Prudence and robustness as explanations for precautionary savings; an evaluation

This paper evaluates approximation methods to make manageable the numerical solution of overlapping generation models with aggregate risk. The paper starts with a model in which households maximize expected utility over their life cycle. Instantaneous utility is characterized by constant relative risk aversion. Prudence, a characteristic of the utility function, leads to precautionary saving. The first-order conditions include expectations. One source of uncertainty is not prohibitive for numerical integration of the expectation term. Because of its accuracy numerical integration results are used as a bench mark. Taylor series approximations can lead to the same results dependent on the linearization point. A linear quadratic approximation of the household model is evaluated subsequently. Alternatively, precautionary saving effects can bethe result of robust decision making. This approach leads to linear policy functions and gives a rather good approximation of the bench mark model, although not as good as the Taylor seriesapproximation.

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