The Armey Curve Hypothesis-based Environmental Kuznets Curve (EKC) Hypothesis Testing Across the US States with Government Spending

: This study re-tests the EKC hypothesis for US states with a new methodology 36 that differs from all previous empirical studies using traditional EKC models. To this aim, 37 this methodology, for the first time, unifies two seemingly different but strongly interrelated 38 hypotheses (models), namely the Armey curve (AC) and traditional EKC models, into one 39 single composite model. The rationale for creating this composite model is twofold. First, 40 the functional propositions of these two hypotheses are depicted with inverted U-shaped 41 curves. Second, they also have economically interrelated-causal relationships. This means 42 that rising government spending (through the AC hypothesis) increases real GDP per capita 43 (RGDPPC) and, consequently, increases in RGDPPC (through the EKC hypothesis) 44 increase CO 2 emissions. The composite model created may also allow US state 45 policymakers to determine a single maximum spending level that will maximize or 46 minimize CO 2 emissions. Empirical findings indicate that the composite model is capable 47 of testing the EKC hypothesis for 7 US states. Additionally, for 7 US states, maximum 48 spending level was calculated to be around 15% of their RGDPPCs. Hence, with this 49 calculated spending level, policymakers of these states may be able to determine-adjust their 50 golden spending levels so as not to cause environmental degradation and declines in GDP. 51


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The roles of the governments in economic growth have been discussed for a long time. In 60 the theoretical discussion, the neoclassical growth model, developed by Solow (1956), 61 postulates that fiscal policies through taxation and government spending can affect the 62 economic growth up to only a steady-state rate of growth, which is determined by the 63 exogenous rate of technological progress. On the other hand, the endogenous growth model, 64 pioneered by Romer (1986), Lucas (1988), and Barro (1990), postulates that a government 65 can affect the economic growth since transition and steady-state growth rates and 66 government is considered endogenous. This means that governments play a serious role in rationale of this expectation is that real GDP per capita will initially increase by increasing 75 productive government spending and eventually decrease after a threshold (turning) point 76 due to different dynamics, such as the crowding-out effect, taxation, the law of diminishing 77 returns, and bureaucratic costs (Bastiat 1983; Barro, 1990;Scully, 1996;Karras, 1997;Chao 78 and Grubel, 1998; Sarte, 2001;Colombier, 2009).  When these two hypotheses (curves) are closely examined, a sequentially causal 98 relationship can be clearly seen from the Armey curve hypothesis to the EKC hypothesis. 99 This means that rises in government spending lead to increases in real GDP per capita in 100 the Armey curve model and, thereby, rises in real GDP per capita lead to increases in CO2 101 emissions in the EKC model. Moreover, this variable-level causal relationship between 102 the two models was constructed on the same inverted U-shaped mathematical proposition.

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Therefore, we believe that these two hypotheses can be jointly examined, both 104 theoretically and mathematically. This means that such similarity may enable us to test 105 the EKC hypothesis through the Armey curve hypothesis (model). Therefore, it can be 106 interpreted that the EKC hypothesis can be potentially tested by a kind of transmission 107 mechanism of the Armey curve model. In this context, a single composite model derived 108 from these two hypotheses (models) can be set up. To the best of our knowledge, this new 109 methodological approach proposed using a single composite model will be the only 110 attempt used in testing the EKC hypothesis in relevant literature. This alternative approach 111 of testing the EKC hypothesis and transmission mechanism can be shown in the following Therefore, we will try to test the EKC hypothesis in this methodological context for 50 US 119 states from 1990-2017 based on the latest available year data. The rationale of a state-level 120 empirical study is that US states have different levels of real GDP per capita, spending, CO2 121 emissions, and energy policies. These differences make the USA a unique sample country.

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Another advantage of sampling US states is that this country provides a wide range of data 123 at the state level for more detailed empirical results. The necessary conditions for testing 124 the EKC hypothesis through the Armey curve model are as follows: first, the Armey curve 125 must be validated for a sample US state. Second, the composite model must be significant 126 for the same US state. This means that the curve shape of the Armey model must be inverted 127 U-shaped. However, significant composite model can be either U-shaped or inverted U-128 shaped. If the composite model's curve is also inverted U-shaped, this will imply that the 129 EKC hypothesis is validated through the Armey curve hypothesis (Case 1 in Figure 4).

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Otherwise, significant but U-shaped curve will not validate this hypothesis through the  To some degree, this proposed methodological approach also enables US state policymakers

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The empirical model of this study was theoretically constructed based on Figure 3  respectively. EC is total energy consumption. According to the EKC hypothesis, the signs 203 for and are expected to be significantly positive and negative, respectively. If these two To determine the maximum (optimal) government spending level that will maximize (Case 220 1 in Figure 4) or minimize (Case 2 in Figure  The sufficient condition for maximization is / = 2 < 0 , so is expected 227 to be < 0. For data consisting of > 1 , is positive, so is expected to be > 0. Later, The value of = − in Eqn.4 will be the optimal CO2 emissions level for Eqn. (3).

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When we insert the value of Additionally, for Gα and Gτ tests, the null hypothesis of no cointegration is defined as H0: 282 pi=0 for all i, while the alternative hypothesis of cointegration is described as H1:pi<0 for at 283 least some i. Gα and Gτ test statistics are computed as shown below:

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After detecting the presence of cointegration in a panel data model, the next step is to     Test results in Table 3 indicate that all variables are integrated of order one (I(1)). This  Table 4.   and − + 2b + 4 < 0 (two inverted U-shaped curves: Case 1 in Figure 4). However, 349 the composite EKC hypothesis is not validated for Colorado, Georgia, and Indiana since <     for the policymakers who will have to choose between lower economic growth and cleaner 419 environment. However, they can determine a golden ratio that will ensure them sustainable-420 compatible economic and energy policies at a lower cost. From the same methodological 421 context, the policymakers of Colorado, Georgia, and Indiana will be able to determine their 422 maximum spending levels that will maximize the real GDP per capita and minimize CO2 423 emissions. Hence, they will know that additional spending after this maximum threshold 424 points will decrease real GDP per capita and increase CO2 emissions. This outcome may give 425 them an ideal (optimal) maximum spending level rather than creating a dilemma, as was the