Posted by Kathryn Schwartz on June 11, 2014

The second issue is that the composition of the group of likely shareholders changes over time, both because the probability of ownership may change over time and because the cut-off point changes. If intertemporal prices were the same across individuals and the utility function depended only on consumption and not on unobserved (or unaccounted for) heterogeneity, this would not be a problem. The measured IMRS would differ from the expected one only because of an expectational error that would average to zero over time. In the presence of unobserved heterogeneity, however, the measured IMRS encompasses both genuine changes in consumption growth and composition effects. This introduces a spurious source of volatility. To make this point clear, suppose that the instantaneous utility function is given by и(с;У;) = (1-гУ'(с’;Г exp(r^), where represents unobserved heterogeneity and we are ignoring the effect of demographic and other observable variables for notational simplicity. The IMRS corresponding to this utility function is:

IMRS = (C,+, \У {Ctl Y exp(p* — «/*_,) „

\ t+ч v / ‘ 1’. If vr is constant over time and the groups are formed consistently, as our procedure requires, the presence of unobserved heterogeneity does not create any problems, as the terms in vlj would drop out of the IMRS. On the other hand, if vht is a random walk with a group specific drift, changes in the compositions of the groups might create some serious distortion in the characterization of the time series properties of the IMRS. For this reason, it might be important to check whether the results change dramatically when we change the way we select the ‘cutoff points5 in our procedure.

As we mentioned above, it should be noted that the presence of unobserved heterogeneity in the utility function is likely to induce serious problems even when panel data are available, if one uses actual ownership. When the unobserved taste shocks v* are correlated with the decision to hold stocks (as is likely), then using individual data and individual specific instruments (even if lagged a few periods) will produce inconsistent estimates. Like any grouping estimator our procedure has an Instrumental Variable interpretation. Averaging over the individuals belonging to a group (defined by a nonlinear function of deterministic variables) avoids the biases caused by individual specific fixed effects. It should be stressed that our procedure relies only on temporal variability to identify the parameters of interest. If there are group specific fixed effects, they can be absorbed in the constant of the equation.

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