Consumption and Time Use over the Life Cycle Online Appendix

This online appendix de\u85nes stationary distribution, details computation steps, and describes calibration procedures. It also includes \u85ve charts that cannot be included in the main paper due to space limitation. 1 Appendix A. De\u85nition of the Stationary Equilib-rium We focus on the stationary equilibrium of the economy where factor prices and agent distribution over state space are constant over time. Each agents state is denoted by x. Let S denote the aggregate housing stock available for renting, D the aggregate consumption of home input, Cm the aggregate consumption of the market good, Ih the aggregate investment on housing, Ik the aggregate investment on physical capital, T c the total transactions costs for trading housing. De nition 1. A stationary equilibrium is given by government policies including tax rate , and pension pen(t); an interest rate r, a rental rate ; and a wage rate w; value functions V (x); allocations cm(x), a0(x), h0(x), d(x), s(x), nm(x), nh(x); bequest b; and a constant distribution of people over the state variables x, (x), such that the following conditions hold: (i) Given the government policies, the interest rate, the wage, and the expected bequest, the value functions and allocations solve the described maximization problem for a household with state variables x. 1 (ii) (:)is the invariant distribution of households over the state variables. (iii) The price of each factor is equal to its marginal product. r = Fm1 (K;L) k; w = Fm2 (K;L): (iv) The expected bequest is consistent with the actual bequest leftZ b(dx) + Z t=0 (a(1 + r) + (1 h)h)(dx) = Z (1 t)[(1 + r)a0 + (1 h)h0](dx): (v) The non-arbitrage condition holds for the rental agency = r + h: (vi) Government budget is balanced at each period Z "etwnm(dx)