We want to look separately at the time series properties of consumption growth of shareholders and non-shareholders. But, since the FES is not a panel, we cannot know whether a particular individual owning shares at a point in time owned shares in the previous quarter or will own shares in the following one. We need to use a grouping estimator to define groups of shareholders and non-shareholders over time.
A first obvious possibility, that is to group individuals at each point in time on the basis of current share ownership is likely to give misleading results because of changes in the composition of the group shareholders over time. Furthermore, share ownership is likely to be endogenous with respect to consumption. Wben hit by a shock, a household might decide to invest in stocks while it was not before (if the shock is positive) or might decide to liquidate its holding of stocks (if the shock is negative).
Our approach is to define the groups in terms of predicted ownership probabilities at a given point in time. Furthermore, we limit the variables that we use to predict ownership to those that do not vary over time or can be predicted perfectly, such as age (see Moffitt, 1993). Given the estimated coefficients we can, for households observed at time /+/, compute the probability of ownership at time t . For each pair of adjacent time periods we define groups of likely shareholders and non-shareholders according to their ownership probability in the first of the two periods and compute the consumption growth for these groups.
where p(Shareholder); is the predicted probability of owning shares and pt is a cut off point. We compute a similar expression for the non-shareholders. We use the actual proportion of shareholders in our sample as the cut-off point in each time period. This implies that the cut-off point changes over the time period. But the groups defined in each subsequent time periods t and t+1 are formed on the basis of the same criterion: the probability of ownership at time t . To compute the time series properties (variability, correlation with expected risk premium, and so on) of the consumption growth of likely shareholders, we compute the averages in equation (10) for all pairs of adjacent time periods in our sample.
ASSET HOLDING AND CONSUMPTION VOLATILITY