Optimal House Acquisition with Stochastic Income

Shaofeng Xu is a Senior Economist in the Monetary Policy and Financial Studies Division of the Canadian Economic Analysis Department. He holds Ph.D. in Economics from the University of California at Davis.is research interests include macroeconomics, financial economics, and housing economics.

This paper studies the impact of idiosyncratic income risk on the consumption-saving decision of a risk-averse household who chooses both the time and size of house acquisition. I derive a closed-form solution for an optimal control-stopping problem characterizing the housing tenure problem. It is found that the timing flexibility of homeownership enables the household to use her saving for home purchase to buffer her non-housing consumption against income shocks. The model offers an explanation for the excess smoothness of consumption as well as the negative relationship between income uncertainty and homeownership as documented in data.