Reliable Statistical Inference with Synthetic Data from Large Language Models

This paper introduces a novel framework for conducting reliable statistical inference using synthetic data generated by large language models (LLMs), particularly in social science research. The authors propose a Generalized Method of Moments (GMM) estimator that effectively integrates both real human-annotated data and LLM-generated synthetic samples. This method aims to improve statistical efficiency and reduce the reliance on costly human labeling, especially in situations with limited labeled data. The research also compares this new GMM-based approach to existing debiasing methods, demonstrating its superior performance in leveraging synthetic data while maintaining statistical validity and providing strong theoretical guarantees.