We estimate a bargaining model of government formation in a bicameral parliamentary democracy where the government is responsible to both chambers ("dual responsibility"). We use the estimated structural model to quantify the effects of dual responsibility on the type of government coalitions that form, and their relative stability. Our main findings are that eliminating dual responsibility does not effect government durability, but does have a significant effect on the composition of governments leading to smaller coalitions. These results are due to an equilibrium replacement effect: Removing dual responsibility affects the relative durability of coalitions of different sizes which in turn induces changes in the coalitions that are chosen in equilibrium.