Multivariate risk aversion and intertemporal substitution

Researchers often assume that preferences over uncertain consumption streams are representable by {Mathematical expression}, where {Mathematical expression}, is (random) period t consumption. It is moreover often asserted that estimates of γ cannot be unambiguously interpreted, since the quantity 1 - γ measures both relative risk aversion and the reciprocal of the elasticity of substitution. Clearly, this ambiguity arises only if 1 - γ indeed measures risk aversion. Although changes in γ cannot reflect changes in risk aversion according to standard definitions of comparative multivariate risk aversion, we show that γ is rationalizable as a risk aversion measure provided that the "acceptance set" of sure prospects is restricted. We also show, however, that there is essentially no relationship between changes in γ and optimal consumption, even in a simple two period model; this finding casts doubt upon the interpretation of γ as a risk aversion measure.