Fiscal stimulus as an optimal control problem

TL;DR

This paper formulates an optimal control model to analyze government fiscal stimulus effects, proving the existence of optimal strategies and showing that loans increase company value, with implications for policy during economic crises.

Contribution

It introduces a generalized optimal control framework for fiscal stimulus, including continuous borrowing and profit behaviors, with rigorous proofs of optimality and impact on firm value.

Findings

Optimal strategies exist for fiscal stimulus policies.

Government loans increase expected net company value.

Different profit-taking behaviors influence stimulus effectiveness.

Abstract

During the Great Recession, Democrats in the United States argued that government spending could be utilized to "grease the wheels" of the economy in order to create wealth and to increase employment; Republicans, on the other hand, contended that government spending is wasteful and discouraged investment, thereby increasing unemployment. Today, in 2020, we find ourselves in the midst of another crisis where government spending and fiscal stimulus is again being considered as a solution. In the present paper, we address this question by formulating an optimal control problem generalizing the model of Radner & Shepp (1996). The model allows for the company to borrow continuously from the government. We prove that there exists an optimal strategy; rigorous verification proofs for its optimality are provided. We proceed to prove that government loans increase the expected net value of a company. We also examine the consequences of different profit-taking behaviors among firms who receive fiscal stimulus.