Posted by Kathryn Schwartz on June 23, 2014

This paper has looked at the empirical failure of the Consumption Asset Pricing Model in the context of recent secular changes in the number and type of shareholders in the UK. Since the first order conditions for the model only hold as an equality for individuals that are currently participating in asset markets, it is natural to look at the consumption behaviour of these individuals rather than the aggregate population. Pursuing this empirical strategy poses a number of problems. Not only do we need household level information on consumption and on asset ownership, but also we have to deal with the fact that asset ownership is neither a permanent nor an exogenous status for the households in the survey. In addition, the data that are available, while providing excellent information on consumption and share ownership, are not a panel. This is problematic since the Euler equation holds only for those owning shares in adjacent periods. To deal with this we present an extension of the synthetic cohort technique which defines groups of individuals with constant membership at adjacent dates on the basis of the estimated probabilities of owning stocks.

We obtain strong results. Firstly, the first two moments of the Intertemporal Marginal Rate of Substitution for the group of likely shareholders are remarkably close to the Hansen-Jagannathan bounds derived from the time series properties of returns on shares and Treasury Bills, which is not the case with aggregate data. Second, when we estimate Euler equations for the same group, both using a single asset and two assets simultaneously, we obtain sensible values for the parameter of interest (the coefficient of relative risk aversion) and we fail to reject the over-identifying restrictions implied by the model. Finally, for the other groups (the total sample and the unlikely shareholders, we either obtain unappealing estimates of the structural parameters (violating concavity of the utility function) or rejections of the over-identifying restrictions. This last result is important in showing that there is some empirical power in our approach. To summarise, we have shown that the time series properties of the consumption of shareholders are very different from those of aggregate consumption. And they are different in a way that is consistent with the implications of the Consumption CAPM.

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