Generational Risk - Is It a Big Deal?: Simulating an 80-Period OLG Model with Aggregate Shocks

The theoretical literature on generational risk assumes that this risk is large and that the government can effectively share it. To assess these assumptions, this paper calibrates and simulates 80-period, 40-period, and 20-period overlapping generations (OLG) life-cycle models with aggregate productivity shocks. Previous solution methods could not handle large-scale OLG models such as ours due to the well-known curse of dimensionality. The prior state of the art uses sparse-grid methods to handle 10 to 30 periods depending on the model's realism. Other methods used to solve large-scale, multi- period life-cycle models rely on either local approximations or summary statistics of state variables. We employ and extend a recent algorithm by Judd, Maliar, and Maliar (2009, 2011), which restricts the state space to the model's ergodic set. This limits the required computation and effectively banishes the dimensionality curse in models like ours. We find that intrinsic generational risk is quite small, that government policies can produce generational risk, and that bond markets can help share generational risk. We also show that a bond market can mitigate risk-inducing government policy. Our simulations produce very small equity premia for three reasons. First, there is relatively little intrinsic generational risk. Second, aggregate shocks hit both the young and the old in similar ways. And third, artificially inducing risk between the young and the old via government policy elicits more net supply as well as more net demand for bonds, by the young and the old respectively, leaving the risk premium essentially unchanged. Our results hold even in the presence of rare disasters, very high risk aversion, persistent productivity shocks, and stochastic depreciation. They echo other findings in the literature suggesting that macroeconomic fluctuations are too small to have major microeconomic consequences.