The distinction between intertemporal substitution and risk aversion features in recent literature on savings behaviour. The former involves the desire to smooth income flows over time, for example in saving for retirement. Precautionary saving occurs when households are risk averse and cannot fully diversify their uncertain future labour incomes. When consumers dislike risk more than they dislike fluctuations over time, they prefer to resolve uncertainty earlier.
Previous work on the effects of uncertain income on saving has, however, introduced risk aversion in the felicity function; this approach does not distinguish between intertemporal substitution and risk aversion. Also, relatively little attention has been paid to the implications for life-cycle consumption of risk aversion and random variations in income. In Discussion Paper No. 359, Research Fellow Frederick van der Ploeg analyses these issues, assuming the decision-maker plays a `min-max' strategy to hedge against shocks that may work to its disadvantage.
The solution method used here for the life-cycle consumption problem yields a rationale for precautionary saving and a larger sensitivity of changes in consumption to income innovations. Under some conditions, van der Ploeg finds analytical decision rules for consumption and saving. Risk aversion increases the sensitivity of changes in consumption to unanticipated changes in income.
This model of precautionary saving can illustrate the controversial issue of whether a tax cut stimulates consumption. In `Keynesian' models, a tax cut boosts disposable income and hence consumption. In `Ricardian' models, however, a debt-financed tax cut simply replaces current taxes with future taxes of equal present value, so the marginal propensity to consume out of the tax cut is zero. Previous work has shown that, if taxes are proportional to labour income, if future labour income is uncertain and if households are risk averse, then Ricardian consumers can display Keynesian behaviour.
In van der Ploeg's model of life-cycle consumption, with a precautionary motive for saving, a tax cut is like a `bird in the hand' to households, boosting current consumption. A high variance of future labour income, a high degree of relative risk aversion and a high degree of intertemporal substitution lead to a high Ricardian marginal propensity to consume, which may even exceed the Keynesian marginal propensity to consume. The risk-sharing effects of a tax cut on consumption can be quite substantial, van der Ploeg concludes.

Risk Aversion, Intertemporal Substitution and Consumption: The CARA-LQ Problem Frederick van der Ploeg

Discussion Paper No. 359, February 1990 (AM)