# 3.3 Decompositions

Having constructed two sets of flows coefficients, relating to pre- and post-GFC periods, along with two vectors of average entrants and numbers on each benefit, this subsection considers what would happen to benefit numbers if transition rates observed during the GFC were to persist until November 2016. Importantly these are 'what if' scenarios, rather than forecasts.[10] The purpose of these calculations is to show the impact that underlying transition probabilities can have on the numbers on benefit, rather than to provide an official estimate of the likely numbers on benefit in the future.[11]

Figure 2 shows the effects on the time profile of total number of benefit recipients over the period from February 2011 to November 2016 of starting from average pre-GFC stocks, holding quarterly inflows constant at their average pre-GFC levels, and using the two different sets of forward flow coefficients. Again the hypothetical nature of these illustrative calculations is worth stressing. In a practical reform analysis, the inflows would not be expected to remain constant and a particular time profile for changes in inflows would be modelled. This can easily be accommodated in the present framework. The simulations illustrate the importance of allowing for the inter-benefit flows when changes take place to a system that is out of equilibrium, and disentangling the effects of inflows and transitions.

First, in each case the simulated benefit numbers do not follow a simple monotonic adjustment towards a final equilibrium stock. Second, the total number of benefit recipients is consistently higher for the post-GFC transitions, reflecting the longer durations for the majority of benefit types. By 2016 the two simulations differ by about 25,000 individuals. These profiles contrast with those shown in Figure 3, which are constructed using the constant post-GFC average entrants and post-GFC initial stocks. The difference between the two totals by November 2016 is similar to that shown in Figure 2, although the time profiles are quite different. In Figure 3, the two simulations consistently increase over the period. As expected, the total number on the benefit system is much higher when the post-GFC birth vectors (and initial stocks) are used.

Simulations of DPB recipients over the same period are shown in Figures 4 and 5, using, respectively, the pre-GFC and post-GFC initial stocks and inflows. Here the different profiles display quite different patterns. The difference produced by the two sets of transitions is also much larger when post-GFC birth vectors are used. As with the total beneficiaries, Figure 4 shows that the use of pre-GFC inflows and initial stocks generates non-monotonic profiles of DPB numbers over time. But in this case the post-GFC transition matrix produces lower stocks of DPB beneficiaries than the pre-GFC matrix in the early years of the projection period, only overtaking the pre-GFC transitions in mid-2014. In Figure 5, which uses the post-GFC birth vector each period, the DPB numbers increase continually over the period for both transition matrices, with the post-GFC transitions overtaking the numbers produced by pre-GFC transitions by early in 2013.

Page top