Generalized Comparative Statics for Political Economy Models

Abstract I investigate the equilibrium properties of a deterministic voting model in which the policy space is multidimensional and politicians have limited ability to commit to platforms. This analysis is useful to answer Political Economy questions in which the multidimensional nature of the policy is crucial to model voters’ trade-offs. The use of unidimensional models to study such problems is prevalent in the literature. This usually implies that one or more policy dimensions are assumed to be exogenous. This choice delivers sharp theoretical predictions, but implies an oversimplification of the problem, which often results in implausible or empirically inconsistent predictions. I show that under suitable restrictions on the individuals’ capability of committing to policy platforms and on individual preferences a Median Voter Theorem holds even if the policy space is multidimensional. Moreover, I show that the comparative statics of the equilibrium policy outcome induced by a change in the voters’ distribution is monotone. I use this tool to extend the Meltzer-Richard model about size of the government. I show this model delivers empirically consistent predictions if a sufficiently rich policy space is assumed. Finally, I show that this framework can be used to study other Political Economy problems beyond simple voting problems