3.6 56.0 8.8 16.6 9.1 58.0 40.1 18.9 203.4 1686.7 2.38
In 1985 international prices. Number of workers. Million tons of oil equivalent (mtoe). Annual average growth rate of mean value across all countries (% per year).
N. Khanna / Ecological Economics 38 (2001) 59–69
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Table A2. Percentage increase in GDP (1990– 2010) under the translog and Cobb–Douglas models. Country
Translog model
Cobb–Douglas model
Australia Austria Belgium Canada Denmark Finland France Germany Greece Iceland Ireland Italy Japan Luxembourg Netherlands New Zealand Norway Portugal Spain Sweden Switzerland UK USA Average
105.1 74.0 43.6 106.0 38.5 49.4 64.8 48.7 65.9 128.7 66.2 45.1 61.0 34.6 56.7 135.5 62.5 59.9 84.2 83.9 81.6 52.6 104.1 71.9
76.3 61.2 23.9 80.3 28.0 36.5 45.5 34.8 56.0 102.3 45.8 33.5 56.8 12.4 36.0 109.5 38.4 34.5 64.2 58.9 73.4 35.3 65.4 52.6
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