Optimal Housing, Consumption, and Investment Decisions over the Life Cycle

We provide explicit solutions to life-cycle utility maximization problems simultaneously involving dynamic decisions on investments in stocks and bonds, consumption of perishable goods, and the rental and the ownership of residential real estate. House prices, stock prices, interest rates, and the labor income of the decision-maker follow correlated stochastic processes. The preferences of the individual are of the Epstein-Zin recursive structure and depend on consumption of both perishable goods and housing services. The explicit solutions allow for a detailed analysis of the links between housing decisions, standard consumption choice, and investments over the life-cycle. We also consider problems with limited flexibility in revising housing decisions and provide estimates of the welfare gain of having access to trade in financial assets that are closely linked to house prices.