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

Olayeni O.R.Foye V. O

Olaoye O. O.

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

),|()},{|( 11 tyttyt FF YXY

)|( ytF

• 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

• 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

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

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

)1,0(),|()),(|( 11 tyttyt QQ YXY

Quantile regression method

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

• where and

),()()()()|( 1111 βzxyz ttttytQ

],,1[ 111 ttt xyz ])(,)(),([)( β

• According to Koenker and Basset (1978):

• where

is a check function. That is the quantile estimator is that minimizes the objective function above.

,)(minarg)(ˆ1

11

T

tttyT βzβ

β

vvv )0( 1

)(ˆ β

Hypothesis

• We test the following hypothesis

• where is the selection matrix and is the estimated causal effects.

)1,0(,0)(ˆ)(ˆ:0 βH

)(ˆ β

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

]1,0[)],1(/[)(ˆ)(ˆ)(ˆ:)(1

ΩTWT

)(supsupW,,1

T iTniW

Computed critical sup-Wald

Table 2: Asymptotic critical values of the sup-Wald test on [0.05,0.95] quantilesq=1 q=2 q=3 q=4 q=5 q=6 q=7

1% 13.07 16.57 19.26 21.78 23.78 25.92 28.225% 9.75 12.77 15.31 17.52 19.56 21.59 23.43

10% 8.12 11.04 13.51 15.58 17.58 19.50 21.29Notes: The results are based on the Monte Carlo simulation that approximates the standard Brownian motions using a Gaussian random walk with 3000 i.i.d normal innovations replicated over 40000 iterations.

Our model

• Dynamic model for causal effects of electricity on GDP

• Dynamic model for causal effects of GDP on electricity

t

q

iiti

q

iitit LELYLY

11

)()()(

t

q

iiti

q

iitit LYLELE

11

)()()(

Optimal lag length

Table 3: Sup-Wald statisticLag G→E E→G

1 1.987 8.4682 4.110 3.9923 2.366 1.6004 4.801 3.7735 3.592 0.9956 3.394 2.3657 0.395 7.890

Quantile causal effects of electricity on GDP

Granger-Yoon decomposition

• One-way causality questioned: G-Y decomposition:

• and

t

jjjt LYLYILY

1

)0(

t

jjjt LYLYILY

1

)0(

Electricity and GDP decomposed

Optimal lag length for decomposed series

Table 4: Optimal lag length for the decomposed serieslag LY-→LE- LE-→LY- LY+→LE+ LE+→LY+ LY+→LE- LE-→LY+ LY-→LE+ LE+→LY-

1 8.253 0.710 5.212 3.599 6.974 3.891 3.649 0.1142 7.339 0.083 3.768 4.538 3.585 1.313 12.888 2.0603 1.940 0.073 1.396 2.814 2.139 3.902 4.276 2.5154 16.663 0.633 2.963 11.294 3.141 2.842 4.820 0.2055 1.675 0.139 3.549 1.109 2.939 5.926 1.906 5.6706 1.172 0.599 0.485 1.104 0.872 1.441 2.130 0.4427 3.150 2.460 1.309 1.781 6.466 6.392 0.423 1.709

Quantile causal effects for decomposed series: Electricity on GDP

Two-way quantile causal effects confirmed

Still two-way quantile causal effects confirmed

Checking for symmetry about the median

• Why would OLS fail to detect causality? Possibility of symmetry about the median

)5.0(ˆ2)1(ˆ)(ˆ)(ˆ iiii

Table ?: Testing symmetry of quantile causal effectPairs

gam1 gam2 gam3 gam4 Joint psi1 psi2 psi3 psi4 Joint psi1 psi2 Joint0.05 0.0000 0.0002 0.0000 0.0000 0.0019 0.0016 0.0003 0.0010 0.0005 0.0026 0.0000 0.0000 0.00050.10 0.0002 0.0005 0.0005 0.0000 0.0048 0.0038 0.0007 0.0024 0.0012 0.0061 0.0000 0.0000 0.00130.15 0.0028 0.0000 0.0005 0.0000 0.0075 0.0086 0.0023 0.0055 0.0032 0.0145 0.0002 0.0000 0.00310.20 0.0023 0.0002 0.0000 0.0001 0.0051 0.0170 0.0070 0.0028 0.0015 0.0205 0.0005 0.0036 0.00490.25 0.0032 0.0000 0.0000 0.0020 0.0072 0.0185 0.0098 0.0021 0.0023 0.0227 0.0021 0.0040 0.00420.30 0.0001 0.0002 0.0012 0.0027 0.0076 0.0153 0.0063 0.0026 0.0014 0.0187 0.0024 0.0048 0.00500.35 0.0005 0.0000 0.0016 0.0048 0.0068 0.0038 0.0095 0.0003 0.0014 0.0103 0.0012 0.0005 0.00120.40 0.0000 0.0000 0.0018 0.0044 0.0057 0.0015 0.0005 0.0000 0.0000 0.0016 0.0000 0.0021 0.00540.45 0.0000 0.0000 0.0035 0.0061 0.0069 0.0011 0.0018 0.0008 0.0000 0.0024 0.0000 0.0000 0.0002

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