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395 AUSTRALIAN JOURNAL OF LABOUR ECONOMICS Vol. 9, No. 4, December 2006, pp 395 - 416 Changes in the Labour Force Status of Lone and Couple Australian Mothers, 1983-2005 Matthew Gray, Lixia Qu and Jennifer Renda, Australian Institute of Family Studies David de Vaus, La Trobe University Abstract Over the last two decades there has been a substantial increase in the proportion of lone mothers employed part-time, while the proportion employed full-time was much the same in 2005 as it was in the early 1980s. The experience of couple mothers is quite different, with both full-time and part-time employment increasing at similar rates. The net effect is that both lone and couple mothers have had similar increases in overall employment rates but that the nature of the growth in employment has been different among the lone and couple mother populations. This paper uses data from the 1986 and 2001 Australian Censuses to explore the possible reasons for the differences in the labour market trends of lone and couple mothers. 1. Introduction Over the last twenty-five years the employment rates of lone and couple mothers with dependent children have increased substantially. Between 1983 and 2005, the employment rate of lone mothers increased from 32.1 per cent to 51.4 per cent. Over the same period, the employment rate of couple mothers increased from 42.1 to 65.4 per cent. Although the increases in employment for lone and couple mothers are of a similar magnitude, the trends in full-time and part-time employment are very different. For lone mothers, virtually all of the increase in employment has been part-time. In contrast, couple mothers have had similar rates of growth in part-time and full-time employment. 1 Understanding the reasons for the different patterns of employment growth for lone and couple mothers is of growing importance as the proportion of families with dependent children that are lone parent families has increased from 13.6 per cent in 1983 to 21.4 per cent in 2005. This is one of the major reasons for the growth in the number of families with children in which no adult is employed over the last twenty- years (Gregory 1999, Dawkins, Gregg and Scutella 2002, Renda 2003). Increasing the rate of employment of those in receipt of income support payments is a clear policy objective (e.g. Budget Paper No 2: Budget Measures 2005-06). Address for correspondence: Matthew Gray, Deputy Director, Australian Institute of Family Studies, Level 20, 485 La Trobe Street, Melbourne, Vic 3000. Email: [email protected] The views expressed in this paper are those of the authors and may not reflect those of the Australian Institute of Family Studies or the Australian Government. Acknowledgement: We are grateful to Prem Thapa, Tess Ridge, Guyonne Kalb and an anonymous referee for comments on an earlier version of this paper. 1 Data are from the Australian Bureau of Statistics (ABS) Labour Force Survey. © The Centre for Labour Market Research, 2006

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Page 1: Changes in the Labour Force Status of Lone and Couple ... · David de Vaus, La Trobe University Abstract Over the last two decades there has been a substantial increase in the proportion

395AUTHORS

Title

395AUSTRALIAN JOURNAL OF LABOUR ECONOMICS

Vol. 9, No. 4, December 2006, pp 395 - 416

Changes in the Labour Force Status of Loneand Couple Australian Mothers, 1983-2005

Matthew Gray, Lixia Qu and Jennifer Renda, Australian Institute of Family StudiesDavid de Vaus, La Trobe University

AbstractOver the last two decades there has been a substantial increase in the proportion oflone mothers employed part-time, while the proportion employed full-time was muchthe same in 2005 as it was in the early 1980s. The experience of couple mothers isquite different, with both full-time and part-time employment increasing at similarrates. The net effect is that both lone and couple mothers have had similar increasesin overall employment rates but that the nature of the growth in employment has beendifferent among the lone and couple mother populations. This paper uses data fromthe 1986 and 2001 Australian Censuses to explore the possible reasons for thedifferences in the labour market trends of lone and couple mothers.

1. IntroductionOver the last twenty-five years the employment rates of lone and couple mothers withdependent children have increased substantially. Between 1983 and 2005, theemployment rate of lone mothers increased from 32.1 per cent to 51.4 per cent. Overthe same period, the employment rate of couple mothers increased from 42.1 to 65.4 percent. Although the increases in employment for lone and couple mothers are of a similarmagnitude, the trends in full-time and part-time employment are very different. Forlone mothers, virtually all of the increase in employment has been part-time. In contrast,couple mothers have had similar rates of growth in part-time and full-time employment.1

Understanding the reasons for the different patterns of employment growthfor lone and couple mothers is of growing importance as the proportion of familieswith dependent children that are lone parent families has increased from 13.6 per centin 1983 to 21.4 per cent in 2005. This is one of the major reasons for the growth in thenumber of families with children in which no adult is employed over the last twenty-years (Gregory 1999, Dawkins, Gregg and Scutella 2002, Renda 2003). Increasing therate of employment of those in receipt of income support payments is a clear policyobjective (e.g. Budget Paper No 2: Budget Measures 2005-06).Address for correspondence: Matthew Gray, Deputy Director, Australian Institute of Family Studies,Level 20, 485 La Trobe Street, Melbourne, Vic 3000. Email: [email protected] views expressed in this paper are those of the authors and may not reflect those of the AustralianInstitute of Family Studies or the Australian Government.Acknowledgement: We are grateful to Prem Thapa, Tess Ridge, Guyonne Kalb and an anonymousreferee for comments on an earlier version of this paper.1 Data are from the Australian Bureau of Statistics (ABS) Labour Force Survey.

© The Centre for Labour Market Research, 2006

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There are a number of possible explanations for the much higher rate of growthof part-time than full-time employment of lone mothers. One set of explanations relateto the financial incentives generated by the income support system. The rapid growthin part-time employment of lone mothers has occurred over a period in which theincome support system has increasingly allowed mothers to combine part-timeemployment with the receipt of government income support.2 Changes have includedincreases in the threshold income beyond which the level of government benefits isreduced (including family payments) and reductions in the taper rates of governmentbenefits. While changes to the income support system that increase the incentives forpart-time employment have been implemented since the mid 1980s, arguably the mostsignificant changes have occurred since 1996.

A second explanation is that the characteristics of the lone mother populationhave changed in such a way as to explain the decline in full-time employment andincrease in part-time employment. A third set of explanations relates to changes in thepreferences for part-time versus full-time employment for lone and couple mothers.The first and third explanations would show up through a change in coefficients in amodel that estimates the probability of employment, whereas the second explanationwould show up through a change in characteristics with the coefficients unchangedover time.

The aim of this paper is to explore possible explanations for the differentlabour force trends of lone and couple mothers, particularly the extent to which thechanges are explained by changes in coefficients (explanations 1 and 3) orcharacteristics (explanation 2) and the extent to which the relative importance of thesefactors differ between lone and couple mothers. The determinants of labour force statusare estimated using data from the 1986 and 2001 Censuses. Census data are usedbecause they provide a consistent basis for estimating the determinants of employmentfor lone and couple mothers. Most other sources of data that provide data since themid-1980s do not have a sufficient sample of lone mothers to allow reliable estimatesto be made.

The rest of the paper is structured as follows. The next section documents thelabour market experience of lone and couple mothers over the period 1983 to 2005.The third section, discusses the conceptual model and empirical specification used toestimate the determinants of employment. In the fourth section, the results of thestatistical modelling are discussed. The discussion focuses on how the determinantsof labour force status have changed over time and whether this differs for lone andcouple mothers. The fifth section presents the results of a decomposition of the sourcesof the changes in labour force status into the component due to changes in characteristicsand the component due to changes in coefficients. The final section concludes.

2 In June 2001, 26.2 per cent of lone parents receiving Parenting Payment Single reported havingearnings (Department of Family and Community Services 2001). The combination of relativelyhigh minimum wages, relatively generous income test tapers, and the provision of in-work benefitsmeans that many lone mothers in Australia combine part-time employment with continued receiptof government income support (Whiteford and Angenent 2001).

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397MATTHEW GRAY, LIXIA QU, JENNIFER RENDA AND DAVID DE VAUS

Changes in the Labour Force Status of Lone and Couple Australian Mothers, 1983-2005

2. Trends in Labour Force Status of Australian MothersIn this section trends in labour force status of lone and couple mothers with a dependentchild over the period 1983 and 2005 are described.3 For lone mothers part-timeemployment grew from 11.8 per cent in 1983 to 28.8 per cent in 2005 (figure 1). Whilethe proportion of lone mothers employed full-time fluctuated with the business cycle,there was an overall increase between 1983 and 1988, from 20.3 to 28.7 per cent. Sincethen it has decreased and was 22.6 per cent in 2005. By 1998 more lone mothers wereemployed part-time than full-time. The increase in participation in part-time employmentcombined with an increase in unemployment has resulted in a substantial decline in theproportion of lone mothers who were not-in-the labour force (NILF).

Figure 1 - Labour Force Status of Lone Mothers, 1983-2005

Source: ABS (various years(a)) and ABS (various years(b)).

In contrast to the experience of lone mothers, couple mothers experiencedsubstantial increases in their level of both full-time and part-time employment (figure2). Between 1983 and 2005, the proportion of couple mothers employed full-timeincreased from 18.3 to 27.7 per cent while the part-time employment rate increasedfrom 23.8 to 37.7 per cent.

Couple mothers have a much lower unemployment to population rate thanlone mothers. Also, their unemployment to population ratio appears less sensitive tothe business cycle. This is not surprising given that the majority of couple mothershave an employed partner and are thus more likely to withdraw from the labour forcealtogether (the so called discouraged work effect) (Lenten 2001). The unemploymentto population ratio of couple mothers declined over the period 1983 to 2005.

3 The data in this section are from the ABS Labour Force Survey. Mothers are defined as womenwho form a parent-child relationship with at least one dependent child, including step children. Adependent child is a child living in the household aged 15 years or younger or a child aged 16 to 24years who is a full-time student.

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398AUSTRALIAN JOURNAL OF LABOUR ECONOMICSDECEMBER 2006

Figure 2 - Labour Force Status of Couple Mothers, 1983-2005

Source: As for figure 1.

3. Modelling the Determinants of Labour Force Status,1986 to 2001This section describes the conceptual framework, estimation method and data used.

Economic ModelThe labour force decision can be viewed as a two-stage process. In the first stage anindividual decides whether or not to supply their labour to the market. In the secondstage whether or not they are employed is determined by a combination of factorsincluding the demand for their labour, their incentives to search actively for work andto accept any job offers they receive.

Individuals make labour supply decisions by maximising a utility functionsubject to a wealth or budget constraint. An individual’s decision to participate in thelabour market (and work a desired number of hours) can be explained in terms of atrade-off between time spent at home on market-substitution activities, leisure, andpaid work. The decision to work or not work depends on a comparison between thewage that can be obtained in the market and the reservation wage (the minimum wageat which a job will be accepted). Family related factors are clearly important for thelabour supply decisions of mothers and a range of models of family labour supplyhave been developed (for a review see Blundell and MaCurdy 1999). These modelsinclude unitary models in which the family aims to maximise total family utility andmodels in which labour supply decisions involve bargaining between family members.

These theoretical labour supply models have a number of implications for whatfactors determine labour supply. The wage that can be obtained in the labour market isa key factor, as is the amount of unearned income received. Clearly specialisation withinthe household between the production of home and market based goods is important.For women, the age of their children is likely to be important in the balance betweenpaid work and child rearing, as child rearing responsibilities change over the lifecycle.

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399MATTHEW GRAY, LIXIA QU, JENNIFER RENDA AND DAVID DE VAUS

Changes in the Labour Force Status of Lone and Couple Australian Mothers, 1983-2005

While the models have differing implications for the way in which the factorsaffect labour supply, data constraints mean that the statistical model used is a reducedform model which cannot distinguish between the underlying models of labour supply.

Econometric Modelling and DataThe dependent variable measuring labour force status is: full-time employment(working 35 hours a week or more); part-time employment; unemployment; and not-in-the labour force. Given that four labour force states are modelled, an appropriatestatistical technique is the multinomial logit model. The multinomial logit model allowsthe dependent variable to take one of four mutually exclusive and exhaustive values,j=1, 2, 3 and 4:

Yi = 1 if person i is full-time employed (FT)

Yi = 2 if person i is part-time employed (PT)

Yi = 3 if person i is unemployed (UE)

Yi = 4 if person i is not-in-the labour force (NILF).

The multinomial model is given by:

(1)

The estimates of the determinants of labour force status are based on the oneper cent sample file from the 1986 and 2001 Censuses. Of crucial importance to thisstudy is the comparability of the census data for 1986 and 2001, which provide aconsistent basis for estimating the determinants of labour force status.4 The censusdata provide detailed information on labour force status, educational and demographiccharacteristics (including the number and age of children) and household level data.

The models are estimated separately for lone and couple mothers for both1986 and 2001. The specification includes a number of variables that the economicmodel described above suggests will be related to employment status, or which previousempirical studies have shown to be important determinants (e.g. Beggs and Chapman1990, Breusch and Gray 2004, Doiron and Kalb 2005, Gray et al. 2002 and Le andMiller 2000).

Age is included as a quadratic to identify life cycle effects and as a measure ofpotential labour market experience. Level of educational attainment is measured by aset of dummy variables: no post-school qualification; vocational qualification; or adegree or diploma level qualification.5

The impact of child rearing on the probability of being in each labour forcestate is captured using a set of dummy variables. The first series of variables reflects

4 There are a number of difficulties with including the 1981 Census data in the analysis of thechanges in labour force status of lone and couple mothers. Information on de facto relationshipswas not collected in the 1981 Census meaning that some couple mothers with de facto partnerswill be misclassified as lone mothers. In addition, information on unemployment was not availablein the 1981 sample file.5 The 1986, 1991 and 1996 Censuses asked about age left school. For the 2001 Census this waschanged to the ‘highest year of schooling’. This change means that it is not possible to construct aconsistent measure of the level of secondary schooling completed for 1986 and 2001.

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whether the age of the youngest dependent child in the household is four years oryounger (pre-school age), 5 to 11 years (primary school age), 12 to 14 years (secondaryschool age, parent eligible for Parenting Payment), or 15 to 24 years (parent not eligiblefor Parenting Payment).6 There is evidence that having more than one young childdramatically reduces the likelihood of a mother being employed (e.g. Breusch andGray 2004) and so a variable which captures the effects of having two or more childrenaged four years or younger is included. Similarly, in order to capture the effects ofhaving additional children aged 5 to 11 years, a variable is included which takes thevalue of one if the respondent has two or more children aged 5 to 11 years or has ayoungest child aged 0 to 4 years and one child aged 5 to 11 years.

The motivation to seek employment and the intensity of job search is likely tobe related to the family’s financial commitments. The stronger the financial need, thestronger the motivation to seek work might be. Since housing costs are a major financialcommitment a set of dummy variables indicating housing tenure (purchasing a house,owning house outright and renting accommodation) is included.

Other explanatory variables include spoken English ability (speaking Englishonly, well, and poorly), being a migrant and arrived in Australia more than five yearsago, being a migrant and arrived in Australia within the last five years and beingAustralian born.7 For couple mothers, partner’s income is included as an explanatoryvariable. Partner’s income squared is included to allow for any non-linear relationship.8

The sample used in the estimation includes all women aged 15 to 64 yearswho had a dependent child aged less than 15 years of age or a dependent child aged 15to 24 years who was a full-time student. The estimation sample for 1986 compriseddata on 13,912 couple mothers and 1,910 lone mothers and for 2001 comprised dataon 14,299 couple mothers and 3,614 lone mothers.9 Summary statistics are presentedin Appendix A.

6 For the period covered in this paper, parents lost eligibility for Parenting Payment (known as soleparent pension or parenting allowance prior to 1996) when the youngest child is aged 16, howeverthe closest age grouping available on the public release data set is 15 to 24 years. In addition, thesole parent may be the primary carer for a Disability Allowance Child over 16 years of age. Fromthe 1 July 2006, significant changes have been made to the income support system includingrestricting Parenting Payment to those whose youngest child is under 6 years for partnered primarycarers and 8 years for single primary carers. Primary carers receiving Parenting Payment prior to1 July will continue to be eligible to receive Parenting Payment until their youngest child is aged16 years. A part-time activity requirement of 15 hours per week applies to those with a youngestchild aged 6 years or older.7 The specification of the model for lone mothers estimated using the 1986 Census differs slightlyto that estimated using the 2001 Census. Due to a small number of migrants in the category,having arrived five to ten years prior to the 1986 Census, length of time since arrival in Australiais captured by two dummy variables: having arrived more than ten years ago and having arrivedwithin the last ten years.8 Geographic remoteness has been shown to impact upon labour force status for a variety of reasons.There are inconsistencies in the measures of geographic remoteness available on the 1986 and2001 Census one per cent sample files and therefore this variable is not included in the estimatesof the determinants of labour force status.9 Exclusions from the estimation sample include mothers living with a same sex partner, for whomthe age of youngest child in the family could not be identified due to the temporary absence ofanother dependent child on census night. Mothers whose partner were temporarily absent on thecensus night are excluded because the Census did not collect income for absent family members.The sample size is further reduced by excluding the ‘not stated’ category in each of the variablesincluded in the analysis.

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401MATTHEW GRAY, LIXIA QU, JENNIFER RENDA AND DAVID DE VAUS

Changes in the Labour Force Status of Lone and Couple Australian Mothers, 1983-2005

4. Estimation Results – Changes in the Determinants ofLabour Force StatusThis section presents the estimates of the determinants of labour force status for loneand couple mothers for 1986 and 2001.10 As the multinomial logit model coefficientsare not straightforward to interpret, the results are presented using the predictedprobability of being in the respective labour force states (coefficient estimates providedin Appendix B).

Given the focus of this paper on why the trends in labour force status of loneand couple mothers have differed so substantially, the presentation of the results focuseson the change in the probability of being in the respective labour force states between1986 and 2001. Specifically, for each set of explanatory variables, the change in thepredicted probability of being in each labour force state between 1986 and 2001 iscalculated holding constant the values taken by all other explanatory variables at the2001 sample mean. This allows the extent to which the effect of each individual variableon labour force status has changed between 1986 and 2001 to be identified and isolatedfrom the effects of changes in the composition of the lone and couple motherpopulations. Tables 1 and 2 show the predicted probabilities of being in the respectivelabour force states in 2001 and the changes in labour force status between 1986 and2001 for each set of explanatory variables for couple and lone mothers respectively.

Age and Number of ChildrenBoth the age and number of children have a strong and statistically significant impactupon the labour force status of both couple and lone mothers. In 2001 couple motherswith a youngest child aged 0-4 years have a predicted probability of full-timeemployment of 18.0 per cent, part-time employment of 33.2 per cent, unemploymentof 2.0 per cent and being not-in-the labour force of 46.9 per cent. The predictedprobability of being full-time and part-time employed increases as the age of theyoungest child increases. There is a corresponding drop in the predicted probability ofbeing not-in-the labour force. Additional children under the age of five dramaticallyreduce the predicted probability of being full-time employed and also reduce theprobability of being part-time employed. Similarly, having an additional child aged 5-11 years reduces the predicted probability of being full-time employed as compared tohaving only one child aged 0-4 years or one child aged 5-11 years.

For lone mothers, the predicted probability of being full-time or part-timeemployed in 2001 is lower for all of the variables relating to age and number of childrenthan for couple mothers. The gap in full-time employment rates for couple and lonemothers’ increases as the age of the youngest child increases until the youngest childreaches 12-14 years and then narrows. Young children, especially an additional childaged 0-4 years or 5-11 years, had a greater negative impact on couple mothers’ predictedprobability of full-time employment as compared to lone mothers, which could be relatedto the fact that the predicted probability of being in full-time employment for lonemothers is lower. Overall, there is a similar pattern for both groups of mothers, withthe rate of full-time employment increasing as the age of the youngest child increases.

The changes in the predicted probability of being in the respective labourforce states are also shown in tables 1 and 2. For the dependent children variables, the10 The estimates pass the Hausman test of the Independence of Irrelevant Alternatives (IIA).

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change in labour force status between 1986 and 2001 are shown graphically in figures3 and 4.

For couple mothers, the predicted probability of being in full-time employmentincreased between 1986 and 2001 for all the family compositions where youngestchild was at least 5 years, while it slightly declined for the families with a child aged0-4 years (figure 3).

On the other hand, the predicted probability of part-time employment for couplemothers increased for all the family compositions examined, especially mothers withyounger children. The increases in employment were greater for couple mothers withyounger children - primarily due to the increases in part-time employment.

For lone mothers the pattern of changes in labour force status between 1986and 2001 is quite different than for couple mothers. Lone mothers experienced adecrease in full-time employment for all the family compositions considered (figure4). In contrast, there was an increase in the rate of part-time employment for all familycompositions – especially among lone mothers with older children. The net effect isthat there has been an increase in employment rates for all family compositions exceptfor lone mothers with two or more children aged 0-4 years.

Table 1 - Predicted Labour Force Status, Couple Mothers, 1986 and 2001

Predicted Probability 2001 Change 1986 to 2001

FT PT UE NILF FT PT UE NILF

Age and Number of Children Per Cent Percentage Point Change

1 child 0-4 years 18.0 33.2 2.0 46.9 -0.6 11.0 -0.2 -10.21 child 5-11 years 31.0 39.9 2.4 26.7 1.5 9.5 -0.8 -10.21 child 12-14 years 39.3 36.8 2.9 21.0 1.9 7.0 0.4 -9.31 child 15-24 years 45.1 34.8 2.4 17.7 1.7 3.6 -0.1 -5.22+ children 0-4 years 9.0 25.7 1.7 63.7 -0.6 9.0 -0.2 -8.21 child 0-4 years and1 child 5-11 years 13.0 32.9 2.0 52.1 -0.2 10.7 -0.7 -9.82+ children 5-11 years 23.9 42.1 2.5 31.5 1.9 10.2 -1.6 -10.4EducationDiploma or higher degree 36.3 40.1 2.1 21.5 1.2 7.4 -0.5 -8.1Vocational qualification 22.5 41.6 2.6 33.3 -1.5 8.8 -0.8 -6.4No post-school qualification 19.8 34.0 2.4 43.8 0.9 10.4 -0.4 -10.9Proficiency in spoken EnglishEnglish only 24.0 40.2 2.2 33.5 1.0 10.1 -0.4 -10.7Well/very well 29.1 31.3 2.9 36.6 -0.6 9.3 -0.9 -7.9Poor/not at all 18.6 15.2 4.8 61.4 -6.1 2.1 -1.6 5.6Year arrived in AustraliaBorn in Australian 24.4 39.7 2.2 33.7 1.4 11.4 -0.5 -12.4Within 5 years 22.9 25.5 4.9 46.8 -3.5 1.6 -0.8 2.7More than 5 years ago 25.9 34.5 2.9 36.6 -1.5 6.5 -0.3 -4.7Home ownershipFully owned 23.1 38.2 2.1 36.5 0.8 11.1 0.1 -12.0Purchasing 27.5 39.6 2.1 30.8 1.6 8.4 -0.8 -9.2Renting 19.7 30.8 4.5 45.0 -2.0 9.8 -0.8 -7.0

Notes: The predicted probabilities of being in the respective labour force states in 2001 arecalculated using the mean values for 2001. Changes in the probability of being in each labourforce state are calculated holding constant characteristics at the 2001 Census sample mean.Source: Derived from Appendix tables A2, B1 and B3.

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403MATTHEW GRAY, LIXIA QU, JENNIFER RENDA AND DAVID DE VAUS

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Table 2 - Predicted Labour Force Status, Lone Mothers, 1986 and 2001

Predicted Probability 2001 Change 1986 to 2001

FT PT UE NILF FT PT UE NILF

Age and Number of Children Per Cent Percentage Point Change

1 child 0-4 years 10.7 25.7 6.7 56.8 -4.0 5.8 0.5 -2.41 child 5-11 years 20.5 32.1 8.5 38.8 -3.0 15.5 0.2 -12.61 child 12-14 years 26.6 31.2 10.5 31.7 -5.0 17.3 1.6 -13.91 child 15-24 years 36.8 28.5 12.1 22.6 -8.0 14.2 5.8 -12.02+ children 0-4 years 3.0 15.7 5.2 76.1 -2.6 5.4 -4.9 2.11 child 0-4 and 1 child 5-11 years 6.3 21.9 7.4 64.4 -2.5 4.0 0.5 -2.02+ children 5-11 years 13.1 29.4 10.1 47.4 -1.6 13.8 0.5 -12.6EducationDiploma or higher degree 31.7 35.7 7.3 25.3 -7.2 4.5 -2.6 5.4Vocational qualification 21.0 36.7 9.0 33.4 -9.8 21.5 1.0 -12.7No post-school qualification 13.2 25.6 9.9 51.3 -1.3 13.1 2.9 -14.7Proficiency in spoken EnglishEnglish only 18.3 31.2 9.3 41.2 -3.4 13.4 1.8 -11.8Well/very well 13.0 22.6 10.6 53.8 -5.5 9.6 -2.0 -2.1Poor/not at all 4.0 10.8 7.3 77.9 -5.1 8.0 -7.6 4.7Year arrived in AustraliaBorn in Australia 17.2 30.6 9.1 43.1 -3.7 14.8 1.8 -12.9Within 5 years 30.2 13.4 10.0 46.4 -4.4 -6.5 0.5 10.4More than 5 years ago 15.5 28.5 10.9 45.0 -4.2 10.1 -0.7 -5.2Home ownershipFully owned 16.0 30.4 7.2 46.5 -3.1 12.6 2.4 -11.8Purchasing 30.9 35.0 6.4 27.6 0.9 12.7 0.2 -13.8Renting 12.6 25.8 11.6 49.9 -5.1 12.2 1.2 -8.3

Notes: As for table 1.Source: Derived from Appendix tables A2, B2 and B4.

Figure 3 - Change in Predicted Labour Force Status by Number and Age ofChildren, Couple Mothers, 1986 to 2001

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Figure 4 - Change in Predicted Labour Force Status by Number and Age ofChildren, Lone Mothers, 1986 to 2001

Educational AttainmentFor both lone and couple mothers, the rate of full-time employment is predicted toincrease as the level of educational attainment increases (tables 1 and 2). The rate ofpart-time employment for both lone and couple mothers is also estimated to increaseas the level of educational attainment increases, although not to the same degree asfull-time employment.

The changes in labour force status by educational attainment between 1986and 2001 are presented in tables 1 and 2 and graphically in figures 5 and 6. For couplemothers there was little change in full-time employment across all education groupswhile there was a substantial increase in part-time employment across all levels ofeducational attainment. The increases ranged from 7.4 percentage points for couplemothers with a degree or higher qualification to 10.4 percentage points for couplemothers with no post-school qualification.

For lone mothers the pattern is very different. There were substantial falls infull-time employment for those with higher levels of educational attainment, with thefall being particularly marked for those who had a post-school qualification. Between1986 and 2001 the predicted probability of a lone mother being employed full-time isestimated to have fallen by 7.4-9.8 percentage points for those who had post schoolqualifications compared to 1.3 percentage point for those who had no post-schoolqualification.

Like couple mothers, the predicted probability of being part-time employedincreased for lone mothers across all education groups. Interestingly, the increases inpart-time employment were highest for lone mothers with a vocational qualification(21.5 percentage points).

For lone mothers, almost all education groups experienced an increase inemployment (part-time plus full-time employment). The only exception is lone motherswith a degree or diploma level qualification who experienced a 5.4 percentage pointfall in employment. When interpreting the change for lone mothers with a degree ordiploma level qualification it should be borne in mind that lone mothers with this levelof education still have the highest employment rate.

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405MATTHEW GRAY, LIXIA QU, JENNIFER RENDA AND DAVID DE VAUS

Changes in the Labour Force Status of Lone and Couple Australian Mothers, 1983-2005

Figure 5 - Change in Predicted Labour Force Status by EducationalAttainment, Couple Mothers, 1986 to 2001

Figure 6 - Change in Predicted Labour Force Status by EducationalAttainment, Lone Mothers, 1986 to 2001

Proficiency in Spoken EnglishFor couple mothers, those who speak English well as a second language had a predictedprobability of full-time employment of 29 per cent. This is slightly higher than therate of 24 per cent for couple mothers who speak only English. Couple mothers withpoor spoken English have a predicted probability of full-time employment of 18.6percentage points. There is a stronger relationship between English proficiency andpart-time employment with probabilities of part-time employment of 40.2 for couplemothers who speak English only, 31.3 per cent for those who speak English well and15.2 per cent for those who speak English poorly.

For lone mothers the effect of English language proficiency on the predictedprobability of part-time and full-time employment in 2001 is more pronounced. Lonemothers with poor spoken English are predicted to have a rate of full-time employmentof only 4 per cent. However, the numbers of lone mothers with poor spoken English isrelatively small and therefore these estimates should be treated with caution.

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The most notable change, between 1986 and 2001, in relation to the effects ofEnglish language proficiency on labour force status is that for both couple and lonemothers with poor English there was a fall in the predicted probability of full-timeemployment (of 6.1 and 5.1 percentage points respectively) while there was an increasein part-time employment (2.1 and 5 percentage points respectively). Overall, bothcouple and lone mothers with poor English experienced declines in their labour forceparticipation rates while couple and lone mothers who spoke English only and spokeEnglish well increased their labour force participation rates.

5. Decomposition of Changes in Probabilities ofLabour Force StatusThe changes in labour force status over the period 1986 to 2001 can be decomposedusing the estimates of the determinants of labour force status into two components—the part due to changes in characteristics and the part due to changes in coefficients.11

This is achieved as follows. Taking lone mothers as an example, the predictedprobability of being in each labour force status is calculated using the coefficients andsample characteristics for lone mothers for 1986 and 2001. These are described as the1986 and 2001 base case probabilities. The difference between the 2001 base caseprobabilities and what the probability would have been if lone mothers in 2001 hadthe same characteristics as lone mothers in 1986 indicates the extent to which changesin the probability of employment is due to changes in characteristics of couple mothers.The remainder of the change in the probability of being in the respective labour forcestates is due to changes in coefficients (also termed ‘determinants’).

This methodology is an extension of the Oaxaca decomposition to non-linearmodels and is similar to the decomposition method proposed by Even and Macpherson(1993) for the case of a binary choice model. A detailed description of how thedecompositions were undertaken is provided in Appendix C. The results of thedecompositions are presented in table 3.

For couple mothers, the 3.8 percentage point increase in full time employmentbetween 1986 and 2001 can largely be explained by changes in the characteristics ofthe couple mother population (3.0 percentage points) with changes in the determinantsof labour force status explaining only 0.8 percentage points of the increase. In contrast,the 9.7 percentage point increase in part time employment was largely explained bychanges in coefficients (8.7 percentage points) with changes in characteristicsgenerating a 1.0 percentage increase in part-time employment.

The majority of the decrease of 12.1 percentage points in the likelihood ofbeing not-in-the labour force is attributable to changes in coefficients (8.4 percentagepoints) with changes in characteristics contributing 3.7 percentage points to the decline.

For lone mothers, the predicted increase in part-time employment was almostentirely due to a change in coefficients (12.5 percentage points) with just 0.7 percentagepoints explained by a change in characteristics. The probability of full-time employmentis predicted to have fallen marginally by 0.8 percentage points. Changes incharacteristics are estimated to have increased full-time employment by 2.3 percentage11 It is also possible to decompose the causes of the differences in labour force status of lone andcouple mothers at a given point in time (e.g Gray et al. 2002).

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points while changes in coefficients are estimated to have decreased the probability offull-time employment by 3.1 percentage points.12 These results suggest that for lonemothers the trends in labour force status are explained either by changes in financialincentives or preferences for part-time employment (explanations 1 and 3), whereasfor couple mothers they are explained both by changes in financial incentives andpreferences for part-time employment but also by changes in the characteristics ofcouple mothers.

Table 3 - Decomposition of Change in Labour Force Status, 1986-2001

Not in labourFull time Part time Unemployed force

Per Cent

Couple Mothers1986 base probabilities 21.9 26.1 4.2 47.92001 base probabilities 25.7 35.8 2.7 35.8Change 1986 to 2001 3.8 9.7 -1.5 -12.1Change in characteristics 3.0 1.0 -0.2 -3.7Change in coefficients 0.8 8.7 -1.3 -8.4Lone Mothers1986 base probabilities 21.7 14.1 7.6 56.62001 base probabilities 20.9 27.3 8.9 42.9Change 1986 to 2001 -0.8 13.2 1.3 -13.7Change in characteristics 2.3 0.7 -0.9 -2.1Change in coefficients -3.1 12.5 2.2 -11.6

Notes: The base case employment probabilities for 1986 and 2001 are calculated using therespective coefficients and sample characteristics for 1986 and 2001. A detailed description of thedecomposition method is provided in Appendix C.Source: Calculations based on Appendix tables A1, A2, B1, B2, B3 and B4.

These results are consistent with those of Doiron (2004), who finds thatchanges in the observed characteristics of lone mothers explains only a small proportionof the changes in labour supply between 1986 and 1990, and that policy reformscaused a substantial increase in employment and, for employed lone mothers, reducedworking hours.

The results for lone mothers are consistent with the expected changes in labourforce status given increased financial incentives for part time work due to the changesto the income support system and due to the increasing availability of part-timeemployment. However, using census data it is not possible to eliminate other possibleexplanations.

12 A similar exercise has been conducted for the period 1986 to 1996. The relative importance ofchanges in characteristics and determinants in explaining the changes in the labour force status oflone and couple mothers over the period 1986 to 1996 are very similar to the results for the period1986 to 2001.

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6. Concluding Comments and Policy ImplicationsOver the last twenty years there has been a substantial increase in the proportion oflone mothers employed part-time, while the proportion employed full-time is muchthe same in 2005 as it was in 1983. The experience of couple mothers is quite different,with both full-time and part-time employment increasing at similar rates. The net effectis that both lone and couple mothers have had similar increases in overall employmentrates but that the nature of the growth in employment has been different among thelone and couple mother populations.

In order to explore the reasons for the different experiences of Australian loneand couple mothers, models of the determinants of labour force status in 1986 and2001 have been estimated. For lone mothers there was a fall in full-time employmentacross virtually all the family compositions (age and number of children) examined.In contrast, there was an increase in part-time employment across all familycompositions, but especially among those with older children.

The estimates are used to decompose the sources of the changes in labourforce status of lone and couple mothers, between 1986 and 2001, into the part due tochanges in the characteristics of the lone and couple mother populations and the partdue to changes in the determinants of labour force status. The results of thisdecomposition are striking. Virtually none of the increase in part-time employment oflone mothers can be explained by changes in the average characteristics of the lonemother population. Much of the explanation lies in changes in the determinants oflabour force status. Although this pattern also applies to couple mothers, changes indeterminants appear to have greater impact on the increase in part-time employmentfor lone mothers than it does for couple mothers.

While the analysis in this paper is not able to disentangle the exact reasonswhy the determinants of employment for lone mothers have changed, some explanationsappear more likely than others. Between 1983 and 2005 there have been changes tothe income support system that have made part-time employment more financiallyattractive. Changes include increases in the real value of the Sole Parent Pension andincreases in earnings disregards of child related income support payments andavailability of rent assistance and other concessions (Stanton and Feury 1995; Whitefordand Angenent 2001).13

However, these changes do not appear to have been of sufficient magnitude tofully explain the changes in lone mothers’ labour force status over this period.Interestingly, the largest changes to the financial incentives of being in part-timeemployment occurred over the period 1996 to 2005, whereas there were increases inpart-time employment over the whole period.14

13 Another factor which may have made part-time work more attractive was the introduction of theChild Support Scheme in 1988. The amount of child support payments received decreases oncethe mother’s earnings cross a threshold amount (in the 1996-97 financial year this amount was$36,130) (Child Support Agency 2003). This is likely to act as a further disincentive to workingfull-time. However, the disincentive to full-time work generated by the child-support scheme islikely to be relatively small, given that only about half of the mothers receiving an income supportpayment receive any child support from the non-resident parent (ABS 1997; Birrell and Rapson1998).14 Relevant changes over the period 1996 to 2005 include increases in the real value of incomesupport payments and child related payments as well as increases in the earnings disregards and areduction in the rate of withdrawal of benefits (the taper rate) (Whiteford and Angenent 2001).

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Given that the changes to the income support system seem unlikely to explainall of the changes in labour force status other factors must also play a role. Anotherpotential explanation for the rapid growth in part-time employment among lone mothersis that an increasing proportion of the additional jobs created between 1986 and 2001have been part-time.15 The growth in part-time employment has been particularly strongin industries and occupations that have a disproportionate number of female employees(ABS 2001; ABS 2002, p. 132). However, this explanation does not account for thefact that for couple mothers there was a similar rate of growth in both part-time andfull-time employment. It appears that there is something about lone and couple mothersthemselves or their access to jobs that is contributing to these different patterns ofemployment growth.

Given that mothers with higher levels of education will, on average, havemore job opportunities, the finding that lone mothers with higher levels of educationalattainment experienced the greater falls in full-time employment but the greaterincreases in part-time employment suggests that there may be an element of choice inreducing the hours of work. Further support of this hypothesis is provided by the factthat lone mothers with the highest level of educational attainment (tertiary qualification)had a fall in the total employment rate between 1986 and 2001.

The finding that the increase in employment for lone mothers is larger amongstwomen with older children (aged 5 years and older), whereas for couple mothers theincreases is larger for women with younger age children (pre school and primary school)suggests that the extra parenting demands placed upon lone mothers makes it moredifficult for those with young children to be in paid employment. However, once thechildren are at school it becomes easier for lone mothers to move to part-timeemployment.

Another possible explanation that is consistent with the pattern of employmentgrowth for lone mothers is that, on average, lone mothers have always been morelikely than couple mothers to prefer full-time employment. This is plausible giventhat lone mothers usually rely on only one income (although many receive child supportpayments). If increasingly lone mothers have been unable to find full-time employment(that is they face a demand constraint), the rising levels of part-time employment willbe reflected in increasing rates of underemployment amongst lone mothers.Unfortunately the data necessary to test this hypothesis are not available. However,we can get some indications by examining the extent to which lone mothers who areworking part-time would prefer to be working full-time. A suitable data set is theHousehold, Income and Labour Dynamics in Australia (HILDA) survey, the first waveof which was collected in 2001. According to the HILDA data, of the lone motherswho are employed part-time, 19.7 per cent would prefer to be working full-time ascompared to just 7.6 per cent of couple mothers.

While this paper has provided some evidence on the reasons for the changes inemployment patterns for lone and couple mothers, further research is needed to clarifywhy these changes have occurred. This information is important when consideringways in which the design of the income support system can be improved in a world inwhich part-time employment of lone mothers is becoming increasingly common.15 The proportion of all new jobs which were part-time increased from 43 per cent in the 1980s to75 per cent in the 1990s (Borland, Gregory and Sheehan 2001).

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Appendix ADescriptive Statistics

Table A1- Descriptive Statistics, 1986 Census

Couple Mothers Lone Mothers

Mean std Mean std

Employment statusFull-time employment 0.22 0.41 0.22 0.41Part-time employment 0.26 0.44 0.14 0.35Unemployed 0.04 0.20 0.08 0.26Not in labour force 0.48 0.50 0.57 0.50Age of youngest dependent children0-4 years 0.43 0.49 0.32 0.475-11 years 0.33 0.47 0.37 0.4812-14 years 0.14 0.35 0.19 0.3915-24 years 0.11 0.31 0.13 0.33Other dependent childrenHaving two or more children aged 0-4 years 0.14 0.35 0.06 0.24Having additional children aged 5-11 years 0.35 0.48 0.24 0.43Age of mothers (years) 36.0 87.78 35.72 8.52EducationDiploma or higher degree 0.11 0.31 0.08 0.27Vocational qualification 0.20 0.40 0.17 0.38No post-school qualification 0.69 0.46 0.75 0.43Proficiency in spoken EnglishEnglish only 0.83 0.37 0.91 0.28Speak English well or very well 0.13 0.33 0.07 0.25Speak English poorly or not at all 0.04 0.20 0.02 0.14Year of arrival in AustraliaBorn in Australia 0.71 0.45 0.77 0.42Arrived within last five years 0.03 0.18 0.02 0.15Arrived more than five years ago 0.26 0.44 0.20 0.40Home ownershipFully owned 0.27 0.44 0.17 0.38Purchasing 0.52 0.50 0.24 0.43Renting 0.21 0.40 0.58 0.49Partner’s income (weekly)* 763 428Number of observations 13,912 1,910

* In constant 2001 dollar.Source: 1986 Census one per cent sample file.

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Appendix A (continued)Descriptive Statistics (continued)

Table A2 - Descriptive Statistics, 2001 Census

Couple Mothers Lone Mothers

Mean std Mean std

Employment statusFull-time employment 0.26 0.44 0.21 0.41Part-time employment 0.36 0.48 0.27 0.45Unemployed 0.03 0.16 0.09 0.28Not in labour force 0.36 0.48 0.43 0.49Age of youngest dependent children0-4 years 0.39 0.49 0.29 0.465-11 years 0.33 0.47 0.38 0.4912-14 years 0.12 0.33 0.16 0.3615-24 years 0.16 0.36 0.17 0.38Other dependent childrenHaving two or more children aged 0-4 years 0.11 0.32 0.06 0.24Having additional children aged 5-11 years 0.32 0.47 0.26 0.44Age of mothers 38.83 7.70 37.99 8.60EducationDiploma or higher degree 0.29 0.46 0.11 0.32Vocational qualification 0.14 0.35 0.21 0.41No post-school qualification 0.56 0.50 0.67 0.47Proficiency in spoken EnglishEnglish only 0.81 0.39 0.87 0.34Speak English well or very well 0.16 0.36 0.10 0.31Speak English poorly or not at all 0.04 0.19 0.03 0.17Year of arrival in AustraliaBorn in Australia 0.71 0.45 0.75 0.43Arrived within last five years 0.05 0.21 0.02 0.15Arrived more than five years ago 0.24 0.43 0.22 0.42Home ownershipFully owned 0.30 0.46 0.16 0.37Purchasing 0.52 0.50 0.26 0.44Renting 0.18 0.39 0.58 0.49Partner’s income (weekly) 892 619Number of observations 14,299 3,614

Source: 2001 Census one per cent sample file.

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Appendix BCoefficient Estimates

Table B1 - Logit Estimates of Probability of Labour Force Status, CoupleMothers, 1986

Part-time Employed Unemployment NILF

Coefficient T-stat Coefficient T-stat Coefficient T-stat

Youngest dependent child 0-4 years 0.5103 4.47 0.7415 2.99 1.7621 16.23Youngest dependent child aged 5–11 years 0.3633 3.89 0.6399 2.85 0.8598 9.42Youngest dependent child aged 12–14 years 0.1017 1.10 0.1763 0.74 0.4266 4.75Has two or more children aged 0–4 years 0.3735 3.44 0.4786 2.94 0.8888 9.41Has additional children aged 5–11 years 0.3398 5.42 0.5779 5.39 0.4197 7.30Age 0.0040 0.13- 0.1947 -3.92 -0.2117 -8.20Age squared 0.0001 0.32 0.0022 3.24 0.0032 9.68Vocational qualification 0.3824 4.46 0.6718 3.40 0.6754 7.71No qualification 0.2913 3.76 0.7188 3.92 1.2344 15.72Good spoken English -0.5667 -6.44 0.1033 0.70 -0.2459 -3.17Poor spoken English -0.9064 -5.14 0.8101 4.09 0.1591 1.29Arrived in Australia within last 5 years -0.3060 -1.83 0.6150 3.00 -0.1839 -1.32Arrived in Australia more than 5 years ago -0.1873 -2.81 0.0011 0.01 -0.2885 -4.61Purchasing -0.0052 -0.08 0.1938 1.42 -0.3386 -5.90Renting -0.2311 -2.72 0.9899 6.77 0.0942 1.28Partner’s weekly income 0.0017 8.66 -0.0003 -0.79 0.0018 9.82Partner’s weekly income squared -5.54 E-07 -6.22 -1.64E-08 -0.09 -5.94E-07 -7.09Constant -1.5794 -2.58 0.6374 0.67 1.0980 2.12Number of observations 13,912Pseudo R-squared 0.08Model chi-square 2635.13

Table B2 - Logit Estimates of Probability of Labour Force Status, Lone Mothers,1986

Part-time Employed Unemployment NILF

Coefficient T-stat Coefficient T-stat Coefficient T-stat

Youngest dependent child aged 0–4 years 1.4541 4.22 1.1026 2.3 1.6571 5.84Youngest dependent child aged 5–11 years 0.8029 2.94 0.9249 2.28 1.0412 4.67Youngest dependent child aged 12–14 years 0.3288 1.22 0.6908 1.74 0.6263 2.91Has two or more children aged 0–4 years 0.3039 0.45 1.4477 2.33 1.1845 2.18Has additional children aged 5–11 years 0.3986 1.74 0.6023 2.23 0.6193 3.33Age -0.0124 -0.14 -0.3638 -3.93 -0.3014 -4.41Age squared 0.0006 0.54 0.0047 3.91 0.0042 4.76Vocational qualification -0.4859 -1.87 0.0077 0.02 1.0718 3.77No post-secondary qualification 0.0652 0.29 0.6264 1.77 2.1846 8.3Good spoken English -0.1495 -0.43 0.6728 1.81 0.2165 0.76Poor spoken English -0.9750 -0.84 1.5557 2.13 1.1981 1.99Arrived in Australia within last 5 years -0.2698 -0.41 -0.2495 -0.39 -0.9481 -1.96Arrived in Australia more than 5 years ago 0.2189 1.06 0.5190 2.06 -0.0492 -0.28Purchasing -0.2270 -1.01 -0.1980 -0.53 -0.7932 -4.16Renting -0.1932 -0.86 0.8498 2.53 0.0759 0.42Constant -1.4196 -0.79 3.6058 1.93 3.3661 2.44Number of observations 1,910Pseudo R-squared 0.11Model chi-square 476.11

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Appendix B (continued)Coefficient Estimates (continued)

Table B3 - Logit Estimates of Probability of Labour Force Status, CoupleMothers, 2001

Part-time Employed Unemployment NILF

Coefficient T-stat Coefficient T-stat Coefficient T-stat

Youngest dependent child 0-4 years 0.8743 9.02 0.7606 3.09 1.8941 17.88Youngest dependent child aged 5–11 years 0.5134 6.71 0.3744 1.78 0.7827 8.93Youngest dependent child aged 12–14 years 0.1941 2.46 0.3282 1.52 0.3092 3.36Has two or more children aged 0–4 years 0.4349 4.03 0.4899 2.29 0.9976 9.68Has additional children aged 5–11 years 0.3119 5.47 0.3222 2.43 0.4254 7.19Age -0.0144 -0.49 -0.1483 -2.54 -0.2089 -7.37Age squared 0.0003 0.80 0.0016 2.10 0.0028 8.02Vocational qualification 0.5149 7.37 0.7038 3.87 0.9179 11.64No qualification 0.4414 8.60 0.7701 5.55 1.3201 22.79Good spoken English -0.4425 -6.10 0.0699 0.43 -0.1027 -1.39Poor spoken English -0.7181 -3.73 1.0136 4.27 0.8594 6.09Arrived in Australia within last 5 years -0.3790 -2.68 0.8784 4.05 0.3905 3.11Arrived in Australia more than 5 years ago -0.2024 -3.32 0.2379 1.58 0.0209 0.32Purchasing -0.1359 -2.62 -0.2155 -1.49 -0.3422 -6.06Renting -0.058 -0.75 0.8965 5.81 0.3653 4.78Partner’s weekly income 0.0006 4.29 -0.0019 -6.01 -0.0008 -5.31Partner’s weekly income squared -1.02E-07 -1.91 7.05E-07 5.35 4.31E-07 7.64Constant -0.6395 -1.07 0.4159 0.36 2.0869 3.65Number of observations 14,299Pseudo R-squared 0.10Model chi-square 3306.1

Table B4 - Logit Estimates of Probability of Labour Force Status, Lone Mothers,2001

Part-time Employed Unemployment NILF

Coefficient T-stat Coefficient T-stat Coefficient T-stat

Youngest dependent child aged 0–4 years 1.1380 5.11 0.6550 2.1 2.1615 9.53Youngest dependent child aged 5–11 years 0.7066 4.54 0.2378 0.97 1.126 6.64Youngest dependent child aged 12–14 years 0.4166 2.68 0.1810 0.73 0.6619 3.91Has two or more children aged 0–4 years 0.7652 1.61 0.9918 1.93 1.5517 3.47Has additional children aged 5–11 years 0.3561 2.41 0.6097 3.23 0.6441 4.45Age 0.097 31.67 -0.0861 -1.18 -0.1795 -3.37Age squared -0.0011 -1.54 0.0006 0.59 0.0025 3.69Vocational qualification 0.4400 2.86 0.613 02.39 0.6891 3.95No post-secondary qualification 0.5439 4.58 1.1736 5.75 1.5843 11.79Good spoken English 0.0209 0.11 0.4710 1.87 0.6102 3.3Poor spoken English 0.4656 0.8 1.2832 2.08 2.1630 4.45Arrived in Australia within last 5 years -1.3899 -3.17 -0.4671 -0.99 -0.4888 -1.44Arrived in Australia more than 5 years ago 0.0340 0.25 0.2835 1.46 0.1472 1.04Purchasing -0.5173 -3.58 -0.7735 -3.02 -1.1798 -7.57Renting 0.0713 0.48 0.7154 3.09 0.3054 2.05Constant -2.5994 -2.2 0.0727 0.05 1.4247 1.32Number of observations 3,614Pseudo R-squared 0.12Model chi-square 1109.5

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Appendix CDetailed Description of the DecompositionThis appendix presents mathematically the decompositions presented in section 4 ofthe paper. We present the decomposition in detail for lone mothers. The decompositionfor couple mothers is very similar. Define the probability that lone mother i in labourforce state j in year k ={1986,2001} as:

(1)

where βkj is a vector of estimated coefficients for labour force state j for lone mothers

in year k, xkj is a vector of characteristics of lone mothers in year k. The average

probability of lone mothers being in labour force state j in year k is derived as:

(2)

where LPS (j)k is the average probability of being in labour force state j for lone mothersin year k and N

k is the number of lone mothers in year k.

The probability of lone mother i being in labour force state j in 1986, if theyhad the lone mothers’ coefficients for 2001 is defined as:

(3)

The average probability of lone mothers being in labour force state j in 1986assuming they had the 2001 coefficients is derived as:

(4)

The difference in the predicted probability of lone mothers being in labourforce state j between 1986 and 2001 can be separated into the component due todifference in coefficients for the two years and the component due to changes in thecharacteristics of the lone mother population between 1986 and 2001. The followingidentity shows this decomposition:

(5)

An analogous procedure is used to calculate the decomposition for couplemothers.

^

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