The political business cycle under a quadratic objective function

Abstract

In this paper, we consider a continuous-time dynamic macroeconomic model of the expectations-augmented Phillips curve for a closed economy. The model is similar to the Nordhaus model of the political business cycle; however, the long-run Phillips curve is assumed to be vertical, i.e., the hypothesis of the natural rate of unemployment holds, and a fiscal policy variable influencing aggregate excess demand is introduced. Moreover, the instantaneous objective function of the voters (and the government) is assumed to be quadratic, penalizing deviations of the objective variables (the rates of unemployment and of inflation) from their desired values, which are assumed to be equal to their long-run equilibrium values. We examine two policy problems for the government: First, an ‘altruistic’ government is considered which plans for an infinite time horizon and optimizes a ‘social welfare function’. It is shown that the optimal policy for an initial situation with positive inflationary expectations consists in monotonically decreasing restrictive fiscal policy actions which lead to convergence of the dynamic system toward its long-run stationary equilibrium. Second, optimal policies of a vote-maximizing government are examined. Here it is assumed that voters are myopic and evaluate the government's performance at the dates of elections according to the development of the objective variables over the past election period only. By means of phase-portrait analysis it is demonstrated that political business cycles may occur under these assumptions. Their particular form is shown to depend on the parameters of the model, in particular on the magnitude of the rate of decay of voter's memory.