Working paper

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

Authors: Omar Aziz, Nick Carroll and John Creedy


This paper presents a social accounting model to examine the entrants, exits and transitions of individuals among a wide range of benefit categories in New Zealand. Transition rates and flows are estimated separately for periods before the global financial crisis (GFC) and periods following the crisis. The data were obtained from the Benefit Dynamics Dataset maintained by the Ministry of Social Development. The model is used to examine, using simulations, the implications for the time profile of changes in the stock of benefit recipients under a range of counterfactual situations. It is suggested that the model can provide a useful tool for policy analysis.

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We are grateful to Jason Raven, Mike O'Rourke and others in the Ministry of Social Development for the support that they have offered to us in accessing and using the Benefit Dynamics Dataset, and for comments on an earlier version of this paper. We are also grateful to Tony Burton, Ben Gleisner and others from the Labour Market and Welfare Team at the Treasury for their comments. We have benefited from comments by Paul Rodway, Nathan Penny and David Rea on an earlier draft.


The views, opinions, findings, and conclusions or recommendations expressed in this Working Paper are strictly those of the author(s). They do not necessarily reflect the views of the New Zealand Treasury or the New Zealand Government. The New Zealand Treasury and the New Zealand Government take no responsibility for any errors or omissions in, or for the correctness of, the information contained in these working papers. The paper is presented not as policy, but with a view to inform and stimulate wider debate.

1 Introduction#

The aim of this paper is to present and explore the use of a model designed to examine the entrants, exits and transitions of individuals among a wide range of benefit categories in New Zealand. It is suggested that an understanding of the factors affecting the number of individuals in receipt of various benefits requires information about movement from one benefit category to another, in addition to flows on and off the benefit system as a whole. The demographic accounting approach seems to be particularly well suited for modelling benefit flows.[1] The transition rates and flows, measured over discrete periods of three months, are estimated separately for a number of periods before the global financial crisis (GFC), which reflect relatively stable patterns of entry and movement, and periods following the crisis, which saw substantial changes, particularly in a number of inflow rates. The data were obtained from the Benefit Dynamics Dataset (BDD) maintained by the Ministry of Social Development (MSD).

The model can be used to make simulations of the number of individuals in the various benefit categories, using assumptions about the variation over time in the inflows to the benefit system and transition rates between benefits. Simulations are reported for several assumptions about economic conditions over the period February 2011 to November 2016.[2] The model is used to examine the implications for the stock of benefit recipients of several counterfactual scenarios which change the inflows and outflows from benefits.

The approach can thus be used to examine the following types of question. How important are the changes in stocks which result from an underlying set of inflow, transition and exit rates, in comparison with those affecting a particular benefit type and resulting from a policy change? How important are flows among benefit categories in understanding the potential effects of a policy reform that concentrates on a single category? How quickly might a change in the inflows to, or exit rates from, a particular benefit category or categories, arising from a policy change, affect the stocks of benefit recipients?[3] The inflows are taken as 'given' here, but of course in using the approach for practical analyses they could be modelled using other methods, including demographic projections.

Section 2 presents the basic framework used. It outlines the relationships between stocks and flows, the calculation of costs and the approach used to consider policy changes. The New Zealand flows data are described in Section 3. This section also defines the benefit categories and the construction of the transition matrices. Summary information regarding inflows and average durations, before and after the global financial crisis, are also briefly discussed. Section 4 reports simulations of benefit numbers up to November 2016 under several assumptions about the economic conditions over the period. Section 5 explores the potential implications of a reduction in inflows to Unemployment Benefits. Conclusions are in Section 6.


  • [1]For an extensive discussion of social accounting models, see Stone, J.R.N. (1973) Transition and admission models in social demography. Social Science Research, 2, pp. 185-230.
  • [2]Official Treasury and MSD forecasts of the number of benefit recipients are provided in the Budget Economic and Fiscal Update, and are based on estimated relationships between GDP and the number of benefit recipients. The purpose of the simulations presented here is to illustrate the impact of different counter-factual scenarios and illustrate the sensitivity of numbers to the underlying flows.
  • [3]One component of welfare reform has been to develop an investment approach, based on an actuarial valuation of the benefit system ( While the approach outlined in this paper uses a flows approach, rather than an actuarial approach, it can be used to inform actuarial assessments of the impact of welfare reform.

2 The Framework of Analysis#

This section presents the basic demographic model of benefit flows.[4] The stock-flow relationships are described in subsection 2.1.[5] In subsection 2.2, the use of the model to deal with policy changes is discussed.


  • [4]Stone (1973) discussed a number of applications, in particular the movement of individuals through the education system. He also suggested an expansion of the model to allow for 'dependence on the past', but the approach would produce too many 'states' in the present context.
  • [5]An indication of how the model can be used to examine benefit costs is outlined in Appendix F.

2.1 Stocks and Flows#

The flows of individuals among defined benefit categories or 'states' from one period to the next can be recorded in a demographic or social accounting matrix. Suppose the accounting period is three months, so that information is available about the state occupied by each individual at the beginning of each quarter. There are m states. Let




) denote the number of people who move from state j to state i from period t to period t+1 (at the beginning of quarter t they are in state j and at the beginning of quarter t+1 they are in state i). These flows are placed in a matrix


. Let Equation. denote the vector whose ith element is the number of people who enter state i from outside the labour market during period t (for example, those leaving full time education and inward migrants): these are referred to as 'inflows'. Similarly


is the vector of exits from the system at the end of period t for various reasons, including migration and death: these are referred to collectively as 'outflows'. Finally,


is the vector of stocks of individuals in each state,


, at the start of period t.








Figure 1 - Relationship between Stocks and Flows


Figure 1 - Relationship between Stocks and Flows.

The information about stocks and flows are placed in a social accounting table shown in Figure 1 (where for convenience, t subscripts have been omitted). A prime attached to a variable indicates transposition, so that, for example,


is the column vector of exits from the system, rewritten as a row vector. In this table, the flows take place from columns to rows. These flows (number of individuals) can be converted into transition rates,


, which denotes the proportion of individuals who started quarter t in state j and moved into state i by the beginning of quarter t+1. The precise timing of the movement is not recorded in this discrete time framework, so moves are effectively assumed to occur at the end of period t.[6] The transition proportions are therefore given by








In matrix terms, this can be written as


, where the 'hat' indicates that the column vector forms the leading diagonal of a square matrix, with zeros in the off-diagonals. Hence








denote a vector of units, the sum of elements in the ith row of S is expressed as Si, and noting that


, the 'closing stocks' are related to the 'opening stocks' and the flows according to:








Hence moving forward one period:










The time profile of the stocks take a particularly simple form if the transition rates and inflows remain constant over time. Thus, becomes:





Here I denotes a unit matrix (a square matrix with a leading diagonal of units, and zeros elsewhere). The column sums of C are less than one and all the elements are non-negative. Hence, if the process continues long enough,




. The vector of equilibrium stocks is therefore:








And the time profile of stocks can easily be obtained from repeated use of the modified form of equation , whereby:





Furthermore, if again the transition rates remain constant, the average time spent in each state (along with its variance) is a simple function of the appropriate diagonal element of the C matrix. It can be shown that the average time in state j is


while the variance of the time in the state is






The outflows can be subdivided into a number of categories. For example, some individuals may leave the benefit system by, for example, migrating, dying, or moving into employment with sufficiently large earnings. Hence the (column) vector


can be redefined as a K by m matrix where


represents the number of individuals who move out of the benefit system from category j for reason k. The corresponding transition proportions are:








And if these are, as with the other transition proportions, assumed to remain constant at


, the numbers in each category in each period are obtained simply from







  • [6]In the discrete time framework, those who enter and leave a benefit category within the period are not recorded. The extent to which individuals may repeatedly enter and leave the benefit system is also not recorded here. It would be possible to redefine states to include some past transitions (allowing for dependence on the past), but this substantially increases the size of the coefficients matrix.

2.2 Examining the Potential Effects of Policy Changes#

Policy changes may be designed to affect a wide range of components of the social accounting framework. For example, changes to eligibility conditions for certain types of benefit may affect the number of people moving onto those benefits (both in terms of 'inflows' and transitions from other benefit categories). In addition, changes to the administration of benefits (including, for example, the monitoring of behaviour relating to moral hazard, the provision of information for potential benefit recipients regarding regulations, and so on) can affect flows of individuals in and out of a range of states. In addition, changes to benefit levels and abatement rates, through their effects on individuals' budget constraints and thus financial incentives, can also influence transitions.

It is therefore possible to use the framework presented here to examine the implications for benefit flows of various policy reforms, given a priori information about the likely effects on particular elements of the accounting matrix. The effects on future total costs of any particular reform are far from obvious, since they depend on the pattern of movements of individuals through the various states. For example, an initiative designed to increase the flow of individuals off a particular benefit type, and which moves those individuals into other states where they are more likely to move into full time employment and off the benefit system entirely, has different implications from a policy which moves individuals away from what may be an expensive benefit but into other states where they are more likely to remain for longer periods.

Changes in flows, in particular the inflows and outflows, also arise from changes that are independent of the benefit system. Structural or cyclical changes to probabilities of becoming unemployed or gaining employment are likely to have significant impacts on flows and costs. Other exogenous changes include, for example, changes in the age composition of the population and fertility rates.

The effects on equilibrium stocks of individuals in the various benefit categories of changes in the inflow vector are easily obtained from equation (6). Letting


denote the 'matrix multiplier', the changes in the stocks are a multiple of the change in the flows for any category. A change in one of the elements of the inflow vector has effects on many of the stocks, not simply the category whose inflow has changed. Thus, if the jth element of b changes, the equilibrium stock changes in all categories, i, for which the ith row element,


, from the jth column of M is non zero. In equilibrium the outflows from each category must precisely match the inflows, so that an increase in the latter can only be matched by outflows after the stocks have built up sufficiently. The extra inflows in any category also lead to higher movements among benefit categories. In a large system, the consequences can easily be obtained from the matrix multiplier, M, but of course the elements of M are not transparent from the flow coefficients, given the matrix inversion involved. The speed of adjustment to the new equilibrium also depends on the speed of convergence of the powers of C towards zero, as is evident from equation (5). The effects of changes in the elements of C itself are also discussed in Appendix E.




3 New Zealand Flows Data#

This section describes the data used to estimate the flows and transitions among benefit categories, and the construction of the matrices used below. Summary information is also reported on the average durations and entrants.

3.1 The Data and Construction of Matrices#

The data used here were obtained from the Benefit Dynamics Dataset (BDD) maintained by MSD. The dataset captures the key variables required for the analysis of individual benefit histories. The BDD includes information on all people who received any main working-age social welfare benefit in the period of study, from February 2005 to February 2011. It provides basic information on their demographic characteristics, and traces their changing benefit status and other circumstances from the beginning of the study period (for benefits current at that date) or from the date they are first granted benefit in that period (for new grants). It also traces the benefit histories of partners and dependent children included in benefits.

The first stage involved constructing the relevant flow matrices and vectors for each quarter over the period, resulting in 24 sets of accounts. At this stage, benefit recipients were divided into 63 categories. After examination of these matrices, the number of benefit categories was cut down to 47 separate types, largely by amalgamating different age groups within a category type: some age groups were found to contain very small numbers of individuals.[7] The final set of categories is described in Table 1.

Examination of the many matrices of transitions between quarters showed a relative stability over the pre-global financial crisis (pre-GFC) periods. There are clearly fewer observations for the post-global financial crisis (post-GFC) period, but again the flows showed little change. Hence, a dividing line was drawn between pre-GFC and post-GFC flows. For this reason, the many matrices were reduced to only two sets of flow matrices and vectors, by computing average flows in the two periods. In view of this averaging process, no explicit allowance is made here for seasonality (particularly regarding unemployment benefit inflows). The full details of the two matrices and their flows coefficients are given in Appendix C, where it can be seen that there are substantial 'off diagonal' movements.

However, it is important to recognise that the coefficients are expected to change over time as a result of policy changes, as discussed earlier, as well as extraneous factors. There have in fact been some policy changes over the relevant periods. In considering a practical policy context the nature of the changes over time in particular transitions would be the focal point of analysis. For present purposes the large changes observed for many flows following the GFC provide useful illustrations of the major benefits of the general approach and the potential value of recognising explicitly that changes take place to a system that is not in equilibrium, so that the consequences of any change can be much wider than anticipated.

A difficulty arises in dealing with exits from benefits. Instead of having a single vector of 'outflows', d, many reasons are recorded. In addition, this part of the dataset has a significant number of missing entries. Appendix A describes the method used to divide the exits into just four categories, involving extraneous information from LEED/MSD Feasibility Study[8]. In particular, it is most useful to have information about the flows of individuals off benefits and into employment.

The average number of entrants into each benefit category, before and after the GFC, are reported in Table 3. The largest increases in average entrants are for those with no earnings in all of the basic categories; these are Domestic Purposes Benefit (DPB), Invalid's Benefit (IB), Sickness Benefit (SB) and Unemployment Benefit (UB). Not surprisingly, the largest increases by far are for UBs, particularly in 18_no and 30_no categories. However, increases in the corresponding SB categories are also substantial.

Table 1 - Benefit Categories
DPB18_0_e  DPB or WB, aged 18 -
DPB18_0_f  DPB or WB, aged 18 -
DPB18_0_no  DPB or WB, aged 18 -
DPB18_5+_no  DPB or WB, aged 18 -
DPB18_5+_wrk  DPB or WB, aged 18 - $0 pw
DPB18_nc_no  DPB or WB, aged 18 -
DPB18_nc_wrk  DPB or WB, aged 18 - $0 pw
DPB30_0_e  DPB or WB, aged 30 -
DPB30_0_f  DPB or WB, aged 30 -
DPB30_0_no  DPB or WB, aged 30 -
DPB30_14_e  DPB or WB, aged 30 -
DPB30_14_f  DPB or WB, aged 30 -
DPB30_14_no  DPB or WB, aged 30 -
DPB30_5_e  DPB or WB, aged 30 -
DPB30_5_f  DPB or WB, aged 30 -
DPB30_5_no  DPB or WB, aged 30 -
DPB30_nc_e  DPB or WB, aged 30 -
DPB30_nc_f  DPB or WB, aged 30 -
DPB30_nc_no  DPB or WB, aged 30 -
DPB60_no  DPB or WB, aged 60 -
DPB60_wrk  DPB or WB, aged 60 - $0 pw
IB18_e  IB, aged 18 -
IB18_f  IB, aged 18 -
IB18_no  IB, aged 18 -
IB30_e  IB, aged 30 -
IB30_f  IB, aged 30 -
IB30_no  IB, aged 30 -
IB60_no  IB, aged 60 -
IB60_wrk  IB, aged 60 - $0 pw
SB18_e  SB, aged 18 -
SB18_f  SB, aged 18 -
SB18_no  SB, aged 18 -
SB30_e  SB, aged 30 -
SB30_f  SB, aged 30 -
SB30_no  SB, aged 30 -
SB60_no  SB, aged 60 -
SB60_wrk  SB, aged 60 - $0 pw
u18  a benefit but aged under 18 years
UB18_e  UB, aged 18 -
UB18_f  UB, aged 18 -
UB18_no  UB, aged 18 -
UB30_e  UB, aged 30 -
UB30_f  UB, aged 30 -
UB30_no  UB, aged 30 -
UB60_no  UB, aged 60 -
UB60_wrk  UB, aged 60 - $0 pw
Misc  other benefits, including CSI and training benefits
Table 2 - Average Entrants per Quarter
States Pre-GFC Post-GFC
DPB18_0_e 192 122
DPB18_0_f 4 4
DPB18_0_no 1,331 1,024
DPB18_5+_no 209 172
DPB18_5+_wrk 40 26
DPB18_nc_no 363 1,096
DPB18_nc_wrk 37 106
DPB30_0_e 127 83
DPB30_0_f 4 4
DPB30_0_no 789 596
DPB30_14_e 89 99
DPB30_14_f 4 7
DPB30_14_no 404 478
DPB30_5_e 282 189
DPB30_5_f 14 14
DPB30_5_no 1,106 925
DPB30_nc_e 111 246
DPB30_nc_f 5 11
DPB30_nc_no 504 1,393
DPB60_no 161 209
DPB60_wrk 46 52
IB18_e 15 11
IB18_f 1 0
IB18_no 163 162
IB30_e 44 35
IB30_f 2 2
IB30_no 714 755
IB60_no 218 297
IB60_wrk 14 14
SB18_e 107 111
SB18_f 6 8
SB18_no 2,824 3,438
SB30_e 198 189
SB30_f 19 21
SB30_no 3,887 4,608
SB60_no 401 589
SB60_wrk 30 36
u18 1,096 1,077
UB18_e 590 923
UB18_f 47 69
UB18_no 6,255 11,833
UB30_e 399 528
UB30_f 55 92
UB30_no 4,495 7,577
UB60_no 365 529
UB60_wrk 46 53
misc 1,166 1,514

3.2 Average Durations#

Details of the average number of quarters spent in each benefit category, along with standard deviations, are given in Table 3, using the expressions given in subsection 2.1 above.[9] The largest increases are for: the DPB categories 18_nc_no (from 18.98 to 22.15 quarters) and 30_nc_no, that is those with no dependent children and no earnings and; IB categories 18_no and 30_no, that is, those without earnings. Smaller increases were found for UB recipients in the same age and employment groups, that is categories 18_no and 30_no. The average duration for those in UB category 60_no actually fell from 6.07 to 4.45 quarters after the GFC, reflecting a higher propensity to move into the corresponding SB category. Reductions in average durations therefore do not necessarily mean that individuals are moving off benefits more quickly, since they may simply be moving to other benefit categories. They may also not result in drops in numbers of benefit to the extent that there is an increase in inflows at the same point.

In judging the changes in average durations it should be remembered that the time units are quarters, so that the change from 19 to 22 (for DPB18_nc_no actually translates to a change of 36 weeks. Another feature of the durations reported in Table 3 is that the standard deviation for the DPB and IB categories mentioned above, for which the increases in average durations are largest and those average durations are themselves high, are much larger than for other benefit types at over 4 quarters.

Table 3 - Time Spent in Each Benefit Category: Quarters
  Pre-GFC Post-GFC
States Average SD Average SD
DPB18_0_e 3.03 1.42 2.61 1.27
DPB18_0_f 1.14 0.38 1.16 0.40
DPB18_0_no 5.67 2.16 4.39 1.84
DPB18_5+_no 4.45 1.86 3.68 1.64
DPB18_5+_wrk 3.19 1.48 2.70 1.30
DPB18_nc_no 18.98 4.24 22.15 4.60
DPB18_nc_wrk 4.90 1.98 4.43 1.85
DPB30_0_e 3.12 1.46 2.67 1.29
DPB30_0_f 1.21 0.46 1.17 0.41
DPB30_0_no 4.80 1.95 3.77 1.66
DPB30_14_e 4.62 1.90 3.63 1.62
DPB30_14_f 1.33 0.57 1.28 0.53
DPB30_14_no 6.39 2.32 4.74 1.93
DPB30_5_e 3.93 1.71 3.15 1.47
DPB30_5_f 1.26 0.51 1.25 0.50
DPB30_5_no 5.07 2.02 3.91 1.71
DPB30_nc_e 6.81 2.41 6.27 2.30
DPB30_nc_f 1.31 0.55 1.43 0.65
DPB30_nc_no 13.42 3.52 21.30 4.51
DPB60_no 8.24 2.69 9.08 2.84
DPB60_wrk 6.54 2.35 6.12 2.26
IB18_e 5.53 2.13 5.22 2.05
IB18_f 1.20 0.45 1.21 0.46
IB18_no 13.85 3.58 17.19 4.02
IB30_e 7.21 2.49 6.48 2.34
IB30_f 1.23 0.48 1.25 0.50
IB30_no 21.60 4.54 24.59 4.86
IB60_no 14.72 3.70 16.26 3.91
IB60_wrk 7.19 2.49 6.27 2.29
SB18_e 2.10 1.05 2.08 1.04
SB18_f 1.14 0.38 1.14 0.38
SB18_no 3.04 1.43 3.47 1.57
SB30_e 3.45 1.57 3.31 1.52
SB30_f 1.25 0.50 1.24 0.49
SB30_no 5.44 2.11 6.24 2.29
SB60_no 5.38 2.09 6.03 2.24
SB60_wrk 4.25 1.80 3.93 1.71
u18 3.28 1.51 3.46 1.57
UB18_e 1.44 0.67 1.59 0.77
UB18_f 1.08 0.28 1.06 0.25
UB18_no 1.87 0.93 2.26 1.12
UB30_e 2.09 1.04 2.29 1.13
UB30_f 1.16 0.40 1.13 0.36
UB30_no 2.70 1.31 3.34 1.53
UB60_no 6.07 2.25 4.45 1.86
UB60_wrk 4.18 1.78 3.14 1.46
Misc 3.92 1.71 4.07 1.75


  • [9]It is perhaps worth stressing that the standard deviations relate to the duration distributions; they are not standard errors of the estimated average durations.

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 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.

4 Simulations of Benefit Numbers#

This section reports a range of simulations, up to November 2016, of the numbers of benefit recipients. These simulations effectively provide counterfactuals against which various policy reforms could be examined. The approach involves taking the actual stocks in each benefit category at November 2010, and then making assumptions about the quarterly entries and transitions over the subsequent quarters. These counterfactuals are described in subsection 4.1. Benefit numbers are reported in subsection 4.2. The implications for the number of beneficiaries who are also employed while in receipt of benefits are shown in Appendix D.

4.1 The Counterfactual Assumptions#

The following graphs show the projected stocks where pre-GFC (2005-08) inflow, outflow and inter-benefit transition rates are applied from February 2011 and continue across the forecast period. This scenario provides benefit recipients under the hypothetical situation whereby there is an immediate return to Pre-GFC transitions on and off the benefit system and between benefit categories. Other profiles incorporate the effect of the GFC (and other structural changes) on benefit numbers, but make assumptions about the timing of the return to pre-GFC transitions. Thus, the profile labelled Post-GFC+Recovery assumes that post-GFC transitions prevail until February 2012 after which beneficiary numbers begin a gradual transition back to Pre-GFC levels. However a complete convergence would not occur inside the forecast period.

The profile labelled Post-GFC->Transition->Pre-GFC assumes that post-GFC transitions prevail till November 2012 but there is a delay before Pre-GFC transitions apply and lead to relatively reduced stocks of beneficiaries. Finally, the Post-GFC profile assumes that post-GFC transitions prevail across the forecast period. As expected, this implies a continued rise in beneficiary numbers across the period. The profile Post-GFC+Recovery suggests that a return to pre-GFC rates by February 2012 results in numbers on a benefit falling to around 325,000 within about 12 months. However, a more delayed return to pre-GFC transition rates could result in benefit numbers being 25,000 higher than with an earlier return to pre-GFC rates; see Figure 8. As these simulations are alternative counterfactuals against which policy changes are to be compared, the assumption that the inflows and transitions remain unchanged for a number of quarters at either their pre- or post-GFC values, or at transitional values, reflects an explicit assumption that there are no policy changes over the projection period.

All simulations thus begin, in the initial period, from the same vector of stocks. These clearly do not reflect a long run equilibrium, especially since the actual November 2010 stocks arise from circumstances which have operated for a relatively short time. As explained in Section 2, the application of fixed inflows and transition rates ultimately produces a long run equilibrium in which the total outflows are matched by inflows, and the vector of stocks of individuals in each benefit category remain fixed. Three of the four counterfactuals ultimately move to, and then continue to apply, the pre-GFC inflows and transition rates. Hence it is clear that these cases will ultimately converge on the same vector of the distribution of individuals across benefit types. It can take many periods to approach the long-run equilibrium, although the stocks for some benefit types may converge more quickly than others. The starting points where the pre-GFC inflows and transition rates apply are obviously different. For example, the benefit numbers are much higher at the point where pre-GFC rates finally operate, for the fourth counterfactual above in which there is a transition period from pre- to post-GFC rates.

An important implication of starting from a disequilibrium stock of beneficiaries is that, when switching to a new set of inflows and transitions which imply lower equilibrium stocks in all benefit categories, the numbers in receipt of some of the benefits need not necessarily initially fall. The numbers in some benefit categories may increase for a period, particularly if the 'starting stocks' involve large (disequilibrium) numbers of those benefit types from which there are significant flows into the category of interest.

4.2 Stocks by Benefit Type#

The time paths of all benefits combined, for each of the counterfactual cases, are shown in Figure 8. The inflows and transition rates observed over the economic cycle clearly have a substantial effect on the total number of benefit recipients and on their changes over time. Even for the three counterfactuals having identical long run equilibrium numbers, there are substantial differences at the end of the projection period. Furthermore, even when the shift to pre-GFC rates implies an immediate fall in total numbers the movement towards the equilibrium is not monotonic. The aggregate number of beneficiaries decreases for about four quarters, until gradually increasing towards the equilibrium.

Figure 8 - All Benefits Combined


Figure 8 - All Benefits Combined.
Figure 9 - Domestic Purposes Benefit


Figure 9 - Domestic Purposes Benefit.

Figure 9 shows the implications for DPB recipients. In this case, the shift from post-GFC inflows and transition rates to pre-GFC rates does not imply a reduction in numbers, but simply a slowing down in their rate of increase, for each of the three less-pessimistic cases. At the end of the projection period, the three counterfactuals continue to produce quite different stocks.

The importance of allowing for the dynamics of inter-beneficiary-category movements is shown in Figure 10 for the case of Invalid's Benefit numbers. This displays the situation where a shift to pre-GFC inflows and transition rates actually leads to higher numbers in receipt of IB than under post-GFC conditions, for all the three relevant counterfactuals. This result is perhaps counter-intuitive, particularly when it is considered that the flows onto IB from outside the benefit system are generally higher under post-GFC conditions and, furthermore, the average time spent in each of the IB categories is higher in the post-GFC transitions than for the pre-GFC transitions. However, the higher IB stock is only a temporary phenomenon, and the fact that equilibrium stocks are eventually lower in the three more optimistic counterfactuals is indicated in Figure 10 which, unlike the other diagrams, extends the projection period further out to November 2022.

As shown in Table 2 of the previous section, the average flows onto SB are very much higher than for any other benefit category, and the increase in the inflows as a result of the GFC is much higher than for the other benefit types. This is especially true of the younger SB categories. A characteristic of the inter-benefit transitions, as shown by the matrices in Appendix C, is that the movement from SB to IB is higher in the pre-GFC period than in post-GFC conditions. These features combine to generate the temporary rise in IB numbers above the post-GFC counterfactual.

The large differences in the inflows to SB categories produce, as expected, quite rapid reductions in SB numbers following the shift from post-GFC to pre-GFC conditions. These are illustrated in Figure 11. Indeed, the two most optimistic counterfactual cases converge quite rapidly towards their long run equilibrium, in view of the dominance of the inflows from outside the benefit system.

Figure 10 - Numbers in Receipt of Invalid's Benefit


Figure 10 - Numbers in Receipt of Invalid's Benefit.
Figure 11 - Numbers in Receipt of Sickness Benefit


Figure 11 - Numbers in Receipt of Sickness Benefit.
Figure 12 - Numbers in Receipt of Unemployment Benefit


Figure 12 - Numbers in Receipt of Unemployment Benefit.

The substantial differences between the inflows to unemployment between the pre- and post-GFC conditions, combined with the small number of movements into the UB categories from other benefit types, means that the three most optimistic counterfactuals shift quite quickly to the long-run equilibrium. These simulations are shown in Figure 12. Finally, Figure 13 shows the results for Miscellaneous and Under 18 Benefits.

Figure 13 - Miscellaneous and Under 18 Benefits


Figure 13 - Miscellaneous and Under 18 Benefits.

5 Effects of Welfare Reforms#

The social accounting model itself does not of course explicitly deal with behavioural responses to changes either in the benefit rates, income thresholds or abatement rates, or indeed in the regulations regarding eligibility or those designed to deal with moral hazard aspects. The transition rates are not based on econometric models in which various rates are estimated as functions of a range of relevant variables, including features of the tax and benefit system: they are based simply on observed flows over a period of time. Indeed, econometric models are seldom capable of handling the precise administrative details of many benefit structures, and to the extent that reforms involve various innovations, empirical evidence regarding behavioural responses are not available anyway.

The counterfactuals reported in the previous section involve simulations. They answer the question, 'what if the inflows and transitions among benefit categories change in well-specified particular ways?' Hence the model provides a useful tool for looking at the broad implications of changes in inflows or transitions which are thought likely to occur. The advantage, as stressed above, is that implications can be examined for benefit types other than those for which reforms are being debated. Furthermore, the dynamics of a system, which is out of equilibrium when a change arises, can be investigated. Given a specified change to one or more features of the benefit system, the potential impact on inflows to selected benefit categories and associated exit rates may be considered, drawing on a range of extraneous information.

Suppose a change in circumstances is expected to arise in May 2013 which influences only the quarterly rate of entrants to the range of unemployment benefits, while all other flows and transition rates remain at the observed post-GFC levels. The details - whether of a change in market circumstances or a change in the eligibility conditions - need not be specified here. Figure 14 illustrates the subsequent time profile of the stock of unemployment benefit recipients over all UB categories, for a range of percentage reductions in the inflows: policies 1a, 1b and 1c respectively involve 2.5, 4 and 6 per cent reductions 'across the board' in UB entrants.

Figure 14 - Projected Unemployment Benefit Stocks over Time


Figure 14 - Projected Unemployment Benefit Stocks over Time.

It has been seen earlier that unemployment stocks move relatively more quickly than other benefit types towards new steady-state values, and this is also observed for this simple change. Changes in other broadly defined benefit types are relatively small in this case.[13]

At the stage when the change is expected to take place, the stock of UB recipients is not in equilibrium even though the various rates were constant, because of the build-up in stocks resulting from the lower post-GFC exit rates (compared with those before the GFC), along with the fact that some movements into UB categories arise from other benefit types within the system, and the stocks in those 'source' categories are not in equilibrium. It is clear from the diagram that the reduction in the stock over time (for each percentage change in the inflow rate), when compared with the stock when the change arises, is smaller than the reduction when measured against the counterfactual of no change in inflows. The contrast between such comparisons would be much greater if the assumed change in the inflow rate were to occur while the counterfactual profile is rising much more steeply. A key point is that the effectiveness of a policy reform needs to be based on a sound counterfactual. In other words, simple ex post comparisons of changing stocks of benefit recipients may therefore not provide an accurate measure of the effectiveness of a policy reform.


  • [13]However, more substantial changes can be observed for particular types of UB claimant, where there are larger movements to other categories.

6 Conclusions#

This paper has presented a social accounting framework designed to examine benefit flows in New Zealand. Quarterly entry, transition and exit rates for 47 benefit types were obtained using average values observed for a number of years before and after the global financial crisis. Simulations over time of the numbers of individuals in receipt of a range of benefits were obtained under alternative assumptions about the recovery from the financial crisis.

One advantage of the approach presented here is that the dynamics and complexities of benefit flows can be investigated in detail. The approach recognises that a change is imposed on a dynamic system that is not in equilibrium. Existing stocks need to 'work their way' through the revised structure, of which just a small number of transition rates are affected by any policy change. The final effect on the number of benefit recipients are not apparent immediately, but may take some time to settle down. In the medium term of three or four years, the stocks can be substantially affected by the economic conditions at the time of the change, and the assumed conditions over the projection period (even when the equilibrium stocks are expected to be the same - as with the three most optimistic counterfactual cases considered above).

The dynamics of adjustments to revised inflow and exit rates, consequent on policy changes, mean that the ex post evaluation of policy initiatives is far from straightforward. The speed and indeed the direction of adjustments to benefit numbers depend on a vast range of flows, not only those flows which are targeted by a policy change. Furthermore, it may in some cases appear that a reform has little or no effect, if the numbers in receipt of a benefit a year or so after the reform are only slightly below those when the reform was enacted. However, the need to consider the numbers in relation to a well-specified counterfactual, not the stock at the time of implementation, is paramount. If the counterfactual suggests that the numbers would increase substantially without a policy change, a policy change which involves only a slight increase, from the time of implementation, might wrongly be judged a failure. Alternatively, and perhaps even more worryingly, a policy change which results in beneficiary stocks that are only slightly below or similar to the counterfactual, which itself implies a large fall in the absence of any intervention, may wrongly be judged to have been successful.

It is suggested that the approach examined here can provide a useful tool for the analysis of alternative policies and exogenous changes in the economy which are expected (or designed) to lead to changes in the pattern of transitions into and among different benefit categories.

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.



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


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


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


. It is desired to adjust the


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









And then obtain:





Along with new values of r using:





Finally, adjust the









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.

Appendix B. The Benefit Dynamics Dataset#

The BDD dataset is derived from the SWIFTT benefit payments system. Historical data generated by taking snapshots of SWIFTT data at given points in time are held on the Information Analysis Platform (IAP). In their raw form, the historical data do not readily permit analysis of benefit dynamics. The variables of interest are distributed across a number of different structures and complex matching routines are required to link them with spells on benefit. In addition, the structures are characterised by a considerable amount of “noise”: multiple records must be examined to establish a chain of events and, in some cases, retrospective action means that these cannot be established by working through records chronologically. The BDD links information recorded in SWIFTT for the same individual over time, strips away the noise in the historical data, and organises the data in a form amenable to longitudinal analysis. In the December 2003 update, the data set was enhanced to incorporate selected variables from the job seeker register system SOLO and the Unified Client View Phase Two (UCVII) system, other administrative data systems held by MSD.

The BDD set is stored in the secure environment of the IAP and access is restricted to a small number of authorised analysts. The data set contains no name and address information that could be used to identify individual benefit recipients.

The dataset covers the period from 1 January 1993 to the date of the most recent update. From October 2010, the data are updated at the end of each month (previously updates were quarterly). These updates are each created with a lag of at least two to three months to allow retrospective action to 'bed down' records for the end of the period.

Because of retrospective action, successive versions of the BDD will give a different benefit history for small numbers of individuals, and analyses repeated on a later version of the data set may produce slightly different results. In order to minimise interruption to projects using a given version of the data set, the most recent update and the one that preceded it are both available through the IAP. The year and month of the update is indicated by the four digits at the end of the name of each file - 1006 indicates the update to 30 June 2010 for example.

For the period up to 1 June 1996, the data set is based on consolidated files of historical SWIFTT data. The consolidated files reflect a snapshot of the situation of each individual in SWIFTT at monthly intervals only. For variables which do not have a change date recorded (such as the partnership status indicator APORT and the district office variable DIST), this leads to some imprecision in the timing of events.

Appendix C. Forward Coefficients Matrices#

This appendix presents the forward coefficients matrices for quarterly movements among benefit categories. Two sets of tables are reported, covering pre-GFC and post-GFC periods. An entry of 0.000 indicates that the proportion moving between the relevant categories was zero to 3 decimal places. Where the values were zero to 4 decimal places, there is a blank entry in the table: in most of these cases there were in fact no recorded flows.

Table 4 - Transition Rates from DPB Part 1: Pre GFC
  DPB 18_0_e DPB 18_0_f DPB 18_0_no DPB 18_5+_no DPB 18_5+_wrk DPB 18_nc_no DPB 18_nc_wrk DPB 30_0_e DPB 30_0_f DPB 30_0_no
DPB18_0_e 0.670 0.392 0.035 0.000 0.005   0.001      
DPB18_0_f 0.007 0.127 0.001              
DPB18_0_no 0.140 0.177 0.824 0.022 0.003 0.004 0.001      
DPB18_5+_no 0.006 0.007 0.021 0.775 0.118 0.002 0.001      
DPB18_5+_wrk 0.027 0.012 0.001 0.046 0.687   0.001      
DPB18_nc_no 0.001   0.005 0.008 0.001 0.947 0.169      
DPB18_nc_wrk 0.001 0.001 0.000 0.000 0.002 0.024 0.796      
DPB30_0_e 0.013 0.004 0.001   0.000   0.000 0.680 0.330 0.038
DPB30_0_f 0.000 0.009           0.007 0.174 0.001
DPB30_0_no 0.003 0.003 0.013 0.001       0.107 0.174 0.792
DPB30_14_e         0.000     0.001    
DPB30_14_f                 0.002  
DPB30_14_no       0.001       0.000   0.002
DPB30_5_e 0.001 0.001   0.002 0.040     0.064 0.025 0.003
DPB30_5_f       0.000 0.001     0.001 0.013  
DPB30_5_no 0.000   0.001 0.044 0.007     0.009 0.011 0.051
DPB30_nc_e         0.000 0.001 0.023 0.001 0.002 0.000
DPB30_nc_f             0.000      
DPB30_nc_no       0.000   0.020 0.005 0.001 0.002 0.003
DPB60_no                   0.000
IB18_no     0.000 0.001            
IB30_no               0.000   0.002
SB18_e         0.000          
SB18_no 0.001 0.001 0.003 0.003 0.000 0.001        
SB30_e               0.000    
SB30_no       0.000 0.000   0.000 0.001   0.003
UB18_e 0.001   0.000 0.000 0.000          
UB18_no 0.001 0.001 0.004 0.004 0.001 0.001 0.000      
UB30_e               0.001   0.000
UB30_no       0.000 0.000     0.001 0.002 0.004
Misc 0.000   0.001 0.001 0.000     0.001   0.002
Table 5 - Transition Rates from DPB Part 2: Pre GFC
  DPB 30_14_e DPB 30_14_f DPB 30_14_no DPB 30_5_e DPB 30_5_f DPB 30_5_no DPB 30_nc_e DPB 30_nc_f DPB 30_nc_no DPB 60_no DPB 60_wrk
DPB30_0_e 0.001     0.001   0.000 0.000        
DPB30_0_no 0.000 0.001 0.003 0.001 0.001 0.006     0.001    
DPB30_14_e 0.784 0.380 0.042 0.030 0.016 0.002 0.003 0.004 0.000    
DPB30_14_f 0.008 0.247 0.001 0.000 0.009     0.003      
DPB30_14_no 0.081 0.132 0.844 0.004 0.003 0.035 0.001   0.005    
DPB30_5_e 0.002   0.000 0.746 0.384 0.054 0.001 0.001      
DPB30_5_f       0.008 0.209 0.002          
DPB30_5_no 0.000   0.004 0.094 0.137 0.803 0.000   0.002    
DPB30_nc_e 0.014 0.013 0.001 0.001 0.000 0.000 0.853 0.460 0.038    
DPB30_nc_f 0.000 0.002     0.001   0.008 0.235 0.001    
DPB30_nc_no 0.004 0.002 0.023 0.000 0.002 0.004 0.092 0.182 0.925    
DPB60_no     0.001     0.000 0.001 0.004 0.010 0.879 0.058
DPB60_wrk 0.001     0.000     0.015 0.021 0.000 0.025 0.847
IB30_e 0.001   0.000 0.000 0.000 0.000 0.000   0.000    
IB30_no 0.001   0.004 0.000 0.000 0.003 0.001 0.003 0.002    
IB60_no                   0.006 0.001
IB60_wrk                   0.000 0.001
SB30_e 0.002 0.002 0.000 0.000     0.000        
SB30_f 0.000                    
SB30_no 0.002 0.002 0.008 0.001 0.001 0.003 0.000   0.001    
SB60_no                   0.000 0.000
SB60_wrk                     0.000
UB30_e 0.003 0.001 0.001 0.000   0.000 0.000        
UB30_f 0.000                    
UB30_no 0.003 0.002 0.009 0.001 0.000 0.003     0.001    
UB60_no                   0.001 0.000
UB60_wrk                     0.000
Misc 0.002 0.001 0.003 0.001 0.001 0.002 0.000   0.001 0.001 0.001
Table 6 - Transition Rates from IB: Pre GFC
  IB18_e IB18_f IB18_no IB30_e IB30_f IB30_no IB60_no IB60_wrk
DPB18_0_f   0.004            
DPB18_0_no     0.000          
DPB18_5+_no 0.000              
DPB18_nc_no 0.000   0.000          
DPB30_14_e         0.001      
DPB30_14_f         0.001      
IB18_e 0.819 0.422 0.022          
IB18_f 0.006 0.168 0.001          
IB18_no 0.101 0.194 0.928          
IB30_e 0.021 0.009 0.001 0.861 0.425 0.015    
IB30_f 0.000 0.009   0.004 0.189 0.000    
IB30_no 0.002 0.004 0.022 0.093 0.188 0.954    
IB60_no       0.001 0.001 0.012 0.932 0.082
IB60_wrk       0.010 0.004   0.008 0.861
SB18_e 0.001              
SB18_f 0.000 0.004            
SB18_no 0.000   0.001          
SB30_e       0.001        
SB30_f       0.000 0.001      
SB30_no       0.001 0.001 0.001    
SB60_no             0.000 0.000
SB60_wrk               0.000
UB18_e 0.000              
UB18_no 0.000   0.000          
UB30_f         0.001      
UB30_no       0.000   0.000    
Table 7 - Transition Rates from SB: Pre GFC
  SB18_e SB18_f SB18_no SB30_e SB30_f SB30_no SB60_no SB60_wrk
DPB18_0_e 0.002   0.001          
DPB18_0_no 0.017 0.015 0.039          
DPB18_5+_no 0.000   0.001          
DPB18_5+_wrk 0.000 0.003            
DPB18_nc_no 0.008 0.008 0.021          
DPB18_nc_wrk 0.001   0.000          
DPB30_0_e       0.000 0.001      
DPB30_0_no     0.000 0.001 0.001 0.002    
DPB30_14_e       0.001        
DPB30_14_no       0.001 0.001 0.001    
DPB30_5_e       0.001   0.000    
DPB30_5_no       0.001 0.001 0.002    
DPB30_nc_e 0.000     0.001 0.001      
DPB30_nc_no 0.000   0.000 0.001   0.002    
DPB60_no             0.001 0.000
DPB60_wrk             0.000 0.002
IB18_e 0.006 0.003 0.000          
IB18_no 0.007 0.003 0.013          
IB30_e 0.000     0.017 0.007 0.001    
IB30_f       0.000 0.002      
IB30_no 0.000   0.000 0.012 0.008 0.029    
IB60_no       0.000   0.000 0.054 0.016
IB60_wrk       0.000     0.001 0.028
SB18_e 0.524 0.271 0.013          
SB18_f 0.013 0.124 0.001          
SB18_no 0.148 0.243 0.671          
SB30_e 0.014 0.003 0.000 0.710 0.335 0.016    
SB30_f 0.000 0.010   0.015 0.203 0.002    
SB30_no 0.002   0.014 0.112 0.221 0.816    
SB60_no       0.001 0.003 0.007 0.814 0.078
SB60_wrk       0.011 0.004 0.000 0.015 0.765
UB18_e 0.004 0.010 0.001          
UB18_f 0.001   0.000          
UB18_no 0.013 0.005 0.025          
UB30_e 0.000     0.002 0.001 0.001    
UB30_f 0.000     0.000 0.002      
UB30_no 0.000   0.000 0.007 0.004 0.015    
UB60_no             0.009 0.004
UB60_wrk             0.000 0.003
Misc 0.003 0.003 0.005 0.002 0.001 0.003 0.001 0.000
Table 8 - Transition Rates from UB: Pre GFC
  u18 UB18_e UB18_f UB18_no UB30_e UB30_f UB30_no UB60_no UB60_wrk misc
DPB18_0_e 0.001 0.000 0.001 0.000            
DPB18_0_no 0.026 0.002 0.003 0.005           0.002
DPB18_5+_no   0.000   0.001           0.000
DPB18_5+_wrk   0.000                
DPB18_nc_no 0.016 0.001 0.001 0.002           0.001
DPB18_nc_wrk 0.001 0.000                
DPB30_0_e         0.001 0.000        
DPB30_0_no         0.001   0.002     0.001
DPB30_14_e         0.001 0.001 0.000     0.000
DPB30_14_no         0.001 0.000 0.001     0.001
DPB30_5_e         0.002 0.001 0.000     0.000
DPB30_5_f           0.000        
DPB30_5_no         0.002 0.001 0.003     0.002
DPB30_nc_e         0.001         0.000
DPB30_nc_f           0.000        
DPB30_nc_no         0.001   0.002     0.002
DPB60_no               0.002 0.001 0.001
DPB60_wrk               0.000 0.002 0.000
IB18_e 0.004 0.000                
IB18_no 0.039 0.000   0.001           0.000
IB30_e         0.001 0.001 0.000      
IB30_no         0.001 0.001 0.003     0.001
IB60_no               0.006 0.001 0.000
IB60_wrk               0.000 0.001  
SB18_e 0.000 0.000   0.001           0.000
SB18_no 0.009 0.004 0.004 0.034           0.010
SB30_e         0.000 0.000 0.003     0.001
SB30_f             0.000      
SB30_no       0.000 0.003 0.002 0.037     0.010
SB60_no             0.000 0.019 0.000 0.001
SB60_wrk               0.003 0.000  
u18 0.695                  
UB18_e 0.003 0.307 0.177 0.017           0.002
UB18_f 0.000 0.011 0.071 0.002           0.000
UB18_no 0.031 0.092 0.144 0.464           0.036
UB30_e   0.006 0.003 0.000 0.522 0.246 0.019     0.002
UB30_f   0.000 0.002   0.021 0.139 0.003     0.000
UB30_no   0.002 0.002 0.008 0.092 0.163 0.630     0.025
UB60_no         0.001 0.001 0.005 0.835 0.080 0.001
UB60_wrk         0.007 0.004 0.000 0.014 0.761  
Misc 0.012 0.003 0.001 0.042 0.004 0.003 0.024 0.003 0.001 0.745
Table 9 - Transition Rates from DPB Part 1: Post GFC
  DPB 18_0_e DPB 18_0_f DPB 18_0_no DPB 18 _5+_no DPB 18 _5+_wrk DPB 18_nc_no DPB 18 _nc_wrk DPB 30_0_e DPB 30_0_f DPB 30_0_no
DPB18_0_e 0.617 0.235 0.024 0.000 0.005   0.001      
DPB18_0_f 0.007 0.140 0.001              
DPB18_0_no 0.132 0.203 0.772 0.018 0.005 0.003 0.000      
DPB18_5+_no 0.005 0.010 0.018 0.728 0.119 0.002 0.000      
DPB18_5+_wrk 0.024 0.028 0.001 0.030 0.629   0.001      
DPB18_nc_no 0.004 0.005 0.020 0.041 0.005 0.955 0.192      
DPB18_nc_wrk 0.004 0.005 0.001 0.001 0.011 0.018 0.774      
DPB30_0_e 0.011 0.005 0.000   0.000     0.626 0.299 0.028
DPB30_0_f               0.008 0.144 0.002
DPB30_0_no 0.002 0.003 0.012 0.001 0.000     0.100 0.179 0.735
DPB30_14_e         0.001     0.001    
DPB30_14_no       0.001 0.000     0.001   0.004
DPB30_5_e 0.001     0.002 0.042     0.060 0.021 0.002
DPB30_5_f       0.000 0.001     0.000 0.007 0.000
DPB30_5_no 0.000   0.001 0.040 0.005     0.009 0.003 0.046
DPB30_nc_e 0.000     0.000 0.001 0.001 0.025 0.007 0.010 0.000
DPB30_nc_f             0.000      
DPB30_nc_no     0.000 0.003 0.000 0.020 0.005 0.003 0.014 0.017
DPB60_no                   0.000
IB18_no     0.001 0.001            
IB30_no               0.000   0.002
SB18_e 0.000   0.000   0.000   0.000      
SB18_no 0.002   0.006 0.005 0.001 0.001        
SB30_no       0.000       0.000   0.006
UB18_e 0.001   0.000 0.000 0.001          
UB18_no 0.002 0.005 0.009 0.008 0.002 0.000        
UB30_e         0.000     0.001 0.003 0.000
UB30_no 0.000   0.000 0.000 0.000     0.001   0.009
misc 0.001   0.002 0.003 0.001     0.002   0.005
Table 10 - Transition Rates from DPB Part 2: Post GFC
  DPB 30_14_e DPB 30_14_f DPB 30_14_no DPB 30_5_e DPB 30_5_f DPB 30_5_no DPB 30_nc_e DPB 30_nc_f DPB 30_nc_no DPB 60_no DPB 60_wrk
DPB30_0_e 0.001     0.001   0.000 0.000        
DPB30_0_no 0.000   0.002 0.001   0.006 0.000   0.001    
DPB30_14_e 0.725 0.354 0.029 0.026 0.018 0.001 0.002 0.001 0.000    
DPB30_14_f 0.010 0.218 0.001 0.001 0.007 0.000   0.001      
DPB30_14_no 0.085 0.143 0.789 0.004 0.007 0.030 0.001 0.001 0.004    
DPB30_5_e 0.001   0.000 0.683 0.302 0.040 0.001        
DPB30_5_f       0.011 0.199 0.002          
DPB30_5_no 0.000   0.003 0.089 0.149 0.744 0.000   0.001    
DPB30_nc_e 0.048 0.030 0.002 0.008 0.005 0.001 0.841 0.498 0.028    
DPB30_nc_f 0.000 0.011   0.000 0.003   0.009 0.299 0.001    
DPB30_nc_no 0.014 0.014 0.080 0.003 0.009 0.021 0.129 0.158 0.953    
DPB60_no 0.000   0.001     0.000 0.001 0.001 0.004 0.890 0.075
DPB60_wrk 0.001     0.000     0.006 0.008 0.000 0.023 0.837
IB30_e 0.000   0.000 0.000              
IB30_no 0.001   0.003 0.000   0.003 0.000 0.001 0.000    
IB60_no                   0.005 0.000
IB60_wrk                   0.000 0.001
SB30_e 0.003 0.001 0.000 0.001     0.000        
SB30_no 0.004 0.003 0.013 0.001   0.006 0.000   0.001    
SB60_no                   0.001 0.001
UB30_e 0.005 0.004 0.001 0.001   0.000          
UB30_f 0.000 0.001                  
UB30_no 0.006 0.003 0.015 0.002   0.008 0.000   0.001    
UB60_no                   0.001 0.000
UB60_wrk                     0.000
misc 0.002 0.003 0.004 0.002   0.005 0.000   0.000 0.001 0.001
Table 11 - Transition Rates from IB: Post GFC
  IB18_e IB18_f IB18_no IB30_e IB30_f IB30_no IB60_no IB60_wrk
DPB18_0_no     0.000          
DPB18_nc_no 0.000 0.006 0.000          
DPB30_14_f         0.003      
DPB30_nc_e       0.000        
DPB30_nc_no       0.000   0.000    
IB18_e 0.808 0.370 0.013          
IB18_f 0.005 0.173 0.000          
IB18_no 0.113 0.161 0.942          
IB30_e 0.019 0.012 0.000 0.846 0.409 0.009    
IB30_f   0.006   0.004 0.202 0.000    
IB30_no 0.002   0.020 0.113 0.165 0.959    
IB60_no       0.001   0.013 0.939 0.094
IB60_wrk       0.009 0.006   0.005 0.840
SB18_e 0.002              
SB18_f   0.006            
SB18_no 0.001   0.002          
SB30_e       0.002 0.006      
SB30_f         0.004      
SB30_no       0.001 0.001 0.002    
SB60_no             0.001 0.001
SB60_wrk               0.001
UB18_no 0.001   0.000          
UB30_e         0.001      
UB30_no       0.000   0.000    
UB60_no               0.000
Table 12 - Transition Rates from SB: Post GFC
  SB18_e SB18_f SB18_no SB30_e SB30_f SB30_no SB60_no SB60_wrk
DPB18_0_e 0.002   0.000          
DPB18_0_f 0.000              
DPB18_0_no 0.010 0.003 0.017          
DPB18_5+_no 0.000   0.001          
DPB18_5+_wrk 0.000              
DPB18_nc_no 0.018 0.011 0.036          
DPB18_nc_wrk 0.002 0.003 0.000          
DPB30_0_e       0.000        
DPB30_0_no 0.000     0.000 0.001 0.001    
DPB30_14_e       0.001 0.001      
DPB30_14_f         0.001      
DPB30_14_no       0.000   0.001    
DPB30_5_e 0.000     0.000        
DPB30_5_f         0.001      
DPB30_5_no       0.000   0.001    
DPB30_nc_e       0.001 0.001 0.000    
DPB30_nc_no 0.000   0.000 0.002   0.004    
DPB60_no             0.001 0.000
DPB60_wrk               0.001
IB18_e 0.003   0.000          
IB18_no 0.007 0.003 0.009          
IB30_e 0.000     0.009 0.006 0.000    
IB30_f       0.000        
IB30_no 0.000   0.000 0.009 0.006 0.020    
IB60_no       0.000   0.000 0.040 0.016
IB60_wrk       0.000     0.001 0.017
SB18_e 0.520 0.261 0.009          
SB18_f 0.014 0.125 0.001          
SB18_no 0.171 0.207 0.712          
SB30_e 0.014 0.011 0.000 0.698 0.304 0.012    
SB30_f 0.000 0.006   0.016 0.193 0.001    
SB30_no 0.003 0.011 0.013 0.135 0.244 0.840    
SB60_no       0.001 0.001 0.007 0.834 0.105
SB60_wrk       0.009 0.005 0.000 0.013 0.745
UB18_e 0.003 0.006 0.001          
UB18_f 0.000   0.000          
UB18_no 0.021 0.023 0.035          
UB30_e       0.003 0.002 0.001    
UB30_f       0.000 0.002 0.000    
UB30_no 0.000   0.000 0.010 0.008 0.019    
UB60_no             0.009 0.007
UB60_wrk             0.000 0.003
misc 0.002 0.014 0.005 0.002 0.002 0.003 0.001 0.001
Table 13 - Transition Rates from UB: Post GFC
  u18 UB18_e UB18_f UB18_no UB30_e UB30_f UB30_no UB60_no UB60_wrk misc
DPB18_0_e 0.001 0.000                
DPB18_0_f     0.001              
DPB18_0_no 0.015 0.001   0.003           0.001
DPB18_5+_no   0.000   0.000           0.000
DPB18_nc_no 0.034 0.002 0.001 0.004           0.002
DPB18_nc_wrk 0.001 0.001 0.001              
DPB30_0_e         0.000          
DPB30_0_no         0.001 0.001 0.001     0.001
DPB30_14_e         0.001 0.000       0.000
DPB30_14_no         0.001 0.000 0.001     0.001
DPB30_5_e   0.000     0.001 0.000 0.000     0.000
DPB30_5_no         0.001 0.001 0.002     0.001
DPB30_nc_e         0.001 0.001 0.000     0.000
DPB30_nc_f           0.000        
DPB30_nc_no         0.002 0.001 0.004     0.003
DPB60_no               0.003 0.002 0.001
DPB60_wrk               0.000 0.002 0.000
IB18_e 0.002 0.000                
IB18_no 0.044     0.001           0.000
IB30_e         0.000          
IB30_no         0.000 0.000 0.002     0.001
IB60_no               0.006 0.001 0.000
IB60_wrk               0.000 0.000  
SB18_e 0.000 0.001   0.001           0.000
SB18_f   0.000                
SB18_no 0.009 0.003 0.003 0.027           0.009
SB30_e         0.001 0.001 0.001     0.000
SB30_no   0.000   0.000 0.002 0.001 0.027     0.008
SB60_no             0.000 0.024 0.002 0.001
SB60_wrk               0.003 0.000  
u18 0.711                  
UB18_e 0.002 0.370 0.212 0.015           0.002
UB18_f   0.009 0.058 0.002           0.000
UB18_no 0.035 0.111 0.201 0.557           0.054
UB30_e   0.006 0.003 0.000 0.562 0.226 0.018     0.001
UB30_f   0.000 0.001   0.021 0.117 0.003     0.000
UB30_no   0.002 0.007 0.008 0.125 0.242 0.700     0.028
UB60_no         0.001 0.001 0.004 0.775 0.110 0.001
UB60_wrk         0.005 0.003 0.000 0.019 0.682 0.000
Misc 0.016 0.003 0.001 0.037 0.003 0.003 0.017 0.005 0.000 0.754

Appendix D. Beneficiaries Working while Receiving Benefits#

This appendix reports simulations, for each of the four cases, of the proportion of beneficiaries who are working, while not earning a sufficient amount to lift them off benefits. Results for all beneficiaries combined are shown in Figure 15.

Figure 15 - All Benefits Combined


Figure 15 - All Benefits Combined.
Figure 16 - Domestic Purposes Benefit


Figure 16 - Domestic Purposes Benefit.
Figure 17 - Invalid's Benefit


Figure 17 - Invalid's Benefit.
Figure 18 - Sickness Benefit


Figure 18 - Sickness Benefit.
Figure 19 - Unemployment Benefit


Figure 19 - Unemployment Benefit.

Appendix E. The Matrix Multiplier#

Consider the simple case of a two-state social accounting model, where the equilibrium stock,


, is given by:












The effect of a change in the vector of 'inflows' is thus straightforward, and is measured by the appropriate elements of the matrix


: in matrix terms


. Consider the effect on, for example,


, of a change in the forward coefficient,


, where:










Differentiation gives:





And using:









Given the definition, , the proportional change in the equilibrium stock of individuals in state 1 arising from the combination of a change in inflows and a change in the proportion remaining in the state from one period to the next is given by:





Appendix F. Benefit Costs per Period#

The accounting framework can be extended to cover the costs associated with the stocks and flows. Suppose the payment received by individuals in state j in period t is denoted,


. In view of the role of income-testing in New Zealand, the existence of some differences in earnings within some benefit categories means that a precise cost per period cannot be given. The term


can therefore be regarded as an average. However, in view of the definitions of states, the range within any category is small. The total cost of transfers during period t, denoted


is thus given by:








Furthermore there are administrative costs associated with the flows of individuals through the system. Suppose that the cost per person of dealing with someone moving from state j to state i from period t to t+1 is equal to


. The total administrative cost in period t, denoted


, is thus: