Analyzing long-term empirical interactions between renewable energy generation, energy use, human capital, and economic performance in Pakistan

Table 3 The results of the Ng-Perron unit root test

Variables	Constant				Constant +trend				No (constant +trend)
Variables	MZ_α	MZ_t	MSB	MPT	MZ_α	MZ_t	MSB	MPT	MZ_α	MZ_t	MSN	MPT
EG_R (1)*	− 1.194	− 0.808	0.860	7.054	− 4.016	− 1.232	0.481	8.629	− 3.031	− 0.247	0.518	9.614
EU_A (1)*	− 0.851	− 0.251	0.711	5.361	− 0.908	− 0.946	0.543	7.175	− 0.076	− 0.038	0.580	8.160
EP (1)*	− 1.078	− 0.014	0.522	5.698	− 16.122	− 1.665	0.216	6.739	− 15.137	− 0.680	0.254	7.724
HC_IN (1)*	− 3.945	− 0.295	0.983	8.293	− 2.345	− 1.138	0.671	9.139	− 1.360	− 0.153	0.708	10.124
ΔEG_R (0)*	− 9.121	− 2.406	0.173	3.793	− 23.942	− 2.542	0.179	4.655	− 22.957	− 1.557	0.217	5.640
ΔEU_A (0)*	− 13.911	− 1.566	0.209	3.279	− 37.600	− 3.386	0.151	3.456	− 36.615	− 2.401	0.188	4.441
ΔEP (0)*	− 13.689	− 1.713	0.221	2.692	− 19.023	− 2.177	0.195	5.539	− 18.038	− 1.192	0.233	6.524
ΔHC_IN (0)*	− 10.156	− 0.999	0.153	1.862	− 27.775	− 6.334	0.083	2.449	− 26.790	− 5.349	0.121	3.434
Ng-Perron critical value 5%	− 7.115	− 0.995	0.270	4.155	− 16.315	− 1.925	0.205	6.465	− 15.330	− 0.940	0.243	7.450

MZ_α modified version of the Phillips (1987) Z_α test, MZ_t modified version of the Phillips-Perron (1988) Z_t test, MSB the Perron and Ng (1996) spectral density test, Modified MPT modified feasible point optimal test, EG_R renewable energy generation, EU_A aggregated energy use, EP economic performance, HC_IN human capital index