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A Stochastic Model with Inflation, Growth and Technology for the Political Business Cycle


This paper analyzes an augmented political business cycle model taking into account the effect of employment creation decisions by the ruling party jointly on inflation and growth. The objective is to maximize voter support in the next election that depends on the rate of unemployment as well as that of growth and inflation. We allow for stochasticity in the New Keynesian Phillips Curve model for the relationship between inflation and unemployment as well as in a benchmark labour productivity function for analyzing the growth rate. We provide explicit solution paths of the affine Markov control problem that results from our formulation. We also provide numerical illustrations with plausible parametric configurations to generate more insight into our model. Our results are broadly in line with the conventional wisdom of Phillips curve, with inflation and unemployment being roughly negatively related. The growth rate is, as expected, negatively related to the unemployment. We observe that, in the sequel, it is the lowering of the rate of inflation that provides support for the ruling party. Thus, electoral pressures drive the government to engage in cost control rather than productive investment (e.g., boosting employment or output growth).

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  1. We do not get into the nuances and alternatives of this, as in Scott Findley (2015) who documents a large body of research in psychology showing an empirical regularity that individuals discount recent memories at a higher rate compared to the rate at which they discount older memories.

  2. Suppose we choose a different cost function which is continuous, and Lipschitz continuous in the state variable uniformly with respect to the control variable, then we can show that the value function is the unique classical solution of the corresponding HJB equation in the class of functions with at most linear growth. However, the HJB equation may not admit an explicit solution and the optimal control may not be unique. Thus in such a situation we have to resort to numerical methods to compute an optimal control. In fact the importance of an explicit solution cannot be overstated.


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Correspondence to Diganta Mukherjee.

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We wish to thank the reviewers for their insightful and constructive comments which have helped us to improve the paper to a considerable extent.

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Basak, G.K., Ghosh, M.K. & Mukherjee, D. A Stochastic Model with Inflation, Growth and Technology for the Political Business Cycle. Comput Econ 53, 125–140 (2019).

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  • Political business cycle
  • New Keynesian Phillips Curve
  • Inflation
  • Growth
  • Technology aversion
  • Stochastic optimal control

JEL Classification

  • C63
  • P16