Despite their widespread adoption, neural conversation models have yet to exhibit natural chat capabilities with humans. In this research, we examine user utterances as causes and generated responses as effects, recognizing that changes in a cause should produce a different effect. To further explore this concept, we have compiled and expanded upon a new dataset called CausalDialogue through crowd-sourcing. This dataset includes multiple cause-effect pairs within a directed acyclic graph (DAG) structure. Our analysis reveals that traditional loss functions struggle to effectively incorporate the DAG structure, leading us to propose a causality-enhanced method called Exponential Maximum Average Treatment Effect (ExMATE) to enhance the impact of causality at the utterance level in training neural conversation models. To evaluate the needs of considering causality in dialogue generation, we built a comprehensive benchmark on CausalDialogue dataset using different models, inference, and training methods. Through experiments, we find that a causality-inspired loss like ExMATE can improve the diversity and agility of conventional loss function and there is still room for improvement to reach human-level quality on this new dataset.