Emotion cause identification aims at identifying the potential causes that lead to a certain emotion expression in text. Several techniques including rule based methods and traditional machine learning methods have been proposed to address this problem based on manually designed rules and features. More recently, some deep learning methods have also been applied to this task, with the attempt to automatically capture the causal relationship of emotion and its causes embodied in the text. In this work, we find that in addition to the content of the text, there are another two kinds of information, namely relative position and global labels, that are also very important for emotion cause identification. To integrate such information, we propose a model based on the neural network architecture to encode the three elements ($i.e.$, text content, relative position and global label), in an unified and end-to-end fashion. We introduce a relative position augmented embedding learning algorithm, and transform the task from an independent prediction problem to a reordered prediction problem, where the dynamic global label information is incorporated. Experimental results on a benchmark emotion cause dataset show that our model achieves new state-of-the-art performance and performs significantly better than a number of competitive baselines. Further analysis shows the effectiveness of the relative position augmented embedding learning algorithm and the reordered prediction mechanism with dynamic global labels.