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We study resource allocation for energy-efficient communication in multi-cell orthogonal frequency division multiple access (OFDMA) downlink networks with cooperative base stations (BSs). We formulate the resource allocation problem for joint BS zero-forcing beamforming (ZFBF) transmission as a non-convex optimization problem which takes into account the circuit power consumption, the limited backhaul capacity, and the minimum required data rate. We transform the considered problem in fractional form into an equivalent optimization problem in subtractive form, which enables the derivation of an efficient iterative resource allocation algorithm. In each iteration, a low-complexity suboptimal semi-orthogonal user selection policy is computed. Besides, by using the concept of perturbation function, we show that in the considered systems under some general conditions, the duality gap with respect to the power optimization variables is zero despite the non-convexity of the primal problem. Thus, dual decomposition can be used in each iteration to derive an efficient closed-form power allocation solution for maximization of the energy efficiency of data transmission (bit/Joule delivered to the users). Simulation results illustrate that the proposed iterative resource allocation algorithm converges in a small number of iterations, and unveil the trade-off between energy efficiency, network capacity, and backhaul capacity: (1) In the low transmit power regime, an algorithm which achieves the maximum spectral efficiency may also achieve the maximum energy efficiency; (2) a high spectral efficiency does not necessarily result in a high energy efficiency; (3) spectral efficiency is always limited by the backhaul capacity; (4) energy efficiency increases with the backhaul capacity only until the maximum energy efficiency is achieved.