Motivated by the facts that mobile terminals have a limited battery life, this paper presents a hierarchical game to model distributed joint power and channel allocation for multi-carrier energy efficient cognitive radio systems. A thorough analysis of the existence, uniqueness and characterization of the Stackelberg equilibrium is conducted. We proved that, at the Stackelberg equilibrium, each of the two users transmits on only one carrier depending on the fading channel gains. This results contrast with capacity-based approaches in which a certain number of carriers is exploited depending on the channel gains. Interestingly, we show that, for the vast majority of cases, introducing a certain degree of hierarchy in a multi-carrier system induces a natural coordination pattern where users have incentive to choose their transmitting carriers in such a way that they always transmit on orthogonal channels. Analytic results are provided for assessing and improving the performances in terms of energy efficiency between the non-cooperative game with synchronous decision makers and the proposed Stackelberg game.