Valid Inference with Imperfect Synthetic Data (arxiv.org)

Researchers introduce a new, practical estimator that lets practitioners combine imperfect synthetic data produced by large language models with real data while still obtaining statistically valid inferences. Framing the problem in a generalized method-of-moments (GMM) setup, the paper gives a hyperparameter-free procedure with provable guarantees that works even when synthetic samples are biased or only partially accurate. This addresses a growing need in computational social science and human-subjects work, where LLMs are increasingly used to generate full synthetic survey responses or simulated units in low-data regimes. The key technical insight is that interactions between the moment residuals from synthetic and real data — i.e., when one set of residuals helps predict the other — can be exploited to reduce estimation error and improve identification of the target parameter. The estimator uses this covariance structure within the GMM framework to correct for imperfections in the generated data without tuning. The authors validate finite-sample performance across several social-science-style tasks and report large empirical gains versus naive pooling or earlier label-only approaches. The result is a principled, theoretically grounded tool for researchers wanting to augment limited datasets with model-generated examples while preserving valid uncertainty quantification and inference.