Periodic Reporting for period 1 - SOLG for Policy (The Old, the Young, and the Uncertain Future: Using High-Dimensional Stochastic Overlapping-Generations Models to Evaluate Fiscal Policies that Shift Risk and Resources Across Generations)
Période du rapport: 2022-10-01 au 2025-03-31
Governments spend enormous resources on policies that affect generations very differently, for instance related to education, infrastructure, or pensions. Moreover, financing of these measures is carried out through means - namely various forms of taxation and government debt - that also have a differential impact on people of different age. Policy choices along those two dimensions thus amount to potentially large transfers across generations. Furthermore, the costs and benefits of these policies, occurring over decades, come with large uncertainty related to, among other aspects, the prospects for productivity growth, and also for demographics itself. Due to the presence of these risks and their impact on fiscal transfers, fiscal policies constitute huge, often inefficient, intergenerational risk-sharing schemes. To assess the welfare impact of such policies, one thus needs to model both the demographic structure of the population as well as the major risks that society faces. Careful modelling of risks is even more important as welfare implications of fiscal policies heavily depend on the risk-premia that lower government borrowing costs relative to the expected return on investments. A model can only properly capture these risk-premia – the excess return of risky assets over risk-free ones – if it includes the risks they derive from and the risk-aversion of households who evaluate them. It is the aim of SOLG for Policy to build stochastic overlapping generations (SOLG) models that integrate the above-mentioned crucial elements in order to try and quantify the welfare implications of fiscal policy choices involving redistribution and risk-sharing between generations. The main challenge for doing so – and thereby going beyond the current state of the literature – is to advance solution methods for solving the resulting high-dimensional SOLG models. Further challenges are the evaluation of welfare in SOLG models and the careful construction and calibration of such complex SOLG models for specific applications. The main objectives of SOLG for Policy are thus as follows: First, develop solution methods for SOLG models. Second, establish a framework for welfare evaluation in SOLG models. Third, evaluate government debt policies in the face of many types of risk. Forth, evaluate intergenerational transfers and risk-sharing through pensions.
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.
Some of the methodological advances we have investigated could substantially advance the possibilities for global solutions of high-dimensional stochastic dynamic models. However, further research and fine-tuning as well as extensive testing is still required. Moreover, these approaches will naturally be tested by applying them to solve large-scale SOLG models for the two main applications of SOLG for Policy, government debt policy and risk-sharing through pensions.