European Journal of Political Economy 7 (1991) 439467. North-Holland The political business cycle under a quadratic objective function* Reinhard Neck zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Vienna University zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA of Economics and Business Administration, A-1090 Wien, Austria Accepted for publication November 1990 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 voters’ memory. 1. Introduction During the last years, the paradigms of Keynesian stabilization policy and of the Tinbergen-Theil theory of quantitative economic policy have been increasingly doubted. In part, this may be due to the fact that fiscal and monetary policies which have been planned according to Keynesian prescrip- tions and with the aid of econometric macro models have not been as successful in reducing unemployment and inflation as had been hoped. But these failures point also toward a more fundamental weakness, namely a tacit *Earlier versions of this paper were presented at the European Public Choice Society Meeting 1989, Linz, March 29-April 1, 1989, and at the Fourth Annual Congress of the European Economic Association, Augsburg, September 2-4, 1989. I am indebted to participants of these conferences and to Richard F. Hart1 for helpful discussions. The responsibility for any errors and shortcomings is mine. 017~2680/91/$03.50 0 1991-Elsevier Science Publishers B.V. All rights reserved