Parsons' scholarly work investigates the ideas and institutions that came together to construct today's Europe; comparisons between the European Union and American federalism; how divisive issues like the authority of the EU affect political parties and democratic representation; and some thorny questions in the philosophy of science and qualitative methodology.
His main current research considers how and why the EU has constructed a "Single Market" that has removed many internal barriers that persist in the United States, and includes collaborations with Andy Smith at Sciences Po Bordeaux and Matthias Matthijs at SAIS Johns Hopkins. Parsons also have a long-running collaboration with Till Weber (Baruch College CUNY) on how political parties manage multiple, cross-cutting issues in Europe and the United States. He is affiliated with ARENA through the project SINGLEMARKETS, which he coordinates, as well as H2020-funded project Differentiation, Dominance, Democracy (EU3D).
Parsons, Craig Alexander (2020). The Extraordinary, Taken-for-granted Achievement of Europe's Single Market. In Jones, Erik (Eds.), European Studies: Past, Present and Future. Agenda Publishing. ISSN 9781788212830. p. 88–94.
Parsons, Craig Alexander (2020). Introduction to Political Science: How to Think for Yourself about Politics. Pearson Education Academic Publisher. ISBN 9780135710104. 528 p.
Parsons, Craig Alexander & Jupille, Joseph (2021). Liberal Intergovernmentalism as a Baseline Theory: A Cautionary Tale.
Parsons, Craig Alexander & Matthijs, Matthias (2021). How Did Europe's Single Market Surpass America's?
Parsons, Craig Alexander & Matthijs, Matthias (2021). Polanyian Means to Hayekian Ends: 'Ordoliberalism on Steroids' in EU Governance.
Parsons, Craig Alexander (2020). The Power of Ideas in Times of COVID-19.