I consider a neoclassical growth model with endogenous labor supply in which agents have private information about their idiosyncratic value of leisure. A key assumption is that these shocks follow a persistent stochastic process over time. For this economy I solve the economy-wide mechanism design problem of a social planner that seeks to maximize the welfare of agents, subject to incentive compatibility, promise-keeping, threat-keeping, and aggregate feasibility constraints. When preferences over consumption and leisure are logarithmic, I obtain a strong analytical result: All macroeconomic variables are exactly the same under private and full information. However, when the stochastic shocks follow a stochastic process that closely resembles a random walk and there is a constant Frisch elasticity of labor supply I find large quantitative effects of the information frictions in a calibrated version of the model: output, investment, consumption, capital, and labor are all 9.5% lower in the steady-state of the private information economy compared to the full information case.