The results for the group of likely shareholders, reported in the first column of Table 4, are remarkably good. The point estimate of the coefficient of the iso-elastic utility function is consistent with concavity. It implies a value of the elasticity of intertemporal substitution of about 0.80, consistent with other estimates of this parameters in the UK reported in the literature.10 Finally, the value of the test of over-identifying restrictions is very low and does not indicate any deviations from the null.
GMM estimation of Euler equation for the return on shares
The point estimates of у obtained for the group of unlikely shareholders and for the total sample are shown in the second and third columns of Table 4. They are either very small (for the whole sample) or negative (for the unlikely shareholders). For the whole sample, the test of over-identifying restrictions has a p-value just above 0.05.
In the empirical asset pricing literature, researchers often reject the over-identifying restrictions implied by the Euler equation for consumption when they consider simultaneously more than one asset. These results are the counterpart to the fact that the first two moments of the IMRS based on aggregate consumption are outside the Hansen Jagannathan bounds. In Table 5 we report the results obtained estimating simultaneously the Euler equation for shares and T-bills returns.
GMM estimation of Euler equation for the return on shares and T-Bills
|‘Likely’ Share owners||Unlikely’ share owners||Whole sample|
|Notes: See Table 4.|
As in Table 4 the results for the group of likely shareowners are very different from those of the other two groups and much more consistent with the predictions of the theory. While the coefficient of the iso-elastic utility function is lower than in the previous case, it is positive and significandy different from zero, even though is not estimated with a great precision. Furthermore, the test of over-identifying restrictions never rejects the null. The message that emerges from the first column of the Table is that even one considers two assets simultaneously for the group of likely shareholders, one does not reject the over-identifying restrictions implied by the theory. Furthermore, one obtains points estimates of the parameter of interest that are not inconsistent with a concave utility function.
The evidence for the other two groups considered is, as in Table 4, quite different. The lack of precision of our estimates does not mean, for these two groups, that our procedure is unable to reject the orthogonaHty restrictions implied by the theory. On the contrary, for both groups we obtain strong rejections of the over-identifying restrictions. For the group of ‘unlikely share holders’, the estimated coefficient of relative risk aversion is again negative, even though is not estimated with any precision.20