3.1  Intergenerational income analysis and social welfare analysis

We want to compare the effect of the policy shock (the change in tax regime in response to the fiscal costs of ageing) on the remaining lifetime incomes of generations alive at the time of the shock as well as future (unborn) generations.

This gives rise to an ethical dilemma. How should the effect of the shock on an individual aged 60 at the time of the shock be compared with the effect on an individual aged 30? Suppose that the 60 year old has a relatively large change in income over each of the remaining 25 years of life, but when summed over the 25 years amounts to less than the sum of smaller changes in income over each of the remaining 45 years of the 30 year old's life. Who is worse off - the 60 year old who suffers a lot for a short period of time or the 30 year old who suffers less in any year but more in aggregate when summed over their remaining lifetime? This is analagous to the comparison of the social benefits of health interventions on a 60 year old compared with a 25 year old. The approach adopted in this paper is to calculate, over the remaining years of life following the shock, the total change in income as a proportion of the income that would have been received in the absence of the shock. In the above example the 60 year old would have a higher proportional drop in income than the 25 year old.

The next step is to determine a social evaluation of the new tax regime. This requires value judgements of an implicit ‘social judge' who evaluates only the aggregate consumption (of goods and leisure) of society in the present and the future. This implies that there is no regard for past consumption of generations still alive. The social welfare function applied here is

where is the aggregate value of the consumption index of all households alive in period j; j=1 in 2015; H is an arbitrarily long time in the future; and V is a measure of discounted social welfare, which we will simply call social welfare.

Although the social evaluation in (6) is concerned only with the aggregate consumption index, it accounts for intergenerational equity indirectly through the parameters that weight future consumption. These parameters are b_s and θ_s, which are analogous in their role to the parameters β and θ in the household's utility function. The parameter θ_s is a social rate of pure time preference, which is the rate at which period j social welfare is discounted in deriving our measure of social welfare. The parameter β_s measures the social degree of aversion to variability in consumption at any given point in time. Both parameters β_s and θ_s discount consumption occurring at different time periods. θ_s discounts a given level of future consumption according to the distance of that consumption in the future, whereas β_s discounts consumption at a given point in the future according to the size of that consumption.[8]

The higher is θ_s the smaller are the future impacts on social welfare from changes in the aggregate consumption index. This will tend to reduce the social weight on the consumption gains relative to the losses because the gains occur in the future. The higher is β_s the smaller the social weight placed on larger consumption gains or losses. This will tend to reduce the social weight on the consumption losses because they are generally larger than the gains even though the gains are spread over a longer period. The simulation outcomes are discussed below in Section 5.