Three issues, arising from the complete lack of a longitudinal dimension in our data, need to be discussed. First, the theoretical model implies the consideration of share ownership at time t for individuals observed at time /+7, while we define the groups on the basis of estimated probabilities of ownership. Second, while the groups are defined consistendy for an}7 two subsequent periods, so that the definition of ‘consumption growth’ makes sense, group membership changes when considering different observations (over time) for the rate of consumption growth. Third, estimating the IMRS in equation (9) involves some aggregation problems that cannot be fully resolved given the lack of a longitudinal dimension. We discuss each of these issues in turn.
where d is a dummy indicating share ownership and the subscript i indicates that the expectation is taken over the cross sectional dimension. But with repeated cross sections we are unable to compute the first of the two terms on the right hand side of equation (11). Having estimated a model for the probability of ownership, it might be tempting to weight individual log consumption at t and t+1 by the estimated probabilities. That is, one would approximate the right hand side of equation (11) by £;n Ct+lE[dt\zt 11 – £Д1п CtE[dt\zt]], where ^ denotes the vector of variables used to model the probability of ownership. This procedure would only be appropriate if share ownership at t and log consumption at /+/, conditional on ^ were uncorrelated, an assumption which is obviously not tenable.