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Student retention and timely graduation are critical for the sustainability of four-year institutions. This study investigates the role of curricular complexity in influencing degree completion. Using a dataset from 26 institutions and 208 disciplines, we employed a cross-classified model for predicting graduation based on curricular complexity, characterized by systems of prerequisite dependencies among courses. As the data structure (students nested in program which are cross-classified within discipline and institution) is too complicated to model directly, we used simulations to facilitate significance testing of program-level predictors. Our findings reveal that curricular complexity impacts graduation overall and negatively impacts men and certain minorities. This research underscores the need for curricular reforms to enhance equity and support timely graduation.