Language change is accelerated by language contact, especially by contact that occurs when a group of speakers shifts from one language to another. This has commonly been explained by linguistic innovation occurring during second language acquisition. This hypothesis is based on historical reconstructions of instances of contact and has not been formally tested on empirical data. In this paper, we construct an agent-based model to formalize the hypothesis that second language speakers are responsible for accelerated language change during language shift. We compare model predictions to a unique combination of diachronic linguistic and demographic data from Maputu, Mozambique. The model correctly predicts an increased proportional use of the novel linguistic variants during the period we study. We find that a modified version of the model is a better fit to one of our two datasets and discuss plausible reasons for this. As a general conclusion concerning typological differences between contact-induced and non-contact-induced language change, we suggest that multiple introductions of a new linguistic variant by different individuals may be the mechanism by which language contact accelerates language change.