Precautionary saving and portfolio allocation: DP by GMM

There is much research on consumption-savings problems with risky labor income and a constant interest rate and also on portfolio allocation with risky returns but non-stochastic labor income. Less is known quantitatively about the interaction between the two forms of risk. Under CRRA utility, undiversifiable income risk should be reflected in both savings rates and portfolio allocations. To quantify these effects in a model of consumption and portfolio choice, we adopt a semi-parametric projection method for solving dynamic programmes, based on generalized method of moments estimation of the parameters of approximate decision rules. We find that background income risk does affect optimal portfolios but that this effect may be difficult to detect empirically.