The English definite and indefinite articles (also known as determiners) are a useful index of early morphosyntactic productivity in children's speech, and give evidence about children's representation of syntactic abstractions. Previous work (i.e. Pine and Lieven, 1997) used a measure of productivity that shows a strong sensitivity to sample size and does not account for the relationship between adult input and children's learning. In this paper, we develop a more robust metric by employing a hierarchical Bayesian model to characterize the degree of generalization implicit in observed determiner usage. By inferring parameters for a generative model over longitudinal corpora, we measure the trajectory of grammatical category abstraction. Our results are consistent with the hypothesis that child learners exhibit adult-like patterns of generalization quite early in the acquisition of determiners.