I examine the impact of idiosyncratic and aggregate shocks/uncertainties to immigrant and native-born households in Australia and Canada. I further investigate the different responses of indigenous and non-indigenous households to such shocks/uncertainties. Within the framework of my investigations I develop a new regression decomposition methodology that greatly improves on the current methods applied to decompose factors contributing to relative social inequality. My research findings will provide useful insights for the planning of labour market intervention, immigration policy, and enhance the understanding of wealth accumulation behaviour and ultimately of macroeconomic stability and growth in Australia and Canada.