Table 3 Simulated power results given \(\sigma \), \(\beta _{1,j}\) , \(\beta _{2,j}\) and \(\beta _{3,j}\) for the homologous and standard cross-sectional hypotheses.

\(\sigma \)	\(\beta _{1,j}\)	\(\beta _{2,j}\)	\(\beta _{3,j}\)	Homologous	t Test	\(\bar{\hat{\rho }}_{0,j}\)	\(\bar{\hat{\rho }}_{1,j}\)
\(\sigma \)	\(\beta _{1,j}\)	\(\beta _{2,j}\)	\(\beta _{3,j}\)	Power	Power	\(\bar{\hat{\rho }}_{0,j}\)	\(\bar{\hat{\rho }}_{1,j}\)
0.4	0	0	0	0.05	0.05	0	0
0.4	0	0	0.5	0.05	0.05	0	0.73
0.4	0	0	1	0.05	0.06	0	0.91
0.4	0	0.5	0	0.05	0.05	0.73	0.73
0.4	0	0.5	0.5	0.05	0.05	0.73	0.9
0.4	0	0.5	1	0.05	0.05	0.74	0.95
0.4	0	1	0	0.05	0.05	0.9	0.9
0.4	0	1	0.5	0.05	0.05	0.9	0.95
0.4	0	1	1	0.05	0.05	0.9	0.97
0.4	0.5	0	0	0.55	0.57	0	0
0.4	0.5	0	0.5	0.54	0.39	0.01	0.74
0.4	0.5	0	1	0.53	0.24	0	0.9
0.4	0.5	0.5	0	0.54	0.31	0.74	0.73
0.4	0.5	0.5	0.5	0.54	0.21	0.74	0.91
0.4	0.5	0.5	1	0.53	0.17	0.73	0.95
0.4	0.5	1	0	0.54	0.17	0.9	0.9
0.4	0.5	1	0.5	0.54	0.14	0.9	0.95
0.4	0.5	1	1	0.54	0.12	0.9	0.97
0.4	1	0	0	0.96	0.97	0	0
0.4	1	0	0.5	0.96	0.85	0	0.73
0.4	1	0	1	0.96	0.56	0	0.9
0.4	1	0.5	0	0.96	0.72	0.73	0.73
0.4	1	0.5	0.5	0.96	0.5	0.74	0.9
0.4	1	0.5	1	0.97	0.35	0.74	0.95
0.4	1	1	0	0.97	0.39	0.9	0.9
0.4	1	1	0.5	0.97	0.29	0.91	0.95
0.4	1	1	1	0.96	0.23	0.91	0.97

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