Modelling And Analysis Of Climate Change

1. Executive Summary

The burning topic throughout the world is “Climate Change?. The close linkage between economic growth of the country and Greenhouse gas emission is indeed a serious debate. Development in industrial sectors will naturally increase GDP accompanied by emissions. However increase in GDP will pay way for higher standard of lifestyle and more income which results in increased consumption of energy and hence more emissions. The alarming global warming and the pressures of international treaties to reduce the emissions have triggered to analyse the relationship between economic growth (GDP) and Carbon dioxide (CO2) emission.

The relationship between GDP and Co2 emission for different countries are studied using regression-correlation model for a particular timeframe and in order to gain further insight on the emission curve, time series analysis is studied for few developed and developing countries. The data for analysis are taken from UN database and World data bank database. The relationship between GDP and Co2 emission could be drawn after analysing the linear regression equation and correlation factors of different countries.

2. Introduction

Climate Change is a serious and long pending issue which seeks continuous solutions. The earth’s climate change is mainly due to greenhouse gases triggered by human activities. Carbon di Oxide (CO2), the principal greenhouse gas is emitted by various means. Industrialization and technology have negatively impacted the environment by emitting the GHGs and discharging other pollutants. Fuel combustion accounts for the high amount of CO2 emission and there exists a strong correlation between total fuel emissions and CO2 emissions. Transportation and energy industries emit more percentage of CO2 emissions. Positive correlation exists between CO2 emission and total energy consumption. Hence the inferred fact is countries that emit more CO2 are those that consume more energy. As seen from the below graph, emission varies

Figure 1: Change in GDP and CO2 emissions for 25 countries.

Source: Change in GDP and CO2 Emissions, Top 25 Emitting Countries, 1992 to 2006

Available online:

3. Literature Review

Various Climate models states that doubling of Green house gases (GHGs) will increase the temperature by 2-5 degree celcius in global mean temperatures. As per forecast, this level may reach by the year 2030 – 2060. There may arise a situation wherein the effect of climate change may cause further amplification by releasing other GHGs. The recent level of greenhouse gases in the atmosphere is equivalent to 430 parts per million (ppm) CO2 compared with only 280ppm before the Industrial Revolution. By 2035, the level of CO2 emission could be reached 550ppm (CO2e) which implies a global increase in temperature of 2 degree Celsius. The below figure depicts the increase in GHGs emiited due to various activities. Increase in CO2, Kyoto gases (include carbon dioxide, methane, nitrous oxide, PFCs, HFCs and SF6) and Clorofluro Carbons(CFCs) are depicted.

Figure 2: Emisiion of Greenhouse gases over time period 1850 – 1990.

Source: Stern review on economies of Climate Change.

Figure 3: Green House gases emissions by Source.

Source: Stern review on economies of Climate Change.

Available at:

Figure 4: World CO2 Emissions by Region - Forecast

Source: World CO2 Emissions by Region,

Available at :

Global emissions are expected to rise due to ‘business as usual’ activities. The Kaya identity identifies total CO2 emissions as factors of population, GDP, energy intensity and carbon intensity.

CO2 emissions from energy ≡

Population x (GDP per head) x (energy use/GDP) x (CO2 emissions/energy use)

Thus any “increases in world GDP will tend to increase global emissions, unless income growth stimulates an offsetting reduction in the carbon intensity of energy use or the energy intensity of GDP? (Stern Report on economies of Climate change). The differing amount of emission is due to varied attributes depending on the country’s economic development. The correlation between CO2 emission per head and GDP per head over the period 1960-1999 for 163 countries was 0.9. A recent research in US claims that 1% increase in GDP per head will cause 0.9% increase in emissions per head.

Figure 5: Projected Co2 emissions.

Source: Stern review on economies of Climate Change.

Available at:

Co2 emissions are high for developed countries than developing countries. Because of technological growth and economic development due to energy intensive industrial sectors in developing countries, the CO2 emission is increasing for developing countries. However in developed rich nations, due to shift towards service based economy and outsourcing activities, the CO2 emissions have decreased after reaching peak.

Environmental Kuznets Curve EKC states that as income increases, the emission also increases upto a threshold limit of income after which the emissions will decrease. This takes a “inverted U shaped? relationship between the variables. From economic theory perspective, two reasoning have arose to explain the linkage between variables (GDP vs emission): First, the Kuznets behaviour is an income effect and initially investment in environmental quality was not encouraged. But when the “turning point? is reached, demand for investments towards environmental quality arises. Thus after turning point, indicators points that there is a decrease in emission.

Second reasoning states that EKC is a replica of the “stages of economic growth?, wherein they make a transition from agricultural to industrial and then from post-industrial to service based economy (Moomaw and Unruh 1997). Since the economy finally moves towards a service based economy, there is downward shift in emission level. In another words, it can be said that “economies pass through technological life cycles, moving from smokestack technology to high technology? (Moomaw and Unruh 1997)

Figure 6: Environmental Kuznets Curve

Source: Moomaw,W.R., Unruh,G.C., Are Environmental Kuznets Curves Misleading Us?,

Available online:

However EKC curve was not accepted by many theorists. Dinda2004 and Stern Review states that since the emissions are mentioned as a function of income. An increase in production/engineering activities causes emission and thereby income. “The corollary is that environment pollution is best addressed through economic growth? (World bank, 1992).

Many argued that Granger causality exists between economic growth and pollution (Coondoo & Dinda, 2002; Dinda & Coondoo, 2006; Akbostanci et al., 2009; Lee & Lee, 2009). Granger Causality does not mean that “X causes Y? instead it implies that “X possesses useful data for predicting Y?. This piece of work raises some question because it considers the relationship between economic growth and pollution in a bivariate environment (Stern, 1993, 2000). The relationship between economic growth and emission trends differs for developed countries, developing countries and Oil rich countries.

Kyoto Protocol:

The Kyoto protocol was established on 11 Dec 1997, is the protocol of  United Nations Framework Convention on Climate Change (UNFCCC ) designed with the objective of lessening global warming by reducing the GHGs emission into the atmosphere. About 187 states signed by Nov 2009. G77 (union of 77 countries) recognized that developed countries contributed high proportion of GHGs in the atmosphere and developing country’s emissions are less and they will emit more percentage of emissions to satisfy their economic needs. The agreement of the Kyoto protocol and further negotiations has triggered the issue on the linkage between CO2 emission and economic growth. Critics claim that economic growth increases emission and any efforts to reduce emissions will have a negative impact on economic growth (The Russian Journal, 2003).

Participation in the Kyoto Protocol, as of June 2009, where dark green indicates the countries that have signed and ratified the treaty, grey is not yet decided and red is no intention to ratify.

Figure 7: Kyoto Protocol Signatories


Available at:

As per Stern review (2004), it was stated that many attributes collage to generate EKC as development in manufacturing/production, change in mix of output/input and technological advancements. Each attribute is decided by various fundamental variables. In theory many factors interact based on assumptions to generate EKC. It is presumed that the economy shifts towards less developed countries as growth occurs.

Due to initial production/manufacturing activities, the pollution per capita increases but gradually it is due to alteration in output mix. Another reasoning assumes that quality of the environment is a costly piece and environmental protection act increases with per capita income. (Grubb et al., nd). Few research states that emissions increases with income growth and few others notice a twist/turning points. Shafik (1994) states that the emissions increases with income and there exists no deviation. However Holtz-Eakin and Selden (1995) claims that the twist arises at a point of $35,418 while Neumayer (2004) mentions the range as $55,000 and $90,000 as deviation point based on assumptions.

The impact of oil price shocks on CO2 emissions of various countries is studied by many analysts. Lanne and Liski (2004) did a study for 16 countries for the years 1870 – 2028 and confirmed that in many cases, the oil price shock resulted in decreased Co2 emission when compared with the past years. The structural developed model indicates the any upsurge in oil prices is associated with the positive to negative emission elasticity (Moomaw and Unruh 1997). Friedl and Getzner (2003) conducted a study for one country Austria and confirmed that amidst oil price blow, CO2 emissions increased with GDP after 1975, but at a slower pace. It is thus worth mentioning that it is the country’s circumstances that decides how it should react to external blows and to change in economic growth.

Based on the varying perspectives of literature, it is necessary to do correlation and regression analysis to state if there is high correlation between GDP and Co2 emission.

4. Data Considerations

The data for analysis is derived from “World data bank? data catalog and UN database. The GDP (billion $) and CO2 emission (billion kg) for the year 2006 for 53 countries are derived from UN database. The sample countries are filtered based on the GDP. Only the countries with GDP of $30000 are taken into consideration. The final sample size is 53.

The data GDP per capita (PPP) and Co2 emission (metric tons per capita) used in Figures 8 to draw trends for a period of 25 years for 5 years are taken from ‘World data bank’ database.

5. Analysis and Interpretation

The variable being predicted or described, denoted by ‘y’ is called dependent variable.

The variable that is used to predict the value of dependent variable is called independent variable. The economic growth of different countries (GDP per capita) is the independent variable along X axis, that is used to estimate the value of CarbondiOxide emission, the dependent variable which is along the Y axis.

Simple Linear Regression Model is the equation which relates how ‘y’ is related to ‘x’ and to an error variable ‘ε’ is given by y = β0 + β1x + ε

Simple Linear Regression Equation is the equation that links the independent and dependent variable and is given by E(y) = β0 + β1x .

The estimated simple linear regression equation developed from sample data is given by ŷ  = b0 + b1x where b0 is the ‘y intercept’ and b1 is the slope and ŷ is the predicted value of y for a given value of x.

5.1. Scatter Diagram

Scatter diagram is used to determine the strength of relationship between GDP and Co2 emission. If the correlation coefficient is zero, it implies that there exists no correlation. However if the value is close to +1, it implies they are perfectly correlated and if the value is -1, it implies they are negatively correlated. The value of correlation coefficient can be found using the CORREL function in MS Excel.

Figure 8 : GDP Vs CO2 emission (for 53 countries) Best Fit Regression model.

The Chart depicts the regression equation and the coefficient of determination.

Y = 0.453x + 96.165

The slope of the line is 0.453 which shows that slope is positive and there exists a positive linear relationship ie as GDP increases CO2 emission also increases. The Y intercept value is 96.165 as seen from chart. The slope and intercept are determined so as to reduce the error in predicting.

Best fit line equation Co2 emission = (0.453 * GDP per capita) + 96.165

R2 = 0.5853 which shows there exists a moderate positive correlation between GDP and CO2 emission. The correlation strength between GDP and CO2 for various countries differs greatly. For developed countries there exists a weak correlation, but for developing countries there exists a strong correlation and hence the final result is a moderate positive factor. Thus the graph depicts that there exists correlation between GDP and Co2 emission. The points that are little farther from the best fit line corresponds to countries like US, UK, Japan, China and India. The GDP and Co2 emission trends for these countries would be discussed in the ‘time series’ analysis section.

To measure the goodness fit for the linear equation, the value of Co2 emission is determined with and without Linear model. (Calculation for best fit without using linear model is listed in Appendix). The performance can be better understood by error reduction in linear model. If the value is near to 0, it implies error is not reduced. In our case, the coefficient of determination is 0.5853 which means that the error variance is lessened by 58.53% using linear model.

5.2. Regression analysis

It depicts how or to what degree the variables are linked with each other and regression analysis cannot be utilized for defining ‘Cause and Effect’ relationship. R2 is the coefficient of determination that is used to evaluate the goodness of fit for the estimated regression equation. Correlation coefficient represents the measure of the strength of linear assosciation between two variable ‘x’ and ‘y’. The scatter plot of GDP Vs Co2 emission can be best fitted by a straight line.

Figure 9: Regression Data analysis Excel Output

5.2.1. t Test :

5.2.2. ANOVA output:

5.2.3. F test:

F test based on the F probability distribution, is used to test for significance The value in cell F12 is the p-value associated with the F test for significance. Given the value of significance α (=0.01), it can be decided if H0 can be rejected or not. H0 can be rejected if p-value is less than alpha (α =0.01).

As per table, the p-value is 2.57E-11 < α (0.01). Hence we can reject the hypothesis H0 and thereby conclude that there exists a significant relationship between GDP and CO2 emission.

The t-test for significance is equivalent to the F-test for significance in simple linear regression and hence the p-values offered by both means are identical. “Significance F? is used to identify the p-value for the F-test for significance.

Standard error occurs twice in the output. In regression statistics, it refers to s , the estimate of α. In estimated regression equation section of the output, it refers to Sb1, the estimated standard deviation of the sampling distribution of b1.

As seen from the Regression statistics output, the coeeficient of determination is 0.585 and the correlation coefficient is 0.577; the standard error that is used to identify the value of s, the estimate of α is 742.02.

5.3. Analysis of Emission and GDP relations:

The relationship between GDP and CO2 emission for different countries will be discussed in this section. The graph shows the GDP- CO2 trends for different countries for the year 2006. The scatter diagram depicts that there exists a positive correlation between GDP and Co2 emission. Only countries with GDP more than 30000 ($) are considered. The list of countries taken as samples are listed in Appendix.

Figure 10: GDP trends for 25 years for 5 countries

Figure 10: CO2 emission trends for 25 years for 5 countries

5.3.1. Time Series analysis for developing nations:

The GDP - CO2 emission trends for few developing countries – India, China, Japan are taken into consideration to study the CO2 emission patterns over the years. Panayotou (2000) states that it is inapt to use static data on CO2 emission and GDP of various countries to determine the linkage between two variables for a country over a timeframe. Hence time series analysis is utilized to analyse the relationship between GDP and CO2 emission for different countries over a period of 25 years.

Figure 11: China’s GDP Vs CO2 emission for 25 year

Figure 12: Japan’s GDP Vs CO2 emission for 25 year

Figure 13: India’s GDP Vs CO2 emission for 25 year

There has been a tremendous significant growth in developing countries in the last 20-30 years. The evolution process of Co2 emission from a timeframe of transition to maturity can be better understood by analyzing the developing countries which have gained noteworthy economic progress. GDP per capita for China was growing much faster than Co2 emission. Japan’s Co2 emission is similar to Uk’s emission and Japan has experienced a high economic progress in the last 20 years. India’s 2002 GDP was 99% that of 1982 GDP and its Co2 emission was 114% that of 1982 emission. This depicts how carbon emissions are highly related with the growth of the nations economy. This is further supported from scatter diagrams of developing countries which represents the coefficient of determination and regression equation.

India , China and Japan exhibits a correlation of 0.93, 0.92 and 0.92 respectively. (Figure 11, 12, 13)

5.3.2. Time Series analysis for Developed Countries:

The figure 10 and 11 shows the GDP and Co2 emission for 5 countries for a period of 25 years. The graph clearly illustrates the the explicit growth of GDP and CO2 emissions of US and UK over the years. UK and US economy were the primitive economies to industrialize and established a stable position in the world market. The increase in GDP for both the countries depicts the steady economic growth over the years. However there exists slight dip in the CO2 emission cureve for both the countries – US and UK which is due to the upsurge of oil price. Inspite of stable growth, the emission per capita for US did not vary much within the 25 years. However for UK, the emission per capita is decreasing over the years. Hence the statement ‘ GDP growth will increase the Co2 emission? is subjected to question.

Figure 14: United State’s GDP Vs CO2 emission for 25 year

Figure 15: United Kingdom’s GDP Vs CO2 emission for 25 year

Hamilton and Turton ( 2000 ) points out that US and UK have taken enormous steps to reduce emission by implementing energy-efficient programs. UK has reduced its fossil fuel consumption and hence there is a downward shift for emission. However in US, the electricity consumption is too high and hence there is no deep fall in Co2 emission. The EU also moved towards energy efficient production system and they adopted to low carbon fuels. Thus the figure 14 and 15 shows that there exists a weak correlation between Co2 emission and economic growth due to above reasons. This clearly proves why we got a R2 = 0.58 in spite of high correlation for developing countries and weak correlation for developed countries.

5.4. Analysis of rates of economic growth and Co2 emission:

Increasing awareness on global warming have paved way for international treaties like Kyoto protocol which sets boundaries for carbon emissions as a basic step to reduce the emissions. The below figure shows the plot for OECD countries for 20 years. OECD countries are listed in Appendix. As seen from the figure, GDP and emissions have increased and decreased over the years and it is thus difficult to conclude if economic progress is linked with either growth or fall in emissions for a time period.

Figure 16: Yearly growth emissions and income for OECD countries

Source: Grubb,M., Butler,L., Feldman,O., Analysis of the Relationship between Growth in Carbon Dioxide Emissions and Growth in Income, Available online:

The below figure shows the percentage change in emission and GDP for EIT (Economy In Transition) countries. Economic growth was visible in many countries after the transition period. Fischer and Sahay (2000) claims that the countries that have adhered strictly to reform measures have experienced faster economic growth. The chart clearly shows that emissions have increased with GDP which supports the statement that GDP growth is linked with Co2 emission but other attributes do play a vital role in maintaining this positive relationship.

Figure 17: GDP and emission changes for EIT countries.

Source: Grubb,M., Butler,L., Feldman,O., Analysis of the Relationship between Growth in Carbon Dioxide Emissions and Growth in Income, Available online:

6. Conclusion:

The core of sustainable development is to reconcile economic growth and quality of the environment. Based on the analysis, it is difficult to firmly state that “Co2 emission increases with GDP always?. The datasets of OECD and EIT countries resulted in different conclusions. Analyzing the real dynamic trajectory by phase diagrams demonstrates that the pollution trajectory pattern depends on internal policy decisions and other exogenous factors. Over the years, economic growth of OECD countries is linked with the increasing, decreasing and steady trends of emissions. However for EIT countries, majority of the countries’ emissions increased with the economic growth but the amplitude of the growth varies greatly due to other attributes. Though there exists a linear relationship between GDP and Co2 emission, it cannot be said that the relationship will be stable forever due to various macroeconomic factors and international pressures. The GDP-CO2 emission relationship for developing/EIT countries is highly correlated and when the country gains the status of mature status, it is the countries’ external factors and its reform measures that decides the relationship between GDP and Co2 emission.

7. References:

Fischer, S., and Sahay, R., 2000. The Transition Economies after Ten Years, NBER Working Paper 7664.

Friedl, B. and Getzner, M., 2003. Determinants of CO2 emissions in a small open economy, Ecological Economics, 45(1), 133-148.

Grubb,M., Butler,L., Feldman,O., Analysis of the Relationship between Growth in Carbon Dioxide Emissions and Growth in Income, Available online:, accessed on 20 june 2010.

Hamilton, C. & Turton, H., 2002. Determinants of emissions growth in OECD countries, Energy Policy, 30, 63-71.

Holtz-Eakin, D., Selten, T.M., 1995. Stoking the fires? CO2 Emissions and Economic Growth, Journal of Public Economics, 57, 85-101.

Lanne, M., and Liski, M., 2004. Trends and Breaks in per-capita Carbon Dioxide Emissions, 1870-2028, The Energy Journal, 25 (4), 41-65.

Moomaw,W.R., Unruh,G.C., Are Environmental Kuznets Curves Misleading Us?, Available online:, accessed on 18 June 2010.

Neumayer, E., 2004. National Carbon Dioxide Emissions: Geography Matters, Area, 36(1), 33-40.

Panayotou, T., 2000. Economic growth and the environment. CID Working Paper 56, Harvard.

Shafik, N., 1994. Economic Development and Environmental Quality: An Econometric Analysis. Oxford Economic Papers, 46, 757-773.

Stern review on economies of Climate Change. Available at: , accessed on 18 June 2010

The Russia Journal, Kyoto Treaty Discrimnates Against Russia, 6th October 2003., accessed on 21 June 2010, accessed on 23 June 2010

World Bank, 1992. The World Bank Development Report 1992: Development and the Environment, Washington DC: The World Bank.