In this paper we present a structural approach to the study of government formation in multi-party parliamentary democracies. The approach is based on the estimation of a stochastic bargaining model which we use to investigate the effects of specific institutional features of parliamentary democracy on the formation and stability of coalition governments. We then apply our methodology to estimate the effects of governmental bicameralism. Our main findings are that eliminating bicameralism does not affect 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 bicameralism affects the relative durability of coalitions of different sizes which in turn induces changes in the coalitions that are chosen in equilibrium.