Parameter interchangeability under recursive utility with housing

We investigate the interchangeability of two central elements of most macroeconomic models, the parameter of intertemporal substitution and time discount rate. We use a recursive utility model during retirement with housing, uncertain life time and risky stock prices since recursive utility is more flexible and general and includes expected utility as a special case. The retiree makes consumption, housing, stock and bond investment decisions. We first provide the analytical solution of retiree decisions. We realistically calibrate our model and simulate the stock returns. Our calibrated model mimics the consumption data for homeowners well. The model qualitatively explains decreasing stock and bond holdings after retirement. Then, we investigate the interchangeability of two important parameters, the parameter of intertemporal substitution and discount rate since they have similar effects on retiree decisions. We show that the parameters of intertemporal substitution and discount rate are not interchangeable analytically. Exploring the interchangeability of parameters is important and fruitful since interchangeable parameters will help to make estimation of some parameters easier. Interchangeability will simplify the solution.