This paper offers a new estimation approach for balancing statistical flexibility and economic regularity in structural econometric models. We focus our analysis on nonparametric demand systems for differentiated goods where such trade-offs are especially salient. Our framework is based on a quasi-Bayes model that transforms a sieve-based estimator of the inverse demand function into a quasi-likelihood, and then uses priors to regularize and enforce economic constraints. The induced quasi-posterior is defined over a complex domain which poses challenges for off-the-shelf sampling methods. We implement novel sampling procedures that (i) repose the heavily constrained target as the limit of a sequence of softly constrained targets, and then (ii) utilize Sequential Monte Carlo algorithms to push and filter samples through this sequence. We evaluate the performance of our approach using both simulations and retail scanner data. We find that our proposed quasi-Bayes framework can more effectively enforce constraints relative to previous methods and, by doing so, improves finite sample performance. Finally, we introduce an accompanying Julia package (NPDemand.jl) to help make nonparametric demand estimation more feasible in applied work.

Large language models (LLMs) have quickly become popular as labor-augmenting tools for programming, writing, and many other processes that benefit from quick text generation. In this paper we explore the uses and benefits of LLMs for researchers and practitioners who aim to understand consumer preferences. We focus on the distributional nature of LLM responses, and query the Generative Pre-trained Transformer 3.5 (GPT-3.5) model to generate hundreds of survey responses to each prompt. We offer two sets of results to illustrate our approach and assess it. First, we show that GPT-3.5, a widely-used LLM, responds to sets of survey questions in ways that are consistent with economic theory and well-documented patterns of consumer behavior, including downward-sloping demand curves and state dependence. Second, we show that estimates of willingness-to-pay for products and features generated by GPT-3.5 are of realistic magnitudes and match estimates from a recent study that elicited preferences from human consumers. We also offer preliminary guidelines for how best to query information from GPT-3.5 for marketing purposes and discuss potential limitations.