Electricity consumption and economic growth in Nigeria: Evidence using causality in quantiles

1. Electricity consumption and economic growth in Nigeria: Evidence using causality in quantiles Olayeni O.R. Foye V. O Olaoye O. O.

2. Methodology • Original idea of causality is in terms of distribution, and we say variable Y does not Granger cause another variable X if where denotes the conditional distribution of variable Y

3. Most studies however concentrates on the mean regression of the d thereby indulging in central tendency for causality. BUT causality in mean will fail to capture the heterogeneity as well as distributional content of the regression. • Hence, the need to employ other techniques one of which is causality in quantiles

4. Quantile regression provides a better approximation to distribution since it divides the distribution into quantiles rather than focusing on the isolated moment of the distribution • C-in-Q applies QR to investigating causal effects

5. Motivation • The review of literature done by Payne (2010) on the relationship between electricity consumption and GDP indicates that all the studies reviewed have used one method or the other that focus basically on the mean. That is, they have used C-in-M. • No known study has employed C-in-Q • Using C-in-Q gives a global view of the distribution; C-in-M deals with an isolated moment and thwarts policy recommendations

6. Way forward • We need to substitute the distribution with the quantile approximation. Thus QR is given by (see Chuang et al, 2009) • This says variable X has no causal effects on variable Y in quantiles

7. Quantile regression method • Koenker and Basset (1978) propose an approach to doing QR and its applications are numerous e.gCAViaR (Engle and Manganelli, 2004). For causality in quantile (Hong et al and Chuang et al), we have: • where and

8. According to Koenker and Basset (1978): • where is a check function. That is the quantile estimator is that minimizes the objective function above.

9. Hypothesis • We test the following hypothesis • where is the selection matrix and is the estimated causal effects.

10. Wald test for the hypothesis • Chuang et al show that the hypothesis can be tested using the Wald statistic given by • and the sup-Wald statistic is

11. Computed critical sup-Wald

12. Our model • Dynamic model for causal effects of electricity on GDP • Dynamic model for causal effects of GDP on electricity

13. Optimal lag length

14. Quantile causal effects of electricity on GDP

15. Granger-Yoon decomposition • One-way causality questioned: G-Y decomposition: • and

16. Electricity and GDP decomposed

17. Optimal lag length for decomposed series

18. Quantile causal effects for decomposed series: Electricity on GDP

19. Two-way quantile causal effects confirmed

20. Still two-way quantile causal effects confirmed

21. Checking for symmetry about the median • Why would OLS fail to detect causality? Possibility of symmetry about the median

23. Conclusion • Causality runs from electricity consumption to economic activity and not the other way around at the aggregated level. • After decomposing the variables into positive and negative components we found that there is a two-way causal relation between the variables • These variables indicate the possibility of observing causal effects in the constituent parts when indeed the aggregate variables do not show any causation