The Long-Run Decline in Hours Worked and PAYG Pensions

"A sustained decline in hours worked per worker reduces pension benefits in a pay-as-you-go (PAYG) pension system while simultaneously weakening productivity growth through learning. We study these effects in an overlappinggenerations model with endogenous labor supply, where two-period-lived individuals have preferences proposed by Boppart and Krusell (2020). Production is subject to a learning externality: supplying more hours raises a worker’s productivity and generates knowledge spillovers to co-workers. The implied Marshallian labor supply is hump-shaped. Despite these nonlinearities, the model admits closed-form transitional dynamics and a unique, stable steady state. Along the balanced growth path, pension benefits grow more slowly than wages because higher wages induce workers to supply fewer hours. The resulting slowdown in learning further dampens both wage and pension growth. Ignoring the endogenous labor supply response substantially overestimates both pension growth and the rate of return of the PAYG system. Due to the learning externality and social discounting, the planner’s and the equilibrium allocations differ. A PAYG pension system financed by a proportional contribution rate applied to individual labor earnings cannot implement the planner’s allocation. By contrast, a PAYG system with lump-sum contributions and benefits combined with a wage subsidy for workers, can."