ASSET HOLDING AND CONSUMPTION VOLATILITY: Aggregation issues

Posted by Kathryn Schwartz on June 13, 2014
ASSET HOLDING AND CONSUMPTION VOLATILITY

The Euler equations used in asset pricing relationships are not necessarily a simple function of consumption growth. Typically, they involve the rate of growth of the marginal utility of consumption. As long as the IMRS can be made a linear function of parameters, this is not necessarily a problem. Indeed, the Euler equations we estimate below (and discuss in Section 2) were log-linearized for this reason. However, non-linearities do constitute a problem if one works with expressions for the IMRS such as that in equation (9) used to compute the Hansen-Jagannathan bounds. This expression involves the interaction of consumption at time t and /+/, which we cannot compute. Therefore, we approximate the left-hand side of (9) by the following expression:
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Taking the ratio of the averages, rather than the average of the ratios obviously introduces some biases. Unfortunately, there is not much we can do about this issue, which may introduce biases of unknown nature. However, we can derive conditions under which there is no bias in following this approximation. If, for instance, the rate of growth of individual consumption is uncorrelated with the initial level of consumption, and consumption is log-normally distributed in the cross section, it can be showed that our approximation does not introduce any bias.

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