Large language models (LLMs) are increasingly used to simulate human behavior, but common practices to use LLM-generated data are inefficient. Treating an LLM's output ("model choice") as a single data point underutilizes the information inherent to the probabilistic nature of LLMs. This paper introduces and formalizes "model belief," a measure derived from an LLM's token-level probabilities that captures the model's belief distribution over choice alternatives in a single generation run. The authors prove that model belief is asymptotically equivalent to the mean of model choices (a non-trivial property) but forms a more statistically efficient estimator, with lower variance and a faster convergence rate. Analogous properties are shown to hold for smooth functions of model belief and model choice often used in downstream applications. The authors demonstrate the performance of model belief through a demand estimation study, where an LLM simulates consumer responses to different prices. In practical settings with limited numbers of runs, model belief explains and predicts ground-truth model choice better than model choice itself, and reduces the computation needed to reach sufficiently accurate estimates by roughly a factor of 20. The findings support using model belief as the default measure to extract more information from LLM-generated data.

翻译：大型语言模型（LLM）越来越多地用于模拟人类行为，但当前使用LLM生成数据的常见做法效率低下。将LLM的输出（“模型选择”）视为单一数据点，未能充分利用LLM概率性质所固有的信息。本文引入并形式化了“模型信念”——一种源自LLM词元级概率的度量，它能在单次生成运行中捕获模型对选择备选项的信念分布。作者证明了模型信念渐近等价于模型选择的均值（这是一个非平凡性质），但构成了一个统计效率更高的估计量，具有更低的方差和更快的收敛速率。类似性质也被证明适用于下游应用中常用的模型信念与模型选择的平滑函数。作者通过一项需求估计研究展示了模型信念的性能，其中LLM模拟了消费者对不同价格的反应。在运行次数有限的现实场景中，模型信念比模型选择本身能更好地解释和预测真实模型选择，并将达到足够准确估计所需的计算量减少了约20倍。这些发现支持将模型信念作为默认度量，以从LLM生成的数据中提取更多信息。