Public Debt and Welfare in a Quantitative Schumpeterian Growth Model With Incomplete Markets

This paper quantifies the welfare effects of counterfactual public debt policies using an endogenous growth model with incomplete markets. The economy features public debt, Schumpeterian growth, infinitely-lived agents, uninsurable income risk, and discount factor heterogeneity. Two versions of the model are specified, one allowing for households to hold equity in the group of innovating firms. The model is calibrated to the U.S. economy to match the degree of wealth inequality, the share of R&D expenditure in GDP, the firms exit rate, the average growth rate, and other standard long-run targets. When comparing balanced growth paths, I find large long-run welfare gains in equilibria characterized by governments accumulating public wealth. In some parameterizations, the equilibrium response of the growth rate is modest. However, welfare effects decompositions show that the growth component is still an important determinant of the welfare gains in the equilibria characterized by public wealth. The version of the model without equity is easier to solve computationally, allowing to consider transitional dynamics. Taking into account the dynamic adjustment to the new long-run equilibrium shows that the transitional welfare costs are not large enough to change the sign of the welfare effects stemming from a change in public debt. I find that eliminating public debt would lead to a 1.7 increase in welfare, while moving to a debt/GDP ratio of 100% would entail a welfare loss of 0.8%