1. United States Environmental Quality and Economic Growth: Time Series Model
Anaisa Cerda
Professor Michael Jonas
Introduction:
In this research project, I am seeking to explore the relationship between Economic
Growth and the Environment Quality by analyzing patterns of environmental
transformation at different income levels in the country. Some of the major questions
and issues I am addressing include:
o Has past Economic Growth been associated with the accumulation of natural
capital or drawing down of natural resource stocks?
o Testing the relationship between income and each environmental indicator
o Showing that environmental policies and investments are worthwhile
o Do indicators improve with higher income or worsen?
o How do relationships vary across different environmental resources?
The Environmental Indicators as independent variables incorporated in the model are:
Carbon dioxide emissions (CO2)
Oil consumption (OIL)
Coal consumption (COAL)
Municipal Solid Waste (MSW)
The dependent variable in the model is:
Gross Domestic Product (GDP)
Original & Lagged Difference Equations:
𝐺𝐷𝑃! =∝!+ 𝛽! 𝐶𝑂2! + 𝛾! 𝑂𝐼𝑙! + 𝛿! 𝐶𝑂𝐴𝐿! + 𝜑! 𝑀𝑆𝑊! + 𝜇!
𝐺𝐷𝑃!!! =∝!+ 𝛽! 𝐶𝑂2!!! + 𝛾! 𝑂𝐼𝑙!!! + 𝛿! 𝐶𝑂𝐴𝐿!!! + 𝜑! 𝑀𝑆𝑊!!! + 𝜇!!!
Histogram and Descriptive Statistics
Independent Variables:

2. Dependent Variable:

3. As noted in all the graphs and statistics see definite upwards trends and fluctuations
across time in Environmental Indicators along with GDP. The objective is to capture
an economic relationship showing the effects of GDP on the indicators are significant.
It is important to note the skewness of the variables as well and how it is varying
across the variables. None are dramatically left or right skewed.
Augmented Dickey Fuller Test
For C02, absolute value of
the t-stat is less that the
Critical values.
Do NOT reject the null as
assume unit root and non
stationary

4.
For Coal: The absolute value of
the t-stat is less than the Critical
values
Do not reject the null and
conclude unit root and non-
stationary
Seems at 3rd
difference can reject
null and sig at the 5&10% level
where = stationary with no unit
root.
For Municipal Waste:
tstat<tcritcal
Do not reject H0= unit root and
non-stationary.

5. It is evident that stationary variables are not present. Moreover, the original variables are not
showing any significance as determined by the p-values.
In the model, I do not want any spurious regression or heteroskedasticity so went along and
corrected for unit roots by lagging and taking the first difference of each of the variables.
Differenced Variables:
For Oil: tstat<tcritical
Do not reject null, unit root = non-
stationary
With First difference of Oil Tstat
becomes 3.83 to get rid of
nonstationarity and can reject null at
1,5, and 10% levels.
Dependent Variable
GDP : tstat<tcritical
Do not reject null, unit root =
non-stationary

6. Lagged Variables:
By adding the lags of certain models, can see a bit more significance in the variables
like oil at (-2) and (-1). Despite the insignificance in the second lag of the carbon
emission, I have decided to add it to the model because of the additional significant
variables, enhancing the model slightly.

7. ARMA 2,3
In order to discover how GDP relates to past values of itself and past values of the error term, ARMA
identification tests were executed. Combining AR&MA describes the current value off GDP depends
linearly on its own previous values plus a combination of current and previous values of the white noise
error term. I wanted to choose lags that minimized my Information criteria. Making sure that these new
added variables explained more than they were costing After multiple tests, I found that ARMA 2,3 was
proving to be the best model. Through looking at the Correllograms it seems to be correctly identified
since the fitted residuals are White Noise. Though MA(3) is showing to not be significant, it would be
likely to delete it. However, upon removing it all other variables became insignificant along with a rising
of the Information criteria. Therefore, I decided to keep the MA(3) term because of its explanatory
power.
The multivariate model does seem to outperform the univariate model. Seen in the Adj
r2 being at its highest along with the AIC and SIC being slightly smaller.
Some of the X variables are showing to be significant like co2 and oil practically being
zero. The model is using their lagged values because of endogeneity bias. Overall, not

8. very much improvement occurred as seen through a very slight difference in the
AIC/SIC and Adjusted R2.
Q-stat
Squared Residuals
By the results of the Qstat, there is white noise meaning that this model does not have
a form of memory or predictability over time. Therfore, this model is claiming to not be
suffering from omitted ARMA factors.
Both the correllogram of Q-stat and of Squared residuals are showing a white noise
process and therefore not seeing presence of an ARCH process and can assume
homoscedasticity.
ARCH effects
ARCH and GARCH tests were done in order to be sure that they would not show any
improvement to my model. Sure enough, they did not. Primarily, looking at the F-stat ,
it was not showing to be significant and not showing evidence of joint significance of

9. the lagged terms .Next, The Resid -1 is the reaction to market shocks at t-1 is a rather
small value which indicates relatively low sensitivity of gdp volatility to recent events.
Below are the included regressions.
F stat is not showing to be significant here, which is not suggesting the presence of
ARCH in GDP . Neither of the coefficients on the residuals are significant .
(GARCH 1,1)
The ARMA terms in the regression are not telling us anything due to their p-values
being very close to 1. But the Lagged Carbon dioxide is showing significance along
with Oil being a significant coefficient.
The ARCH term is significant and the GARCH term, which is the error variance, is
not as significant as we hoped it would. This implies a carry over effect that was not
very strong on the GARCH side.
(Seen Below)

10. GARCH conditional Variance
This Graph is providing a forecast of the market variance.
STRUCTURAL BREAKS
CHOW TEST 1989
Here with a p-value of 0.5836, we do not reject the null of zero break points/ structural
stability and conclude that there does not seem to be evident structural break points.
Without a structural break/ regime shift, we can assume a constant mean, variance,
auto correlation, marginal effects, and ARMA structure.
.

11. Quandt-Andrews Test:
Based on the sample size being limited to 53 it was too small to run this test due to the
trimming effect of this model. Due to not being able to run this model I decided to still
go forth and run a tar model because of the potential breaks in the model that may not
could have been
Ramsey Reset Test:
In the Ramsey Reset Test we are testing whether the quadratic fitted independent
variable terms are significant in determining the level of the dependent variable. The
Ramsey test in my regression is testing whether the relationship between
GDP(economic growth) and my explanatory variables is linear or not.
In the output we take note of both F= 0.34 with pvalue =. 5620 and X^2=0.000326 and
pvalue = 0.1392 , it is seen that there is no apparent non-linearity in the regression
equation and conclude that the linear model for Economic Growth/GDP is
appropriate.

12. TAR Multivariate Model
I have chosen to use my dependent variable D(GDP) as my forcing variable.
In the threshold it is also lagged tracking that GDP rising before is going to keep rising
depending on which state it is in. Where current GDP is being changed by the lags.
The dummy variables are the determining factors to which state we are in: Above 0 or
below 0. Dummy variables are used commonly as a way of solving structural breaks,
not involving splitting the data. I have included the output along with grouped TAR
indicating which state I am in across time.
Grouped Tar:

13. In the Next model clearly do see improvement, incorporating the lags:
The forcing variable in this Model is D(GDP)(-1) and the threshold is zero.
In the regression output our adjR^2 is at its highest along with AIC/SIC being at its
lowest which outperforms our linear model. This is the SETAR model where the
regime switch is determined by my dependent variable relative to the threshold.
Overall claiming that GDP (which I lagged) behaves differently when rising vs.
falling. If GDP was rising before then it will keep rising, the current GDP will be
determined by the lag.
The dummy variables alone determine the regression shift. Here showing a large
difference in states. Z1 variable being significant at 645.08 and Z2 is -187.79 There is
evidently large intercept with a large change / shift from one state to another.

14. Through this model, observing the joint significance across states to see whether or not
they belong to the model. In looking at this regression, all AR terms are proving to be
significant except for lagged carbon dioxide emissions in state 2, Lagged MSW in state
2 and Lagged oil in state 2.
The coefficients in regression are proving that states do matter in this research. For
variables such as co2 and oil there is a small change but not much different from one
another. The shape of the regression is showing to be highly sensitive to coal and msw
due to a big percent change in the coefficients.
D(GDP)=
α 1+𝛽1𝐷(𝐺𝐷𝑃)(−1)𝑡 − 1 + 𝛿1𝐷(𝐶𝑜2)(−1)𝑡 − 1 + 𝛾1𝐷(𝐶𝑜𝑎𝑙)(−1)𝑡 − 1 + 𝜆1𝐷(𝑀𝑆𝑊)(−1)𝑡 −
1 + 𝜓1𝐷(𝑜𝑖𝑙)(−1)𝑡 − 1 + 𝜇1𝑡
If ∆𝐷(𝐺𝐷𝑃)(−1)𝑡 − 1 > 0
α 2+𝛽2𝐷(𝐺𝐷𝑃)𝑡(−1) − 1 + 𝛿2𝐷(𝐶𝑜2)(−1)𝑡 − 1 + 𝛾2𝐷(𝐶𝑜𝑎𝑙)(−1)𝑡 − 1 + 𝜆2𝐷(𝑀𝑆𝑊)(−1)𝑡 −
1 + 𝜓2𝐷(𝑜𝑖𝑙)(−1) 𝑡 − 1 + 𝜇2𝑡
If ∆𝐷(𝐺𝐷𝑃)𝑡 − 1 ≤ 0
Dummy Z1t= 1 if Δ𝐷(𝐺𝐷𝑃)(−1)𝑡 − 1 > 0
Dummy Z2t= (1-Z1t)
LOGISTIC STAR MODEL
Estimating the LSTAR model using Non-Linear Least Squares

15. I tried this model various times and some type of error is occurring where all my
coefficients resulted in N/A. For the L-star estimation, for a given threshold, we must
find optimal values of alpha 0, alpha 1, Beta, and theta. Using the NLS to minimize
SSR. The generated gamma would be the state sensitivity parameter, as it increases a
small change in forcing variable GDP will have a large outcome on the state out come
of theta. The sensitivity parameter will tell us very much about the degree of state
dependence that will occur.This model will help me determine whether there is state
dependence rather than single dependence between X and Y.
VAR
The Variance Auto Regressive allows for all variables in the system to be endogenous,
depending on lags of all other variables. I am running this in my model to provide
more accurate forecasts and to accomplish the estimation of an identified VAR by
OLS. I am tracking whether shocks to Carbon Dioxide emissions, Oil, Coal, and
Municipal Solid Waste boost GDP. My goal is to show that certain resources are very
informative about GDP and that GDP is a good indicator about the use of the
resources. Throughout all testing, keeping in mind, do the amount of emissions affect
output in the economy? If so, what is the transmission mechanism by which these
effects occur?
Specific Cholesky Ordering is a crucial part to identify a structural or primitive system
to be estimated by OLS. In my model I have come up with the following order:
DOILàDMSWàDCOALàDCO2àDGDP
Here DOIL is serving as my “contemporaneously exogenous” variable and DGDP is
serving as my “contemporaneously endogenous” variable.
Based on my chosen order:
𝐷𝑂𝑖𝑙! influences, 𝐷𝑀𝑆𝑊!,𝐷𝐶𝑂𝐴𝐿! 𝐷𝐶𝑂2! and 𝐷𝐺𝐷𝑃!
contemporaneously, and is
influencd by𝐷𝑀𝑆𝑊!,𝐷𝐶𝑂𝐴𝐿! 𝐷𝐶𝑂2! and 𝐷𝐺𝐷𝑃!
only
at
a
lag.

16. 𝐷𝑀𝑆𝑊! influences 𝐷𝐶𝑂𝐴𝐿!, 𝐷𝐶𝑂2! and 𝐷𝐺𝐷𝑃!
contemporaneously
and
is
influenced
by, 𝐷𝐶𝑂𝐴𝐿!, 𝐷𝐶𝑂2! and 𝐷𝐺𝐷𝑃!
only
at
a
lag..
𝐷𝐶𝑂𝐴𝐿!influences
𝐷 𝐶𝑂2! and 𝐷𝐺𝐷𝑃! contemporaneously and is influenced by 𝐷𝐶𝑂2!
and 𝐷𝐺𝐷𝑃! only at a lag
𝐷𝐶𝑂2! influences 𝐷𝐺𝐷𝑃! contemporaneously and is influenced by 𝐷𝐺𝐷𝑃! only at a lag
𝐷𝐺𝐷𝑃! has no contemporaneous effect on the other variables
I have come up with this order on the idea that oil next in sequence because of the
large commodity that it is overall in the economy and furthermore because of the
overwhelming dependency that the country and better yet, world has on the
production and trade of oil. However, due to this dumping, production, and spills
there is severe damage that is caused in all other areas of the environment. This all
leads to the contemporaneous influences on Coal and waste. For example, oil refining
produces solid waste that contains high levels of metals and toxic compounds.
Following Oil, I have included Municipal Solid Waste. The high amount of waste that
exists in our nation has to be burned. Upon burning this produces toxic pollutants and
emissions. The more waste we have the more it directly influences the coal that is
needed to burn all this waste.
This leads me to my next variable; Coal is used to burn oil at power plants as well as
municipal solid waste as a couple examples. I have placed coal as third because when it
is burned, it releases carbon dioxide as one of its major emissions.
Next, I have carbon emissions because they are universally distributed and naturally
present in the atmosphere. It is the primary greenhouse gas that is emitted through
human activities. It comes from a variety of natural sources, but human related
emissions are responsible for the increase that has occurred since the Industrial
Revolution. Hence, carbon dioxide emissions being influenced by all other variables
like oil, coal, and waste contemporaneously.
Below are the Cholesky Ordering Equations:

18. Without taking the difference of the environmental variables:
Upon running this regression, I instantly note the changes in AIC, SIC, and the log
likelihood. It has definitely minimized in comparison to other models that were run,
even the Threshold Auto Regressive model. I proceeded to run the Impulse Response
Functions, generating the responses of my environmental variables to shocks in
DGDP. I was anticipating seeing significance and unfortunately, found none. This was
not an expected result. Zero is clearly within the confidence interval and I cannot
reject the null that the change in DGDP with additive “s” terms (future periods) in the
future is zero. I did run the test without the differenced environmental variables out of
curiosity and in terms of the IRF there seems to be a bit of significance but still not as
much as had been assumed.
Results & Conclusion
Overall, a lack of data in environmental quality indicators has posed a problem in
proving the capability of this model to show more significance. The earliest data that
has been revealed has been from the 1960’s, which results in a small sample. The size
has prevented from running certain models, like the Quandt –Andrews, which would
capture the potential of any significant breaks that were not captured by other models.
Furthermore, there are definitely more environmental indicators that could have been
incorporated into the model, which is proof of omitted variable bias. Factors such as
water, deforestation, and other toxins were not readily available to serve as additional
explanatory variables in finding an economic relationship between economic growth

19. and environmental indicators. If such variables were included this could change results
greatly. Theoretically, it may not be possible to predict how environmental quality will
evolve with changes in GDP, but from this data can observe some clear patterns.
Unfortunately, not as much significance as would have been hoped for but after
running the various models there was evidence of improvements that were achieved.