Militaries are needed to protect the state from external threats, but what protects the state from coups led by the military? As Plato asked, who guards the guards? Besley and Robinson develop a simple two-period model of coups. In period one, the government collects revenue (perhaps a function of natural resources), pays a wage to the military, and purchases public goods, which the military values at some discount; for instance, the military would not value money that is siphoned off by lower ministers, but would value money pumped into military depots. In period 2, the military can either mount a coup or not; if not, the government then pays them a new wage. If the government cannot commit to the second period wage, then they essentially pay the military only enough to keep the army from deserting. Whether or not they can commit, states where the military does not value the public goods the government likes to buy will see more coups, and therefore the state will choose a suboptimal army size in order to prevent the coup. This paper is somewhat less convincing that the model by Acemoglu et al also discussed today on this site.
“Quis Custodiet Ipsos Custodes?: Civilian Control over the Military,” T. Besley & J. Robinson (2010)