Access to research data is a critical feature of an efficient, progressive, and ultimately self-correcting scientific ecosystem. But the extent to which in-principle benefits of data sharing are realized in practice is unclear. Crucially, it is largely unknown whether published findings can be reproduced by repeating reported analyses upon shared data ("analytic reproducibility"). To investigate, we conducted an observational evaluation of a mandatory open data policy introduced at the journal Cognition. Interrupted time-series analyses indicated a substantial post-policy increase in data available statements (104/417, 25% pre-policy to 136/174, 78% post-policy), and data that were in-principle reusable (23/104, 22% pre-policy to 85/136, 62%, post-policy). However, for 35 articles with in-principle reusable data, the analytic reproducibility of target outcomes related to key findings was poor: 11 (31%) cases were reproducible without author assistance, 11 (31%) cases were reproducible only with author assistance, and 13 (37%) cases were not fully reproducible despite author assistance. Importantly, original conclusions did not appear to be seriously impacted. Mandatory open data policies can increase the frequency and quality of data sharing. However, suboptimal data curation, unclear analysis specification, and reporting errors can impede analytic reproducibility, undermining the utility of data sharing and the credibility of scientific findings.