ASSET HOLDING AND CONSUMPTION VOLATILITY: The Consumption CAPM model 3

Posted by Kathryn Schwartz on May 24, 2014
ASSET HOLDING AND CONSUMPTION VOLATILITY

In the absence of measurement error, and under the assumption of rational expectations, any variable dated t-1 or earlier is a valid instrument Considering equations (5) and (6) for two different assets, j and iy we can obtain a log-linear version of equation (4). After some manipulation, it is possible to derive: Source
w6567-6
Notice that, since consumption growth enters only through its conditional covariance with asset returns, the identification of the curvature of the utility function is harder then in equation (5). If the conditional second moments on the right-hand-side of equation (7) are not predictable, neither are excess returns. Moreover, in such a situation one would not be able to identify the curvature parameterу Mankiw and Zeldes (1991) rely on an unconditional version of equation (7). Under the assumption of log-normality, taking unconditional expectations of equation (7) yields:
w6567-7
As у is the only parameter to be estimated, it can be identified by making the sample equivalents of the unconditional moments equivalent to the population moments in equation (8). This approach is appealing because it relates the estimate of the parameter of interest directly to the time series properties (variance and correlation) of rates of return and consumption growth. However, it exploits a single orthogonality condition to estimate the unknown parameter and is therefore less efficient than the other methods discussed above. For this reason we do not use it.

Tags: , ,