There is growing evidence for the impact of arts engagement on later life cognition. However, confounding by socioeconomic factors may have led to an overestimation of this association. We analyzed data from 4,344 older adults in the Wisconsin Longitudinal Study. We measured participatory (e.g. painting, making music, crafts) and receptive (e.g. concert, play, museum) arts engagement separately. Participants completed six neurocognitive tests measuring two distinct domains of cognitive function (episodic/working memory and executive function/language) concurrently and seven years later. We used inverse probability of treatment weighting (IPTW) to remove confounding by a range of demographic and socioeconomic factors. Engaging in participatory or receptive arts for up to one hour per week (but not more frequently) was associated with better subsequent executive function/language. Similarly, engaging in receptive arts activities for up to three hours per week (but not more frequently) was associated with better subsequent episodic/working memory. These effects were of similar sizes to doing vigorous physical activity for up to one hour per week. However, our findings also highlight key methodological issues when exploring the relationship between arts engagement and cognition that should be considered in future studies, including measurement bias, life-course stage, length of follow-up, variation in outcomes, attrition, and missing data.