Mortgage loan and housing market

Focusing on the evolution of identical single-cohort households concerning their housing service consumption in the life-cycle context, this paper studies the impact of fixed-rate mortgage loans on both the rental and owner-occupied housing markets. Unlike the arbitrarily divided life span usually seen in literature, we "naturally'' divide the household's life cycle into three separate but continuous stages according to their involvement with their mortgage. Then, using inter-stage smoothing conditions, we solve optimal control problems for each life stage. In addition to proposing an implicit method for dealing with durable goods such as housing, we endogenize the housing tenure choice by considering the conversion of a housing renter to a housing owner for a household at different life stages. Our baseline model successfully generates results that are consistent with the empirical evidence. Our numerical comparative statics results reveal the long-run effect of the down-payment ratio, the mortgage interest rate, and the mortgage duration on the equilibrium values of rental housing rate, time for housing purchase, the quantity of housing purchase, and the minimum requirement of housing service to maintain a standard of living. Interpreting these results in terms of homeownership rate, we find that only the mortgage duration positively affects the homeownership rate in the long run.