We investigate energy efficiency (EE) optimization for single-cell massive multiple-input multiple-output (MIMO) downlink transmission with only statistical channel state information (CSI) available at the base station. We first show that beam domain transmission is favorable for energy efficiency in the massive MIMO downlink, by deriving a closed-form solution for the eigenvectors of the optimal transmit covariance matrix. With this conclusion, the EE optimization problem is reduced to a real-valued power allocation problem, which is much easier to tackle than the original large-dimensional complex matrix-valued precoding design problem. We further propose an iterative water-filling-structured beam domain power allocation algorithm with low complexity and guaranteed convergence, exploiting the techniques from sequential optimization, fractional optimization, and random matrix theory. Numerical results demonstrate the near-optimal performance of our proposed statistical CSI aided EE optimization approach.