The Shonkwiler–Yen two-step correction is widely used to address zero purchases in applied demand system estimation. Despite its influence, empirical applications differ substantially in how the first-stage participation equations are specified, how endogeneity is handled, whether theoretical restrictions are imposed, and how elasticities are computed. This paper examines the sensitivity of censored Quadratic Almost Ideal Demand System (QUAIDS) estimates to these implementation choices. Using quarterly county-level NielsenIQ Retail Scanner data on conventional milk, lactose-free milk, organic milk, plantbased milk alternatives, and ultra-filtered milk from 2014 to 2023, we compare a baseline censored QUAIDS specification with several alternative implementations. The results show that seemingly minor modeling choices can lead to economically meaningful differences in expenditure and price elasticity estimates. The findings underscore the importance of transparent reporting, careful first-stage specification, appropriate treatment of endogeneity, and consistent elasticity calculations in censored demand system applications.
