The data were comprised of annual information from 2001 to 2016. Nineteen high-income countries were selected for the study. In this chapter, we studied the causal relationships of energy–growth nexus, domestic credit, and environmental sustainability in two ways, namely (1) the bivariate relation between variables and (2) the elaboration of a PVAR with the performance of the Granger causality test. António Cardoso Marques, in The Extended Energy-Growth Nexus, 2019 6.5 Conclusion > grangertest(GDP ~ DEF,order = 2,na.action = na.omit) > grangertest(DEF ~ GDP,order = 2,na.action = na.omit) Therefore, one can conclude that there is unidirectional causality from GDP Deflator growth (DEF) to real GDP growth (GDP) (similar results are obtained with four lags, not reported here). On the other hand, lagged values of GDP in the DEF equation are not statistically significant ( F = 0.386, P-value = 0.68), so GDP does not Granger cause DEF. Since, lagged values of DEF in the GDP equation are statistically significant as a group ( F value of 9.96, P-value = 0.00015), DEF Granger causes GDP. If the lagged values of DEF are statistically significantly different from zero, then DEF Granger causes GDP. Granger causality tests can be done by estimating two equations for each variable: one with the lags of both variables (in this case GDP and DEF), and the other one with only the lagged values of the dependent variable (GDP). Granger causality tests support this finding. Therefore, one can argue that a higher inflation (measured with GDP deflator) precedes a lower real GDP growth. These results suggest that, in general, the growth in GDP Deflator precedes real GDP growth with a relatively high negative correlation. The correlation is higher if the GDP Deflator is lagged up to five periods (close to negative 0.6 at lags 3 and 4). For example, with both variables at zero lags, the correlation is negative 0.39. Cross-correlations help to see how two variables are related with lags. It is important to find out how these correlations change with lags in one of the variable. Simple correlation gives the degree of the relationship of two variables at the same time period.
Both variables seem to have deterministic trends. Real GDP is positively related to time ( r = 0.50), and the GDP Deflator is negatively related to time (− 0.66). Mariano, Suleyman Ozmucur, in Handbook of Statistics, 2020 3.2.4 Correlations and cross-correlations: GDP and GDP deflatorĪ simple correlation matrix indicates that the correlation between GDP and Deflator is negative 0.39.
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