Open access (OA) has mostly been studied by relying on publication data from selective international databases, notably Web of Science (WoS) and Scopus. The aim of our study is to show that it is possible to achieve a national estimate of the number and share of OA based on institutional publication data providing a comprehensive coverage of the peer-reviewed outputs across fields, publication types and languages. Our data consists of 48,177 journal, conference and book publications from 14 Finnish universities in 2016-2017, including information about OA status, as self-reported by researchers and validated by data-collection personnel through their Current Research Information System (CRIS). We investigate the WoS, Scopus and DOI coverage, as well as the share of OA outputs between different fields, publication types, languages, OA mechanisms (gold, hybrid and green), and OA information sources (DOAJ, Bielefeld list and Sherpa/Romeo). We also estimate the role of the largest international commercial publishers compared to the not-for-profit Finnish national publishers of journals and books. We conclude that institutional data, integrated at national and international level, provides one of the building-blocks of a large-scale data infrastructure needed for comprehensive assessment and monitoring of OA across countries, for example at the European level.