The effects of global warming have been observed around the world in the form of more frequent wildfires, longer droughts, and stronger tropical storms, which can have negative impacts on the Earth’s societal, ecological, and environmental systems (The National Aeronautics and Space Administration, 2014). Carbondioxide (CO₂) emissions contribute to global warming through the greenhousegas (GHG) effect by holding heat energy from the sun in the Earth’s atmosphere, producing increases in global average temperatures (The U.S. Environmental Protection Agency, 2015). The Intergovernmental Panel on Climate Change (2014) reported that CO₂ accounted for 57% of total global GHG emissions in 2004 and was the largest single source of emissions. They also reported that CO₂ emissions produced by the transportation sector accounted for as much as 13% of total global GHG emissions from the combustion of fossil fuel¹⁾.

Among the five economic sectors in the U.S. (electricity, transportation, industry, commercial and residential, and other), CO₂ emissions from the transportation sector ranked second highest, explaining 32% of total U.S. GHG emissions in 2012 (The U.S. Environmental Protection Agency, 2013). Although CO₂ emissions from the transportation sector have increased, they reached a peak in 2007 (Fig. 1). Regarding the reduction after 2007, Choi et al. (2014) and Choi and Roberts (2015) suggested a couple of possible factors: 1) a government policy change (stricter federal regulations for GHG emissions) towards CO₂ emission reduction, and 2) a decline in fuel consumption caused by higher oil prices led to increases fuel economy, production from alternative sources, and fewer miles travelled by light duty vehicles²⁾.

Fig. 1. 
CO₂ emissions from the U.S. transportation sector, 1990 to 2012.

For the last two decades, increasing interest in reducing CO₂ emissions has generated numerous studies of the major CO₂ emitting sectors (e.g., power, industry, transportation, etc.) mainly using the Laspeyres or the Divisia methods to attribute the growth in CO₂ emissions to the potential driving forces. However, those methods are limited by their inability to consider the effects of qualitative factors, such as a change in environmental policy, while leaving to speculate the effects of an environmental policy change on CO₂ emissions. In contrast, other researchers have incorporated an environmental policy factor while studying CO₂ emission changes in passenger transport, freight transport, transport land use, and highway accidents when focusing on forecasting CO₂ emissions, the effects of an environmental policy change, or revealing the relationship between CO₂ emissions and their potential driving factors (Diakoulaki et al., 2007; Al-Ghandoor et al., 2009; Choi et al., 2010; Chung et al., 2013; Barido and Marshall, 2014; Kim et al., 2016; Park et al., 2016; Zhang et al., 2016).

Even though quantitative and qualitative analyses of CO₂ emissions have been performed, to the best of my knowledge no research has been conducted with statistical validation process since 2007 to evaluate the effects of climate change policy on CO₂ emissions produced by the U.S. transportation sector. Thus, the objectives of this study are to: I) identify whether climate change policies can reduce CO₂ emissions from the U.S. transportation sector with appropriate statistical validation tools; ii) quantify the effects of U.S. climate change policy on CO₂ emissions in the 49 contiguous U.S. states and for the nation ³⁾; and iii) determine whether the effects of U.S. climate change policy are consistent states. The findings of this study will be helpful to state and federal policy planners in evaluating the effects of climate change policy within their boundaries and nation wide and will provide a base on which to improve and accelerate the trend of CO₂ emission reduction through the implementation of stricter environmental regulations all over the world.

Various independent variables⁴⁾ in the literature were taken into account to explain the factors of CO₂ emission reduction in the transportation sector; therefore, the seven in dependent variables, including the implementation of a climate change policy, were all initially examined by a stepwise regression even though the effects of such apolicy are of primary interest in this study. The stepwise regression automatically selected the most important in dependent variables for modeling the mean dependent variable based on a t-test, and the brief procedures used are explained as follows: 1) all possible onevariable models of a linear form were fitted; 2) the best twovariable model of the form was selected through there maining (k—1), where k is the number of independent variables; and 3) the researchers checked for the third independent variable and this process continued until further independent variables did not appear to contribute to a significant p-value with the variables already in the model (Mendenhall and Sincich, 2011).

After the procedures, the four independent variables (fuel consumption, regulation of CO₂ emissions, VMT, and GDP in the transportation sector, ordered by the lower p-value and statistically significant at the 10% level) remained. However, due to the high possibility of multicollinearity between the four variables, the variance inflation factor (VIF) was tested for each variable. Excluding the regulation of CO₂ emissions, the three variables were highly correlated, showing a VIF greater than 10 (Mendenhall and Sincich, 2011); thus, only the variable of fuel consumption, which is directly connected to CO₂ emissions, remained and the others were dropped. Finally, the two independent variables (fuel consumption and regulation of CO₂) were selected. The former variable was obtained from the online data base of the U.S. Energy Information Administration (2015) and was measured in billion Btu. The latter variable was produced through a qualitative variable technique based on information regarding a climate change action planfrom Table 2. For the dependent variable, CO₂ emissions were derived from the USEPA and measured in MMT (The U.S. Environmental Protection Agency, 2014). All the data ranged from 2007 to 2012 by state.

An entity fixed-effects panel regression model was utilized to estimate the effects of climate change policy on CO₂ emission reduction in the U.S. transportation sector. The empirical econometric model for the pooled data and each group is as follows (Pindyck and Rubinfeld, 1997; Stock and Watson, 2011):

where, β₀, β₁, β₂, y₃, …, y_n+1 are unknown coefficients; X_1it is the implementation of a climate change policy by state i in year t; X_2it is the transportation sector fuel consumption by state i in year t; D2_i is a qualitative variable that equals 1 when i = 2 and 0 otherwise; D3_i is a qualitative variable that equals 1 when i = 3 and 0 otherwise, and so on; u_it and is an error term.

n—1 qualitative variables were used to avoid the dummy variable trap by omitting the first qualitative variable, D1_i. The rest of the qualitative variables take care of the effects of all the omitted variables that are not the same from each state to another but are constant over time. To summarize, the processes of the model performed in this study are as follows. First, the author extracted the appropriate regressors for the model by the stepwise regression and multicollinearity test. Second, the author tested whether the entity fixed-effects regression model is the best among other possible panel models, such as the time fixed effects, one-way random effects, and two-way random effects, by using F statistics and comparing the overall model fit and the estimated coefficients’ statistical significance. Third, a couple of statistical tests for verifying the serial correlation and heteroskedasticity were processed by the Durbin-Watson test and the Breusch-Pagan test, and the problems found were fixed by heteroskedasticity and autocorrelationconsistent (HAC) standard errors. Fourth, the author regressed the panel model and then analyzed the regression results based on the estimated coefficients’ p-values at the 10%, 5%, and 1% significance levels.

The empirical findings regarding the effects of climate change policy on CO₂ emission reduction in the U.S. transportation sector from 2007 to 2012 are summarized in two partspooled data and each group-in Table 3 and Table 4. In both tables, the F statistic’s null hypothesis, which is no fixed effects, was rejected at the 1% level of significance. A couple of OLS regression assumptions were tested and the test results are shown with the existence of positive serial correlation and heteroskedasticity since the Durbin-Watson tests were less than 2 and the null hypothesis of homoskedasticity in the Breusch-Pagan tests were rejected at the 5% significant level, respectively.

To address these problems, HAC standard errors were used in the entity fixed-effects models. The HAC standard errors functioned to make the regression errors remain randomly correlated within a grouping and uncorrelated across groups (Stock and Watson, 2011). Additionally, to consider the potential omitted variable bias arising from omitting both technological advancements in fuel efficiency and the U.S. economic recession, the two control variables⁵⁾ were utilized in the regression models. The concept of a control variable replaced the first least squares assumption of exogeneity with conditional mean in dependence⁶⁾ to prevent the estimated causal effect of interest from suffering from endogeneity (Wooldridge, 2012). As Stock and Watson (2011) explained in 2011, this study distinguished between regressors for which we have an interest in estimating a causal effect and a control variable. By establishing the alternative assumption, “the OLS estimator of the effect of interest was unbiased, but the OLS coefficients on control variables were in general biased and did not have a causal interpretation” (Stock and Watson, 2011, p. 231).

In Table 3, an overall effect of a climate change action plan on CO₂ emission reduction in the U.S. transportation sector across the 49 U.S. states was estimated and its coefficient shows a negative value of —0.413. If a state’s policy plan of CO₂ emission reduction took effect during the period of 2007∼2012, then it on average has reduced the CO₂ emissions per year by 0.413 MMT. Since the 31 states have completed such a CO₂ emission reduction policy plan through a climate change action plan, their total reduced CO₂ emissions reached 12.803 MMT in 2012, which was bigger than the entire transportation CO₂ emissions of West Virginia in 2012, 11.75 MMT. As the author expected, the fuel consumption in the transportation sector has had a positive impact on CO₂ emissions, technically 1 billion Btu in fuel consumption by transport in a state per year on average, increasing the CO₂ emissions by 0.000077 MMT.

Table 4 provides the effects of the climate change policy on CO₂ emission reduction in the three groups. Overall, the stability of average and standard deviation of CO₂ emission by each group would not seem to be deteriorated when considering the difference of the levels of CO₂ emission. The major group shows the most significant CO₂ emission reduction through the climate change action plan, followed by the middle and minor groups. The policy plan of CO₂ emission reduction in a state in the major group on average has almost three times as powerful a CO₂ emission reduction effect than that of the middle group, while a state in the minor group has on average only one-tenth of the CO₂ emission reduction effect compared with the major group. Since a climate change action plan exerts different effects within the groups, if the time and financial resources available are limited in the nation, then it is recommend to focus on letting the federal government first support the states in the major and middle groups⁷⁾ rather than the minor group.

The human activities for industrialization have been accelerating and raising the global temperature for centuries, due to the increasing CO₂ emissions released into the atmosphere by most of the economic sectors in a nation. As a result, we are unexpectedly experiencing severe natural disasters in many areas worldwide more frequently than in the past and thereby more people are being exposed to danger to their life and property.

A positive environmental policy change will be an essential factor in protecting public health and the coexistent needs of current and future generations; as Benjamin Franklin (Sussman, 2006) emphasized in 1963 at the University of North Dakota, the environment is an important public policy concern. In the U.S., such a change to relax the current high-level global warming and reverse it to a moderate level of around 1990 has been evident in various social and economic sectors; among them, the transportation sector, which emits one-third of the total CO₂ emissions in the U.S., has been quickly adapting by implementing a climate change action plan to reduce its CO₂ emissions.

This study revealed how effectively a climate change policy can function in the U.S. transportation sector by estimating the quantified climate change policy impacts not only for the national level, but also for the major, middle, and minor CO₂ emission groups. The empirical findings using an entity fixedeffects model with various valid statistical tests shows an evidently positive effect of the existence of a climate change policy in a state on decreasing its CO₂ emissions, even in the case of the minor CO₂ emission group. If all of the 49 states can implement climate change action plans, the U.S. transportation sector can reduce its CO₂ emissions by 20.2 MMT per year, and for the next 10 years, the cumulated CO₂ emission reduction will reach 202.3 MMT, which is almost equivalent to the CO₂ emissions produced by the transportation sector in 2012 in California, the largest CO₂ emitting state in the nation. All of this finally suggests the importance of implementing a climate change policy to reduce CO₂ emissions in the transportation sector.

The author tried to find out scientific proofs regarding implementing effective climate change policies in the transportation sector as using an econometric tool which was well known in the econometrics. We probably think that decrease of fuel consumption will step out of CO₂ emissions in the air more and more, but regardless of intuitive awareness, evident proofs need to be revealed. In this study, the author macroscopically found out the CO₂ reduction effect of climate change policies, but in the next study microscopic effects of each climate change policy needs to be reviewed for the detailed policy effect analysis.