Birnbaum's research at the Stockholm Resilience Centre focuses on environmental ethics, international justice, and the link between standards of legitimacy and compliance with environmental regulations. His contribution to the project Regime Shifts in the Baltic Sea Ecosystem, funded by Formas, aims to shed light on some of the key conditions for successful governance structures to meet environmental targets.

These efforts are mainly focused on two areas of research. Firstly, he is developing a theoretical framework for the assignment of responsibility for eutrophication in the Baltic Sea. How should the required nutrient reductions be allocated between the countries affected? Which principles could articulate our moral intuitions in this complex issue, and help to guide our debates and decisions in these matters? This aspect of his work serves to provide a foundation for examining the question of fairness in the allocation of burdens, and to clarify the moral bases of the competing claims at stake. Secondly, Birnbaum examines rival conceptions of political legitimacy in the context of fisheries management. When and why do institutions and policies for sustainable fisheries fail?

The relevance and importance of perceived legitimacy for key agents' compliance with regulations is now broadly recognized in the literature. On closer scrutiny, however, the interpretation of these connections in existing empirical research, and the political prescriptions derived from it, harbours many different and sometimes diverging notions of legitimacy. So, which aspects of legitimacy seem to matter the most to compliance?

By drawing on the theoretical literature on political legitimacy, Birnbaum's research seeks to contribute to a more nuanced and precise understanding of the linkages between legitimacy deficits and noncompliance with environmental regulations.

Birnbaum was previously a visiting graduate, with a scholarship from STINT, at the Department of Politics and International Relations, University of Oxford, during six months in 2006-2007. He was a Postdoctoral Fellow at the Hoover Chair of Economic and Social Ethics, Catholic University of Louvain, in the fall of 2008, and at the Stein Rokkan Centre for Social Studies in Bergen (within the framework of the Nordic Centre of Excellence, NordWel) during five months in 2009 and 2010. More recently, Birnbaum was a Fellow at the Swedish Collegium for Advanced Study in Uppsala (in the fall of 2011).
 
He is the author of Basic Income Reconsidered: Social Justice, Liberalism, and the Demands of Equality (Palgrave Macmillan, 2012).

Birnbaum's other publications have appeared in Politics, Philosophy and Economics, Critical Review of International Social and Political Philosophy (CRISPP), Mind, Basic Income Studies, Tidsskrift for velferdsforskning, Statsvetenskaplig tidskrift, Tidskrift för politisk filosofi, and several edited volumes.

His article in CRISPP was awarded the essay prize for "the best article published in volume 132010".

Birnbaum has been an associate editor of Basic Income Studies since 2006. He is also a representative of the Nordic Network for Political Ethics (NNPE), and a member of the International Advisory Board of the Basic Income Earth Network (BIEN).