# A Dynamic Causality Study between Electricity Consumption and Economic Growth for Global Panel: Econometric Methodology

The empirical investigation of the dynamic causal relationship between electricity consumption and economic growth based on modern econometric techniques involves the following three steps. At the first step whether each panel variable contains a unit root is examined. If the variables contain a unit root, the second step is to test whether there is a long run-cointegration relationship between the panel variables. If a long-run relationship between the variables is found, the final step is to estimate panel vector error correction model in order to infer the Granger causal relationship between the variables. Finally using the GMM technique the long-run and short-run elasticities of economic growth with respect to electricity consumption are estimated for five different panels.
Panel Unit Root Tests
Since none of the panel unit root tests is free from some statistical shortcomings in terms of size and power properties, so it is better for us to perform several unit root tests to infer an overwhelming evidence to determine the order of integration of the variables. In this paper three panel unit root tests: Im, Peasaran and Shin (IPS, 2003), Maddala and Wu, and Choi tests are applied. The IPS and MW tests are based on the assumption of cross-sectional independence. This assumption is likely to be violated for the income variable. It is found by Banerjee, Cockerill and Russell that these tests have poor size properties and have a tendency to over-reject the null hypothesis of unit root if the assumption of cross-section independence is not satisfied. Choi is derived another test statistic to solve this problem. so
Both ai and p in equation and are allowed to vary across countries. The null hypothesis to be tested is that each series in the panel contains a unit root, i. e.
There are two stages for constructing the t-bar statistic which is proposed by Im, Pesaran and Shin. At the first stage the average value of the individual ADF t-statistic for each of the countries in the sample is calculated which is given by— 1 n tnT    1 tiT (pi)    n i=1 i where t (p ) is the calculated ADF test statistic for country i of the panel (i = 1, 2,……,n). The second step is to calculate the standardized t-bar statistic which is given by; ^ It – I E(t1Tpi Z- = L. =1    J ~ N nT    in-1 var(tITpi pi=1 where n is the size of the panel, which indicates the no. of countries, E(tiT(pi)) and var(tiT(pj)) are provided by IPS for various values of T and p. However, Im, et al. suggested that in the presence of cross-sectional dependence, the data can be adjusted by demeaning and that the standardized demeaned t-bar statistic converges to the standard normal in the limit.
Maddala and Wu proposed a Fisher-type test which combines the p-values from unit root tests for each cross-section i. The test is non-parametric and has a chi-square distribution with 2n degrees of freedom, where n is the number of countries in the panel. The test statistic is given. The Maddala and Wu test has the advantage over the Im, et al. test that it does not depend on different lag lengths in the individual ADF regressions. Maddala and Wu performed Monte Carlo simulations showing that their test is superior to that proposed by Im, et al.. In addition Choi derived another test statistic which is given.

Table-2 IPS, MW , and Choi panel unit root tests results for five panels

 IPS Test Prob. MW Test Prob. Choi Test Prob. [High Income Panel; Constant and Trend Terms are Included in the Model [Level Form] lnPGDP -1.4741 0.0712 46.8343 0.8927 1.3456 0.9108 lnEC 0.74169 0.7709 67.71 52 0.2307 1.3273 0.9078 Model w ith Only Cons tant Term [ Fir ■st Difference d Form] AlnPGDP -18.5510* 0.0000 447.422* 0.0000 -17.099* 0.0000 AlnEC -15.1447* 0.0000 365.974* 0.0000 – 1 4.7413* 0.0000 Upper Middle Income Panel; Constant and Trend Terms are Included in the Model [Level Form] lnPGDP 0.18274 0. 5729 26.9947 0.9422 1.36183 0.9134 lnEC -1.64503 0.0500 43.4734 0.3257 -0.7331 0.2318 Model with Only Constant Term [ First Differenced Form] AlnPGDP -19.3034* 0.0000 390.064* 0.0000 -16.5037* 0.0000 AlnEC -13.8171* 0.0000 291.839* 0.0000 -13.5598* 0.0000 Lower Middle Income Panel; Constant and Trend Terms are Included in the Model [Level Form] lnPGDP 2.1013 0. 9822 16.8526 0.9995 3.54398 0.9998 lnEC -2.4278* 0.0076 48.5668 0.1660 -1.9675* 0.0246 Model with Only Constant Term [ First Differenced Form] AlnPGDP -18.7508* 0.0000 397.672* 0.0000 -16.6208* 0.0000 AlnEC -19.3710* 0.0000 419.841* 0.0000 -16.759* 0.0000 Low Income Panel; Constant and Trend Terms are Included in the Model [Level Form] lnPGDP 1.5828 0. 9433 8.9726 0.7053 2.4071 0.9920 lnEC -3.5461* 0.0002 32.5079* 0.0012 -3.3349* 0.0004 Model with Only Constant Term [ First Differenced Form] AlnPGDP -10.4517* 0.0000 120.762* 0.0000 -8.6467* 0.0000 AlnEC -12.6833* 0.0000 146.074* 0.0000 -10.5931* 0.0000 Global Panel; Constant and Trend Terms are Included in the Model [Level Form] lnPGDP 0.0592 0. 5236 99.6542 0.9997 4.0383 1.000 lnEC -2.6339* 0.0042 192.262* 0.0 1 50 -1.4885 0.0683 Model with Only Constant Term [ First Differenced Form] AlnPGDP -34.1038* 0.0000 1401.61* 0.0000 -31.1291* 0.0000 AlnEC -30.1175* 0.0000 1265.29* 0.0000 -28.2836* 0.0000

Table-3 Kao Cointegration Test Results for Five Panels

 Different Panels Kao cointegration test Probability High income panel -7.1061* 0.0000 Upper middle income panel -4.1765 * 0.0000 Lower middle income panel -0.4343 0.3320 Low income panel 0.1025 0.4592 Global panel -5.9069* 0.0000

Table -4 Results of the Johansen based Panel Conintegration Test for Five Panels

 Number of Coint. Eqn. Model 1 Trace Tes t Prob. Max-Eigen Value Test Prob. Model 2 Trace Test Prob. Max-Eigen Value Test Prob. High Income Panel None 298.3* 0.0000 289.4* 0.0000 252.0* 0.0000 222.3* 0.0000 At Most 1 93.67* 0.0035 93.67* 0.0035 92.65* 0.0044 92.65* 0.0044 Upper Middle Income Panel None 146.0* 0.0000 140.4* 0.0000 143.8* 0.0000 119.6* 0.0000 At Most 1 60.37* 0.0203 60.37* 0.0000 63.79* 0.0098 63.79* 0.0098 Lower Middle Income Panel None 108.8* 0.0000 112.3* 0.0000 104.3* 0.0000 103.1* 0.0000 At Most 1 39.67 0.4849 39.67 0.4849 36.03 0.6377 39.03 0.6377 Low Income Panel None 47.61* 0.0000 66.69* 0.0000 54.31* 0.0000 42.09* 0.0000 At Most 1 16.42 0.1730 16.42 0.1730 24.60** 0.0168 24.60** 0.0168 Global Panel None 606.60* 0.0000 588.5* 0.0000 554.4* 0.0000 487.0* 0.0000 At Most 1 210.1* 0.0013 210.1* 0.0013 217.3* 0.0004 217.3* 0.0004

Table-5 Panel Granger F-test Results

 Dependent Variables AlnEC AlnPGDP ECM High Income Panel [ VEC Model] AlnPGDP 6.4359* (0.0000) -2.80476* (0.0051) AlnEC 31.6363* (0.0000) 1.87976** (0.0603) Upper Middle Income Panel [VEC Model] AlnPGDP 1.9366** (0.0859) -4.94594* (0.0000) AlnEC 6.0683* (0.0000) 2.87282* (0.0042) Global Panel [VEC Model] AlnPGDP 2.4059 * (0.0000) -2.54997* (0.0108) AlnEC 9.5215*(0.0000) 6.19110* (0.0000) Lower Middle Income Panel [VAR Model] AlnPGDP 0.3695 (0.775019) AlnPGDP 0.6602 (0.5175) lnEC 0.7740 (0.4621)

Table-6 Panel Long-run and Short-run Elasticities

 Different Panels Long-run Elasticity [ lnPGDP is the Dependent variable] lnEC AlnEC ECM Coefficient t-Test Coefficient t-test Coefficient t-Test High income panel 0.5958* 12.1476 0.1429* 3.8152 -0.0072 -1.5674 Upper middle income 0.6027* 7.9218 0.2122* 5.5597 -0.0211* -6.3097 Global panel 0.8125* 48.9068 0.1336* 7.2043 0.0009 0.4544 Lower middle income 0.2871* 8.8280 0.1288* 5.0831 Low income panel 0.2145* 17.3557 0.00278* 4.4163