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An Analysis of Benefit Flows in New Zealand Using a Social Accounting Framework WP 13/01

Appendix A. Adjustment of Exit Frequencies

In examining the reasons for leaving each benefit type, it was mentioned above that the data relating to reasons for leaving benefits contain many cases where no code is given. This appendix explains how extraneous information about the distribution of reasons for exit in aggregate, for each group of benefits, can be used to adjust the data.

Let Equation. denote the number of individuals in benefit category j who exit the benefit system at the end of the quarter, for whom no reason is given. As above, let Equation. denote the number moving from benefit type j for reason i. The number for whom a reason is known is thus:


The aggregate proportion leaving for reason i, for those for whom a reason is known, is given by:


In addition, information about these proportions is available from another data source. Denote the extraneous values by Equation. . It is desired to adjust the Equation. by allocating the unknown values in such a way that the new aggregate proportions approximately match the values from the additional data source.

First, adjust all Equation. using:


And then obtain:


Along with new values of r using:


Finally, adjust the Equation. using:


This procedure was used to benchmark the exit rates in the social accounting framework. As mentioned earlier, there are many reasons for a person on benefit to leave the benefit system. The four main reasons are: finding work; death; migration and; a change in circumstances such as re-partnering.

The data for exits in the Benefit Dynamics Dataset were accurate in aggregate; they correctly captured the total number of people leaving the benefit system in a particular quarter. However, they did not provide much detail on why they were leaving. Therefore exit rates were derived from the 2008 'Linked Employer-Employee Data' feasibility study. This study documented the reasons why people left the benefit system in great detail. For example the study found that of the people who moved off the Unemployment Benefit between July 1999 and June 2005, 48 per cent left because they had obtained work, 0.1 per cent died, 5.1 per cent left New Zealand and the rest left for a variety of other reasons. Similar statistics were available for other benefit types.

It was assumed that the exit statistics detailed in the study applied to the corresponding aggregates of all the benefits in the model. However, since the model further divides these benefits into sub-categories (for example, UB is divided into 8 sub-categories), the above procedure was used to derive exit rates for each of the sub-categories without altering the overall exit rate for a particular benefit. This accounts for the fact that exit rates are not uniform across the sub-categories, for example older beneficiaries in receipt of a particular benefit are more likely to exit due to 'death' than beneficiaries in lower age-groups. Similarly, lower-age groups are more likely to exit due to migration or finding work. The procedure described above was used to account for this unevenness in the reasons for people leaving the benefit system.

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