Posted by Kathryn Schwartz on June 09, 2014

The expression for the consumption growth of likely shareholders on the right hand side of equation (10) differs from the expression on the right-hand side of equation (11) by four terms reflecting prediction errors from the probit. Two possible misclassifications can occur. Individuals who hold shares can have p{.) < pt and hence their consumption

If the Probit discussed above predicted share ownership perfecdy, AInCf’+1 = AlnC^, and we would be measuring the consumption growth of actual shareholders at time t. When this is not the case, one wants to estabHsh whether the fact that the last four terms in (12) are not zero introduces a bias in the estimates of the structural parameters and in the tests of over-identifying restrictions. To do so, one has to evaluate the covariance between these (unobserved) terms and the instruments used in the GMM procedure described below. As we use instruments that are lagged two periods our procedure should still yield consistent estimates unless there are reasons to believe that the terms on the right hand side of (12) exhibit serial correlation.

Three points should be stressed. First, even when panel data are available, if ownership is not perfecdy predictable because of the presence of unobserved heterogeneity, using the consumption growth of actual owners might introduce important biases, as we discuss below. Second, using the consumption of actual share holders at time t and that of predicted share holders at time /+7 would be inappropriate as the two groups would not be homogenous. Our procedure, instead, defines groups consistently between adjacent time periods. Finally, our procedure is, at the very least, a test of the null hypothesis that limited stock ownership is not the explanation of the empirical failure of the consumption CAPM. We check whether the consumption behaviour of what we define as the likely shareholders is systematically different from the rest of the population.

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