Is the Economic Growth in the United States Influenced by Its Fossil Fuel-based Carbon Dioxide Emissions ?

For the first time in the scientific literature, this research establishes empirical evidence for the existence of a causal relationship among fossil fuel-based carbon dioxide (CO2) emissions in the United States (US), her gross domestic product (GDP) and world crude price. Estimated long-run income elasticity of CO2 emissions is as high as 3.2% in the US. A strong bi-directional long-run causality is found between CO2 emissions and GDP. Short-run causality runs from crude price to CO2 emissions to GDP. Monte Carlo stochastic simulations of the model developed reveal even a small increase in the reference real GDP growth rate causes considerable increase in the future CO2 emissions in the US. Results of this study therefore suggest urgent policy actions are imperative in the US to decouple the strong causal relationship existing between her CO2 emissions and GDP, and to ensure sustainable economical development in the US.


Introduction
A century after the pioneering work of the influence of atmospheric carbon dioxide (CO 2 ) concentration upon global surface temperature (Arrhenius, 1896), the Intergovernmental Panel on Climate Change (IPCC, 1996) concluded that fossil fuel use was responsible for significant increase in atmospheric concentrations of greenhouse gases (GHG), inclusive of CO 2 .IPCC (2007) states that average global surface temperature is likely to rise 1.1 to 6.4℃ during this century which has the potential to cause irreversible impact on ecosystems.With the intention of stabilizing atmospheric GHGs at levels that would slow down climate change, on 11 th December 1997, world leaders adopted the Kyoto Protocol.In November 1998, the United States (US) signed the Kyoto Protocol which required the US and other economically developed countries to reduce their GHG emissions from 1990 levels by specified amounts during 2008 to 2012.In March 2001, the US announced that it would not ratify the Protocol.
In high income economies, such as the US, service sector dominates over manufacturing sector and changes in electricity-mix take place (Aldy, 2005).These factors together with technological progress have led to the popular concept that environmental pollution, inclusive of GHG emissions, in a country might decrease with income once the country surpasses a threshold income (Beckerman, 1992), which is known as the Environmental Kuznets Curve (EKC) hypothesis (Grossman & Krueger, 1991;Holtz-Eakin & Selden, 1995;Shafik & Bandyopadhyay, 1992).In case of GHG emissions complying with the EKC hypothesis, emission reductions similar to those suggested by the Kyoto Protocol would have been welcomed as achievable by economically developed countries, and as plausible by economically developing countries.The reality was the opposite.Adhering to the provisions of the Kyoto Protocol was seen as incompatible with achieving economic growth (Commonwealth of Australia, 2003;US Congress, 1997).
A recent inventory of GHG emissions and sinks in the US, published by the US Environmental Protection Agency (US EPA, 2010), states CO 2 emission from fossil fuel combustion has grown from 77% of total global Since the above tests establish that CO 2 emissions, real GDP, and crude real price are I(1) series, and that they are cointegrated, direction of Granger causality among them are examined using the error-correction based Granger causality tests (Acaravci & Ozturk, 2010).Granger causality results have immediate policy implications.For instance, if CO 2 emission Granger causes GDP then reduction in emissions in the US could harm her economy.On the other hand, if GDP Granger causes CO 2 emission then CO 2 emission reduction is possible in the US without harming her economic growth.
Forecasting is undertaken in cointegration studies (Amarawickrama & Hunt, 2008) by estimating future values of the dependent variable using the ECM developed for several different potential future scenarios of explanatory variables predicted in relevant official sources (Akashi et al., 2011;Amarawickrama & Hunt, 2008).In this study, Monte Carlo stochastic simulation (Mooney, 1997) of the ECM is used in forecasting CO 2 emissions since this technique has the power to convert the uncertainties in the future GDP growth rate of US and world crude price growth rate into probability distributions over the future CO 2 emissions in the US.
A brief review on the research literature on CO 2 emission-economic growth nexus for the US is given in Section 2, data used are presented along with model rationale in Section 3, a brief account of the econometric methodologies used is given in Section 4, and empirical results and discussion in Section 5.The potential use of the model in CO 2 emissions-economic growth related policy formulations in the US is discussed in Section 6, and Section 7 concludes.

Literature Review
Past research studies on CO 2 emission-economic growth nexus focused primarily upon the said relationship's ability to describe an EKC model.While Shafik and Bandyopadhyay (1992) and Shafik (1994) found CO 2 emissions per capita to increase with rising per capita income within the sample periods studied, Dijkgraaf and Vollebergh (1998) and Schmalensee et al. (1998) reported EKC-type relationships for CO 2 emissions-income nexus.Carrying out a comprehensive survey of empirical evidence and possible causes of EKCs describing pollution-income nexus, Lieb (2003) concluded that emission-income relationship monotonically rises for global pollutants, such as CO 2 .Perman and Stern (2003) altogether negated the existence of EKC on the ground most of the EKC literature was devoid of testing for stochastic trends in the time series data used, and for spurious correlations of the models developed.
Testing the time series concerned for stationarity and cointegration was first introduced to the emissions-income research literature by Friedl and Getzner (2003) who found cointegration between Austrian yearly emissions and income time series during 1960-1999. Aldy (2005) ) tested for cointegration among emissions, income, and income-squared state-specific time series for the US using state-level yearly data spanning 1960-1999.Aldy found evidence for cointegration in 8 of the 48 states for production-based CO 2 emissions, and in 7 states for consumption-based CO 2 emissions.Dinda and Coondoo (2006) carried out a panel data-based cointegration analysis for 88 countries with annual data in the range of .Their results showed the null hypotheses of no cointegration between per capita CO 2 emission and per capita GDP could not be rejected for country groups such as North America, South America, Asia and Oceania.Therefore, they concluded long-run causality among the variables concerned was not probable for these country groups that included the US.
Arguing that countries in a group need not have similar economic dynamics, Soytas et al. (2007) investigated, for the US, Granger causality relationships among CO 2 emissions, real GDP, energy consumption, labour, and investment in fixed capital using annual data during 1960-2004. Using Toda and Yamamoto (1995) procedure, they found no causality between real GDP and CO 2 emissions and concluded that the US could reduce their carbon emissions without harming her economic growth.Causal relationship among CO 2 emissions, economic growth and energy consumption has also been investigated for China (Zhang & Cheng, 2009), five OPEC countries (Sari & Soytas, 2009), Turkey (Halicioglu, 2009), India (Ghosh, 2010), BRIC countries (Pao & Tsai, 2010), and for 19 European countries (Acaravci & Ozturk, 2010) among others.Conclusions reached in these studies varied from one country to another.None of the above studies used energy price as an explanatory variable despite the local peaks experienced by CO 2 emissions in the US in 1973 and in 1979 during the oil shock decade.It was Unruh and Moomaw (1998) first showed, using phase diagrams, that per capita CO 2 emission's trajectories of the US and another 15 high income economies reached their respective peaks during the oil shock decade.In modelling both short-term and long-term dynamics of emissions in Sweden since 1870, Lindmark (2002) utilized a structural time series model with stochastic components having GDP and fuel prices as explanatory variables.Lindmark concluded that a combination of nuclear power, low economic growth, and increasing fuel prices had caused reduction in CO 2 emissions since early 1970s in Sweden.
In modelling CO 2 emissions in Austria since 1960, Friedl and Getzner (2003) pointed out that the sag in the N-shape (cubic) Austrian emissions versus income profile was caused by stringent environmental policies that came into effect following the oil shock decade.They also added that the upward trend found in the Austrian emissions in 1990s and in early 2000s could be explained as a 'recovery-effect' because the impact of the oil shock decade could have been much reduced in the 1990s and after.Lanne and Liski (2004), working with data for the period 1870-1998 for 16 'early developed' countries, inclusive of the US, observed that the downward sloping trends in per capita CO 2 emissions caused by the oil shock decade were not stable, except for United Kingdom and Sweden.They used the additive outlier modelling approach which assumes structural changes in emissions trajectories being the results of sudden breaks in the trajectories caused by external shocks.Huntington (2005) found variations in fuel prices during 1890-1998 to have statistically insignificant impact upon CO 2 emissions per capita in the US.He used econometric techniques fit for stationary time series, and concluded that 1% growth in real GDP per capita caused 0.9% growth in CO 2 emissions per capita when holding technological progress, proxied by time trend, constant.Shanthini and Perera (2007) exposed the role of crude real price fluctuations in accounting for structural changes in CO 2 emissions versus income profiles of 17 high-income economies.They used a set of year-group dummy variables, the choice of which was solely guided by world crude real price fluctuations.A predictive model for Australia's per capita CO 2 emissions with per capita real GDP and world crude real price as explanatory variables was developed by Shanthini and Perera (2010) who used the ARDL bounds testing approach to cointegration for the first time to study the emissions-income-crude price nexus of a nation.Their study showed that world crude real price variations had very little influence on the emission-income nexus of Australia, which they attributed to Australia's possession of rich fossil fuel reserves.Similar analyses have been carried out in this study for the US.

Data and Model Rationale
Figure 1 shows the variations in annual CO 2 emissions stemming from fossil-fuel burning, cement manufacture and gas flaring in the US (Marland et al., 2010) against her annual real GDP (Bureau of Economic Analysis, 2010) during 1950-2007.CO 2 emissions data are in teragram (= 10 12 g) of CO 2 equivalent, denoted by TgCO 2 , and real GDP data are in billions of constant 2005$.Time period chosen for the analysis covers the period of intense CO 2 emissions growth and GDP growth in the US, which commenced in the 1950s (Figure 1).Choice of the end year as 2007 was dictated by CO 2 emissions data availability in the data source used.
As seen in Figure 1, CO 2 emissions in the US increased sharply with increasing real GDP till 1973, which was followed by a sharp reduction in emissions till 1975.Consequent recovery of the growth in emissions once again experienced a sharp reduction in 1979.Since 1982, CO 2 emissions increased with real GDP.However, it must be noted that the rate at which CO 2 emissions increased with real GDP since 1982 was much lower than the corresponding rate till 1973.It is therefore evident that statistical modelling of the relationship between CO 2 emissions and real GDP requires the use of suitably selected dummy variables or yet another explanatory variable that could account for the aforementioned discontinuities experienced by the CO 2 emission-real GDP relationship.
Figure 2 shows the annual variations in average world crude oil real price (British Petroleum, 2010) in constant 2009$ per barrel.World crude real price experienced very little fluctuations till 1973, then a sharp increase during 1973 to 1974, and another increase during 1978 to 1979.This decade of two major oil shocks was followed by a general decline in crude real price till 1986.Crude real price fluctuated about a near steady value till 2002 or so before setting up on an upward trend till 2007.
It is noteworthy that the decade of oil shocks, which is the 1970s, is nearly the same as the decade during which CO 2 emissions-real GDP relationship in the US experienced discontinuities (Figure 1).It is probable that abrupt increases experienced by crude real price during 1973 to 1974 and during 1978 to 1979 caused the breaks in emissions in 1973 and in 1979, respectively (Figure 1).It is therefore, I attempt to model CO 2 emissions in the US using real GDP and world crude real price as explanatory variables.
Inferring from the information presented above, I hypothesize, during the sample period 1950 to 2007, CO 2 emission time series of the US is strongly and positively correlated with her real GDP time series, and is negatively correlated with world crude oil real price.A time trend term is included in the model to explain any possible gradual reduction in emissions which could have been prompted by technological progress (Huntington, 2005) and other emissions reductions policies and strategies which have evolved during the past half century.I hypothesize that the coefficient of the time trend is therefore negative.Since I am interested in the temporal growths of the variables concerned, I use natural logarithms of the variables for model development.The hypothetical model therefore takes the following form: where C, G and O represent the natural logarithms of fossil fuel-based CO 2 emissions in the US, real GDP in the US and world crude oil real price, respectively, t represents the time in year, and the Greek letters represent the coefficients to be determined.

Order of Integration of the Time Series
The time series considered in this study exhibit discontinuities (Figure 1 and Figure 2), and therefore augmented Dickey-Fuller and other conventional tests may not correctly identify the order of integration (Perron, 1989).The series must therefore be tested for unit roots in the presence of structural breaks.To this effect, I employ the recently developed unit root testing methodologies of Popp (2008) and Narayan and Popp (2010).A distinctive feature in these two unit root tests is that they allow for structural break(s) under both the null hypotheses of the presence of unit root and the alternative of stationary series.They were also shown, via Monte Carlo simulations, to have stable power and to identify the true break date(s) very accurately even for small breaks (Narayan & Popp, 2010;2012).Moreover, the unit root test of Popp (2008) is novel in the sense the coefficients of the test equation are nonlinearly related to each other.Owing to the novelty of these tests, they have been briefed in Appendix A of this paper.

ARDL Cointegration Analysis
ARDL bound testing approach to cointegration (Pesaran et al., 2001), in comparison with other cointegration methods (Engle & Granger, 1987;Johansen & Juselius, 1990), has the following advantageous features: (i) variables considered could be of different order of integration, (ii) efficient estimator even in small samples (iii) unbiased estimator of the long-run model even with endogenous regressors (iv) optimal order of lags of the series need not be the same, (v) current first-differenced regressors could be used as explanatory variables, and (iv) a single reduced form equation is used.
First step in the ARDL approach is to estimate the following unrestricted ECM.
where β 0 is the intercept, β 1 , β 2 , β 3 and β 4 are the parameters of the long-run equilibrium ensemble, a i , b i , and d i are the short-run dynamic parameters with m, n and p specifying the optimum lag lengths selected based on Akaike's Information Criterion (AIC) or Schwarz Criterion (SC), and ε(t) is white noise.
Second step is to compute the F-statistic, at the selected optimum lag lengths, under the null hypothesis β 1 = β 2 = β 3 = β 4 = 0 (that is, no cointegration) against the alternative hypothesis that they are not.Computed F-statistic is then compared with the finite sample critical value bounds (Narayan, 2005).If it lies above the upper bound critical value then the null of no cointegration is rejected.If it lies below the lower bound critical value then the null cannot be rejected.If it lies within the bounds, then no conclusive decision could be drawn without knowing the order of integration of the regressors involved.

Long-run Equilibrium and Short -run Dynamics
If the null of no cointegration is rejected, then it is certain that the variables concerned are locked in a long-run equilibrium relationship, which is estimated starting from an ARDL model as the one given below: where μ 0 is the constant term, μ t is the coefficient of the time trend, i  , j  and k  are the coefficients of the first-differenced series, m, n and p denote the optimum lag lengths selected based on AIC/SC statistics, and ECT(t) are the serially uncorrelated residuals known as the equilibrium correction term.
ARDL(m,n,p) model is estimated using OLS procedure, and the coefficients of the corresponding long-run equilibrium relationship along with the standard errors and t-statistics are estimated using the Delta method (Pesaran & Shin, 1999).Conditional ECM corresponding to the chosen ARDL(m,n,p) model paves the way for estimating the short-run dynamic equation governing the variables C, G and O.In the conditional ECM, first difference of C is regressed on its lagged terms, current and lagged first differences of G and O and a one period lag of ECT using OLS regression (Pesaran et al., 2001).
Residuals of the conditional ECM are then tested for non-rejection of the null hypotheses of no residual serial correlation, no heteroskedasticity among the residuals, and normally distributed residuals.Stability of the estimated parameters are tested employing Ramsey regression specification error test (RESET), cumulative sum of recursive residuals (CUSUM) test and cumulative sum of squares of recursive residuals (CUSUMSQ) test.

Granger Causality Analysis
In case of cointegrated I(1) series, existence of Granger causality among them is tested using the following pair of equations (Acaravci & Ozturk, 2010;Narayan & Singh, 2007;Oxley & Greasley, 1998): where i  (i=1,2,3) are the intercepts, ,2,3; j=1,2,3; k=1,2,..p) are the coefficients of the lagged first-differenced variables, p is the optimum lag length selected based on AIC/SC, i  (i=1,2,3) are the coefficients of the lagged ECT, and i  (i=1,2,3) are the zero mean, constant variance, independently and normally distributed residuals.Short-run (or weak) Granger causality tests are conducted by generating 2  statistic using the F-test of the lagged explanatory variable to establish rejection or non-rejection of the relevant null hypothesis, denoted by H 0 .For example, ∆G Granger causes ∆C in the short-run if H 0 : causality tests are conducted by assessing the significance of the t-statistics on the coefficients of the lagged ECT, which are i  (i=1,2,3).

Order of Integration of the Time Series
Results obtained with unit root testing methodologies incorporating structural breaks (described in Appendix) are tabulated in Table 1 and Table 2. Since the primary interest is the unit root properties of the series tested, test statistics , explained in Appendix A, tabulated in the tables are compared with the respective 5% critical values provided below the respective tables.Since none of the test statistics surpass the corresponding 5% critical values, null of unit root could not be rejected in any case studied, and therefore I concluded all three variables are I(1) series at 5% level of significance.
It is noteworthy to mention that all 12 models tested have highly significant coefficients of the break dummies, 1  and 2  , explained in Appendix A. For crude real price, the first and the second break years are identified as 1973 and 1978, respectively, which correspond to the years of oil shocks, strongly supporting the model with two breaks in the levels (column 7 of Table 1).For real GDP, the first break year is identified as 1981 and the second break year as 1990 or 1991.For CO 2 emissions, M1 model identifies the first break year as 1973 and M2 model identifies it as 1981.The second break year is identified as 1975 by M1 and 1989 by M2.Statistical significance of the corresponding level and slope dummies, however, do not provide consistent evidence to conclude on the nature of structural break(s) in G and C.

Cointegration
As the next step, cointegration among C, G and O is tested using the ARDL bound testing procedure (Section 4.2).Both AIC and SC statistics select the optimum lag lengths in equation ( 1) as m = 0, n = 3 and p = 0 starting with the maximum lag length of 4 in each case which is adequate for annual data (Narayan & Smyth, 2005).Corresponding F-statistic is 10.107 for a sample size of 53 spanning 1955 to 2007.Since the upper bound critical value at 1% level of significance is 6.790 for a sample size of 50 and is 6.578 for a sample size of 55 (Narayan, 2005(Narayan, , p.1989)), the null hypothesis β 1 = β 2 = β 3 = β 4 = 0 (no cointegration) is rejected at 1% level of significance when C is the dependent variable.When C and G are interchanged in equation ( 1), both AIC and SC select m = 2, n = 1 and p = 1, and the F-statistic is 5.453 for a sample size of 53.Since the upper bound critical values at 5% level of significance are 5.030 for a sample size of 50 and 4.955 for a sample size of 55 (Narayan, 2005(Narayan, , p.1989), null of no cointegration is rejected at 5% level of significance when G is the dependent variable.

Long-run Equilibrium
Rejection of the null of no cointegration assures the variables concerned are locked in a long-run equilibrium relationship.Starting from ARDL(4,4,4), the following long-run equilibrium relationship based on AIC statistic is estimated using the procedure outlined in Pesaran and Shin (1999): where t-statistics, given within the brackets, are computed using the Delta method (Pesaran & Shin, 1999), and their numerical values render statistical significance to the corresponding estimated parameters.SC statistic chooses ARDL(1,3,0) model, the coefficients and the t-statistics of which are very similar to those of equation (4).
Long-run equilibrium estimates in equation ( 4) show 1% growth in real GDP is associated with 3.2% growth in CO 2 emissions, when crude real price is frozen in time, and in the absence of progressive technological and policy-based CO 2 emissions reduction strategies, proxied by time trend.Decline in CO 2 emissions as a result of climbing crude real price, in the absence of technological and policy-based interventions, is realizable only if GDP growth is limited to a maximum of 2.4 (= 0.078/3.2) percent.These results also imply that technological and policy-wise interventions, under constant crude real price scenario, cause CO 2 emissions to decline only if real GDP grows at a rate less than 2.8 (= 0.09/3.2) percent.

Short-run Dynamics
Short-run dynamic equation is estimated from the conditional ECM corresponding to ARDL(1,4,1) using the OLS procedure.The general to specific procedure guided by minimising AIC statistic gave the following statistically significant conditional ECM: where ECT(t-1) is given by equation ( 4), and the statistical significance of the estimated parameters are testified by the corresponding t-statistics given within the brackets below the parameters concerned.
Equation ( 5) is estimated to have an adjusted R 2 of 69%, and a Durbin Watson statistic of 2.13.Estimated chi-squared statistics of Breusch-Godfrey serial correlation LM test, Jarque-Bera normality test, and ARCH heteroskedasticity test are and the corresponding P-value is 0.86.Null of no misspecification in the model such as non-inclusion of all relevant variables is therefore rejected.Plots of CUSUM and CUSUMSQ test results, shown in Figure 3, confine themselves within the critical bounds of 5% significance.This implies the estimated coefficients of equation ( 5) are nearly constants from one sample period to the other, despite crude real price series experiencing two structural breaks within the sample period.In interpreting equation ( 5), it must be noted that the coefficient of the equilibrium correction term ECT(t-1), known as the adjustment parameter, not only has the expected negative sign implying negative feedback mechanism but also is highly significant (with the t-statistic of -6.23), which can be taken as further proof of the existence of a stable long-run equilibrium relationship (Banerjee et al., 1998).Numerical value of the adjustment parameter reveals that any deviation from the long-run equilibrium following a short-run disturbance is corrected by about 25% in a year.Coefficient of ΔG(t) reveals there is a 1:1 short-run dynamic relationship between GDP growth and CO 2 emission growth in a given year.

Granger Causality
Having estimated ECT by equation ( 4), long-and short-run Granger causalities are analyzed (Section 4.4).SC selected an optimum lag length of unity in equation ( 3) with the constant terms being replaced by the break dummies DB 73 = 1(t = 1974) and DB 81 = 1(t = 1982) to account for the structural breaks in the variables (Section 5.1).Other criterions such as AIC, Hannan-Quinn information criterion, and final prediction error selected the lag length to be six which is too large in comparison to the sample size of 57, and therefore not considered.F-test results of the lagged first-differenced explanatory variables, coefficients of the lagged ECT, and the corresponding P-values are tabulated in Table 3.
Table 3 shows, in the short-run, crude real price is significant at 5% level in the CO 2 emission equation whereas real GDP is not.In the real GDP equation, CO 2 emission is significant at 1% level in the short-run whereas crude real price is not.In the long-run, lagged ECT is significant at 1% level in the CO 2 emission equation and at 5% level in the real GDP equation.In both cases, coefficients of lagged ECT terms have the correct signs.In the crude real price equation, as anticipated, no term is statistically significant.
Empirical evidence, therefore, suggests, as could be visualized in Figure 4, in the short-run, Granger causality runs from world crude oil real price to CO 2 emissions to real GDP.Deviations from long-run equilibrium Granger cause changes in both CO 2 emissions and real GDP.That is, bi-directional long-run Granger causality runs between CO 2 emissions in the US and her GDP through the equilibrium correction term.It must be noted that Soytas et al. (2007) found no evidence for long-run causality (in any direction) between CO 2 emissions and real GDP in the US.Their approach however did not include crude real price as one of the explanatory variables.

Potential Use of the Model as a Policy Tool
It would be of considerable interest for the policy makers if reliable forecasts of future CO 2 emissions could be made using the ECM developed in this study.Forecast equation can be obtained (Amarawickrama & Hunt, 2008) by substituting the long-run equilibrium relationship (equation 4) in the conditional ECM (equation 5), and then by simplifying it as follows: In-sample CO 2 emissions forecasted by dynamical simulation of the compound model are shown along with the actual CO 2 emissions in Figure 5. Dynamical simulation is carried out using the actual values of real GDP and crude real price, with the actual value of CO 2 emissions at 1953 as the initial input.As could be observed in Figure 5, compound model is able to closely predict the in-sample actual emissions, which is expected considering the stability of the estimated coefficients of the conditional ECM (Section 5.4).
Out-of sample forecasting of CO 2 emissions requires reliable real GDP and crude real price future projections be made available.Taking into account the uncertainties associated with such future projections, I use random number generators to provide future projections of real GDP and crude real price growth rates.Real GDP is generated using a triangular distribution having 1.8%, 2.4% and 3.0% as the minimum, reference and maximum real GDP growth rates till 2035.These rates are obtained from Annual Energy Outlook 2010 (AEO, 2010) published by the US Energy Information Administration (US EIA, 2010).World crude real price is generated using another triangular distribution with a reference growth rate of 1.1% (US EIA, 2010), and with minimum and maximum growth rates so chosen that they give about 50 and 200 constant 2009$ at 2035 (US EIA, 2010).
Results of 25 000 Monte Carlo simulations of equation ( 10), generated using MATLAB TM package, are shown in Figure 6.The 50 th percentile of Figure 6 gives the median emissions which could be taken as the most expected CO 2 emissions forecast.The 2.5 th and 97.5 th percentiles bound the emissions range of 95% confidence level.Thus, when real GDP and crude real price are confined to the AEO2010-defined limits, it is most likely that the fossil fuel-based CO 2 emissions in the US will be below the 1990 emissions level beyond 2020, and will reach 3885 TgCO 2 in 2035.At 95% confidence level, it could be said that CO 2 emissions will be below the 1990 level beyond 2024, and that emissions will be confined to the range of 3560-4240 TgCO 2 in 2035.
In order to study the sensitivity of the CO 2 emissions forecast to the reference real GDP growth rate used in the simulations, I replaced the reference real GDP growth rate of 2.4 in the triangular distribution by 3.0.Results of 25 000 Monte Carlo simulations of equation ( 10), shown in Figure 6, reveal that it is most likely that the fossil fuel-based CO 2 emissions in the US will be below the 1990 emissions level beyond 2026, and will reach 4500 TgCO 2 in 2035.At 95% confidence level, it could be said that CO 2 emissions will be confined to the range of 4100-4950 TgCO 2 in 2035.
The above analyses in emission forecasts prove that increase in the reference real GDP growth rate has significant impact upon the future CO 2 emissions in the US for a business-as-usual scenario.

Conclusion
With the prime objective of learning from the fossil fuel-based CO 2 emissions-economic growth-world crude oil price nexus of a leading economy of the world, the underpinning nature of the relationship among them is investigated for United States (US) for the period 1950 to 2007.
Widely fluctuating nature of CO 2 emissions and crude real price called for the use of unit-root testing methodologies for series with structural break(s).Test results provide empirical evidence for all series being non-stationary.The relationship among the series considered is therefore analysed using a cointegration methodology.
ARDL bounds testing approach to cointegration provides empirical evidence for the existence of a long-run equilibrium relationship with 1% growth in real GDP being tied up with 3.2% growth in fossil fuel-based CO 2 emissions in the US, and 1% growth in crude real price being tied up with 0.08% decline in CO 2 emissions.The long-run model also captures the tendency for emissions growth to very gradually reduce with time.
The equilibrium correction model developed reveals any deviation from the long-run equilibrium relationship is corrected within a 4-year period.And, the short-run dynamics are such any change in the current annual growth in real GDP is tied up with equivalent change in the annual growth in emissions.
Granger causality analyses provide empirical evidence for short-run Granger causality running from world crude real price to CO 2 emissions to real GDP, and bi-directional long-run Granger causality running between CO 2 emissions in the US and her GDP.Policy implication of the existence of such bi-directional long-run Granger causality is that considerable reduction in fossil fuel-based CO 2 emissions in the US could hinder her economic growth.And, strong GDP growth in the US could be a cause for increase in fossil fuel-based CO 2 emissions.
Stability test results illustrated the model developed in this study is free of model misspecification such as non-inclusion of all relevant variables and the estimated coefficients are nearly constants from one sample period to the other.Therefore, the model developed is suitable for forecasting for a Business-as-usual scenario.Monte Carlo stochastic simulations of the compound model developed reveal, for a business-as-usual scenario, a small increase in the reference real GDP growth rate, such as from 2.5% to 3.0%, causes considerable increase in the future CO 2 emissions of the US.
The results of this study clearly demonstrate that it is the rate of economic growth and not the level of economy that decides on the CO 2 emission intensity of a high income economy, in contrast to the general belief CO 2 emission reduction is plausible once the economy is grown to satisfactory levels (the familiar EKC hypothesis).It is therefore evident that US needs to invest both on urgent policy-based solutions and long-term technological solutions to weaken the strong cointegrating relationship existing between CO 2 emissions and GDP. for a sample size of 50, and are -3.498 and -4.316 for a sample size of 100.They are obtained from Table 3 of Popp (2008) and Table 3 of Narayan and Popp (2010), respectively.
02 [0.89], respectively.P-values of the given chi-squared statistics, provided within the brackets, testify non-rejection of the null hypotheses of no residual serial correlation, no heteroskedasticity among the residuals, and normally distributed residuals.Stability of the estimated parameters is assessed by the chi-squared statistic of RESET which is )

Table 1 .
Test statistics of unit root tests with structural break(s) in the level (model M1).Notations used are explained in Appendix A

Table 2 .
Test statistics of unit root tests with structural break(s) in the level and slope (model M2).Notations used are explained in Appendix A Same as in Table 1 except for the critical values which are -4.168 for for a sample size of 50, and are -3.953 and -4.937 for a sample size of 100.

Table 3 .
Results of error-correction based Granger causality tests Notes: *** and ** represents 1% and 5% significance levels, respectively.P-values are provided within the parenthesis.