The causal relationship between renewable energy and economic growth in the US

The result of drawing is a bunch of values which form a posterior distributions for ,, and other coefficientsin the VECM. The means of the obtained posterior distributions could be considered as the coefficient values.

In the last part of the analysis, the orthogonal impulse response functions with the 90% confidence interval are constructed on the basis of the estimated model.This instrument is important because it allows us to observe a continuous change of a particular variable over the given period after response to shocks in another variable of interest. The reaction of variables in Orthogonalised IRF is clean from the system of equations' noise, in which obtained equations' coefficients are influenced by all variables. A horizon chosen is equal to 20 (), because in this study case such a period gives information about the variable behavior sufficiently. Impulse response functions are produced by using the VAR model

, (12)

where , is the lag order, is the matrix of coefficients, is a structural coefficients indicating the bivariate correlation between observed variables, .

The impulse responses are calculated through recursion equation:

, (13)

where is the index for each forecast step, ; the initial value of is . Orthogonalised impulse responses are calculated as

, (14)

where is the lower triangular Choleski decomposition of ; is considered to be an identity matrix (Pesaran & Shin, 1998).

5. Results

The first step of the algorithm was determining the optimal lag order.

The AIC and SIC showed that the 7 lag order was optimal.

The next step was the implementation of the stationarity augmented Dickey-Fuller test with constant and trend.

The results, which are shown in Table 4, indicate that all variables are stationary in the first difference.

Table 4. Augmented Dickey-Fuller test results

Note: the specification of the Augmented DF test is one with constant and trend, and with the 7 lag order.

The Johansen cointegration procedure with trend and 7 lag order was the following step of the analysis. The Johansen cointegration procedures with other specifications also were carried out, but the results occurred to be the same. Since the test statistics is greater than the critical values for the hypothesis, the hypothesis about existence of one long-run relationship between the variables was confirmed. The results for cointegration test are shown in Table 5.

Table 5. Johansen cointegration procedure results

After conducting the necessary tests, the Bayesian VECM has been estimated, with non-informative prior and the initial values from Table 3.For its computation 15000 iterations have been carried out. The resulted coefficients are the means of total draws, produced by collapsed Gibbs sampler. The coefficients for and quarters are shown in Table 6. The long-run coefficients of are shown in equation (15). The rest of the coefficients are given in the Appendix.

Table 6. The coefficients for and seasonal dummies

, (15)

After the Bayesian vector error correction model has been estimated, the Orthogonal Impulse Response Functions between Consumption of renewable energy and economic growth have been constructed on the basis of the model. They are shown in Figure 11.

Figure 11 Orthogonal Impulse Response Functions for GDP and Non-Renewable Energy consumption

As can be seen from the figure, there are no significant results indicating a causal relationship between analyzed variables, so that `theneutrality hypothesis' has been confirmed. Apart from it, the Orthogonalised impulse response functions have been constructed for non-renewable energy consumption and GDP too. The results are illustrated in the Figure 12.

Figure 12 Orthogonal Impulse Response Functions for GDP and Non-Renewable Energy consumption

As can be seen from the figure, there is a unidirectional positive causality running from non-renewable energy consumption to GDP in the first year. As for GDP, it has no effect on non-renewable energy consumption.

Conclusions

Overall, the analysis of the problem has been carried out. The results indicated that there is no causal relationship between renewable energy consumption and economic growth. Such a result is consistent with the result of the study, in which Toda-Yamamoto causality test was employed (Payne, 2009). The absence of causality could indicate that the development of renewable energy sources could not enhance economic growth in the short-run period. However, the development of renewable energy sources also could not undermine economic growth, so the transition towards renewable energy consumption potentially could be an appropriate option for the transformation of the energy sphere.

The absence of a causal relationship may be attributable to the presence of nonrenewable energy consumption in the model, which along with renewable energy consumption is analyzed. Therefore, in the further analysis the effect of nonrenewable energy consumption should be taken into consideration, because of its possible overlapping property. Along with analyzed variables, there are other factors that could be included, like technology development, the investment rate, institutional and social indicators.

Overall, this study contributes to the present literature on the causal relationship between renewable energy consumption and economic growth. A similar analysis could be done also for other countries, which dispose of much less information about their macroeconomic indicators. The scientific novelty is the first application of the Bayesian inference to this problem. However, the limitation of the study is the fact that the latest specification of BVEC Mapply only normal distribution for its priors. Besides, the Bayesian inference is supposed to be more subjective because of priors, which contains the researcher's consideration about phenomena.

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Appendix 1

Table 7. Descriptive Statistics for Variables in Natural Logarithms, 1973Q1-2018Q3

Appendix 2

Table 8. Mean of the parameters draws for differenced lagged endogenous variables

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