Ogawa (Int Tax Public Financ 20(3):474–484, 2013) discusses the analysis of Kempf and Rota-Graziosi (J Public Econ 94(9–10):768–776, 2010a) by taking into account capital ownership in the government’s objective functions. He establishes that the unique subgame perfect Nash equilibrium (SPNE) of the endogenous timing game corresponds to the simultaneous Nash equilibrium. This result contrasts with Kempf and Rota-Graziosi (J Public Econ 94(9–10):768–776, 2010a) who conclude to the existence of two Stackelberg outcomes at the SPNEs. Highlighting the role of plain complementarity or substitutability, we obtain conditions under which leadership still emerges at the equilibrium of the endogenous timing game when capital ownership is considered. Numerical simulations confirm this finding and display a case where plain properties are not monotone and a well-identified Stackelberg outcome is the SPNE.