Welfare cost of suboptimal allocations under recursive settings

We first investigate a household's asset allocation, housing and consumption decisions with a multi-period model under recursive utility function. We obtain both the analytical and numerical solutions for the optimal policies. We focus just on the period after retirement. In light of the empirical evidence that the elderly people do not down-size or liquidate their housing, we assume that the household buys a house initially and then keeps it until he dies. Our analysis indicates that the composition of the liquid portfolio between stocks and bonds do not depend on the elasticity of intertemporal substitution or the weight of housing in utility parameters. We find that optimal decisions of the household depend on intertemporal elasticity of substitution, risk aversion, weight of housing in utility and characteristics of the financial assets. Our calibrated model can generate empirically documented consumption patterns of the elderly homeowners. Second, we analyze and quantify the cost of various suboptimal allocations in housing, consumption, bond and stock holdings in the light of extensive empirical evidence that investors make suboptimal decisions in different ways. We find that suboptimal stock holdings impose only modest costs on the household. This may have a merit in explaining the limited stock market participation in the data. While the model generated cost of suboptimal bond holdings is higher than that of stocks, they are still small. This may partially explain why many people hold more bonds than stocks. We find asymmetric and high utility cost for suboptimal housing allocations. Positive deviations are less costly relative to the negative deviations from the optimal level. This may help us to explain why the elderly people are over consuming housing in data. The cost of suboptimal consumption is quite high and the highest of all. Our paper suggests that the most important household decisions in terms of welfare are how much wealth to use for consumption and how much for housing. The composition of liquid savings is not that important in terms of welfare.