[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

Derek Applegate Economics major

Psych minor

Cell: 518-852-1648

Home: 518-355-1824

Econ/Finc classes:

Econ 101,102, 201,202, 210, 300,340 and 430

Career Goals: I want to possibly be a market analyst or work in the emerging green sector. I also wouldn’t mind opening up my own business at some point down the road if I get the opportunity and capital to do so.

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

Can forest area be used an indicator of carbon emissions?

Hypotheses and inspiration: Countries with higher percentage of forest will have lower carbon

emissions during the year of 2005. I want to see if having a large body of forests in a country is

an indicator of low carbon emissions for each individual country. I decided to do this regression

because I had heard of the carbon capture concept in Professor Booker’s class and wanted to see

if the data would hold up in a regression. This data is arithmetical in how the carbon capture is

calculated but it is still worth it in determining forest area’s role in carbon emissions.

Variables

1. Forestry (percent of land area): Forest area is land under natural or planted stands of trees

of at least 5 meters in situ, whether productive or not, and excludes tree stands in

agricultural production systems (for example, in fruit plantations and agroforestry

systems) and trees in urban parks and gardens2. Urban population: Urban population refers to people living in urban areas as defined by

national statistical offices. It is calculated using World Bank population estimates and

urban ratios from the United Nations World Urbanization Prospects.3. Energy Use per Capita: Energy use refers to use of primary energy before transformation

to other end-use fuels, which is equal to indigenous production plus imports and stock

changes, minus exports and fuels supplied to ships and aircraft engaged in international

transport.4. Energy Production per capita: Energy production refers to forms of primary energy—

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

petroleum (crude oil, natural gas liquids, and oil from nonconventional sources), natural

gas, solid fuels (coal, lignite, and other derived fuels), and combustible renewables and waste--and primary electricity, all converted into oil equivalents.

5. C02 Emissions per capita: Carbon dioxide emissions are those stemming from the

burning of fossil fuels and the manufacture of cement. They include carbon dioxide

produced during consumption of solid, liquid, and gas fuels and gas flaring.

Initial run

Model Summaryb

Model R R Square Adjusted R Square Std. Error of the

Estimate

1 .907a .823 .813 .0027021

a. Predictors: (Constant), Energy Production Per Capita, Urban Population, Forest Area

(percentage of land area), Motor Vehicles (per 100 people), Energy Use Per Capita

b. Dependent Variable: C02 Emissions per capita (kt)

Coefficientsa

Model Unstandardized Coefficients Standardized

Coefficients

t Sig.

B Std. Error Beta

1 (Constant) .001 .001 2.400 .018

Motor Vehicles (per 100 people) 8.853E-007 .000 .032 .450 .654

Forest Area (percentage of land area) -2.372E-005 .000 -.080 -1.736 .086

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

Urban Population 2.200E-012 .000 .025 .569 .571

Energy Use Per Capita 1.842E-006 .000 .771 8.687 .000

Energy Production Per Capita .084 .035 .151 2.394 .019

a. Dependent Variable: C02 Emissions per capita (kt)

In my initial run I found the R squared to be .823 and only two of variables to have passed the T-

test. I am not going to be discounting these values yet as I have to still correct for any outliers

and determine if there is any multicollinearity, auto correlation, or Heteroschadisticity between

my explanatory variables which would throw off the T-stat.

Casewise Diagnosticsa

Case Number Std. Residual C02 Emissions per

capita (kt)

Predicted Value Residual

86 -6.297 .0074 .024443 -.0170160

114 2.120 .0244 .018624 .0057273

144 -2.496 .0092 .015909 -.0067454

185 -2.009 .0057 .011137 -.0054281

a. Dependent Variable: C02 Emissions per capita (kt)

In my first run, I found that there is a significant outlier in my regression. I checked my data and

found that Iceland was throwing out my data due to emitting lower C02 per capita than the rest

of my data. After conducting some research I found that Iceland gets 81% of its energy from

renewable resources and derives 19% of its energy from oil and other fossil fuels. This 19%

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

percent energy use in fossil fuels is what accounts for the.0074 C02 emissions per capita. I will

be taking Iceland out of my regression and running the regression anew. I realized that this tells

me something about the rest of the data in my regression. This means that most of the countries

in my regression heavily rely on fossil fuels because if they did not Iceland would be an outlier

and instead could possibly be the norm for this regression.

Second Run (without Case 86 or Iceland).

Model Summary

Model R R Square Adjusted R Square Std. Error of the

Estimate

1 .962a .925 .921 .0017666

a. Predictors: (Constant), Motor Vehicles (per 1000 people), Urban Population, Forest

Area (percentage of land area), Energy Production Per Capita, Energy Use Per Capita

After taking out Iceland my R squared jumped to .925 which is a significant jump from the .823

that I had previously reported. This details that 92.5% of C02 emissions per capita is explained

by Motor Vehicles per 1000 people, Urban Population, Percentage of forest area, Energy

Production per capita, Energy Use per capita. The other interesting point I found was that the

adjusted R squared in this regression was only off by .004 in this regression as opposed to a

difference of .010 in the previous regression. This means that the variables in my regression are

pulling their weight in this regression stronger than they were previously.

Coefficientsa

Model Unstandardized Coefficients Standardized

Coefficients

t Sig.

B Std. Error Beta

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1 (Constant) .001 .000 2.892 .005

Forest Area (percentage of land area) -3.187E-005 .000 -.106 -3.555 .001

Urban Population 6.988E-013 .000 .008 .276 .783

Energy Production Per Capita .003 .024 .006 .133 .894

Energy Use Per Capita 2.508E-006 .000 .980 16.567 .000

Motor Vehicles (per 1000 people) -1.525E-006 .000 -.054 -1.169 .246

a. Dependent Variable: C02 Emissions per capita (kt)

This regression gave me back some very interesting values as far as the T- stat. The most

important difference I see is that Forest Area has passed the t-stat while in the first run it failed

that test. Energy use remained the same with the t-stat while urban population and energy

production per capita saw a more pronounced failing of the t-stat. There is a negative slope on

forest area which is what I expected out of the regression. Urban population has a positive slope

which is what I expected. Energy use also had a positive slow which is what I expected to occur.

I expected motor vehicles to have a negative slope and the data confirmed it. The only slope that

did not fall according to my data was energy production. I expected it to have a negative slope

but instead it had a positive slope. This makes sense in practicality because energy production

should increase with C02 emissions given my observance above of countries relying heavily on

fossil fuels that produce C02 emissions.

A more in depth look at these variables shows that percentage of forest area can be used

as an explanation for the C02 emissions since the data passes the 5% t-stat test as well as the 1%

test. I could still be off but the IPSS has only shown the number out to the thousandth’s place.

This means that forest area does have an impact on the C02 emissions per capita in a given

country.

Urban population failed the t-test with a sig value of .783. This means that if I were to

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

reject the null hypotheses for urban population I would be wrong 78.3% of the time. With this

knowledge I can safely say that urban population is not statistically significant in impacting C02

emissions per capita.

Energy production also failed the t-test with a sig value of .894. This means that if I were

to reject the null hypotheses I would be wrong 89.4% of the time. With this knowledge I can

suggest that energy production is not statistically significant in determining C02 emissions.

Energy use per capita passed the t-test with a .000. This means that I can reject the null

hypotheses and would be wrong 0% of the time. I could still be wrong on this but IPSS has only

reported out to the thousandth’s place. From this I can infer that energy use per capita does have

a statistically significant impact on C02 emissions.

Motor Vehicles per 1000 people failed the t-test with a value of .246. This means that if I

were to reject the null hypotheses I would be wrong 24.6% of the time. This means that motor

vehicles per 1000 people is not a statistically significant indicator of C02 emissions.

Practical significance is another issue entirely which is very intertwined in my regression.

It is not statistically significant that urban population affects C02 emissions yet in my regression

it is statistically significant for energy use to affect C02 emissions. This means that the urban

population does not matter but rather how that population uses energy influences C02 emissions.

To clarify, a population that uses a lot of energy per capita is going to be influencing the C02

emissions of that particular country more than a population that does not use a lot of energy per

capita. A high urban population will not matter if the people who are in that population do not

use a lot energy per capita. This logic can be applied to energy production per capita as well.

Producing more energy per capita does not in any way necessitate that the population will be

using the energy which is the key in how much C02 is produced. This essentially comes down to

how much a nation uses C02 producing energy will result in higher C02 emissions. This can also

apply to motor vehicles as well. Having more motor vehicles per 1000 people doesn’t suggest

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

that they will use those vehicles but rather the energy use per capita will be a indicator of how

much they use those vehicles. Using vehicles is simply a means of energy use which is why I

postulate that it fails the t-test by a smaller margin than energy production or urban population.

This is something that I had not initially thought about when running my regression. This

however leaves a gray area of forestry and how it falls into being practically significant given

that is the crux of my regression.

Multicollinearity

After running a pearson correlation I found that there were two separate cases of

multicollinearity. The first case is between energy production per capita and energy use per

capita with a pearson correlation value of .661. Under Professor Trees rule of thumb anything

over .6 is considered a strong correlation. The other multicollinearity issue is with energy use per

capita and motor vehicles per 1000 people with a pearson correlation of .691. This a much more

problematic issue because they are not measured the same way and are therefore more

problematic to interpret. I am going to focus more on the energy use and energy production

problem instead.

I am going to run another regression using energy use and production to determine if

multicollinearity is still present.

Model Summary

Model R R Square Adjusted R Square Std. Error of the

Estimate

1 .781a .610 .607 1710.575

a. Predictors: (Constant), Energy Production Per Capita

This is a strong case for the existence of multicollinearity with these two variables. The major

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

problem with trying to correct for this by dividing all of the explanatory variables by energy

production or energy use is that it will be far more problematic as they are all measured

differently besides energy use per capita and energy production per capita. Instead I am going to

take out each variable individually to try to correct for multicollinearity. The first variable I am

going to remove is energy production.

Model Summary

Model R R Square Adjusted R Square Std. Error of the

Estimate

1 .962a .925 .922 .0017569

a. Predictors: (Constant), Energy Use Per Capita, Urban Population, Forest Area

(percentage of land area), Motor Vehicles (per 1000 people)

Coefficientsa

Model Unstandardized Coefficients Standardized

Coefficients

t Sig. Fraction Missing Info.

B Std. Error Beta

1 (Constant) .001 .000 2.907 .005

Urban Population 6.664E-013 .000 .008 .266 .791

Motor Vehicles (per 1000 people) -1.600E-006 .000 -.056 -1.367 .175

Forest Area (percentage of land area) -3.184E-005 .000 -.106 -3.572 .001

Energy Use Per Capita 2.522E-006 .000 .985 23.998 .000

a. Dependent Variable: C02 Emissions per capita (kt)

After examining my previous R squared with energy production in it. I can see that the R squared

has remained the same and I have successfully rid my regression of that particular

multicollinearity.

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

I am going to attempt to solve the multicollinearity issue with motor vehicles and energy use by

removing motor vehicles as that variable has failed it’s t-test.

Model Summary

Model R R Square Adjusted R Square Std. Error of the

Estimate

1 .967a .936 .934 .0018705

a. Predictors: (Constant), Energy Use Per Capita, Urban Population, Forest Area

(percentage of land area)

Coefficientsa

Model Unstandardized Coefficients Standardized

Coefficients

t Sig.

B Std. Error Beta

1 (Constant) .000 .000 1.376 .171

Urban Population -1.745E-013 .000 -.001 -.067 .946

Forest Area (percentage of land area) -1.914E-005 .000 -.061 -3.039 .003

Energy Use Per Capita 2.555E-006 .000 .958 47.517 .000

a. Dependent Variable: C02 Emissions per capita (kt)

Interestingly enough I have removed motor vehicles from the equation and the R squared has

jumped by .11. This shows that motor vehicles was not pulling its weight in this regression as

well as contributing to the problem of multicollinearity. There has been trend in each of these

tests as well. As I have removed a variable that has contributed to multicollinearity the t-stat on

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

my energy use variable has increased sharply with each test. There is another phenomenon that I

have noticed as well during this test, the t-stat on the forest area continues to move positively

after each variable that I have removed.

Autocorrelation

Autocorrelation is not a particular issue for cross-sectional analysis but it is worth going

over to check to see if my regression suffers from it. The test I will be conducting is the Durbin-

Watson.

Model Summaryb

Model R R Square Adjusted R Square Std. Error of the

Estimate

Durbin-Watson

1 .962a .925 .921 .0017666 1.679

a. Predictors: (Constant), Motor Vehicles (per 1000 people), Urban Population, Forest Area (percentage of land

area), Energy Production Per Capita, Energy Use Per Capita

b. Dependent Variable: C02 Emissions per capita (kt)

I found the value of my DL to be 1.69261 and Du to be 1.76991. My DL-4 equals -2.3079 and

my Du-4 equals 2.2009. My Durbin Watson is 1.679 which means that I do have autocorrelation

but I have cross-sectional data which means I still do not have autocorrelation.

Heteroscedasticity

As a means to test for Heteroscedasticity I will be graphing the unstandardized residual against

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

the unstandardized predicted value to determine if I have hetero for this regression.

Based on this graph there seems to be a moderate degree of heteroscedasticity.

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

This graph indicates that there is a small amount of heteroscedasticity

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

This graph indicates that there is a little heteroscedasticity.

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

This graph indicates that there is a large degree of heteroscedasticity.

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

This graph indicates that there is little heteroscedasticity.

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

This graph indicates that there is little heteroscedasticity.

Heteroscedasticity test 2: Glejser test.

To be certain that I do not have heteroscedasticity I will be performing the glejser test on all of

my explanatory variables. I have taken all of the residual values that I had previous attained by

my first heteroscedasticity test ran them through excel using the the heteroscedasticity absolute

value function. The only data that makes me question my original findings is energy use per

capita which had a graph that had a strong indication of heteroscedasticity. I am going to start

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

simply by running energy use as an explanatory variable while absolute value of the residuals

will be the dependent.

Model Summary

Model R R Square Adjusted R Square Std. Error of the

Estimate

1 .000a .000 -.011 .00172780

a. Predictors: (Constant), Energy Use Per Capita

Coefficientsa

Model Unstandardized Coefficients Standardized

Coefficients

t Sig.

B Std. Error Beta

1 (Constant) -1.220E-018 .000 .000 1.000

Energy Use Per Capita .000 .000 .000 .000 1.000

a. Dependent Variable: Unstandardized Residual

The R squared on this regression is zero and the t-stat is zero. This would suggest that there is

no heteroscedasticity. I am going to run another regression with the absolute value of the residual

as dependent and square root of energy use per capita as explanatory variable. This test will be

the second part of determining if energy use per capita has heteroscedasticity.

Model Summary

Model R R Square Adjusted R Square Std. Error of the

Estimate

1 .075a .006 .001 .0010145

a. Predictors: (Constant), square root of energy us per capita

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Coefficientsa

Model Unstandardized Coefficients Standardized

Coefficients

t Sig.

B Std. Error Beta

1 (Constant) .001 .000 5.621 .000

square root of energy us per capita -2.856E-006 .000 -.075 -1.087 .278

a. Dependent Variable: Abs. residual

The R squared in this case is still below zero and doesn’t explain the absolute value of the

residuals enough to suggest that there is heteroscedasticity. From this test as well I can suggest

that there is no heteroscedasticity in this regression.

The final test I will be running to determine if I have heteroscedasticity will be using energy use

per capita divided by one and the absolute value of the residual.

Model Summary

Model R R Square Adjusted R Square Std. Error of the

Estimate

1 .051a .003 -.003 .0009679

a. Predictors: (Constant), 1/energy use per capita

Coefficientsa

Model Unstandardized Coefficients Standardized

Coefficients

t Sig.

B Std. Error Beta

1 (Constant) .000 .000 5.677 .000

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1/energy use per capita -.009 .014 -.051 -.655 .513

a. Dependent Variable: Abs. residual

As I have state before the R squared is not enough to explain the possible heteroscedasticity. The

t-stat is also below 2 which would indicate that there is no heteroscedasticity.

From these two tests I can easily see that it simply a graphing anomaly that explains why

the graph was indicating that I had heteroscedasticity when all of the numbers in the regressions

point to heteroscedasticity being very small or non-existent in the overall regression. I am going

to assume that heteroscedasticity plays a negligible role in my regression.

Conclusion and final runs:

I am still at a loss for how forest area fits into the practical significance of my original hypothese

despite it confirming my original hypotheses. To illuminate forest area more I am going to run a

few more regressions.

Model Summary

Model R R Square Adjusted R Square Std. Error of the

Estimate

1 .971a .942 .941 .0017760

a. Predictors: (Constant), Energy Production Per Capita, Rural Population, Forest Area

(percentage of land area), Energy Use Per Capita

Coefficientsa

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Model Unstandardized Coefficients Standardized

Coefficients

t Sig.

B Std. Error Beta

1 (Constant) .001 .000 2.118 .036

Forest Area (percentage of land area) -1.700E-005 .000 -.054 -2.828 .005

Energy Use Per Capita 2.284E-006 .000 .856 28.111 .000

Rural Population 3.034E-013 .000 .004 .188 .851

Energy Production Per Capita .076 .018 .131 4.305 .000

a. Dependent Variable: C02 Emissions per capita (kt)

I ran this regression without motor vehicles and instead of using urban population I ran the

regression with rural population. What I have found here is that is different from the rest of the

regression run up to this point is that energy production has passed the t-stat and my R squared is

significantly higher than I have previously reported. I am going to do away with rural population

in this regression and run it with GDP per capita instead.

Model Summary

Model R R Square Adjusted R Square Std. Error of the

Estimate

1 .975a .950 .949 .0016798

a. Predictors: (Constant), GDP per Capita, Energy Production Per Capita, Forest Area

(percentage of land area), Energy Use Per Capita

Coefficientsa

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[Type text] Can forest area be used an indicator of carbon emissions? [Type text]

Model Unstandardized Coefficients Standardized

Coefficients

t Sig.

B Std. Error Beta

1 (Constant) .001 .000 2.507 .013

Forest Area (percentage of land area) -1.644E-005 .000 -.052 -2.812 .006

Energy Use Per Capita 2.220E-006 .000 .827 27.210 .000

Energy Production Per Capita .103 .018 .171 5.676 .000

GDP per Capita -3.046E-009 .000 -.007 -.400 .689

a. Dependent Variable: C02 Emissions per capita (kt)

My R squared is higher than it was before but GDP per capita still fails it t-test. It is also worth

noting that in these two regressions that I have multicollinearity for energy use and production. I

also noticed that the beta2hat for gdp per capita is negative which is opposite of what I was

expecting. This means that the less gdp per capita a nation has the more C02 emissions will be

produced by that nation.

I think I figured out that possibly my hypotheses was wrong not because the data doesn’t

confirm it but rather that the relationship my data is telling me is a far more compelling story. I

have noticed that after I solved for multicollinearity the t-stat on energy use and forest area

would both move positively the more I corrected for multicollinearity. Statistically this makes a

lot sense to correct for multicollinearity but it tells me something even deeper about the nature of

energy use and forest area. The t-stat was always being reported as less than it actually was

which was understating the effects of energy use and increasing the role forest area played into

C02 emissions. This essentially means that energy use tends to fluctuate with forest area but why

would that matter? This would matter because it is essentially suggesting that countries with

higher energy use tend to adopt policies that will decrease the area of forests. This inverse

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relationship tells me that the smaller the forest area percentage is in a country the more energy

use. My initial hypothesis was wrong because forest area contributes to the rise of C02 emissions

through its relationship with energy use. Without the relationship with energy use, forest area is

not itself an indication of C02 emissions.

Another alternative to this is that the less forest area a nation has can also be an indicator

of the amount deforestation that occurs as well. For instance, forest area is negatively sloped

with C02 emissions which can suggest that the more a nation uses energy the more likely that

nation is also taking a pro-deforestation stance since it requires the use of fossil burning fuels at

greater amounts to cut down forests that could contribute to higher C02 emissions.

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