The Optimal Control of Government Stabilization Funds

Ricardo Huamán-Aguilar,Abel Cadenillas

doi:10.3390/math8111975

Ricardo Huamán-Aguilar, Abel Cadenillas

Open Access

https://doi.org/10.3390/math8111975

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Abstract

We study the optimal control of a government stabilization fund, which is a mechanism to save money during good economic times to be used in bad economic times. The objective of the fund manager is to keep the fund as close as possible to a predetermined target. Accordingly, we consider a running cost associated with the difference between the actual fiscal fund and the fund target. The fund manager exerts control over the fund by making deposits in or withdrawals from the fund. The withdrawals are used to pay public debt or to finance government programs. We obtain, for the first time in the literature, the optimal band for the government stabilization fund. Our results are of interest to practitioners. For instance, we find that the higher the volatility, the larger the size of the optimal band. In particular, each country and state should have its own optimal fund band, in contrast to the “one-size-fits-all” approach that is often used in practice.

Highlights

The most recent fiscal crises have led to more interest in countercyclical fiscal policies to mitigate the negative consequences of a crisis
We model the control of a stabilization fund as a stochastic singular control problem
We analyze the effects of the cost k L of making deposits, the stabilization fund volatility σ, the long-term mean of the fund θ, and the speed of convergence λ on the optimal stabilization fund band [ a, b]

Summary

Introduction

The most recent fiscal crises have led to more interest in countercyclical fiscal policies to mitigate the negative consequences of a crisis. We study the optimal interventions of a government to manage its stabilization fund. The only theoretical literature on the control of government stabilization funds is the one related to Rainy Day Funds, such as Joyce [2], Navine and Navine [3], and Vasche and Williams [4]. They have not addressed the issue of the optimal band and size of such funds. The optimal singular control can be described, roughly speaking, as the intervention of the government to ensure that the stabilization fund stays within the band.

The Stabilization Fund Model

The Value Function and a Verification Theorem

The Analytical Solution

Time to Increase or Decrease the Stabilization Fund

Analysis of the Solution

Comparative Statics Analysis

Findings

Conclusions