This article presents a novel customer satisfaction (CS) estimation method that outputs both turn-level and call-level estimations simultaneously. Our key idea is to directly apply turn-level estimation results to call-level estimation and optimize them jointly; previous works treat both as being independent. Our proposal applies long short-term memory recurrent neural networks (LSTM-RNNs) to turn-level and call-level CS estimation to capture long-range sequential context in contact center calls. In addition, both networks are hierarchically stacked so as to use turn-level estimation results for call-level estimation directly. In order to learn the relationship between the two tasks, we also introduce joint optimization training to the stacked model. Several analyses of turn-level and call-level CS are provided on acted and real calls to support the proposed method. Experiments show that the proposed framework outperforms the conventional methods in both turn-level and call-level estimations.