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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.

Figure 2 - Effects of Different Transitions with Pre-GFC Stocks and Inflows: All Benefits Combined
Figure 2 - Effects of Different Transitions with Pre-GFC Stocks and Inflows: All Benefits Combined.
Figure 3 - Effects of Different Transitions with Post-GFC Stocks and Inflows: All Benefits Combined
Figure 3 - Effects of Different Transitions with Post-GFC Stocks and Inflows: All Benefits Combined.

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.

Figure 4 - Effects of Different Transitions with Pre-GFC Stocks and Inflows: DPB
Figure 5 - Effects of Different Transitions with Post-GFC Stocks and Inflows: DPB

Decompositions using different combination of transition matrices, initial stock and flow vectors, are shown for IB beneficiaries in Figures 6 and 7.[12] In this case the pattern of changes over time and differences between numbers using pre- and post-GFC transitions are similar. The number of IB beneficiaries rises consistently over the projection period. But in this case the stock of IB recipients under pre-GFC transitions is consistently higher than obtained under post-GFC transitions, irrespective of the inflow vector and initial stocks used. This result has interesting implications for the counterfactual cases examined in the following section. It may be expected, in view of the larger inflows to IB and the typically longer average durations in the various IB categories post-GFC, that the pre-GFC transitions would produced lower stocks of IB beneficiaries. This is indeed the case in the long-run equilibrium situations: the profiles in Figures 6 and 7 eventually intersect. However, as in all the cases considered in this section, the adjustment to an equilibrium stock can take many years. Inflows to IB from other categories (notably from some SB states) are in fact higher for the pre-GFC period than during the post-GFC years, and this type of inter-benefit transition influences the results in these two decompositions. This characteristic has important implications, as discussed further below, for evaluating both the possible need for policy intervention and the effectiveness of any policy designed to reduce inflows to certain benefits. In the case of unemployment stocks (not shown here) the stocks reach their equilibrium values relatively quickly in each case, mainly because the inflows from outside are large and the durations are relatively shorter than for the other beneficiary types discussed in this subsection. It also highlights the point that numbers of different types of benefit may not all move counter-cyclically.

Figure 6 - Effects of Different Transitions with Pre-GFC Stocks and Inflows: IB
Figure 7 - Effects of Different Transitions with Post-GFC Stocks and Inflows: IB


  • [10]Official forecasts of benefit numbers are provided in the Budget Economic and Fiscal Update.
  • [11]The differences between periods are assumed to arise from the GFC, but in some of the non-work focused benefits they may reflect other changes over the period.
  • [12]There have been policy changes regarding IB beneficiaries over the period though, as explained earlier, the present illustrations ignore such changes.
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