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While joint models have been developed for many NLP tasks, the vast majority of event coreference resolvers, including the top-performing resolvers competing in the recent TAC KBP 2016 Event Nugget Detection and Coreference task, are pipeline-based, where the propagation of errors from the trigger detection component to the event coreference component is a major performance limiting factor. To address this problem, we propose a model for jointly learning event coreference, trigger detection, and event anaphoricity. Our joint model is novel in its choice of tasks and its features for capturing cross-task interactions. To our knowledge, this is the first attempt to train a mention-ranking model and employ event anaphoricity for event coreference. Our model achieves the best results to date on the KBP 2016 English and Chinese datasets.