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In health economics applications involving outcomes (y) and covariates (x), it is often the case that the central inferential problems of interest involve E[y|x] and its associated partial effects or elasticities. Many such outcomes have two fundamental statistical properties: y≥0; and the outcome y=0 is observed with sufficient frequency that the zeros cannot be ignored econometrically. This paper (1) describes circumstances where the standard two-part model with homoskedastic retransformation will fail to provide consistent inferences about important policy parameters; and (2) demonstrates some alternative approaches that are likely to prove helpful in applications.