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

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### Monthly Archives: June 2014

**Problems**

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 growthâ€™ 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.

**The methodology**

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.

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Following Hansen and Jagannathan, 1991, we use the observed data on asset returns to compute volatility bounds on the IMRS, expressed as mean-standard deviation pairs. This is given by the shaded area in Figure 4. For illustration, we also use quarterly data on aggregate total expenditure from the UK National Accounts to compute estimates of the IMRS. Assuming that within-period utility functions exhibit Constant Relative Risk Aversion, and maintaining the assumption of inter-temporal separability, the IMRS is given by:

Real quarterly returns to shares and 3-month Treasury Bills are plotted in Figure 3 and summarized in Table 2. The share returns are given for the UK 500 share index. The main facts about the returns on shares and T-bills are not surprising. Over the period as a whole, as in the US, the share returns are substantially higher and more volatile than the returns on Treasury Bills. Given the large changes in share ownership that occurred during the mid 1980s, it is interesting to consider the behaviour of asset returns before and after these changes. The stock market crash of 1987 constitutes a natural breaking point both because it occurs at the end of the increase in ownership and because it allows us to define two periods that are not affected by a single large observation.

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