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Welfare benefits and the duration of single parenthood.


The number of one parent families has risen by about 80 per cent since 1971, reaching just over a million in 1986. (Haskey 1989). In 1986, they made up 14 per cent of all families with dependent children, and the primary reason for this large increase is marital breakup: about 70 per cent of the increase is attributable to the growth in the number of divorced and separated mothers. At present, 90 per cent of single parents are women, and 3/4 of mothers heading one parent families have previously been married.

The proportion of families with dependent children who are headed by a single parent depends on the rates of inflow to single parenthood, through first births outside of marriage and particularly through marital dissolution. But it also depends on how long people remain single parents. The duration of single parenthood depends, in turn, on how quickly single parents marry or remarry.

About 70 per cent of one parent families currently receive Income Support, the primary welfare benefit. Politicians and other commentators have contended that higher welfare benefits are at least partly responsible for the increase in the number of one parent families. For instance, in its special article on Welfare and Work, The Economist argues that `It is work that offers the only way to give a single mother a decent life, without paying her so much in welfare that she is discouraged from marrying for fear of losing her benefit.' (26 November 1988, p.28). Furthermore, it is argued that politicians' fears that larger benefits for single parents encourage more one parent families are a barrier to better provision for single parent families.(2) The evidence presented in this paper indicates that such fears have little foundation. The paper focuses on measuring the effect of welfare benefits on the duration of single parenthood.

The duration of single parenthood.

The analysis uses data from the demographic and employment histories of women collected in the British Women and Employment Survey (WES) (see Martin and Roberts 1984 for details). The WES collected marital, childbearing and employment histories from 5,320 women aged 16-59 in 1980. The focus on women is not an important limitation because, as noted earlier, 90 per cent of one parent families are headed by the mother. It is, unfortunately, not possible to identify consensual unions in the WES demographic histories. Thus, while we would ideally like to characterise, at each point in time, a mother with a dependent child(ren) by whether she is in a union with a man or not, our characterisation is in terms of whether she is married or not.

Our definition of a single parent is, therefore, a mother with dependent children who is not married. A dependent child is defined as being less than 16 years of age in our analysis.

On this definition, about 800 of the women in the WES were single parents at least once during their lives. Starts and ends of marriages, as well as births, are dated (by month) in the Survey, but there is an asymmetry. Starts of marriages generally refer to the legal date of the marriage, while ends of marriages refer to the de facto end as reported by the woman, rather than the date of the legal divorce.(3)

Of the two types of single mothers, the start of single motherhood for the never-married is the date of her first birth, and it is the date of the marital dissolution for the previously married. The outflow from single motherhood occurs through (re)marriage or the youngest child reaching adulthood (16 years of age). The proportions of previously married and never-married single mothers remaining single mothers at yearly intervals since the start of single parenthood, computed from our data by lifetable methods (the Kaplan-Meier estimator), are shown in chart 1. These estimates indicate a median duration of single motherhood of 59 months for previously married single mothers. In contrast, never-married mothers leave single parenthood much quicker, exhibiting a median duration of 34 months. Thus, one of the reasons that single mothers represent a relatively small proportion of single mothers is their much shorter average duration as single parents.

The distribution of the duration of single parenthood among previously married mothers illustrated in chart 1 reflects the distribution of the age of the youngest child at marital dissolution in the sample, because it determines the length of time before the youngest child reaches adulthood. We investigate whether welfare benefits or characteristics of a woman or her family influence the duration of single parenthood.

In order to do so, we only need to study how these variables affect a single mother's marriage chances. The probability of a mother leaving single parenthood because of the maturity of her youngest child is zero until the month the child reaches 16, and it is one in that month. Thus, while the maturity of the youngest child and marriage are `competing risks' for the exit from single motherhood, welfare benefits and a woman's characteristics only influence the duration of single parenthood through their influence on the marriage rate.

The marriage analysis employs the so called proportional hazards model. What statisticians call the marriage `hazard', and what we shall call the marriage rate, is the probability of marrying in a month conditional on being a single mother up to that time. In this model, the marriage rate at duration of single parenthood t, h(t,X), is given by: (1) h(t, [X.sub.t])= [Lambda] (t) exp([X.sub.t] [Beta]) where [Lambda] (t) is a function of duration t; [X.sub.t] is a vector of characteristics of the mother, her family and aspects of her environment (e.g. welfare benefits) at duration t; and [Beta] is a vector of parameters to be estimated. We have allowed for some of the elements of [X.sub.t] (e.g. welfare benefits) to vary over time. If all of the elements were fixed, the relationship between the marriage rate and duration would be the same for everyone, but its level would vary proportionally with a mother's characteristics X. The parameters of the model are estimated by maximum likelihood using methods described in Allison (1982).(4)

The duration of single parenthood is measured from the date of the (de facto) end of the first marriage (previously married) or the date of a woman's first birth (never-married). The date of marriage is the legal date, which may be after the date when the new union is formed. If a woman's youngest child reaches the age of 16, her duration is treated as `censored' (as is also the case when the survey intervenes before (re)marriage), because she is no longer a single mother according to the definition used here.

Effects of welfare benefits on duration

Welfare benefits are defined as the real value of Supplementary Benefit (deflated by the RPI) that would be received by a single mother if she is not employed. They vary both over time, as benefit rules and rates change, and over women because benefits vary with the number of children. A measure of them is constructed by computing the amounts of Supplementary Benefit, including payments for housing, that single mothers with different numbers of children would receive in each year (computed from Department of Health and Social Security 1984), and these amounts are allocated to women's months of single parenthood according to the year that they occur and the number of children the woman has in that month. There was an upward trend in real welfare benefits over the sample period 1948-80. Indeed, welfare benefits generally increased faster than women's wages until 1967, but during 1968-80 they fell substantially relative to average women's hourly pay (by about 35 per cent).

Welfare benefits can have both direct and indirect effects on marriage by single mothers. As a source of income outside of marriage, we expect that higher welfare benefits would discourage (re)marriage. Higher welfare benefits also discourage employment (Ermisch and Wright 1989b). If women in jobs have a different marriage rate from women not employed, then welfare benefits could affect marriage chances indirectly by affecting the proportion of single mothers in jobs.

The focus of this paper is on the effects of welfare benefits, but in measuring these effects we must also allow for other aspects of the economic environment and for characteristics of a woman and her family to affect the marriage rate. For instance, the WES reports a number of characteristics of a woman and her family that might affect her remarriage rate, and these are shown in table 1. All of these variables are measured at or before the end of the first marriage. In addition, we consider characteristics that change over time, including whether the woman is employed or not, work experience, age of the youngest child (in categories), and other variables that do not refer to the woman but to her economic environment.(5)

These latter variables are: the ratio of average women's to men's hourly wages (for adults of each sex working full-time in manual occupations), which is taken as an indicator of changes over time in the gains from the division of labour within marriage (Becker 1973);(6) women's average real hourly wage (for full-timers in manual occupations), which is another indicator of income outside of marriage; and the unemployment rate in the economy. A higher unemployment rate may indicate poorer alternative sources of income for a woman, but it may also be associated with poorer marriage offers.

None of these `macro' variables appear to be stationary time series, and their trends over time make them strongly correlated with one another. This can make it difficult to estimate the impacts of these variables on the marriage rate with any precision. It also may make the estimated effect of any one macro variable strongly dependent on which of the other macro variables are included in the equation.

Results: previously married mothers

We started with a general model including all of the variables in table 1 plus variables indicating a woman's current employment status or work experience to date and the `macro' evironmental variables, including welfare benefit. Then we estimated more parsimonious models, which eliminated particular variables and re-grouped categories of categorical variables, and tested whether these restrictions were statistically acceptable using likelihood ratio tests. Table 2 shows the estimates of the parameters ([Beta]) and their standard errors for a statistically acceptable restricted version of the general model. The discussion focuses on the estimated impacts of welfare benefits and employment status (see Ermisch and Wright 1989a for a fuller discussion).

In a general model including all of the macro variables, in addition to the characteristics of a woman and her family in table 2, only women's real wages and real welfare benefits approach statistical significance, and estimates of the parameters associated with the unemployment rate and the ratio of women's to men's hourly wages never exceed their standard error in any specification. We therefore concentrate on the effects of women's real wages and real benefits.

Direct effect of welfare benefits

When the logarithmn of real benefits is the only macro variable included, its impact on the remarriage rate is positive, but statistically insignificant ([X.sup.2] = 1.16), and when the log of the real wage is the only macro variable, it has a negative effect which is insignificant ([X.sup.2] = 1.25). When both of these variables are in the model, their estimated parameters are statistically significant with opposite signs, but of the same size. As this suggests, a statistically acceptable simplication is to include the logarithm of the ratio of benefits to women's hourly wages as the only macro variable, and this is the estimated model shown in table 2. This ratio measures benefits deflated by women's wages rather than prices, and it could be interpreted as being proportional to an average benefit `replacement ratio'.

These results suggest that when women are able to earn more in a job, they are less likely to remarry, and they remain single parents longer. This is consistent with the negative impact of a woman's own employment on remarriage discussed below. The estimated tendency for higher real welfare benefits to encourage remarriage is, however, surprising and difficult to explain.

Because the size and significance of the benefits' parameter depends so much on the inclusion of women's real wages in the model, and vice versa, we estimated some other specifications to examine the robustness of the effects of these variables. All of these show a positive coefficient for welfare benefits; they are discussed in Ermisch and Wright (1989a).

While we are concerned that the impacts of the women's real wages and real welfare benefits may be spurious, we have certainly found no evidence that higher benefits discourage remarriage. This result is consistent with the evidence, from Duncan and Hoffman (1988), that American AFDC (Aid to Families with Dependent Children) benefits to single mothers do not discourage remarriage, and with the finding, by Hannan, Tuma and Groeneveld (1977), that different levels of income maintenance in American negative income tax experiments have no discernible impact on the remarriage rate.

Indirect effect of welfare benefits

Current employment status is a dichotomous variable indicating whether a woman is employed or not in each month. Being in a job reduces the remarriage rate by 30 per cent. Thus, single mothers dependent on welfare benefits are more likely to remarry, and if this is a true `structural effect', higher welfare benefits would encourage remarriage by discouraging women from working (Ermisch and Wright 1989b).

One interpretation of this finding is that mothers with better earning opportunities find marriage less attractive. But it also may be the case that women who are not very interested in remarrying look to the labour market for their present and future livelihood. In other words, there may be an unobservable trait, call it `taste for marriage', which is negatively correlated with participation in paid employment, so that the coefficient on employment status is at least partly reflecting this unobserved trait. Indeed, there may be no `structural effect' of employment on the remarriage rate. To address this issue, we would need to model remarriage and participation in paid employment jointly, allowing for unobserved hetereogeneity. But this is a much more formidable estimation task, which is beyond the scope of this paper.

The implications of these estimated effects for duration can be seen more easily when we use the parameters of the remarriage rate model in table 2 to calculate the expected (mean), median and first quartile durations of single parenthood for women with different attributes. These are shown for some selective cases in table 3. The reference woman has the mean attributes for continuous ones (like age) and the modal attributes for categorical ones (cf. table 1), and the year is taken as 1980.

The reference woman can expect to remain a single parent for 7.7 years on average, but because of the skewness of the duration distribution, half of women with her characteristics would remain so for 5.3 years or less, and a quarter remain single parents for 2.2 years or less. This compares with a median duration for all previously married single mothers of 4.9 years (cf. chart 1). If, however, she took a job when she became a single parent and remained in employment, her expected duration would be about 3 years longer than the reference woman.(7) If the ratio of welfare benefits to women's real wages returned to its higher level in 1968 (about a 55 per cent increase in benefits relative to wages), then the mean duration would be 2.5 years shorter. But, as noted earlier, we are sceptical about the measured effect of this ratio on remarriage.

Results:Never-married mothers

In addition to the macro variables considered above, the analysis considered a large number of characteristics of a never-married mother that might affect her marriage rate. These include her last occupation before having a child, including whether she had a job before becoming a mother, the year in which she gave birth, her own birth cohort, her educational qualifications, her age at becoming a single mother, her work experience before her motherhood, and whether she was currently in a job or not. Of these many variables, only a mother's age at childbirth and her current employment status had a significant impact on her marriage rate, and these estimated impacts are shown in table 4.

There is no evidence that welfare benefits have a direct effect on marriage by never-married mothers. But never-married mothers in employment are about 45 per cent more likely to marry than other single mothers, resulting in a median duration of single parenthood about 16 months shorter for a continuously employed mother than one who is never in a job.(8) This probably reflects in part better opportunities to find a husband and lower search costs for women who have jobs. This finding implies that never-married mothers dependent on welfare benefits are less likely to marry. Thus, by discouraging employment, higher welfare benefits may indirectly prolong single parenthood.

The positive association between employment and marriage could, however, also reflect some unobserved differences between women. Never-married mothers with the ability and motivation to be in employment may also be more attractive in the marriage market.


The analysis indicates that there are a number of characteristics of a woman and her family which are associated with the length of time that she remains a single parent. For the largest group of single parents, previously married mothers, there is no evidence that higher welfare benefits prolong the length of single parenthood, neither directly nor indirectly. Among never-married mothers, there is evidence that welfare benefits may prolong single parenthood indirectly by reducing the probability that the mother works. The association of employment with a shorter duration may not, however, be a structural effect, but rather a reflection of unmeasured attributes of a woman that favour both employment and marriage. Comparable analysis of marital dissolution among mothers finds no evidence that more generous welfare benefits encourage divorce (Ermisch and Wright, forthcoming). The lack of evidence that higher welfare benefits prolong single parenthood or encourage divorce probably reflects the low level of welfare benefits relative to the share of income in marriage going to a mother and her children.

Strictly speaking, these results only apply to the effects of Supplementary Benefit (now called Income Support). Because the size of this benefit is relatively high however, it is more likely to influence divorce and (re)marriage decisions than other benefits for one parent families, like One Parent Benefit or proposed child care subsidies for single parents, Thus, the results probably apply to other benefits as well.

Ermisch and Wright (1989b) show that higher Income Support benefits discourage employment, but payments that increase a parent's net income in a job, such as higher One Parent Benefit, larger child benefit, child care allowances or larger child maintenance payments would substantially increase the percentage of single mothers in employment. This contrast arises because of the implicit 100 per cent tax rate in the Income Support system. If, therefore, the groundless fears of encouraging more single parents were laid aside, we could adopt policies that make single parent families more independent while also improving their living standards. [Chart 1 Omitted] [Tabular Data 1 to 4 Omitted]

NOTES (1)NIESR and Birkbeck College respectively. We are grateful to the Joseph Rowntree Memorial Trust and the Economic and Social Research Council (programme grant on `Economic Inequality, Gender and Demographic Differentials') for financial support for the research upon whichthis paper is based. They are not, however, responsible for the views presented in the paper. (2)See for instance, Polly Toynbee, in Part Two of her Observer series on Divorce Today (10 September 1989). (3)It is worth noting, however, that 10 per cent of previously married singlemothers remarried within one year, and 20 per cent remarried within 2 years. Murphy (1984) found that the median time between separation and legal divorce among women aged under 50 in 1980 who had experienced a separation some time in their lives was 2.5 years. Thus, it appears that in the WES a substantial number of women dated their marital dissolution closer to their legal divorcedate than their date of separation from their husband. Inaccuracy in the dating of `ends of marriages' has been reported as a general problem in retrospective surveys (e.g. see Peters 1988). She notes that the unpleasant memories often associated with divorce, the fact that divorce is more in the nature of a process than an event and the ambiguity of `when did this marriage end?' in questionnaires can contribute to inaccurate responses. These probably also play a role in explaining the apparent `quick' remarriages in the WES. (4)In this type of model, the pattern of duration dependence, must be specified. As a compromise between flexibility and the number of parameters to be estimated, it was assumed that, given the values of the explanatory variables, the hazard is constant within each of five duration segments, but can vary between the segments. These segments were constructed so that each contributes about a fifth of the monthly `exposures to risk'. In the analysis of remarriage (table 2), a constant hazard (exponential duration distribution) is statistically acceptable; in the analysis of marriage of never-married mothers (table 4), a Weibull distribution of durations is acceptable (i.e. log [[Lambda] (t)] = ([Gamma] - 1)log(t)). (5)In the estimation, months of single parenthood, rather than women, are the observations. Characteristics of a woman and her family are `attached' to each month of single parenthood contributed by her, as are environmental variables that vary annually. (6)As women, on average, receive lower pay than men, when this ratio is higher the benefits from conventional marital division of labour are lower, thereby tending to reduce the (re)marriage rate. Ermisch (1981) found that this ratio had a negative influence on first marriage rates in Britian. (7)As we cannot measure whether women form unions without legal marriage, the impact on the duration of single parenthood could be overstated to the extent that women inemployment are more likely to form such consensual unions, but this is unlikely to account fully for the large impact of employment on the remarriage rate. (8)According to the estimates in table 4, the reference woman (aged 20, not employed) has a median duration of 33.4 months, while a mother continously employed has a median duration of 17.7 months.
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Author:Ermisch, John; Wright, Robert E.
Publication:National Institute Economic Review
Date:Nov 1, 1989
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