We propose STAR, a structure-to-text data generation method for complicated structure prediction tasks that first generates complicated event structures (Y) and then generates input passages (X), all with Large Language Models. We further reduce errors and improve data quality through self-reflection error identification and self-refinement with iterative revision. We show that the data generated by STAR significantly improves the performance of low-resource event extraction and relation extraction tasks, even surpassing the effectiveness of human-curated data.