Political coalition formation games can describe the formation and dissolution of nations, as well as the creation of coalition governments, the establishment of political parties, and other similar phenomena. These games have been studied from a theoretical perspective, but the resulting models have not been used extensively in empirical work. This paper presents a method of estimating political coalition formation models with many-player coalitions, and then illustrates this method by estimating structural coefficients that describe the behaviour of municipalities during a recent set of municipal mergers in Japan. The method enables counterfactual analysis, which in the Japanese case shows that the national government could increase welfare via a counter-intuitive policy involving transfers to richer municipalities conditional on their participation in a merger.