The first half of the project period focused largely on advancing methods for solving high-dimensional SOLG models. We explored several enhancements to the adaptive sparse grid method and investigated alternative new approaches for high-dimensional approximations, such as tensor train decompositions and shape-preserving neural networks. We also worked on continuous-time SOLG models, focusing on leveraging their structural characteristics for numerical solution methods. Regarding the other objectives of SOLG for Policy, we have begun analyzing the properties of social welfare functions in SOLG environments and modeling intergenerational transfers and risk-sharing mechanisms through pension systems. As for government debt policies, we have already carried out a first self-contained analysis. While it retains the small-scale OLG structure used in earlier research, it substantially goes beyond that research in incorporating endogenous labor supply and a larger set of drivers for the gap between government borrowing rates and the risky rate of return: convenience benefits of public debt, idiosyncratic return risk, and aggregate risk. Using numerical solutions with sparse grids, our analysis focuses on contrasting a purely fiscal perspective with a welfare perspective. For this purpose, we establish the concepts of deficit-maximizing debt (DMD) and welfare-maximizing debt (WMD) - the debt-to-GDP ratios that maximize either the average deficit a government can run or the (long-run) welfare of households. Our analysis shows that the following insights are of quantitative relevance. First, it is rather the rule than the exception that DMD and WMD differ strongly. Second, WMD can be substantially lower than DMD, implying that it may not be desirable to take advantage of all available deficits, even if they seem to be a free lunch form a purely fiscal perspective. Third, lower risk-free rates may or may not, depending on the root cause, speak in favor of higher debt-to-GDP ratios: increased risk, longevity, and convenience benefits do; reduced growth or government spending do not. Fourth, market power of firms tilts the welfare evaluation strongly in favor of lower public debt. Finally, the impact of higher debt on households varies widely, depending on their reliance on different production factors. While the wealthy often benefit from debt levels exceeding DMD, such levels tend to harm the middle class significantly. Building on the first project, we have started a new project that focusus on optimal state-contingent debt policy, thus answering questions about how governments should respond to (large) fiscal shocks and how debt accumulated during crises should be dealt with.
