Number 14: The dynamics of participating in Parenting Payment (Single) and the Sole Parent Pension

This report was published by the former Department of Families, Community Services (FaCS).

Executive summary

This paper  uses the Department of Family and Community Services’ Longitudinal Data Set to analyse the length  of time lone-parent families  spent  on the Parenting Payment  (Single) (PPS)/ Sole Parent Pension  (SPP) in the period  June 1995–June 1999.1  In the first component of the analysis, the paper  presents various  summary statistics describing features of the composition of the PPS caseload at a point in time, and the population of PPS recipients over time. In the second  component, the length  of time lone parents remain  in receipt of program payments is formally  analysed.

The main findings  were that:

  • over the four-year  data period, the average time spent  on payment by a PPS recipient was 55 fortnights;
  • a variety  of time patterns of PPS receipt was evident. Of the lone parents who  received the PPS during  the data period: one subset  were ‘short-term recipients’ (18 per cent  received the PPS for six months  or less)  while another  were ‘long-term, continuous recipients’ (15 per cent  remained on the program for the full data period). Cycling on and off the program was also common  (25 per cent  experienced multiple episodes of PPS receipt); and
  • of new  episodes of PPS receipt that began  during  the data period, 25 per cent  ended  within 10 fortnights, 50 per cent  ended  within 32 fortnights, 62 per cent  ended  within two years and approximately 25 per cent  remained in progress after four years.

In examining the impact  of individual characteristics, labour  market  conditions and program parameters, it was found that:

  • lone mothers, relatively younger and older  lone parents, and those  with  younger children had lower exit  rates from PPS;
  • there  is evidence that lone parents in public housing (particularly in NSW/ACT) had longer stays on PPS;
  • lone parents with  some job attachment had much  shorter  stays on PPS, and the greater their earnings the higher  their  exit  rate;
  • the unemployment rate was not significantly associated with  the length  of stay on PPS; and
  • the effect of payment levels  on the length  of time on PPS could  not be firmly identified from the data (without making  arbitrary assumptions about the costs of children).

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1  Introduction

In 1996, there  were 467 000 lone-parent families  in Australia, accounting for approximately 20 per cent  of all families  with  dependent children (ABS 1998, p. 26). Over 73 per cent  of these families  received the Sole Parent Pension  (SPP)1  during  that year  (ABS 1998, p. 120), and program expenditures amounted to $2.8  billion  in 1995–96. The PPS (SPP) program is clearly a very important program, both in terms  of the number  of recipients and the resources devoted to it; however, relatively little  is known about the time pattern of PPS participation. This is an important gap in our knowledge, for there  is little  understanding of whether PPS acts as a long-term  substitute for labour  market  income, whether it provides effective temporary support for lone parents during  a period  of financial crisis, or whether it is associated with  a continuing cycle of poverty and dependence on public assistance.

The objective of this report  is to provide  an analysis of the time pattern of PPS participation based  on the Department of Family and Community Services’ (FaCS) recently constructed Longitudinal Data Set (LDS). The analysis presented in this report  consists of two components:

  • The first component is descriptive. A series  of cross-tabulations are presented to provide  a picture of the composition of the PPS caseload at a point in time and to describe the characteristics of lone parents who  participated in the PPS. The total time lone parents spent  in receipt of PPS payments during  the sample  period  is also examined.
  • The second  component provides a formal analysis of the length  of time lone parents spent in receipt of PPS payments. This analysis is conducted in a hazard  function  framework and provides estimates of the marginal effect of individual characteristics and program parameters on the program exit  rate (equivalently, the expected length  of time on the program).

The empirical analysis is based  on the LDS, which is derived from the administrative records of 1 per cent  of individuals who  received FaCS payments during  the period  from 23 June 1995  to 18 June 1999. The LDS has a number  of properties that make it very suitable for an analysis of PPS dynamics. Firstly, the data contain  fortnightly information on PPS participation, which is the time unit by which the program is administered. This enables the precise length  of PPS stays to be determined and thereby avoids the problems of time aggregation experienced with annualised data (Hoynes  1996). Additionally, since  the data were generated from computerised administrative records, the LDS provides reliable information on the time pattern of program participation. This is a key advantage of the LDS, since  the data are not subject to the problems of systematic non-response or recall  error as experienced with  retrospective survey-based longitudinal data.

However, it is noted  that the data have several  important limitations. Like most administrative data sources, there  is no information on individuals when  they  are not participating in a FaCS program. Consequently, it is not possible to distinguish between destination states  for people who  exit  PPS, such as through re-partnering or full-time employment.2  Furthermore, the administrative data contain  only a limited  amount  of socioeconomic information on PPS

recipients. In particular, the LDS does not record  PPS recipients’ market  wage  or information on their  employment history, which may be important in explaining the dynamics of PPS participation. These limitations are addressed in the analysis by using  estimation techniques that allow  for the effects  of unobserved individual characteristics (unobserved heterogeneity). The report  is organised as follows. In Section  2, the institutional features of the PPS are briefly described and a dynamic model  of PPS participation is discussed. Section 3 describes the properties of the LDS, including variable definitions, in some detail. The methods used in the analysis are outlined in Section 4 and the results  of the empirical analysis are presented in Section 5. Concluding comments are presented in Section 6.

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2  Program structure and theoretical model

The structure of Parenting Payment  (Single) (PPS) is detailed in Centrelink (2000, pp. 92–93) (and the structure of the Sole Parent Pension  is detailed in Centrelink [1998]). To be eligible for PPS payments, a lone parent  must be the primary carer  for a child  under  16 years  of age.3  The basic  PPS payment at the end of the data period  was $361.40 per fortnight.4 If a lone parent had fortnightly income in excess of $124.00, the basic  payment was reduced by 50 cents per dollar of income above this ‘free area’.5 If fortnightly income exceeded $857.60,6  no PPS benefit was payable. An assets  test is also applied to the PPS. If the lone parent  was a non-homeowner, the PPS payment was reduced by $3 for every  $1 000 of assets  above the threshold level  of $215  750.00 ($125 750.00 for homeowners).

Lone parents in receipt of the PPS may receive additional payments, the most important of which is the Family Payment  (FP—now known as Family Tax Benefit). Unlike the basic  PPS payment, the family payment does depend on the number  and age of dependent children. At the end of the data period, the FP was $99.00 per fortnight for each  child  of 0–12 years  of age, and $128.80 per fortnight for each  child  aged  13–15  years.7 The FP for recipients of the PPS was not subject to the regular FP income or asset tests; however, PPS recipients are required to take ‘reasonable action’ to obtain  child  support from the non-custodial parent.8  Income  from child support payments does affect the level  of FP.9 Additional  payments that a PPS recipient may receive include Rent Assistance (payable only to those  in private rentals), Remote  Area Allowance, the Pharmaceutical Allowance ($5.40 per fortnight at the end of the data period) and an Education  Entry Payment  ($200) or Employment Entry Payment  ($100).10

Given the structure of the PPS program, there  are a number  of events  that may cause  a recipient to exit  the program. One avenue of program exit  is through employment. A lone parent  may obtain  a job that pays in excess of the PPS income cutoff (see  Murray [1997a, 1997b] for an analysis of the static  labour  supply incentive effects  of SPP/PPS). Another avenue of program exit  is through partnering or re-partnering (see  Fitzgerald  [1991] for an analysis of welfare participation in the United States that incorporates features of the ‘marriage market’). Finally, a lone parent  may cease  being  the primary carer  for a ‘qualifying child’ due to, for example, a child  turning  16 years  of age or a change in custody arrangements.

Since the LDS only follows  individuals while they  are in receipt of a FaCS payment, it is not possible to determine the destination states  for those  who  exit  PPS, and hence it is not possible to distinguish between the different  exit  routes. Although  it would  be valuable to analyse the alternative exit  routes  separately, it is not possible with  the available data. Consequently, in interpreting the effects  of socio-demographic characteristics, program parameters and labour market  conditions on PPS exit  rates, it is important to keep  in mind these  very different avenues of exit.

Given the structure of the PPS program, there  are a number  of events  that may cause  a recipient to exit  the program. One avenue of program exit  is through employment. A lone parent  may obtain  a job that pays in excess of the PPS income cutoff (see  Murray [1997a, 1997b] for an analysis of the static  labour  supply incentive effects  of SPP/PPS). Another avenue of program exit  is through partnering or re-partnering (see  Fitzgerald  [1991] for an analysis of welfare participation in the United States that incorporates features of the ‘marriage market’). Finally, a lone parent  may cease  being  the primary carer  for a ‘qualifying child’ due to, for example, a child  turning  16 years  of age or a change in custody arrangements.

Since the LDS only follows  individuals while they  are in receipt of a FaCS payment, it is not possible to determine the destination states  for those  who  exit  PPS, and hence it is not possible to distinguish between the different  exit  routes. Although  it would  be valuable to analyse the alternative exit  routes  separately, it is not possible with  the available data. Consequently, in interpreting the effects  of socio-demographic characteristics, program parameters and labour market  conditions on PPS exit  rates, it is important to keep  in mind these  very different avenues of exit.

2.1   A dynamic model of PPS participation

It is useful  to consider theoretical models  of PPS participation in order  to structure the empirical analysis and help  interpret the results. The basic  principle underlying the analysis of participation is that a lone parent  (on the program) decides to either  continue receiving PPS or exit  the program depending on which alternative offers the greater level  of wellbeing. If the lone parent’s wellbeing in the next  fortnight is expected to be greater on PPS, then the current spell  will  be extended. Alternatively, if utility  is expected to be greater off the program (due  to accepting an offer of a well-paying job or through re-partnering), then the lone parent  exits  PPS.

Assume for simplicity that a lone parent  has to choose  between two discrete alternatives: working full-time or receiving PPS.11  The choice of states  is based  on the comparison of utility under  each  alternative. The lone parent’s utility  when  working full-time will  be a function  of demographic characteristics, the wage  rate and per-period costs of full-time employment, such as child  care. Assume that the potential wage  is stochastic and increasing in the length  of time previously spent  employed (due  to the accumulation of job skills and experience) but decreasing in the time previously spent  on PPS (due  to human  capital atrophy or employer screening). The presence of either  human  capital atrophy or employer screening implies negative duration dependence in the PPS exit  rate.

A lone parent’s utility  when  participating in the PPS program will  be a function  of personal and family characteristics, the level  of program payments and the length  of the current PPS spell. The length  of the current PPS spell  may directly affect a lone parent’s utility  if participation in the PPS alters  an individual’s income–leisure trade-off or changes the non-monetary ‘stigma’ costs of participation. These latter  effects  are further  potential sources of state dependence in PPS participation.

The lone parent’s decision process can be considered in the context of a search  model. New values  of the offered  wage  arrive  at random  intervals and when  this information arrives  the lone parent  chooses the preferred alternative that maximises current utility. This stylised model suggests the following reduced-form specification for the exit  rate from welfare, b:

formula

where Xt is a vector  of personal characteristic, Bt is the level  of benefits, dt  denotes per-period costs of employment, URt represents labour  market  variables, such as the unemployment rate, which affect the arrival  rate of job offers12, T is the length  of time on PPS in the current spell and P represents an individual’s past receipt of PPS.

It is straightforward to derive  the following predictions:

formula

Higher PPS payments are a disincentive to supplying labour  and therefore have a negative effect on the PPS exit  rate. Higher costs of employment decrease the relative attractiveness of employment thereby reducing the PPS exit  rate. An increase in the unemployment rate is equivalent to a decrease in the arrival  rate of job offers, which also leads  to a decline in the exit rate. Furthermore, as the length  of the current spell  increases, the effects  of human  capital atrophy, employer screening, changes in preferences over income–leisure or in stigma  costs of participation lead to a decreasing exit  (or hazard13) rate. By the same reasoning, past PPS spells may have a similar  dampening effect on the exit  rate. The latter  two predictions correspond to forms of state dependence discussed in Heckman  and Borjas (1980).

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3  The FaCS Longitudinal Data Set

The data analysed in this report  were derived from the fortnightly administrative records of the PPS program for the period  23 June 1995  to 18 June 1999.1 The LDS is a 1 per cent  random sample  of individuals who  received a FaCS payment during  the sample  period. The set of PPS payment records were drawn  from the LDS: there  were 363 145 fortnightly records generated by 6 643 individual lone parents. The composition of the PPS caseload, and the PPS population, are described using  this set of records.

The (fortnightly) information available in the LDS and used in the analysis include basic demographic variables such as the lone parent’s gender, age, country of birth, whether the individual identifies as an Aboriginal  or a Torres Strait Islander, the number  of dependent children (and number  aged  from 0–12 years, between 13 and 15 years, and number  over 15 years  of age), plus the age of the youngest child. There is also detailed information on home ownership or type  of rental  accommodation. This information is used to create a set of variables indicating whether the individual is a homeowner, is purchasing their  own  home, has some other  form of homeownership (such  as joint ownership), is renting privately, is renting from a government authority, has some other  form of rental  (such  as board and/or lodging  or site fees), is neither a homeowner nor pays rent, or whether this information is missing. The LDS also includes the individual’s postcode, which was used to create a series  of variables indicating State of residence. The State of residence and record  date were then used to match  the LDS data with  the local  unemployment rate.

The LDS contained a range  of information on the financial position of PPS recipients. In particular, the LDS records information on receipt of child  support payments plus earned and unearned income. The amounts  of these  income components, plus variables indicating whether or not the lone parent  received income from these  sources, is used in the analysis. Furthermore, the LDS contained detailed information on program payments, including the actual  amount  of the following payments: PPS, Family Payment  (now  Family Tax Benefit), Pharmaceutical Allowance and Rent Assistance. In addition, information from the program rules  and the lone-parent family’s  characteristics were used to construct maximum potential payment levels (before  the application of the income test)  for use in the empirical analysis. All nominal  values were inflated  to June 1999  dollars  using  the national CPI.

3.1   Duration information

To analyse the length  of time lone parents spend  on the PPS, it is necessary to construct ‘spells of PPS receipt’. A ‘spell’ is a sequence of consecutive fortnights of PPS receipt. A spell  therefore aggregates information on a period  of equivalent behaviour. To minimise the effects  of coding errors  and the appearance of false transitions, an exit  was defined  as two consecutive fortnights not in receipt of PPS payments.14 For spells  beginning after 23 June 1995, it was possible to determine the precise length  of the spell  unless  the spell  was still in progress in mid-June 1999. Spells in progress at the end of the data period  are ‘right-censored’ (that  is, the ending  date and hence total duration of the spell  is not observed). The econometric methods take this censoring into account.

A substantial number  of spells  were in progress at the beginning of the data period. The LDS does record  the length  of time the individual had been  on the current payment and so it is possible to determine the duration of these ‘interrupted spells’. However, if the analyst  is interested in the ‘completed spell  distribution’, and intends  to make inferences about the effects of individual characteristics and program parameters on the expected time on the program (or expected program expenditures), then the analysis must be based  on ‘fresh’ spells  that began during  the sampling window. As proved  by Heckman  and Singer  (1984, 1985),‘interrupted spells’ are a special subset  of spells  that are atypically long. In essence, of all the spells  that began on a particular day prior to the start of the data period, only those  spells  that are sufficiently long make it into the data period. The interrupted spells  therefore form a ‘length- biased  sampled’ (see  Lancaster  1990  for a discussion of this issue), which leads  to sample selection bias analogous to the well-known problems of selection bias experienced in analysing cross-sectional data. Consequently, the selection mechanism (which may depend on calendar time effects, time-varying covariates and unobserved individual effects)  causing the interrupted spells  to enter  the data period  must be controlled for, otherwise models  estimated with  the interrupted spells  will  give biased  estimates and potentially misleading inferences. As a result, in the present analysis, the set of interrupted PPS spells  are treated as if they  are ‘left-censored’, and although descriptive statistics for these  spells  are presented, they  are not used in the estimation of the duration models. The sample  of fresh PPS spells  form the basic  unit for the duration analysis; for each  of these  spells  there  is information on duration (measured in fortnights) and whether it is right-censored, plus the other  variables available from the LDS as listed  above.

An issue  of key policy interest is the effect of PPS payments on the program exit  rate. Consequently, it is critical to consider the source of variation between spell  durations (or PPS exit  rate)  and program payments underlying the estimation results. Firstly, it is important to obtain  a measure of payment levels  that is exogenous to the behaviour of the individual lone parent. For this reason, it is inappropriate to use the actual  level  of payments made  to a lone parent, since  this is affected  by their  earned income. For instance, low benefit  payments may be correlated with  short spell  durations (and high payments with  long spell  duration); however, it would  be erroneous to attribute this difference to a behavioural effect of payments levels. A lone parent  may receive relatively low payments because of a high level  of earned income and hence it may be their  strong  attachment to the labour  market  (which may in turn be a function of their  level  of education or some other  characteristic) which is responsible for their  shorter stay on the program. Since actual  payments are affected  by an individual’s labour  supply, this measure of program payment is endogenous and cannot  be used to identify  a program impact. By this reasoning, it is more appropriate to examine the effect of maximum potential payments on exit  behaviour, since  potential payments are beyond  the control  of an individual (they  are set by legislation) but are likely  to influence an individuals’ PPS participation and labour market  activity.

Variation  in potential payments provides the key for identifying the impact  of payment levels  on exit  behaviour. Unfortunately, there  is very little  variation in potential PPS payments during  the data period. The nominal  PPS basic  payment was increased marginally twice a year  in line with changes in the CPI over the data period. Consequently, the real level  of potential PPS payments was effectively constant over the period  of the analysis. Real Family Payments were similarly constant over the data period.

However, it is useful  to note that the potential PPS payments are a flat rate, independent of family size, while potential Family Payments are a function  of the number  and age of dependent children. If family needs  do vary with  family size, then the flat rate PPS payment will  have a greater effect on improving the wellbeing of families  with  few children than the larger  families. In addition, if the increase in Family Payments for each  additional child  do not completely off- set the costs associated with  the extra  child, this will  lead to further  variation in potential program payments and family wellbeing by family size and composition.15 The differences in ‘adult-equivalent’ payment levels  and family wellbeing may then induce differences in the exit behaviour according to the size and age composition of families. Therefore, one potential source of identification for the effect of program payment levels  on the exit  rate is through the nonlinearity of adult equivalence scales.16

Based on this reasoning, several  measures of ‘adult-equivalent’ payment levels  are considered in the estimation: total payments to the family, per-person payments, and total payments divided  by three  alternative measures of ‘adult  equivalents’ (the  square-root of family size, the OECD adult equivalent scale  and the scale  implicit in the Henderson poverty lines). The use of total family payments implies that the payment is spent  on pure  public goods within the household (such as shelter or heating), while the use of per-person payments implies the payments are spent  on pure  private goods (such  as food). These two benefit  measures represent the extreme adult equivalence scales. The other  three  scales  assume  a mixture of within-family public and private goods. The number  of children enters  linearly in the OECD scale  (each  child  is equivalent to 0.5 adults)  and non-linearly in the other  two scales. The Henderson scale  also recognises differences in family needs  depending on whether the lone parent  is employed. The sensitivity of the estimated impact  of program benefits on exit  behaviour is examined below. However, it is important to note that the identification of the effect of payment levels  on the exit  rate is based  on the non-linearity of the payment scale  and the choice of the ‘appropriate’ adult equivalence scale.17

An issue  in the estimation of duration models  is the specification of the covariates as either fixed throughout a spell  or as varying  over time as the spell  progresses. The analysis presented in this report  treats  all variables as fixed  throughout the spell  (at the start-of-spell values). Given the relatively short time period  covered by the sample  (four years), it was felt that allowing for time-varying covariates was a minor issue  in the duration model  estimation.

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4  Methods

4.1   Description of PPS population

The first component of the analysis simply  describes the composition of the PPS caseload in an average fortnight. The information is then aggregated for each  individual lone parent, and the characteristics of the ‘average’ PPS recipient is described. In addition, the PPS population is broken  down  into groups  corresponding to the total time spent  on PPS during  the data period, and whether the lone parent  experienced one or multiple episodes of benefit  receipt. This exercise provides a comparison of the characteristics of lone parents who  exhibited different patterns of program participation.

4.2   Duration analysis

The second  component of the research project involves  the formal analysis of the length  of time spent  on PPS using  a hazard  function  framework. The analysis proceeds by first estimating the empirical hazard  or exit  rate and survival  probability functions. The estimate of the hazard rate at duration T is calculated as the number  of spells  which terminated in fortnight  T as a fraction  of spells  at risk of terminating in fortnight T. The survival  probability function  simply reports  the proportion of spells  that are at least T fortnights in duration. The empirical hazards and survival  probabilities are equivalent ways  to summarise the pattern of PPS exits  as a function of time on the program which do not require the imposition of a parametric function on the underlying distribution.

A limitation of the empirical hazard  rate estimator is that it treats  the population as homogeneous. Spell lengths potentially vary according to the characteristics of the lone parent, with  labour  market  conditions and program parameters. To control  for covariates, the proportional hazard  duration model  is used whereby

formula

where bi(t) is the hazard  for person  i, bo(t) is the baseline hazard  common  to all individuals, zi(t) is a vector  of observable characteristics (which may vary with  t) and symbol is a parameter vector  to be estimated. For different  values  of symbol, the hazard  function  for individual i is shifted  proportionally up or down  relative to the baseline.

The estimation approach implemented for this report  is an extension of Prentice and Gloeckler (1978) and is detailed in Meyer (1988, 1990) and Lancaster  (1990, pp. 172–208). The baseline hazard  is estimated non-parametrically as a piece-wise constant function. The time axis is divided into a finite number  of intervals and a separate baseline hazard  parameter is estimated for each  interval. This approach provides a very flexible method  for estimating the baseline hazard  function  and avoids the imposition of a parametric functional form on the baseline. This is an important advantage of the specification for it has been  shown  that mis-specifying the baseline hazard  is a major source of error in drawing inferences concerning both the presence of duration dependence (Manton, Stallard  & Vaupel  1986; Blank 1989) and the impact  of covariates (Heckman & Singer  1985, Dolton & van der Klaauw  1995).

The log likelihood function  for this model  with  a sample  of N welfare spells  is given  by:

 

formula

where ki is the observed length  of the ith welfare spell, symbol equals one if the spell  terminates before  being  right-censored and symbol is zero if the spell  is censored. In maximising the log likelihood, the formula are treated as parameters to be estimated.18

The proportional hazard  model  may be extended to allow  for unobserved individual characteristics. Assuming  that the unobserved heterogeneity takes  a multiplicative form, the hazard  rate is given  by

formula

where symbol is a non-negative random  variable assumed  to be independent of zi(t).19 Maximum likelihood estimates of the parameter vector  and baseline hazard  are then obtained by conditioning the likelihood function  on 8iand then integrating over the distribution ofsymbol. This approach requires specifying a distribution function  for symbol. One popular distribution is the gamma, which gives a closed  form expression for the likelihood function. Alternatively, the unobserved heterogeneity distribution can be estimated nonparametrically. The log-likelihood functions for these  models  are presented and discussed in Meyer (1988, 1990), Dolton and van der Klaauw  (1995) and Barrett (2000). Estimation of the duration model  with  each  type  of unobserved heterogeneity was attempted but difficulties in empirically identifying the heterogeneity terms  were encountered and are discussed in Section 5 below.

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5  Empirical results

5.1   Describing the PPS caseload  and population

Summary  statistics for the sample  of PPS records extracted from the LDS are presented in Table 1. Note that each  record  is a ‘person-fortnight’, and so the reported sample  averages in Table 1 show  the composition of the PPS caseload in an average fortnight. The sample  averages show that at a point in time the vast majority of PPS recipients are lone mothers. The average age of PPS recipient in a given  fortnight was approximately 34 years, 80 per cent  of the PPS recipients were born in Australia  and 5 per cent  identified as Aboriginal  or Torres Strait Islander.  The average number  of dependent children was 1.75  (with 1.4 aged  under  13 years), while the average age of the youngest child  was 6.2 years. In terms  of homeownership status, 13 per cent were homeowners, while a further  7.8 per cent  were either  paying off a home or held some form of joint ownership of a home. The large  majority (71.7  per cent)  of PPS recipients were renters; 44 per cent  of them at a point in time rented  privately while 20 per cent  rented  from a government authority, 7 per cent  had some other  rental  arrangement (such  as board and lodging) while almost 3 per cent  paid no rent. Across the sample, the average amount  of rent paid was $144  per fortnight ($201 averaged across  those  who  pay some form of rent). The distribution of PPS recipients across  the States and Territories shows  that NSW/ACT accounts for the largest  fraction  with  over one-third  of the caseload, while the Northern  Territory  has the smallest fraction  with  1.9 per cent.

Turning  to the financial variables, approximately 44 per cent  of the PPS recipients in an average fortnight received some child  support. The average fortnightly amount  of child  support was $85 ($195 among  those  who  received child  support). Just over one-quarter of PPS recipients in a typical fortnight received earned income, which averaged $101  ($372 for those  with  positive earnings). Only 16 per cent  of PPS typically received some unearned income, which averaged $8 per PPS recipient per fortnight ($48  for those  with  unearned income).20 In terms  of program payments, the average fortnightly PPS basic  payment was $308  and the average Family Payment to a PPS recipient was $185. Approximately 43 per cent  of PPS recipients at a point in time also received Rent Assistance (the  large  majority of PPS recipients paying rent to a private landlord) with  an average Rent Assistance payment of almost $31 ($72  averaged across  those  receiving Rent Assistance).

The fortnightly PPS records were then aggregated for each  individual lone parent  who  received a PPS payment during  the sample  period. The 363 145 person-fortnight records summarised in Table 1 were generated by 6 643 lone parents who  experienced an average of 55 fortnights on the program. Table 2 presents the average characteristics of these  PPS recipients. Note that Table 1 is equivalent to Table 2 where each  PPS recipient in Table 2 receives a weight equal  to the number  of fortnights that they  were on the program. Consequently, higher  averages for a characteristic in Table 2 relative to Table 1 (such  as the fraction  of PPS recipients who  were lone fathers) indicates that characteristic was associated with  less time on the program. Column 1 of Table 2 presents the sample  means  for all lone parents grouped together. In contrast to the caseload averages at a point in time, the average PPS recipient over the data period  was slightly younger, more likely  to be male and have marginally fewer  children. The average PPS recipient was also more likely  to be a homeowner and less likely  to be in rental  accommodation. In terms of their  location, the lone parents observed over the data period  were slightly less likely  to be from NSW/ACT or Victoria  but marginally more likely  to be from Queensland than suggested by the point-in-time  caseload averages.

The dynamics of participation in Parenting  Payment (Single) and the Sole Parent Pension

Table 1: Sample of fortnightly PPS records
  Sample  average
Demographic characteristics
Sole mother 0.9312
Sole father 0.0688
Age (yrs) 34.0511
Australian-born 0.8011
Identifies  as Indigenous 0.0544
Number children under  13 years 1.4359
Number children over 13 years 0.3200
Age of youngest child 6.1614
Homeownership and rental type
Private  rent 0.4419
Govt. rent 0.2034
Other rental 0.0720
No rent paid 0.0294
Homeowner 0.1312
Purchasing home 0.0344
Other homeowner 0.0440
Missing 0.0436
Rent paid ($) 143.80
State of residence
NSW/ACT 0.3544
Vic 0.2111
Qld 0.1957
SA 0.0863
WA 0.1052
Tas 0.0284
NT 0.0190
Financial variables
Whether received Child Support 0.4362
Amount Child Support 84.96
Whether earnings>0 0.2708
Earned income 100.78
Whether unearned income >0 0.1614
Unearned income 7.70
Program variables
Family Payment  amount 184.98
Basic payment entitlement 308.32
Pharmaceutical Allowance 5.42
Whether received Rent Assistance 0.4289
Rent Assistance entitlement 30.71
Total observations (SP-fortnights) 363,145

The sample  of PPS recipients was then divided  into groups  according to the total time they were on PPS payments during  the sample  period. Column  (2) presents the average characteristics of those  lone parents who  received the PPS for a total of 13 or fewer  fortnights during  the sample  period. Columns  (3)–(6) show  the average characteristics for the set of PPS recipients with  progressively greater total time on PPS, with  column  (6) summarising the characteristics of those  with  the maximum possible observed length  on time on the program of 105 fortnights. From Column  (2) it is apparent that those  who  spent  less total time on the program were, on average, marginally older  and substantially more likely  to be a lone father, compared to the average of all PPS recipients. In addition, they  were more likely  to have some form of homeownership and less likely  to be renting, and much  less likely  to be in public housing (especially in NSW/ACT). Lone parents who  were on the program for at most 13 fortnights during  the sample  period  accounted for approximately 18 per cent  of all PPS recipients observed during  the sample  period, and as a group  they  accounted for 2.2 per cent of the total time spent  on the program and 2 per cent  of total PPS program expenditures.

For brevity, column  (6), which summarises the characteristics of those  who  were most dependent on the program during  the data period, is compared with  column  (2). Almost 15 per cent  of the PPS recipients observed in the data period  remained on the program for the full 105 fortnights. This group  of PPS recipients accounted for approximately 30 per cent  of both the total time spent  on the program and total program expenditures over the data period. Relative  to column  (2), this group  of PPS recipients is more likely  to be composed of lone mothers, those  born in Australia  and identifying as Aboriginal  or Torres Strait Islander. The ‘long-termers’ on average have slightly more children, with  the youngest marginally younger than that for those  PPS recipients with  the shortest  stay. The PPS recipients with  the longest period  on the program are substantially less likely  to have some form of home ownership and more likely  to be renting, especially from a government authority. The sample  of PPS recipients was then divided  into two groups  according to whether the parent experienced a single  or multiple episodes of benefit  receipt over the course  of the data period. Approximately three-quarters of the lone parents experienced only a single  spell. Those who  had multiple spells  experienced 2.4 spells  on average, and spent  an additional two fortnights (on average) on the program over the course  of the data period. Relative  to lone parents who  had only a single  spell, those  with  multiple spells  were more likely  to be female, have younger children, be Australian-born and identify  as Aboriginal  or Torres Strait Islander. Lone parents who  had repeat episodes were also less likely  to have some form of homeownership and more likely  to be in rental  accommodation, were more likely  to reside  in Queensland or Western Australia  and less likely  to reside  in New South Wales  (and the ACT) or Victoria. Interestingly, the total time on program and total program expenditures accounted for by each  group  was equal  to their  population shares.

Table 2: Sample of PPS recipients
Total time on program (fortnights) 105 Single spell Multiple spells
Characteristics   All recipients Jan-13 14–39    40–78    79–104
Total time on PPS 54.6658 6.7431 25.7814 58.0087 93.3990 105.0 54.0748 56.5224
Sole mother 0.9089 0.8505 0.8951 0.9134 0.9451 0.9486 0.9067 0.9158
Age 32.6125 33.7046 32.5426 31.9156 31.4142 34.0809 33.3545 30.2815
Total children 1.7000 1.6778 1.6551 1.6304 1.7523 1.8558 1.6970 1.7095
Age of youngest child 5.1143 5.6280 5.2312 5.0389 4.4734 5.2198 5.3741 4.2980
Australian-born 0.7974 0.7921 0.7821 0.8042 0.8090 0.8024 0.7869 0.8304
Identifies as Indigenous 0.0476 0.0361 0.0436 0.0488 0.0676 0.0413 0.0367 0.0817
Private rent 0.4031 0.4158 0.4068 0.4114 0.3922 0.3810 0.3991 0.4158
Govt. rent 0.1451 0.0876 0.1042 0.1354 0.1716 0.2631 0.1455 0.1440
Other rental 0.0978 0.0928 0.1030 0.0959 0.1167 0.0766 0.0933 0.1122
No rent paid 0.0622 0.0464 0.0714 0.0784 0.0592 0.0413 0.0576 0.0767
Home owner 0.1492 0.1856 0.1592 0.1470 0.1260 0.1220 0.1558 0.1284
Purchasing home 0.0446 0.0722 0.0600 0.0389 0.0245 0.0212 0.0478 0.0343
Other home owner 0.0443 0.0232 0.0366 0.0442 0.0507 0.0736 0.0472 0.0349
Missing 0.0537 0.0765 0.0587 0.0488 0.0592 0.0212 0.0538 0.0536
NSW/ACT 0.3497 0.3110 0.3582 0.3678 0.3601 0.3377 0.3568 0.3273
Vic 0.2034 0.1985 0.1977 0.1888 0.2046 0.2419 0.2161 0.1633
Qld 0.2073 0.2397 0.2135 0.2051 0.1885 0.1855 0.1969 0.2400
SA 0.0860 0.0962 0.0840 0.0744 0.0845 0.0988 0.0863 0.0848
WA 0.1040 0.1031 0.0998 0.1133 0.1006 0.0998 0.0988 0.1203
Tas 0.0291 0.0275 0.0284 0.0314 0.0330 0.0232 0.0266 0.0368
NT 0.0178 0.0215 0.0139 0.0180 0.0245 0.0111 0.0153 0.0256
NSW*Govt. rental 0.0565 0.0275 0.0354 0.0616 0.0710 0.0978 0.0576 0.0530
Rent paid ($) 1.3076 1.3975 1.3283 1.3497 1.3499 1.3521 1.3360 1.4079
Average basic payment 308.32 292.45 308.28 308.25 312.06 322.69 309.98 303.11
Average Family Payment 184.98 170.41 176.43 185.79 197.72 199.14 182.29 193.45
Number of spells 1.3373 1.1177 1.3544 1.5572 1.4937 1.0000 1.0000 2.3971
Individual sole parents 6643 1164 1583 1721 1183 992 5039 1604
Share SPP Pop. 1.0000 0.1752 0.2383 0.2591 0.1781 0.1493 0.7585 0.2415
Share Total Time 1.0000 0.0216 0.1124 0.2749 0.3043 0.2868 0.7503 0.2497
Share PPS Exp. (BP) 1.0000 0.0205 0.1124 0.2749 0.3080 0.3002 0.7544 0.2454
Share PPS Exp. (BP+FA) 1.0000 0.0203 0.1104 0.2753 0.3144 0.3034 0.7488 0.2513

5.2   Analysing the length of PPS spells

The next  step of the research is to more formally  analyse the length  of ‘spells’ of PPS receipt. The cross-tabulations summarised above provide  a series  of correlations between two variables. It is not clear  from these  tabulations what  is the partial  correlation (or marginal effect)  of a variable with  the length  of time on PPS. The estimation of the duration models  uncovers these marginal effects. Additionally, by considering the source of variation in the covariates, it is possible to determine whether the behavioural effects  of program parameters on PPS can be identified in the data.

To undertake the duration analysis, spells  of PPS receipt were constructed. The 6 643 PPS recipients experienced a total of 8 884 spells. Summary  statistics for the sample  of PPS spells are presented in Table 3. The hazard  models  were estimated using  the fresh spells  of column (3). For these  spells, the average duration was 28.5  fortnights, 90 per cent  were experienced by lone mothers, the average age at spell  commencement was 32years, 81 per cent  were experienced by lone parents who  were born in Australian  and 6.8 per cent  were by individuals who  identify  as Aboriginal  or Torres Strait Islander. The average number  of children was 1.75, and the average age of the youngest child  in the family was 4.7 years. To allow  for non-linearity in the effect of the age of youngest child, series  of dummy  variables were constructed indicating whether the youngest child  was aged  0–4 years, 5–11 years, 12–14  years and 15+ years. For more than 58 per cent  of the sample, the youngest child  was aged  4 years  or younger, while for 2 per cent  the youngest child  was age 15. In terms  of accommodation arrangements, 15 per cent  of the spells  were experienced by lone parents who  were home owners, 6 per cent  were paying off their  home while approximately 42 per cent  rented  from a private landlord, 10 per cent  were in public housing, another  11 per cent  paid for board or lodging  and a further  14 per cent  neither owned a home nor paid rent. Only 28 per cent  of families  received some child  support, almost 20 per cent  had some employment income (the  average earnings for those  who  worked was $98.24/0.1958=$501 per fortnight) while 15 per cent  received some unearned income. The average PPS payment at the commencement of these  spells  was $281  per fortnight, and the average FP was $190  per fortnight. Approximately 38 per cent  also received Rent Assistance. In total, there  were 5 685 ‘fresh’ spells, of which 39 per cent  corresponded to a repeat spell  by a lone parent, and 55 per cent were ongoing at the end of the data period.

The summary statistics for the ‘interrupted’ spells  are shown  in column  (2) of Table 3. As is clear from the first row of Table 3, the average observed duration of the interrupted spells  is much longer  than for the fresh spells. As will  be apparent from the estimation results  presented below, the set of interrupted spells  have a concentration of observed characteristics which are associated with  longer  spell  duration. Moreover, as Heckman  and Singer  (1984, 1985) proved, this set of spells  also has a concentration of unobserved individual characteristics which are associated with  longer  spell  lengths. Therefore, in order  to derive  unbiased estimates of the underlying distribution of completed spells, the duration models  are estimated with  the sample of fresh spells  summarised in column  (3).

Table 3: Sample of PPS
  Total spells Interrupted spells Fresh spells
Duration (fortnights) 40.9905 63.3326 28.4185
Demographic characteristics
Sole father 0.0893 0.0650 0.1029
Age (yrs) 32.4439 33.6774 31.7498
Identifies  as Indigenous 0.0615 0.0497 0.0681
Australian-born 0.8058 0.8046 0.8065
Number children 1.7384 1.7118 1.7534
Age of youngest child: 0–4 yrs 0.5349 0.4508 0.5822
Age of youngest child: 5–11 yrs 0.3371 0.3907 0.3069
Age of youngest child: 12–14  yrs 0.1013 0.1238 0.0887
Age of youngest child: 15 yrs 0.0267 0.0347 0.0222
State of residence
NSW/ACT 0.3407 0.3482 0.3365
Vic 0.1929 0.2160 0.1799
Qld 0.2175 0.1932 0.2311
SA 0.0861 0.0878 0.0851
WA 0.1093 0.1028 0.1129
Tas 0.0298 0.0313 0.0290
NT 0.0213 0.0166 0.0239
Homeownership and rental type
Private  rent 0.4145 0.4095 0.4172
Govt. rent 0.1440 0.2173 0.1027
Other rental 0.0971 0.0819 0.1057
No rent paid 0.0593 0.0475 0.0660
Homeowner 0.1427 0.1275 0.1513
Purchasing home 0.0460 0.0197 0.0609
Other home-owner 0.0386 0.0660 0.0232
Missing 0.0577 0.0306 0.0730
Rent paid ($) 139.16 139.73 138.84
Financial variables
Whether received Child Support 0.3145 0.3711 0.2827
Amount Child Support 52.13 56.96 49.41
Whether earnings>0 0.2165 0.2532 0.1958
Earned income 95.98 91.95 98.24
Whether Unearned Income  >0 0.1526 0.1566 0.1504
Unearned Income 7.74 6.96 8.18
Program variables
Family Payment  amount 153.38 88.87 189.68
Basic payment entitlement 287.70 299.01 281.34
Pharmaceutical Allowance 4.96 5.17 4.84
Whether received Rent Assistance 0.3890 0.4079 0.3784
Rent Assistance entitlement 28.25 29.58 27.51
Repeat  spell 0.2523 0.3942
Previous  duration 5.3515 8.3629
Unemployment rate (%) 8.1933 8.0490 8.2745
Right censored 0.5824 0.6324 0.5543
Observations (spells) 8884 3199 5685

Empirical hazard rate estimates

The empirical hazard  rate function  for the sample  of fresh spells  is plotted in Figure 1A. The hazard  plot shows  that the exit  rates generally declined with  spell  duration, although the hazards rates at the longest  spell  durations are somewhat erratic due to the small number  of observations ending  at these  durations. The exit  rate from PPS starts at 3.4 per cent  in the first fortnight of a spell, declines to 2.4 per cent  by the sixth  fortnight of a spell, and although the hazard  rate is somewhat erratic, there  is a general decline over longer  spell  durations. For example, by fortnight 13 the hazard  is 2.2 per cent, at fortnight 26 it is 1.7 per cent, at fortnight 52 it is 0.55  per cent  and at fortnight 78 it is 0.93  per cent. The uneven decline in the exit  rate with  spell  duration suggests that it would  be inappropriate to impose  a smooth, parametric functional form on the hazards.

An alternative description of the spell  data is provided by the survival  function  plot in Figure 1B. The survival  functions show  the proportion of spells  that are at least x months  long. It is apparent that 25 per cent  of all spells  end within 10 fortnights, 33 per cent  have ended within 15 fortnights while 50 per cent  have ended  after 32 fortnights of benefit  receipt (the median  spell  length). A total of 38 per cent  of spells  are still in progress after 52 fortnights (2 years), 29 per cent  are ongoing after 78 fortnights (3 years) and 25 per cent  remain  in progress after 100 fortnights (almost  4 years).21

The set of PPS spells  were stratified according to one set of characteristics at a time. The empirical hazard  rate and survival  function  for the various  divisions of the sample  are illustrated in the series  of Figures  2A–19B (see  Appendix B). A subset  of the survival  probabilities is reported in Table 4. By stratifying the sample  along  one dimension at a time, it is possible to obtain  a better  sense  of the relationship between that characteristic and spell  duration.

Figure 1A: Empirical  Hazard Rate Functions:  SPP/PPS  Spells

Figure 1A: Empirical  Hazard Rate Functions:  SPP/PPS  Spells

Figure 1B: Empirical  Survival Functions:  SPP/PPS  Spells

Figure 1B: Empirical  Survival Functions:  SPP/PPS  Spells

The figures  show  that substantial differences in exit  behaviour were evident along  the dimensions of gender, age of youngest child  and age composition of children, state of residence, lone parent’s labour  force status (presence of earned income) and whether the spell  is a repeat spell.

The shape  of the empirical hazard  and survival  functions indicate a degree of negative duration dependence; the longer  a lone-parent family remains on the PPS, the (marginally) less likely  it is they  will  exit. However, the decline in the exit  rates is minor, plus this apparent duration dependence may be a reflection of differences in individual characteristics rather  than true state dependence. The results  from the duration model  estimation, which controls  for observable characteristics and unobserved heterogeneity, are presented in the next  section.

Table 4: Empirical survival probabilities
  Fortnight
Characteristics 6 13 26 32 78 100
Population 0.8306 0.6966 0.5459 0.3836 0.2909 0.2527
Sole mother 0.8359 0.7055 0.5584 0.3969 0.3040 0.2634
Sole father 0.7842 0.6181 0.4357 0.2667 0.1741 0.1558
Age<= 31.88  years 0.8509 0.7191 0.5534 0.4013 0.3079 0.2585
Age>31.88  years 0.8095 0.6731 0.5385 0.3647 0.2725 0.2462
Not identify  as Indigenous 0.8313 0.6993 0.5518 0.3876 0.2937 0.2538
Identifies  as Indigenous 0.8210 0.6594 0.4655 0.3301 0.2533 0.2400
Australian-born 0.8283 0.6968 0.5463 0.3821 0.2891 0.2526
Foreign-born 0.8401 0.6958 0.5445 0.3904 0.2988 0.2545
1 child<13  years  old 0.8499 0.7332 0.5850 0.4288 0.3290 0.2843
2+children<13 years  old 0.8240 0.6808 0.5356 0.3831 0.3013 0.2678
0 children>13years 0.8364 0.7075 0.5571 0.4032 0.3126 0.2707
1+children>13years 0.8063 0.6504 0.4986 0.2971 0.1939 0.1731
Youngest child<=4 years  old 0.8422 0.7140 0.5647 0.4096 0.3151 0.2689
Youngest child> 4 years  old 0.8097 0.6651 0.5119 0.3360 0.2449 0.2243
NSW/ACT 0.8491 0.7359 0.5767 0.4194 0.3241 0.2918
Vic 0.8453 0.7257 0.5932 0.4124 0.3265 0.2912
Qld 0.8123 0.6444 0.4802 0.3274 0.2427 0.2106
SA 0.8045 0.6483 0.5193 0.3595 0.2561 0.1655
WA 0.8157 0.6899 0.5429 0.3797 0.2744 0.2309
Tas 0.8587 0.7081 0.5660 0.3824 0.3002 0.3002

Duration model estimates

Effects of demographic and economic characteristics

The estimates of the piece-wise constant proportional hazard  models  are presented in Tables 5 and 6 (pp. 26–29).22 Model 1 only includes controls  for basic  demographic characteristics. It is clear  that the relatively small number  of lone fathers  have a substantial and statistically significant higher  exit  rate from PPS compared to lone mothers. The exit  rate is increasing with age, up to approximately 32 years, and then it declines. The number  of dependent children is found to have a positive and significant effect on the exit  rate. The direction of this effect indicates that families  with  more children have shorter  stays on the program, which is somewhat surprising. The age of the youngest child  has a substantial and significant effect on the exit  rate. Relative  to families  in which the youngest child  is aged  5–11 years, families  where the youngest is an infant have a 7.5 per cent  lower exit  rate. For families  where the youngest child  is aged  12–14  the exit  rate is 29 per cent  higher, and where the youngest is aged  15 years the exit  rate is a substantial 133 per cent  higher.23 This latter  estimate is unsurprising since lone-parent families  are no longer  entitled to PPS once  the youngest child  turns 16 years  of age. Further, the point estimates indicate that lone parents who  identify  as Aboriginal  or Torres Strait Islander  tend to have significantly higher  exit  rates from PPS.

Model 2 includes variables indicating the housing situation of the lone-parent family. The reference category (or omitted group) are those  who  rent from a private landlord. Relative  to this baseline, the estimates suggest that those  in public housing and those  who  own  their  own home tend to have a lower exit  rate. Even so, the differences in the exit  rate from PPS by accommodation status are statistically insignificant.

The next  model  includes the set of variables that indicate State of residence. The reference category is NSW/ACT. There are large  and significant differences in the exit  rate by location. Lone parents who  reside  in Queensland, South Australia  and Tasmania  have substantially higher exit  rates from the PPS. The differences in the exit  pattern by location may reflect  regional differences in labour  markets, the ‘marriage market’, costs of living  or social  support networks.

As a first attempt to uncover the source of the regional variation in exit  rates, the NSW/ACT indicator variable was interacted with the public housing variable and included in model  3. The housing market  in NSW, and Sydney  is particular, has experienced rapidly increasing house prices and private rents. Consequently, the real value  of public housing may be much  higher  in NSW than other  States and Territories, which would  give NSW PPS recipients in public housing an incentive to remain  on the program longer. The point estimates reveal  that lone parents in NSW/ACT who  are in public housing have a 32 per cent  (0.0316–0.3493) lower exit  rate from PPS then their  counterparts who  rent privately. This point estimate is substantial and statistically significant.

The specification was then augmented to include information on the private income of PPS recipients. Dummy variables indicating whether the pensioner received any employment income, unearned income or child  support payments are included in model  4. The results  show that lone parents with  some attachment to the job market  do exit  the PPS at a significant and substantially higher  rate. Those with  any form of paid employment have a 15 per cent  higher exit rate than those  with  no employment income. The receipt of unearned income was not significantly related to the exit  rate, whereas lone parents who  received some child  support payments had a significantly higher  exit  rate from PPS. This latter  finding  indicates that lone parents who  receive child  maintenance payments from the non-custodial parent  are less reliant on public income support.

Model 5 then includes the actual  amount  of income received from the three  private sources. The estimates show  that lone parents with  some earnings were significantly more likely  to exit, and the probability of exit  increased by a further 6 per cent  with  every  $100  of fortnightly earnings.

Although  it is clear  that job attachment is associated with  higher  exits  from PPS, it is difficult  to pinpoint the underlying cause  of this association. For example, this association between earning and PPS exits  may reflect  the important effects  of work  experience in generating better  job opportunities that ultimately lead to economic self-sufficiency. Alternatively, this association may simply  be the reflection of other  underlying factors, such as the lone parent’s level  of education, prior employment history  or simply  their  motivation and ingenuity, which may explain both the presence of earnings and the high exit  rate. Additional data providing information on these  factors  are required in order  to identify  the causal  effect of work  experience and earnings on PPS exit  patterns.24

The level  of unearned income, as well  as its incidence, was found to be insignificantly related to the PPS exit  rate. The point estimate for the effect of the level  of child  support payments is negative but also statistically insignificant. However, the direction of these  effects  is consistent with  the predictions of a static  labour  supply model, where unearned income and private transfers  have a pure ‘income effect’ which acts to reduce labour  supply (and increase program participation).

Model 6 includes a variable indicating whether a spell  corresponds to a repeat spell, plus another variable measuring the length  of the most recently observed PPS spell  for the lone parent. The presence of state dependence, where past experiences on PPS induce greater reliance on the program, imply  that the coefficients on these  two variables should  be negative. However, as shown  in model  6, the coefficient on the repeat spell  indicator variable is positive and highly  significant. The coefficient estimate reveals  that repeat spells  have a 15 per cent higher  exit  rate than first (observed) spells. This finding  likely  reflects the short length  of the sample  period. Recall  that the sample  period  is only 105 fortnights long and therefore an individual must have relatively short spells  in order  to experience multiple spells  during  this time frame. However, the coefficient on previous duration is negative and highly  significant, indicating that repeat spells  tend to be longer  the longer  was the prior spell. Overall, the mixed findings  about occurrence and lagged  duration dependence are instructive in highlighting the difficulty of testing  for state dependence with  a relatively short panel  data set.

The final model  presented in Table 5 includes the unemployment rate. The PPS spells  were matched with  the State unemployment rate at the date of spell  commencement. The inclusion of the State dummy  variables in the specification implies that the only source of variation identifying the unemployment coefficient is time series  variation within States (and not average differences in the unemployment rate across  States). The estimated coefficient is positive, suggesting that an increase in the unemployment rate is associated with  a higher  exit  rate, but this effect is statistically insignificant. Indeed, the large  standard  error indicates this coefficient is not well  identified. It is difficult  to determine whether the State unemployment rates may be a poor proxy  of local  labour  market  conditions or other  factors  may underlie the regional variation in the exit  rates. The extension of the LDS to cover  a complete business cycle may help  resolve  this issue.

Effects of program payments

A question of wide  policy interest is the impact  of PPS payment levels  on the program exit  rate. One possible (though not ideal)  strategy for identifying this impact  is from the nonlinearity of the payment scale  relative to the ‘true’ adult equivalent scale. In Table 6, models  8–12 include a potential payment level  deflated by alternative adult equivalence scales  (thereby providing measures of the level  of family wellbeing implied by the payment levels). Model 8 simply includes the maximum potential level  of total payments that the lone-parent family may receive.25 In model  9 total potential payments are deflated by family size, in model  10 total potential payments are deflated by the square-root of family size, in model  11 by the OECD adult equivalence scale  and in model  12 by the scale  implicit in the Henderson poverty lines.

Comparing the results  across  model  8–12 shows  that the choice of equivalence scale  has important consequences for the estimated effect of program payments (as well  as the coefficient on the number  of children and child  support payments). The coefficient on the payment variable in model  8 is negative but insignificant, indicating that an extra  $100  per fortnight of potential payments under  the PPS reduces the exit  rate by a modest  3.4 per cent. Model 9 with  per-capita payment implies the largest  labour  supply disincentive effects  of payment level  (which is statistically significant) and model  8 with  total payment level  implies the smallest (and insignificant) disincentive effect. The use of the alternative adult equivalence scales  in models  10–12  results  in estimates between these  two extremes (the  OECD and Henderson scales  are associated with  statistically significant estimates). Across the five models/ equivalence scales, the implied change in the exit  rate due to a $100  per-adult  equivalent increase in maximum payments ranges  from (a significant) –13 per cent  to (an insignificant) –3 per cent. Given the much  smaller  changes in maximum PPS payment levels  actually implemented in recent times (of the order  of $10), the models  suggest that changes in payment levels  have had an economically insignificant impact  on changes in the PPS exit  rate over the data period.

However, as discussed in section 3, total potential payments are a function  of the number  (and age)  of dependent children. The inclusion of a payment variable has important consequences for the estimated impact  of the number  of children. In model  8, additional children are associated with  a 7 per cent  higher  exit  rate, while in model  9 they  are associated with essentially no change in the exit  rate, while in model  6 (with no payment variable) additional children are associated with  a 4 per cent  higher  exit  rate. A comparison of models  8–12 shows that the choice of equivalence scale  has important consequences for both the estimated impact of payment levels  and the effects  of family size on the exit  rate. Overall, the chief  lesson  from the estimation is that the impact  of payment levels  on PPS durations is at best tenuously identified in this sample  and is based  on the somewhat arbitrary choice of the appropriate adult equivalence scale.26

Table 5: Duration model estimates (and standard errors), PPS spells
Variable Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7
Sole father 0.2935 (0.0585) 0.2949 (0.0588) 0.2750 (0.0591) 0.3320 (0.0601) 0.3356 (0.0604) 0.3256 (0.0188) 0.3257 (0.0599)
Age (10yrs) –0.0188 (0.0317) –0.0227 (0.0332) –0.0200 (0.0334) –0.0383 (0.0339) –0.0360 (0.0340) –0.0294 (0.0192) –0.0295 (0.0341)
Age2 –0.0756 (0.0241) –0.0713 (0.0242) –0.0736 (0.0242) –0.0667 (0.0243) –0.0648 (0.0245) –0.0623 (0.0192) –0.0622 (0.0246)
No. children 0.0424 (0.0203) 0.0408 (0.0205) 0.0409 (0.0205) 0.0415 (0.0207) 0.0423 (0.0206) 0.0402 (0.0177) 0.0404 (0.0206)
Youngest: 0–4yrs –0.0744 (0.0459) –0.0773 (0.0460) –0.0860 (0.0461) –0.0683 (0.0463) –0.0667 (0.0464) –0.0560 (0.0319) –0.0557 (0.0466)
Youngest: 12–14yrs 0.2861 (0.0736) 0.2821 (0.0736) 0.2857 (0.0734) 0.2837 (0.0737) 0.2816 (0.0736) 0.2873 (0.0443) 0.2874 (0.0733)
Youngest: 15yrs 1.3270 (0.1368) 1.3340 (0.1368) 1.3588 (0.1390) 1.3569 (0.1397) 1.3361 (0.1378) 1.3326 (0.0229) 1.3324 (0.1386)
Foreign-born 0.0088 (0.0475) 0.0090 (0.0476) 0.0022 (0.0479) –0.0212 (0.0482) –0.0190 (0.0482) –0.0158 (0.0339) –0.0161 (0.0480)
Identifies as Indigenous 0.1760 (0.0687) 0.1966 (0.0705) 0.1390 (0.0730) 0.1567 (0.0728) 0.1666 (0.0729) 0.1354 (0.0476) 0.1354 (0.0737)
Rent—govt.   –0.0825 (0.0616) 0.0316 (0.0712) 0.0350 (0.0711) 0.0410 (0.0714) 0.0364 (0.0524) 0.0365 (0.0716)
Rent—other   –0.1215 (0.0656) –0.1085 (0.0663) –0.0971 (0.0665) –0.0966 (0.0665) –0.0910 (0.0195) –0.0912 (0.0666)
Rent—Paid 0   –0.0907 (0.0711) –0.0814 (0.0710) –0.0742 (0.0708) –0.0716 (0.0707) –0.0707 (0.0414) –0.0715 (0.0709)
Own home   –0.0705 (0.0572) –0.0567 (0.0572) –0.0677 (0.0576) –0.0585 (0.0576) –0.0448 (0.0338) –0.0448 (0.0572)
Purch. home   0.0530 (0.0784) 0.0503 (0.0790) 0.0365 (0.0792) 0.0280 (0.0794) 0.0429 (0.0217) 0.0430 (0.0796)
Other homeowner   –0.1459 (0.1206) –0.1082 (0.1208) –0.1355 (0.1216) –0.1251 (0.1213) –0.1324 (0.0444) –0.1323 (0.1200)
Rent/own missing   –0.0751 (0.0749) –0.0673 (0.0754) –0.0561 (0.0757) –0.0477 (0.0752) –0.0354 (0.0313) –0.0356 (0.0754)
Vic     –0.0300 (0.0564) –0.0247 (0.0566) –0.0168 (0.0566) –0.0231 (0.0423) –0.0296 (0.0630)
Qld     0.2409 (0.0503) 0.2375 (0.0501) 0.2464 (0.0502) 0.2304 (0.0385) 0.2206 (0.0668)
SA     0.1735 (0.0695) 0.1715 (0.0695) 0.1745 (0.0693) 0.1683 (0.0360) 0.1561 (0.0883)
WA     0.1054 (0.0633) 0.1026 (0.0632) 0.1123 (0.0630) 0.0989 (0.0342) 0.1011 (0.0639)
Tas     0.0224 (0.1111) 0.0321 (0.1117) 0.0412 (0.1119) 0.0254 (0.0581) 0.0082 (0.1379)
NT     0.2091 (0.1174) 0.2015 (0.1179) 0.1907 (0.1170) 0.1661 (0.0718) 0.1763 (0.1274)
NSW*Rent—govt.     –0.3493 (0.1294) –0.3548 (0.1298) –0.3705 (0.1298) –0.3502 (0.0794) –0.3507 (0.1305)
Earnings>0       0.1543 (0.0451) 0.1593 (0.0454) 0.1498 (0.0155) 0.1499 (0.0452)
Unearnt Inc.>0       0.0396 (0.0534) 0.0433 (0.0534) 0.0401 (0.0276) 0.0404 (0.0533)
Child Sp.>0       0.1301 (0.0405) 0.1256 (0.0405) 0.0898 (0.0332) 0.0896 (0.0413)
Earnings ($100) Unearnt income ($100) Child A27Sp. ($100)         0.0560 (0.0133) –0.0119 (0.0419) –0.0257 (0.0184) 0.0521 (0.0112) –0.0186 (0.0175) –0.0284 (0.0159) 0.0522 (0.0129) –0.0187 (0.0418) –0.0285 (0.0182)
Repeat spell Previous dur. (1 yr)           0.1464 (0.0344) –0.2420 (0.0392) 0.1465 (0.0399) –0.2414 (0.0428)
Unemployment rate (10%)             0.0636 (0.2862)
Log likelihood function –13963.03 –13958.87 –13933.01 –13921.04 –13912.25 –13885.92 –13885.89

 

Table 6: Duration model estimates (and standard errors), PPS spells
Variable Model 8 Model 9 Model 10 Model 11 Model 12
Sole father 0.3233 (0.0599) 0.3228 (0.0598) 0.3227 (0.0599) 0.3225 (0.0599) 0.3225 (0.0598)
Age (10yrs) –0.0295 (0.0341) –0.0313 (0.0340) –0.0302 (0.0340) –0.0306 (0.0340) –0.0307 (0.0340)
Age2 –0.0622 (0.0246) –0.0605 (0.0246) –0.0617 (0.0246) –0.0613 (0.0246) –0.0613 (0.0246)
No. children 0.0724 (0.0306) –0.0002 (0.0284) 0.0410 (0.0207) 0.0198 (0.0230) 0.0235 (0.0220)
Youngest: 0–4yrs –0.0553 (0.0466) –0.0537 (0.0466) –0.0551 (0.0466) –0.0549 (0.0466) –0.0553 (0.0466)
Youngest: 12–14yrs 0.2930 (0.0734) 0.3019 (0.0736) 0.2971 (0.0735) 0.2993 (0.0735) 0.2992 (0.0735)
Youngest: 15yrs 1.3399 (0.1383) 1.3575 (0.1379) 1.3477 (0.1380) 1.3503 (0.1380) 1.3498 (0.1380)
Foreign-born –0.0156 (0.0479) –0.0164 (0.0479) –0.0158 (0.0479) –0.0160 (0.0479) –0.0159 (0.0479)
Identifies as Indigenous 0.1331 (0.0736) 0.1352 (0.0734) 0.1336 (0.0735) 0.1341 (0.0735) 0.1338 (0.0734)
Rent—govt. 0.0365 (0.0714) 0.0352 (0.0714) 0.0359 (0.0714) 0.0357 (0.0714) 0.0351 (0.0714)
Rent—other –0.0939 (0.0666) –0.0938 (0.0665) –0.0947 (0.0666) –0.0950 (0.0665) –0.0955 (0.0665)
Rent—paid 0 –0.0752 (0.0708) –0.0774 (0.0708) –0.0767 (0.0708) –0.0774 (0.0708) –0.0779 (0.0708)
Own home –0.0505 (0.0572) –0.0557 (0.0573) –0.0531 (0.0573) –0.0544 (0.0573) –0.0548 (0.0573)
Purch. home 0.0422 (0.0795) 0.0368 (0.0795) 0.0404 (0.0795) 0.0392 (0.0795) 0.0395 (0.0795)
Other homeowner –0.1375 (0.1201) –0.1453 (0.1203) –0.1407 (0.1202) –0.1425 (0.1202) –0.1430 (0.1202)
Rent/own missing –0.0458 (0.0756) –0.0546 (0.0757) –0.0507 (0.0757) –0.0531 (0.0757) –0.0540 (0.0757)
Vic –0.0242 (0.0564) –0.0235 (0.0564) –0.0242 (0.0564) –0.0242 (0.0564) –0.0243 (0.0564)
Qld 0.2309 (0.0502) 0.2317 (0.0501) 0.2311 (0.0501) 0.2311 (0.0501) 0.2312 (0.0501)
SA 0.1658 (0.0691) 0.1648 (0.0691) 0.1650 (0.0691) 0.1646 (0.0691) 0.1644 (0.0691)
WA 0.0971 (0.0631) 0.0955 (0.0631) 0.0963 (0.0631) 0.0959 (0.0631) 0.0959 (0.0630)
Tas 0.0264 (0.1123) 0.0247 (0.1121) 0.0258 (0.1122) 0.0253 (0.1122) 0.0254 (0.1122)
NT 0.1645 (0.1181) 0.1588 (0.1181) 0.1622 (0.1181) 0.1606 (0.1181) 0.1614 (0.1181)
NSW*Rent—govt. –0.3528 (0.1304) –0.3541 (0.1304) –0.3536 (0.1304) –0.3541 (0.1304) –0.3542 (0.1304)
Earnings>0 0.1446 (0.0453) 0.1407 (0.0453) 0.1424 (0.0453) 0.1413 (0.0453) 0.1387 (0.0454)
Unearnt Inc.>0 0.0377 (0.0533) 0.0374 (0.0532) 0.0374 (0.0533) 0.0374 (0.0532) 0.0371 (0.0532)
ChildSp.>0 0.0805 (0.0419) 0.0742 (0.0421) 0.0769 (0.0420) 0.0752 (0.0421) 0.0746 (0.0420)
Earnings ($100) 0.0518 (0.0129) 0.0517 (0.0129) 0.0518 (0.0129) 0.0518 (0.0129) 0.0518 (0.0129)
Unearnt income ($100) –0.0194 (0.0417) –0.0202 (0.0417) –0.0198 (0.0417) –0.0200 (0.0417) –0.0199 (0.0417)
ChildSp. ($100) –0.0342 (0.0189) –0.0365 (0.0190) –0.0358 (0.0190) –0.0365 (0.0190) –0.0369 (0.0190)
Repeat spell 0.1558 (0.0406) 0.1585 (0.0404) 0.1583 (0.0405) 0.1592 (0.0405) 0.1598 (0.0405)
Previous dur. (1 Yr) –0.2376 (0.0428) –0.2349 (0.0428) –0.2357 (0.0428) –0.2349 (0.0428) –0.2344 (0.0428)
PPS payments  ($100) –0.0341 (0.0238) –0.1373 (0.0663) –0.0541 (0.0297) –0.0643 (0.0321) –0.0873 (0.0410)
Adult equivalence scale Total Per-person (Family Size)1/2 OECD Scale Henderson Scale
Log likelihood function –13884.9 –13883.9 –13884.4 –13884.04 –13883.79

Baseline estimates and unobserved heterogeneity models

The baseline hazard  estimates for models  1 and 8 are reported in Table 7, and the baseline for model  8 is illustrated in Figure 21. As indicated by Table 7, the baseline hazard  estimates are very similar  across  the different  model  specifications, and they  exhibit a very similar  pattern to the empirical hazard  function  in Figure 1A. The baseline hazard  rates decline marginally with spell  duration. The decline in the exit  rate with  spell  length  is very small and, at most, suggests a minor degree of negative duration dependence.

The models  incorporating unobserved heterogeneity were also estimated. However, in the model with  unit gamma  heterogeneity, the estimate of the variance term always converged toward zero even  when  the estimation routines were run using  a range  of starting  values. In the model  incorporating nonparameteric heterogeneity, the heterogeneity distribution is approximated by a discrete multinominal distribution. The heterogenity distribution is theoretically identified by fixing  the location of one masspoint and constraining the sum of probabilities across  the masspoints to sum to one. In estimating the model  with  two masspoints, the most simple  specification of this model, the estimated location of the free masspoint converged to the value  of the fixed  masspoint. Consequently, results  from these models  are not reported,27 and they  suggest that unobserved heterogeneity may not be an issue with  the models  presented in Tables 5 and 6.28

Figure 21: Baseline Hazard Rate Functions for Model 8

Figure 21: Baseline Hazard Rate Functions for Model 8

Table 7: Baseline hazard rate estimates
    Model 1   Model 8
Duration Estimate (Std.Err) Estimate (Std.Err)
1 0.0320 (0.0029) 0.0312 (0.0046)
2 0.0261 (0.0025) 0.0255 (0.0039)
3 0.0308 (0.0029) 0.0301 (0.0046)
4 0.0319 (0.0030) 0.0313 (0.0047)
5 0.0305 (0.0030) 0.0300 (0.0046)
6 0.0230 (0.0025) 0.0227 (0.0037)
7 0.0264 (0.0028) 0.0260 (0.0041)
8 0.0275 (0.0029) 0.0271 (0.0043)
9 0.0271 (0.0029) 0.0268 (0.0042)
10 0.0228 (0.0026) 0.0225 (0.0037)
11 0.0221 (0.0026) 0.0219 (0.0037)
12 0.0211 (0.0026) 0.0209 (0.0036)
13 0.0218 (0.0027) 0.0216 (0.0037)
14 0.0168 (0.0024) 0.0168 (0.0031)
15 0.0200 (0.0026) 0.0200 (0.0035)
16 0.0211 (0.0028) 0.0210 (0.0037)
17 0.0238 (0.0030) 0.0237 (0.0041)
18 0.0190 (0.0027) 0.0189 (0.0035)
19 0.0262 (0.0033) 0.0262 (0.0045)
20 0.0173 (0.0026) 0.0173 (0.0033)
21 0.0150 (0.0025) 0.0150 (0.0030)
22 0.0158 (0.0026) 0.0158 (0.0032)
23 0.0155 (0.0026) 0.0155 (0.0032)
24 0.0144 (0.0025) 0.0144 (0.0030)
25 0.0177 (0.0029) 0.0178 (0.0035)
26 0.0170 (0.0028) 0.0170 (0.0034)
27–28 0.0125 (0.0018) 0.0126 (0.0023)
29–30 0.0158 (0.0021) 0.0158 (0.0028)
31–32 0.0194 (0.0024) 0.0194 (0.0033)
33–34 0.0127 (0.0020) 0.0127 (0.0025)
35–36 0.0150 (0.0022) 0.0150 (0.0028)
37–38 0.0133 (0.0021) 0.0134 (0.0026)
39–42 0.0145 (0.0017) 0.0146 (0.0024)
43–46 0.0138 (0.0018) 0.0138 (0.0024)
47–50 0.0149 (0.0020) 0.0149 (0.0026)
51–54 0.0101 (0.0017) 0.0102 (0.0020)
55–58 0.0126 (0.0020) 0.0126 (0.0024)
59–62 0.0125 (0.0021) 0.0126 (0.0025)
63–74 0.0121 (0.0015) 0.0124 (0.0020)
75–100 0.0186 (0.0045) 0.0187 (0.0056)

[ Return to Top   Return to Section ]

6  Conclusion

From analysing the LDS it was found that a substantial number  (15 per cent)  of PPS recipients remained on the program for the entire  sample  period. As a group  they  accounted for 29 per cent  of the total time spent  on the program and 30 per cent  of total expenditures, over the entire  data period. These lone parents were more likely  to be women, to be Australian-born, to have more children and to be in rental  accommodation (especially public housing).

The duration analysis of stays on PPS payments revealed that the lone parent’s gender (lone fathers  had much  shorter  stays on PPS) and the age of the youngest child  (more  so than the number  of children) were important explanatory variables. The youngest and more elderly lone parents tended to have longer  stays on the program. Lone parents in public housing, particularly in NSW/ACT, had longer  periods of time in receipt of PPS. It was clear  that lone parents with some job attachment had much  short stays on PPS, and the greater their  earnings the higher their exit  rate from PPS. In analysing the impact  of payment levels on the length of time on PPS, it was found that this effect could  not be firmly identified from the effects  of number of children or their  age composition. Any inference on the effects  of program payments would  also be sensitive to the choice of an appropriate adult equivalent scale.

[ Return to Top   Return to Section ]

Appendix A: Table 8

Table 8: Empirical hazard rate and survival probability estimates
Duration Hazard rate Survival probability Duration Hazard rate Survival probability
Estimate (Std.Err.) Estimate (Std.Err.) Estimate (Std.Err.) Estimate (Std.Err.)
1 0.0338 (0.0024) 0.9662 (0.0024) 51 0.0072 (0.0025) 0.3858 (0.0076)
2 0.0276 (0.0022) 0.9396 (0.0032) 52 0.0055 (0.0023) 0.3836 (0.0076)
3 0.0323 (0.0024) 0.9092 (0.0038) 53 0.0160 (0.0039) 0.3775 (0.0076)
4 0.0333 (0.0025) 0.8789 (0.0044) 54 0.0097 (0.0031) 0.3738 (0.0076)
5 0.0317 (0.0025) 0.8510 (0.0048) 55 0.0131 (0.0036) 0.3689 (0.0077)
6 0.0240 (0.0023) 0.8306 (0.0050) 56 0.0103 (0.0032) 0.3651 (0.0077)
7 0.0273 (0.0025) 0.8079 (0.0053) 57 0.0106 (0.0033) 0.3612 (0.0077)
8 0.0284 (0.0025) 0.7849 (0.0056) 58 0.0132 (0.0038) 0.3565 (0.0077)
9 0.0278 (0.0026) 0.7631 (0.0058) 59 0.0137 (0.0039) 0.3516 (0.0077)
10 0.0234 (0.0024) 0.7452 (0.0059) 60 0.0083 (0.0031) 0.3487 (0.0077)
11 0.0227 (0.0024) 0.7282 (0.0061) 61 0.0135 (0.0040) 0.3440 (0.0078)
12 0.0216 (0.0024) 0.7125 (0.0062) 62 0.0104 (0.0036) 0.3404 (0.0078)
13 0.0224 (0.0025) 0.6966 (0.0063) 63 0.0094 (0.0035) 0.3372 (0.0078)
14 0.0172 (0.0022) 0.6846 (0.0064) 64 0.0097 (0.0036) 0.3340 (0.0078)
15 0.0205 (0.0025) 0.6706 (0.0065) 65 0.0114 (0.0040) 0.3302 (0.0079)
16 0.0214 (0.0026) 0.6562 (0.0066) 66 0.0044 (0.0025) 0.3287 (0.0079)
17 0.0241 (0.0027) 0.6404 (0.0067) 67 0.0107 (0.0040) 0.3252 (0.0079)
18 0.0193 (0.0025) 0.6280 (0.0067) 68 0.0111 (0.0042) 0.3216 (0.0079)
19 0.0264 (0.0030) 0.6114 (0.0068) 69 0.0131 (0.0046) 0.3174 (0.0080)
20 0.0174 (0.0025) 0.6008 (0.0069) 70 0.0069 (0.0034) 0.3152 (0.0080)
21 0.0150 (0.0023) 0.5917 (0.0069) 71 0.0177 (0.0056) 0.3096 (0.0080)
22 0.0158 (0.0024) 0.5824 (0.0069) 72 0.0056 (0.0032) 0.3079 (0.0080)
23 0.0154 (0.0024) 0.5734 (0.0070) 73 0.0038 (0.0027) 0.3067 (0.0081)
24 0.0143 (0.0024) 0.5652 (0.0070) 74 0.0179 (0.0059) 0.3012 (0.0081)
25 0.0175 (0.0027) 0.5553 (0.0070) 75 0.0103 (0.0046) 0.2981 (0.0081)
26 0.0169 (0.0026) 0.5459 (0.0071) 76 0.0106 (0.0047) 0.2950 (0.0082)
27 0.0113 (0.0022) 0.5397 (0.0071) 77 0.0044 (0.0031) 0.2937 (0.0082)
28 0.0134 (0.0024) 0.5325 (0.0071) 78 0.0093 (0.0046) 0.2909 (0.0082)
29 0.0197 (0.0030) 0.5220 (0.0072) 79 0.0097 (0.0048) 0.2881 (0.0083)
30 0.0113 (0.0023) 0.5161 (0.0072) 80 0.0025 (0.0025) 0.2874 (0.0083)
31 0.0170 (0.0028) 0.5073 (0.0072) 81 0.0026 (0.0026) 0.2866 (0.0083)
32 0.0210 (0.0032) 0.4967 (0.0072) 82 0.0028 (0.0028) 0.2858 (0.0083)
33 0.0109 (0.0024) 0.4913 (0.0073) 83 0.0145 (0.0064) 0.2817 (0.0084)
34 0.0139 (0.0027) 0.4845 (0.0073) 84 0.0062 (0.0043) 0.2800 (0.0084)
35 0.0165 (0.0030) 0.4765 (0.0073) 85 0.0096 (0.0055) 0.2773 (0.0085)
36 0.0125 (0.0027) 0.4705 (0.0073) 86 0.0167 (0.0074) 0.2726 (0.0086)
37 0.0135 (0.0028) 0.4641 (0.0073) 87 0.0074 (0.0052) 0.2706 (0.0087)
38 0.0126 (0.0027) 0.4583 (0.0074) 88 0.0197 (0.0087) 0.2653 (0.0088)
39 0.0123 (0.0027) 0.4527 (0.0074) 89 0.0088 (0.0062) 0.2630 (0.0089)
40 0.0158 (0.0031) 0.4455 (0.0074) 90 0.0144 (0.0083) 0.2592 (0.0090)
41 0.0099 (0.0025) 0.4411 (0.0074) 91 0.0000 (0.0000) 0.2592 (0.0090)
42 0.0175 (0.0034) 0.4334 (0.0074) 92 0.0000 (0.0000) 0.2592 (0.0090)
43 0.0140 (0.0031) 0.4273 (0.0075) 93 0.0065 (0.0064) 0.2575 (0.0091)
44 0.0151 (0.0033) 0.4209 (0.0075) 94 0.0072 (0.0072) 0.2556 (0.0092)
45 0.0133 (0.0031) 0.4153 (0.0075) 95 0.0000 (0.0000) 0.2556 (0.0092)
46 0.0100 (0.0027) 0.4111 (0.0075) 96 0.0000 (0.0000) 0.2556 (0.0092)
47 0.0110 (0.0029) 0.4066 (0.0075) 97 0.0000 (0.0000) 0.2556 (0.0092)
48 0.0153 (0.0035) 0.4004 (0.0075) 98 0.0114 (0.0113) 0.2527 (0.0096)
49 0.0192 (0.0040) 0.3927 (0.0076) 99 0.0000 (0.0000) 0.2527 (0.0096)
50 0.0105 (0.0030) 0.3886 (0.0076) 100 0.0000 (0.0000) 0.2527 (0.0096)

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Appendix  B: Figures 2A to 20B

Figure 2A: Empirical  Hazard Rate Functions by Gender

Figure 2A: Empirical  Hazard Rate Functions by Gender

Figure 2B: Empirical  Survival Functions  by Gender

Figure 2B: Empirical  Survival Functions  by Gender

Figure  3A: Empirical  Hazard  Rate  Functions  by  Age

Figure  3A: Empirical  Hazard  Rate  Functions  by  Age

Figure 3B: Empirical Survival Functions by Age

Figure 3B: Empirical Survival Functions by Age

Figure 4A : Empirical  Hazard Rate Functions  by  Age of Youngest Child

Figure 4A : Empirical  Hazard Rate Functions  by  Age of Youngest Child

Figure  4B: Empirical  Survival Functions  by Age of  Youngest Child

Figure  4B: Empirical  Survival Functions  by Age of  Youngest Child

Figure 5A: Empirical  Hazard Rate Functions  by Indigenous Status

Figure 5A: Empirical  Hazard Rate Functions  by Indigenous Status

Figure 5B: Enpirical Survival Functions by Age

Figure 5B: Enpirical Survival Functions by Age

Figure 6A: Empirical  Hazard  Rate Functions by Immigrant Status

Figure 6A: Empirical  Hazard  Rate Functions by Immigrant Status

Figure 6B: Empirical  Survival Functions  by  Immigrant  Status

Figure 6B: Empirical  Survival Functions  by  Immigrant  Status

Figure 7A: Empirical  Hazard Rate Functions by Number of  Children

Figure 7A: Empirical  Hazard Rate Functions by Number of  Children

Figure 7B: Empirical  Survival Functions  by Number of  Children

Figure 7B: Empirical  Survival Functions  by Number of  Children

Figure 8A: Empirical  Hazard Rate Functions  by  Number of Children

Figure 8A: Empirical  Hazard Rate Functions  by  Number of Children

Figure 8B: Empirical  Survival Functions  by  Number of Children

Figure 8B: Empirical  Survival Functions  by  Number of Children

Figure 9A: Empirical Hazard Rote Functions by State of Residence

Figure 9A: Empirical Hazard Rote Functions by State of Residence

Figure 9B: Empirical Survival Functions  by   State  of   Residence

Figure 9B: Empirical Survival Functions  by   State  of   Residence

Figure 10A: Empirical  Hazard Rate Functions by  State  of  Residence

Figure 10A: Empirical  Hazard Rate Functions by  State  of  Residence

Figure 10B: Empirical  Survival Functions  by   State  of  Residence

Figure 10B: Empirical  Survival Functions  by   State  of  Residence

Figure 11A: Empirical Hazard Rate Functions by Housing Type

Figure 11A: Empirical Hazard Rate Functions by Housing Type

Figure 11B: Empirical Survival Functions by Housing Type

Figure 11B: Empirical Survival Functions by Housing Type

Figure 12A: Empirical Hazard Rate Functions by Housing Type

Figure 12A: Empirical Hazard Rate Functions by Housing Type

Figure 12B: Empirical Survival Functions by Housing Type

Figure 12B: Empirical Survival Functions by Housing Type

Figure 13A: Empirical Hazard Rate Functions by Labour Force Status

Figure 13A: Empirical Hazard Rate Functions by Labour Force Status

Figure 13B: Empirical Survival Functions by Labour Force Status

Figure 13A: Empirical Survival Functions by Labour Force Status

 

Figure 14A: Empirical Hazard Rate Functions by Unearned Income

Figure 14A: Empirical Hazard Rate Functions by Unearned Income

Figure 14B: Empirical Survival Functions by Unearned Income

Figure 14B: Empirical Survival Functions by Unearned Income

Figure 15A: Empirical Hazard Rate Functions by Payment Level

Figure 15A: Empirical Hazard Rate Functions by Payment Level

Figure 15B: Empirical Survival Functions by Payment Level

Figure 15B: Empirical Survival Functions by Payment Level

Figure 16A: Empirical Hazard Rate Functions by Payment Level

Figure 16A: Empirical Hazard Rate Functions by Payment Level

Figure 16B: Empirical Survival Functions by Payment Level

Figure 16B: Empirical Survival Functions by Payment Level

Figure 17A: Empirical Hazard Rate Functions by Child Support Receipt

Figure 17A: Empirical Hazard Rate Functions by Child Support Receipt

Figure 17B: Empirical Survival Functions by Child Support Receipt

Figure 17B: Empirical Survival Functions by Child Support Receipt

Figure 18A: Empirical Hazard Rate Functions by Rent Assistance

Figure 18A: Empirical Hazard Rate Functions by Rent Assistance

Figure 18B: Empirical Survival Functions by Rent Assistance

Figure 18B: Empirical Survival Functions by Rent Assistance

Figure 19A: Empirical Hazard Rate Functions by Spell Number

Figure 19A: Empirical Hazard Rate Functions by Spell Number

Figure 19B: Empirical Survival Functions by Spell Number

Figure 19B: Empirical Survival Functions by Spell Number

Figure 20A: Empirical Hazard Rate Function for Population

Figure 20A: Empirical Hazard Rate Function for Population

Figure 20B: Empirical Survival Function for Population

Figure 20B: Empirical Survival Function for Population

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Endnotes

1     The Parenting Payment  (single) (PPS) program replaced the Sole Parent Pension  (SPP) program from 20 March 1998. Reference throughout the paper  to the PPS program is taken to include the SPP program.

2     It is possible to track  people in the LDS who  exit  PPS and move to another  FaCS payment (such  as Disability  Support  Pension  or ‘more  than minimum rate’ Family Payment). Unfortunately, the transition from PPS to another  payment type  in the LDS does not provide comprehensive coverage of any exit  route  (such  as re-partnering or full-time employment). However, the analysis of transitions across  income support programs by lone parents represents an important area for future  research.

3     Alternatively, the lone parent  may be the primary carer  for a Disability  Allowance Child over 16 years  of age. In addition  to having  a ‘qualifying child’, there  are also residency requirements: see Centrelink (1998).

4     This description of payment rates is based  on the program parameters that applied during the final fortnight of the data period  4–18 June 1999.

5     The ‘free area’ of $124  applies to a lone parent  with  one child, and amount  increases with additional children.

6     This figure  includes the Pharmaceutical Allowance, which raises  the income cutoff from $846.80 to $857.60. The income cutoff is higher  if Rent Assistance is also paid to the lone parent.

7     Additionally, for each  dependent child  aged  16–18  years  who  were full-time students, the FP was $23.70 per fortnight.

8     If a PPS recipient does not meet  the maintenance action  test then the minimum rate FP of $23.70 per child  per fortnight is payable.

9     The child  support income ‘free area’ was $951.60 per annum, plus $317.20 for each additional child. Child maintenance income above that amount  reduces the FP by 50 cents per dollar until the minimum FP of $23.70 per child  per fortnight is reached. Child support income does not affect other  FaCS payments. Further, PPS recipients are not subject to tax on child  (or spousal) support.

10   PPS recipients may also receive a range  of State and local  government benefits.

11   As noted  above, the LDS does not contain  information on the exit  state (for example, work versus  re-partnering). Therefore a two-state  framework is adopted (on- versus  off-PPS). As an organising principle, the off-PPS is labelled ‘full-time  employment’ in the discussion in this section. Nevertheless, in interpreting the empirical results, it is important to keep  in the mind the range  of events  leading to exit  and hence possible destination states.

12   The arrival  rate of job offers reflects demand  side constraints on PPS participation. It is straightforward to extend the search  model  by specifying the arrival  rate as a function of covariates.

13   Formally, the term ‘hazard  rate’ signifies  an exit  rate defined  as a function  of time.

14   Alternative definitions of program exit, such as 3 or 4 consecutive fortnights not in receipt of PPS payments, were also used. By construction, these  alternative definitions lead to marginally fewer  repeat spells  and hence marginally longer  average spell  durations. However, the qualitative results  reported below were not sensitive to the particular definition of program exit  implemented.

15   For example, if family needs  increase by more (less)  than $99.00 for each  child  aged 0–12 years, then the welfare of these  families  will  be lower (higher) than other  families  on the program and hence, other  things  being  equal, their  exit  rate will  be higher  (lower).  

16 This issue  of identifying benefit  effects  from the non-linearity of the payment scale  and the choice of adult equivalent scale  is examined in Barrett (2000). Binh and Whiteford (1990) and Whiteford (1985) provide  a comprehensive treatment of the range  of adult equivalence scales  derived for Australia.

17   Nevertheless, any strategy for identifying the effect of program benefit  levels  on the exit rate must (at least implicitly) entail  an assumption about the appropriate adult equivalent scale.

18   The models  were estimated with  40 baseline hazard  parameters. The baseline included individual parameters for each  fortnight  1–26, and then intervals for fortnights 27–28, 29–30, 31–32, 33–34, 35–36, 37–38, 39–42, 43–46, 47–50, 51–54, 55–58, 59–62, 63–74 and 75–100.

19   This specification treats  the unobserved heterogeneity component as spell-specific rather than individual specific. An alternative is to assume  that 8ivaries  across  individual, and is constant across  all spells  experienced by the individuals.

20   Unearned income is exclusive of child  support.

21   The empirical hazard  rate and survival  probability function  estimates, and associated standard  errors, are also reported in Table 8. If the confidence bands were included in Figures  1A and 1B, the estimated functions would  simply  appear as thick  lines.

22   The continuous variables, which measure age, earnings, unearned income, child  support payments, previous durations and payment levels  were transformed to deviations from their respective mean  values. The reference group  (or baseline) then corresponds to the average levels  for these  variables.

23   An alternative methodology is to treat the aging  of the youngest child  as a separate exit route  (from a combined employment–repartnering exit  route)  in a competing risk framework. At most only 113 spells  end through this route, and hence it is not possible to estimate the parameters associated with  this risk. However, consistent with  this framework, if the spells  associated with  exit  due to the aging  of the youngest child  are treated as right- censored, the estimates of the model  for the combined employment–re-partnering risk are almost identical to those  presented in Table 5.

24   In addition, due to the tax-back  of benefit  payments beyond  the ‘free-area’, eventually additional earnings will  lead to disentitlement.

25   Maximum  potential payment under  the PPS is defined  here  as the sum of the maximum basic  rate and maximum Family Payment. It is the potential payment since  the income and assets  test reductions are not taken  into account.

26   A firmer foundation for selecting the appropriate adult equivalent scale, and identifying the impact  of PPS payments levels  on the exit  rate, is to actually estimate the scale  as part of a consumer demand  system  using  data on the expenditure patterns of low income families. This task is beyond  the scope  of the present project

27   The estimates for the baseline hazards  and covariates were virtually identical to the corresponding models  in Tables 5 and 6.

28   Empirical  studies  based  on the flexible duration model  used in this analysis (Barrett  2000, Dolton & van der Klaauw  1995, Meyer 1990) have found that allowing for unobserved heterogeneity does not affect the estimated impact  of covariates on the exit  rate. At most, the form of the heterogeneity distribution affects the shape  of the estimated baseline. Nevertheless, an interesting avenue for future  research is to incorporate alternative specifications of the unobserved heterogeneity component, such as allowing for individual- specific, rather  than spell-specific, unobserved characteristics.

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Content Updated: 19 June 2013