Event Causality Extraction (ECE) aims to extract the cause-effect event pairs from the given text, which requires the model to possess a strong reasoning ability to capture event causalities. However, existing works have not adequately exploited the interactions between the cause and effect event that could provide crucial clues for causality reasoning. To this end, we propose an Implicit Cause-Effect interaction (ICE) framework, which formulates ECE as a template-based conditional generation problem. The proposed method captures the implicit intra- and inter-event interactions by incorporating the privileged information (ground truth event types and arguments) for reasoning, and a knowledge distillation mechanism is introduced to alleviate the unavailability of privileged information in the test stage. Furthermore, to facilitate knowledge transfer from teacher to student, we design an event-level alignment strategy named Cause-Effect Optimal Transport (CEOT) to strengthen the semantic interactions of cause-effect event types and arguments. Experimental results indicate that ICE achieves state-of-the-art performance on the ECE-CCKS dataset.