# Stochastic Olg Models And Transition Path, With Numerical Computation Using Gpu Computing And Machine Learning

#### Abstract

This paper provides with a general framework for solving stochastic overlapping-generations model with heterogeneous finitely-lived households with elastic labor supply, exposed to both idiosyncratic income risk and aggregate production risk, using GPU computing in parallel. Markets are incomplete both within and between generations, and the fiscal policy space includes debt, progressive taxes, and a lifetime-based redistribution program (social security). Machine learning methods including neural networks and kernel regression are applied in order to improve the accuracy of the perceived law of motions. The presence of idiosyncratic shocks enables the Krusell-Smith algorithm to perform well in stochastic steady-state by smoothing out zero-wealth corner constraints across the measure of households. The model produces a wide range of realistic pricing moments (equity premium, risk-free rate, and key covariances) with standard CRRA preferences set at a modest level of risk aversion (gamma=3). Auto-correlation in productivity shocks produces realistic business cycles that typically cause the demand for safe assets to increase after a negative shock by more than the supply of new debt consistent with realistic counter-cyclical government spending. As a result, the risk-free rate \textit{falls} despite an increase in the debt-output ratio. However, a systemic increase in debt produced by a change in the fiscal policy itself produces sharp increases in the risk-free rate and marginal product of capital, while reducing the equity premium, wages, and GDP. Transition paths are calculated by including a large matrix of Krusell-Smith coefficients indexed by time into the fixed-point algorithm, which also allows for the construction of confidence intervals across time. Changes in welfare, calculated as equivalent variations, can be reported across the measure of households and across generations, including households of different ages at the time of reform as well as future generations (the unborn). Additional model enhancements, including a distinct unemployment risk, are considered to investigate the role of risk vulnerability'' (Gollier and Pratt (1996)) caused by the interaction of idiosyncratic and aggregate risk.