The Optimal Level of Government Debt and Wealth Inequality

Rapidly growing public debt to GDP in the U.S. makes the question of the optimal level of public debt extremely relevant. The answer to this question will help to explore whether the U.S. government should conduct a contractionary fiscal policy in order to reduce the debt burden and increase social welfare or there should be no concerns about the level of the government debt to GDP. To address this issue correctly it is important to consider heterogeneous agents model instead of the model with a representative agent to account for more realistic wealth and income distributions. The model in this paper is mainly based on the works of Aiyagari, McGrattan (1998) and Achdou et al. (2017, 2020). It is conducted in continuous time, using such tools as the Hamilton-Jacobi-Bellman equation, Kolmogorov forward equation with finite differences approach. To calibrate the income distribution in the model, I used the NMAR process for Markov transition matrix discretization, which differs from the standard lognormal income process widely used in the literature. This paper also augments the literature by introducing a portfolio choice in heterogeneous agents model with government debt, as well by accounting for the rare jump shock hitting the whole economy. This makes the work extremely relevant for the analysis of the current worldwide crisis. Optimality of the government debt here is considered in the context of social welfare maximization, taking into account the wealth and income distributions, as well as incompleteness of markets because of the borrowing constraints. In the result of the analysis, I have obtained that the optimal level of government debt to GDP in the U.S. ranges from 120% to 140%, which is in line with the related literature.