Political Competition in a Model of Economic Growth; Some Theoretical Results

We study a one-sector model of economic growth in which decisions about capital accumulation and consumption are made through a political process of two candidate competition. Each voter's utility for a consumption stream is the discounted value of that voter's utility of consumption in each period. We consider the case when voters' one period utility functions for consumption are identical but discount factors are different. We are particularly interested in the conditions under which neoclassical optimal growth paths occur, and conditions in which political business cycles occur. The answer depends on the ability or inability of the candidates to commit to multi-period investment strategies. If candidates can commit indefinitely into the future, then a political (majority rule) equilibrium path will not exist if all discount factors are different. For any feasible consumption path, there is a perturbation which is majority preferred to it. For any neoclassical optimal path there exists a perturbated path that is preferred to it either unanimously or by all but one voter. These results are true even if the perturbations can differ at no more than three consecutive periods from the original path. If candidates are unable to commit to multi-period plans, we show there is a unique subgame perfect, stationary, symmetric equilibrium to the infinite horizon two candidate competition game; namely the optimal consumption path for the median voter. The equilibrium is unique in the following sense: It is the unique limit of subgame perfect equilibria to the finite horizon electoral game. In the case when candidates can commit for a finite time into the future, we show that a stationary minmax path (a path which minimizes the maximum vote that can be obtained against it) yields a political business cycle.