In this paper we derive the exact distribution of the indirect least squares estimator of the coefficients of the Cobb-Douglas production function within the context of a stochastic production model ...

While this is an improvement on the basic Cobb-Douglas model, it still implies logically that the contribution of energy to production could be nil: just set its exponent g to zero.

S. AQDAS ALI KAZMI, A Note on Cobb-Douglas Production Function, Pakistan Economic and Social Review, Vol. 10, No. 2 (DECEMBER 1972), pp. 239-252 ...