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ABSTRACT

This paper seeks to determine the causes of the well-documented wage penalty experienced by mothers compared to women without children. Using data from Waves 1-11 of the British Household Panel Survey I show that such a penalty exists in the UK while analysing the role played by unobserved heterogeneity, human capital, compensating differentials, work effort, employer discrimination and work flexibility in explaining this 'family gap' in pay. Importantly, I discover that OLS estimations understate the negative returns to motherhood. For the average woman in our sample, controlling for differences in human capital, job characteristics and household responsibilities can explain the entire observed wage gap. My contribution to the literature is to evaluate the validity of the work-flexibility hypothesis and to explore whether the child penalty differs by marital status. Unlike the majority of previous studies, I check and confirm that my results are robust to sample selectivity bias.

Section 1: Introduction

Over the last century, a dramatic increase in gender equality has led to a closing of the 'gender gap' between the wages of men and women in the developed world. However, in its place has developed a substantial 'family gap': a differential between mothers and non-mothers' wages. This pushes us to ask: does having children have a direct negative effect on women's wages? The overwhelming answer from previous empirical research has been that it does (Waldfogel 1995; Buding & England 2001; Molina and Montuenga 2009). This paper provides evidence to show that such a 'child penalty' exists for a cohort of British women and discusses some competing and complementary explanations.

Thus far, there have been six hypotheses put forward to explain this phenomenon (Budig & England 2001; Anderson, Binder and Krause 2003). First, some of the unobserved person-specific characteristics which are responsible for reduced earnings may also encourage child-bearing. Second, having children may induce women to interrupt their career with deleterious effects on their human capital stock. Third, mothers may choose to trade off lower wages for certain job characteristics which make it easier to balance their work and family needs. Fourth, children may be responsible for mothers being less productive at their jobs because they are exhausted or distracted. Fifth, employers may discriminate against mothers while making hiring and promotion decisions. Finally, the penalty may be a result of the work-schedule conflicts created when children demand their mother's time.

A number of recent articles have explored these hypotheses for data from developed countries: Korenman and Neumark (1992), Waldfogel (1995; 1997a; 1997b; 1998a;1998b), Lundberg and Rose (2000), Budig and England (2001), and Anderson, Binder and Kraus (2003), Molina and Montuenga (2009). I build upon all of these studies by empirically exploring all six hypotheses. Firstly, I will investigate whether the OLS estimates used in previous cross-sectional research may underestimate the negative returns to motherhood, in comparison with the fixed-effects panel estimations presented here. Secondly, I will explore the variation in the penalty by marital status, education level, and employment type and discuss what it implies about the nature of the penalty. Unlike most previous research, I also evaluate whether the work-effort and work-flexibility hypotheses can be complementary explanations of the child penalty as a result of mothers' strained resources.

Research has consistently shown that despite increased female labour force participation, women remain predominantly responsible for child-care among other household responsibilities (Fox and Nichols 1983, Milkie Raley and Bianchi 2009). Both mothers and fathers enjoy the benefits of parenthood - but if mothers bear most of the indirect costs of child-rearing through lower wages, this penalty will contribute to the gender wage gap. Moreover, the act of child-rearing produces positive externalities beyond the home (Coleman 1993; Risman and Ferree 1995): good parenting increases the likelihood that a child will grow up to be a well-behaved, productive adult. This results in lower crime rates, increased productivity, political stability and economic efficiency. A wage penalty implies that mothers disproportionately bear the cost of child-rearing while other people who benefit from their labour- fathers, neighbours, employers, spouses, friends and fellow citizens - are free-riding. Moreover, in a nation such as Britain with an ageing population, an indirect cost of child-rearing that is disproportionately borne by mothers may induce women to have fewer children and cause fertility rates to decline further (as suggested by Bélanger and Oikawa 1999). Given the increasing numbers of single mothers in recent years, it is also important for us to understand whether these penalties are affected by marital status. Understanding the causes and nature of this family gap in mothers' wages is crucial to determine appropriate and effective policies to both reduce the child penalty and also mitigate its effects.

Section 2 introduces the theoretical background for this study by discussing the six hypotheses that may explain the child penalty, offering a concise and intuitive outline of the economic theory behind each model. Section 3 provides a brief review of the literature, focussing mainly on previous empirical evidence. Section 4 presents the results of my own empirical study, where I attempt to evaluate the strengths of several nested models and also to answer certain questions which I have identified as requiring attention. Section 5 concludes by summarizing my findings and discussing their policy implications.

Section 2: Theoretical Background

Six hypotheses have been put forward to account for the negative association between motherhood and wages, these are discussed below.

Unobserved Heterogeneity

One simplistic explanation of the motherhood wage penalty is that it is inherently a form of omitted variable bias. If workers are heterogeneous in their skills and abilities, but these differences are unobserved, it is possible that certain types of workers in higher paying jobs are also less likely to have children. This explanation centres on some unobserved characteristics which are exogenous to both fertility and earnings but which influence both in opposite directions, resulting in a negative correlation between motherhood and earnings which is mistaken to be causation. The hypothesis implies negative selectivity into motherhood: some of the unobserved traits which make a woman more likely to have higher wages also reduce her propensity to have children. For example, Budig & England (2001) consider that women who have poor academic skills are likely to have children early because they realise their career prospects are limited and they may believe child-rearing will yield greater satisfaction. Additionally, women who derive more utility from relationships than material things i.e. care more about family than affluence may have more children and in addition they are more likely to trade-off of lower wages for other job values. Certain women may also have a present-orientation, i.e. they are more susceptible to the temptation of instant gratification. These women are more likely to become pregnant unintentionally and may also show lower self-discipline in their studies, training, and work which will result in lower earnings. Other such unobserved characteristics could include motivation, career ambition, the desire to be professional, and interest in completion of tasks. (Molina & Montuenga 2009)

Human Capital

One of the great success stories of modern labour economics is Mincer's (1974) human capital earnings function:

ln (w) = ß0 + ß1 s + ß2 x + ß3 x2 + u

The coefficient ß1 provides an estimate of the positive rate of return to education (s), and the concavity of the earnings profile is captured through quadratic terms for experience, x and x2, whose coefficients are expected to be positive and negative respectively. 'This function assumes that the skills acquired by the worker through education and on-the-job training can be regarded as a stock of homogenous human capital which increases the worker's productivity by the same amount in all lines of work for all employers.' (Willis 1986 pp542). Since experience involves training which makes workers more productive, the neo-classical predictions of human capital theory postulate that experience and tenure should have significant positive returns to wages (Mincer and Polachek 1974). Experience may also increase wages for other reasons not related to productivity, such as familiarity with organisational culture and policies as well as institutional inertia.

Much of the research that has been conducted on the motherhood wage penalty has focussed on the role played by the differences in experience between mothers and non-mothers. Motherhood is generally negatively related to experience because it induces many women to take time out of employment - this career interruption can range from the period of a few months before/after childbirth to several years for mothers who decide to stay home to provide care for their children full-time. A key line of thought is that during these periods of absence from the labour market mothers do not accumulate further human capital and thus fall behind non-mothers. Moreover, pre-existing human capital depreciates as qualifications and training become obsolete or are forgotten (Mincer and Ofek 1982). Therefore if a mother interrupts her career in order to care for her children, she will face lower wages than her childless counterpart who has been continuously employed.

Becker (1964) likens human capital to a means of production - one must invest in it through training in order to increase its rate of return. Furthermore, he shows that the incentive to invest in human capital specific to a particular activity is strongly positively related to the time spent performing that activity. Therefore, if mothers spend less time at work compared to non-mothers, either due to frequent career breaks or part-time working, they face a lower incentive to engage in human capital accumulation, especially when it is costly in terms of money, time or effort. Furthermore, in order to determine the optimal amount to invest in human capital, an individual must consider the prospective utilisation of this capital - thus the individual's plans for future marital, fertility and labour market decisions play an important part in determining how much human capital they accumulate. Therefore Corcoran (1978) reasons that if we take expectations into account, workers who anticipate a labour-market withdrawal such as young women planning on starting a family may decide to invest less in on-the-job training in the period preceding the interruption. She also points out that if employees pay the cost of on-the-job training though lower wages, women who expect a long family-related career interruption may choose jobs where they receive less on-the-job training but enjoy higher starting salaries. In this case these women will face flatter career profiles, with fewer promotion opportunities and slower wage growth.

An obvious application of this human capital model is the study of statutory maternity leave policies and their effect on mother's wages. Maternity leave may have negative effects on wages by inducing mothers who may otherwise have only taken a short period of sick leave to be absent from the labour market for a longer period of time and allow their human capital to depreciate. Moreover, if women value maternity leave, its mandated provision will increase the supply of female labour: some women will be willing to work for lower wages and some who were unwilling to work earlier will now enter the labour market. This will shift the long-term labour supply curve to the right, and lower wages while raising employment.[1] Thus on the surface it might appear that introducing maternity leave should increase supply (mothers' labour force participation) and decrease price (wages). However, Waldfogel (1995;1997a;1997b;1998) has conducted extensive research on this relationship between maternity leave and women's pay and finds that using maternity leave has a significantly positive effect on mothers' employment as well as wages. Human capital theory explains this through the positive returns to experience: utilising maternity leave is associated with a premium because it prevents the loss of general and firm-specific experience. It enables mothers to return to their previous employers to benefit from their accumulated firm-specific human capital, and continue to receive rents from a good job match while maintaining their positions on the company's internal promotion ladder. Moreover, mothers who may have left the labour market altogether may be induced to return at the end of their leave period - thereby preventing some of the human capital loss and deterioration which would otherwise have taken place.

Compensating Differentials

Rosen (1986) defines 'compensating differentials' to be the observed wage differentials required to equalize the total monetary and non-monetary advantages or disadvantages among work activities and among workers themselves. These are also known as 'equalizing differences' and are very useful as a theory of supply of workers who are heterogeneous in their tastes and abilities to labour activities which are heterogeneous in their environments, skills and requirements. Thus an acceptable 'sale' occurs when the employee finds the job attributes to be the most desirable and the employer finds the worker characteristics to be the most productive. Holding a worker's wage-relevant characteristics constant, she will pay a positive price to acquire preferred non-wage amenities or to avoid non-wage dis-amenities which the employer will simply subtract from her wage payment. Thus the theory of equalizing differences centres around the choices made by workers with given personal characteristics (X) regarding jobs which offer different combinations of wages (w) and non-pecuniary characteristics (Z). The specification is a semi-log equation,

ln (w) = ß1 X + ß2 Z + u

where u is a random disturbance and Z is a vector of non-pecuniary characteristics.

Frank (1978) presents evidence that some of the gender wage gap can be attributed to the fact that many women subordinate their careers to that of their husbands', and as a result they tend to accept jobs for which they are over-qualified and underpaid in return for convenient locations and fewer work hours. Blair-Loy (2003) found that even after controlling for hours worked, mothers are more likely than fathers to perceive that doing their jobs compromises their child-rearing responsibilities. Thus there is a reasonable basis for modifying and extending Frank's argument to the case of women with children, hypothesising that they may accept jobs with lower wages in return for mother-friendly job characteristics, resulting in a negative equalizing difference. The most obvious attractive feature of a job for a mother is the ability to work part-time. Other appealing features which may play a part in mothers' employment decisions include characteristics such as flexi-time working, personal phone calls, on-site childcare, nearby location, limited work-related travel, and maternity leave and pay.

Work-Effort

In the past century, increasing equality between the sexes has meant that women have become a much bigger part of the labour market. However, research has consistently shown that despite their increase participation in the labour force, most women remain largely responsible for child-care and other household responsibilities (Stafford 1980; Fox and Nichols 1983). These responsibilities, it has been argued, have a negative effect not only on the continuity of labour force participation and the types of work women are employed to do, but also their orientation toward that work (Polachek 1979). Becker (1985) initially postulated the 'work-effort' hypothesis to explain the disparities between the economic attainments of men and women: since women perform a significantly greater portion of household chores, they would have less energy leftover and they would therefore offer lower work 'effort'. Thus an hour of a male employee's labour may be of greater value to an employer than an hour of a female employee's time if she has more household responsibilities.

The same argument can be adapted for the case of the family gap in wages. It is reasonable to assume that non-mothers spend more of their time outside of work and household chores in leisure activities while mothers must dedicate some or most of it to childcare. Since caring for a child is more labour-intensive and therefore more tiring than leisure - mothers will be left with less energy for the office than non-mothers. They may also be storing energy in anticipation of the work they have to do when they get home. Budig and England (2001) argue that mothers may also be less productive at work because they spend time worrying about their children or calling them at home, and they may also take sick leave to care for ill children. A combination of all these factors may reduce the average productivity of mothers compared to non-mothers, and employers may respond to this by offering them lower wages.

Discrimination

One explanation that has been put forward to explain the child penalty is that mothers as a group are discriminated against by others in their work environment, and their lower wages are a consequence of this behaviour.

Taste discrimination

Cain (1986) explores the idea of psychic disutility as part of a useful definition of economic discrimination. Psychic disutility would exist for mothers if an employer feels a disutility in hiring a worker solely because she has children, which by itself has no effect on her productivity. Using this definition, Becker (1971) would define a discrimination coefficient (di) for such an employer to be a non-monetary cost of production such that when this employer is faced with the monetary wage rate wm for a particular factor (mothers' labour), he acts as if wm(1 + di) is the net wage rate, where di is positive and measures the intensity of his disutility against this factor. Initially, if for a discriminating employer the market wage rate wn of a perfect substitute (non-mother's labour) is lower than wm(1 + di), then the demand for the non-mothers would increase, raising their price wn until it equals wm(1 + di), in equilibrium. Thus competition in the labour market will result in a uniform 'product price' with separate wages for mothers and non-mothers: the differential in money labour costs is compensated for by a differential in psychic costs. This is the intuition of the taste discrimination explanation - sophisticated models will account for the distribution of employer's tastes, the form of production functions, the amount of competitiveness in industries, and the ratio of mothers to non-mothers in the labour market.

Statistical discrimination

The theory of statistical discrimination was developed by Arrow (1973) and Phelps (1972) separately and is a useful tool for studying various labour market phenomena. 'It occurs when rational, information-seeking decision makers use aggregate group statistics, such as group averages, to evaluate individual personal characteristics, such that individuals belonging to different groups may get treated differently even if they share identical observable characteristics in every other aspect' (Moro 2008 pp1). In the case of the motherhood case penalty, this may occur if, net of other employee characteristics which employers can screen cheaply (such as education and experience), mothers are on average less productive than non-mothers. Since employers cannot easily screen the productivity of each mother who approaches them for a job, they offer her a wage equal to the expected productivity of the group. Thus employers will theoretically create a pay-gap between mothers and non-mothers which is commensurate with the estimated productivity gap.

Following from Akerlof's (1970) ground-breaking theories of information asymmetry, we can theorise that the motherhood wage penalty may be a form of 'lemon market effects'. Due to employers' asymmetric information and beliefs, mothers who are more productive than average are paid less than their true worth given their human capital. Depending on the opportunity cost of their time spent in labour, they may decide to accept these lower earnings, or to leave the job market (which would result in self-selection and bias the results). Employers will then need to revise their expectations of the productivity of the group and offer a wage equal to the new average productivity. This cycle continues until an equilibrium is reached when the only people left in the market face an opportunity cost that is lower than the current wage on offer. Therefore, due to this adverse selection, any remaining mothers in the labour market are the 'worst' with regards to productivity, and so they earn lower wages than their childless counterparts.

However it can be argued that the underlying assumption of mothers being less productive on average is open to debate. An alternate model of statistical discrimination considers the probability of labour market participation. It is a well-documented fact that mothers have much lower labour force participation rates than non-mothers (Gustafsson,Wetzels, Vlasblom and Dex 1995). Employers who provide on-the-job training would like to invest the most in those employees who are likely to remain in the full-time labour force the longest so that they can re-coup their investment. Thus employers who do not know a mother's true probability of remaining in the labour market must depend upon the average probability for the group to compute her wages and decide how much to invest in her training. 'Any employer faced with these different probabilities will practice statistical discrimination, even though there are millions of women who will be in the full-time paid labour force for their entire lifetime' (Albert & Cabrillo 2000 pp5)

However a major critique of this latter model is that ex ante, employers cannot ascertain the true probability of a female employee becoming a mother (thus decreasing the likelihood of being a lifetime year-round full-time worker and increasing the likelihood of exiting the labour market or switching to part-time work). Therefore it might be rational for him to discriminate against all young women who are potential mothers by assigning them to jobs with less training, leading to them experiencing flatter career profiles with fewer promotions and smaller wage increases. In this case, the occurrence of statistical discrimination should lead to a gender gap in young women's wages compared to that of men and an age gap in young women's wage growth compared to that of older women, rather than specifically a family gap between the wages of mothers and non-mothers. The likelihood of this occurring increases in countries with high fertility rates and without statutory maternity leave (i.e. much of the developing world) due to the increased probability of a young woman having a child and leaving the job without being able to return.

There may also be an institutional aspect to statistical discrimination, for example Piore (1970) argues that the initial placement of disadvantaged workers into low-wage low-training jobs could create attitudes and habits which will perpetuate their low status. To explore this let us utilise Arrow's (1973) model where employer's initial differential beliefs can be confirmed in equilibrium even though the two groups are ex-ante identical. Suppose that employers assume mothers are less likely to invest in on-the-job training and experience because they expect to take family-related career breaks. The employer typically promotes workers who emit a signal (e.g. pass a qualifying test or work significantly more overtime hours) which passes a certain threshold - but because of his pessimistic beliefs about mothers, the threshold for mothers is kept higher than that of non-mothers. This affects the worker's investment decision: mothers (who are held to a stricter standard) have less incentive relative to non-mothers (who are held to a more lax standard) to study for these tests or work overtime because even though both groups are equally able, the probability of mothers passing the 'mother' threshold is much smaller than that of non-mothers passing the 'non-mother' threshold. This behaviour will confirm the employer's initial asymmetric beliefs that mothers are less committed to their jobs and less likely to invest in human capital.

Work-schedule flexibility

Anderson, Binder and Krause (2003) propose a theory of work-schedule flexibility which is both a modification and complement to Becker's work-effort hypothesis. They believe that mothers face lower wages due to the work-schedule conflicts created by child-related commitments not only with respect to energy but also with respect to time. They identify the three inputs of work to be: time during standard office-hours, time outside of office hours, and effective effort which is an increasing function of education (Mincer (1974) showed that education increases productive human capital). Work requiring time during standard office hours has the greatest potential to create scheduling conflicts for working mothers because these are the hours during which children are most active and husbands are most likely to be working themselves. Therefore Anderson et al (2003) theorize that a worker who is time and effort constrained may be able to avoid a wage penalty by making offsetting adjustments between these three inputs. The ability of a worker to make these adjustments depends on her human capital, the nature of the job and other commitments in her life.

Section 3: Literature Review

Unobserved heterogeneity

Some studies have found that controlling for subject-specific heterogeneity tends to reduce the estimated child penalty, suggesting that women with certain pay-enhancing characteristics are less inclined to have children. This would encourage us to think of the unobserved heterogeneity as an omitted variable whose absence in the regression causes the negative coefficient on children to be biased away from 0. Most previous research regarding this hypothesis has utilised person-fixed effects modelling methods to control for this bias and investigate whether heterogeneity of unmeasured traits can explain the motherhood wage penalty[2]. Korenman and Neumark (1991) find that moving from OLS to first differences renders the penalty to be statistically insignificant, suggesting that mothers only suffer a wage penalty because they differ in certain time-constant pay-relevant ways from non-mothers. However their finding is the exception rather than the rule, as most studies (including Budig and England 2001; Anderson Binder and Kraus (2002,2003); Waldfogel 1998a) have found that controlling for unobserved heterogeneity may reduce the negative coefficient on children, but a statistically significant wage penalty still persists afterwards. Thus while it is true that some of the child penalty may include a form of omitted variable bias because unobserved heterogeneity may exaggerate the negative returns of children, there is a considerable amount of evidence to suggest that controlling for such characteristics cannot entirely explain the motherhood wage penalty.

Human Capital

Since it is relatively common for women's life-cycle labour force participation to be interrupted by family commitments, many of the studies of the child penalty have focused on investigating the consequences of career interruptions. Mincer and Polachek (1974) argue that career breaks influence wages through human capital depreciation and under-investments in on-the-job training. They performed a cross-sectional study of the 1967 National Longitudinal Survey of Women and found that a home-time interval for marriage or children results in a net depreciation rate of 1.5% per year for the average woman, and of 4.3% for a woman with some college education. Kim and Polachek (1994), using 1976-1987 panel data from the PSID, utilised more robust econometric specifications to take into account problems of heterogeneity and endogeneity and found much larger estimates of the average depreciation rates, ranging from 2.6% to 26.5%.

Gupta & Smith (2002) performed a more recent study of the effect of motherhood and confirmed that the main effect of children appears to be the loss of human capital which occurs during and shortly after childbirth period. They also finds that, holding experience constant, there is evidence that in the long-term children have little effect on the earnings potential of their mothers. This implies that there is a catch-up process between the wages of mothers and non-mothers, indicating that experience has diminishing marginal returns. Lundberg and Rose (2000) find that mothers' wages fall by 5% on average after the first birth, but mothers who are continuously employed face no penalty at all. This suggests that preventing the deterioration of human capital can play a significant role in avoiding the wage penalty. However Phipps, Burton and Lethbridge (2001) find that women who return to a different job after a career interruption face a significantly larger penalty than women who return to the same job. He suggests that a 'human-capital deterioration' explanation may be deficient, and that firm-specific human capital, rents from good job matches, and loss of position in a firm's internal labour market should also be important.

Waldfogel (1995;1998;2003) has conducted extensive research into the effects of maternity leave on mothers' wages. She finds that women who use maternity leave and return to their jobs immediately after enjoy a wage premium of 6% which nearly cancels out the average child penalty of 8% (Waldfogel 1998a). She reasons that this is because it allows women to continue to reap the benefits of tenure, firm-specific training/knowledge, and good job matches. In addition, women who may have left the labour market altogether may decide to instead return by the end of the leave period in order to maintain employment continuity.

However Gupta & Smith (2002) find that wages grow more slowly for mothers in the period just after childbirth compared to the wage growth experienced by non-mothers, even if the women take no time out of employment i.e. experience no human capital deterioration or loss of good job match. This suggests that despite the strong evidence in support of the human capital model, differences in education and experience cannot completely explain the motherhood wage gap. We must continue to look for something else that negatively affects the earnings potential of mothers, particularly when their children are young - by this criterion, both the compensating differentials model and work effort hypothesis fit the bill.

Compensating differentials

Felfe (2008) finds that after childbirth women are disposed to pay significant amounts to avoid a job involving certain undesirable characteristics, and that the more financial resources and education a woman has, the more willing she is to give up a portion of earnings in order to avoid these dis-amenities. In particular, she finds that women are willing to accept a wage cut of almost 35% to be able to work during the evening and of 57% to be able to work rotating shifts. Felfe (2006) also finds more direct evidence to support the 'compensating differentials' hypothesis- upon including non-monetary dis-amenities such as night work, stressful work, distance to workplace, and hazardous conditions in the regression, she finds the child penalty is reduced by almost 10%.

The most desirable 'mother-friendly characteristic' of a job is the ability for mothers to work part-time, but part-time jobs have been associated with a significant penalty for women. Manning and Petrongolo (2008) find a part-time penalty for identical women to be about 10% if one does not take account of differences in occupations and 3% if one does. This implies that occupational segregation can explain most of the part-time penalty, and so women can escape it if they stay with the same employer/occupation. Unfortunately, they offer considerable evidence that a lack of flexibility in hours within British jobs means that women who want to switch to part-time work are forced to change their employers and occupations, resulting in a loss of good job matches. Moreover, this transition nearly always results in downward occupational mobility. To make things worse, returns to experience and education for women in part-time positions is much lower - probably because full-time work carries greater value in the labour market (Dolton, Joshi and Makepeace, 2002). If part-time working is the most popular job amenity chosen by mothers to balance work and family needs, it will result in a large compensating differential in the form of lower pay.

Waldfogel (1997) found that net of experience and education, adding controls for part-time work and part-time experience reduced the wage penalty from 6% to 4% for one child and from 15% to 12% for two children. Budig and England (2001) studied whether mothers choose less demanding jobs and found that controlling for job characteristics reduced the net penalty by 21%, leaving a penalty of 3.7% to explain. Thus there is considerable evidence to support the idea that certain job characteristics may be responsible for some of the lower wages experienced by mothers, there is still a significant 'unexplained' penalty to be accounted for.

Work Effort

Kalist (2008) uses the Ladies Professional Golf Association to study the effect of motherhood on productivity and, in turn, wages. It is a unique setting because productivity is directly observable through players' scores, and discrimination is not possible because earnings are strictly determined by relative performance (ranking). Using panel data to study female golfers who become mothers, he finds that their performance is improving before giving birth and worsening after birth. This evidence confirms the idea that motherhood has a direct treatment effect of reducing productivity, and rejects the idea that women who become mothers are inherently poor players, or that children are endogenous such that women whose careers are going badly will choose to have children. However it can be argued that this study only considers physical productivity which is more vulnerable to the effects of motherhood because childcare may strain a person's physical rather than mental or intellectual resources.

It is difficult but certainly not impossible to find evidence to support the claim that mothers exert less work effort generally compared to non-mothers. A comprehensive study was carried out by Bielby and Bielby (1988) who used Quality of Employment Surveys to conduct probit analyses to investigate the work-effort hypothesis. Although the focus of the study was to explore the differences between men and women rather than mothers and non-mother, they found that in 1977 compared to women with no children in similar jobs, women with children under the age of 6 scored nearly one whole standard deviation lower on the underlying effort dimension and women with children older than 6 scored exactly half a standard deviation lower. Phipps et al (2001) conduct a study of the family gap in wages for Canadian mothers and find that controlling for total hours of unpaid work reduces the penalty from -0.123 to -0.052. Due to the limited availability of comprehensive datasets containing measures of housework responsibilities, there have been relatively few studies which have explored the work effort hypothesis directly, and to my knowledge this paper is the first to have done so specifically for mothers in the United Kingdom.

Employer discrimination

Since it is practically impossible to measure employer discrimination, the vast majority of literature has relegated this hypothesis to be akin to a residual effect, i.e. after controlling for all the 'observable' characteristics of the woman and her job if a significant penalty persists it is usually attributed to a discrimination effect. However it may be possible to evaluate the veracity of this hypothesis through social experiments, as some more recent studies have attempted to do. Correll (2007) conducted such a laboratory experiment to see if status-based discrimination played a part in employers' hiring decisions. In this study, participants evaluated application materials for pairs of same-gender equally qualified candidates who only differed by parental status. The experiment found that mothers were penalized compared to non-mothers on a host of measures including competence and commitment. Mothers were significantly less likely to be recommended for hire, promotion, management training, and their suggested starting salaries were on average 7.9% lower than otherwise equivalent childless women.

Work-flexibility

Bonke, Datta-Gupta, and Smith (2003) report that women face a greater penalty if they conduct housework immediately before or after work. They find the penalty to be larger for employees on fixed work schedules, and insignificant for those who enjoy flexible schedules. Although a study has not been conducted specifically for the case of mothers, it is reasonable to assume that a significant portion of child-care activities must take place in the morning and afternoon- getting children ready, preparing their lunches, picking them up from school, extra-curricular activities etc. Thus we may be able to find some support for Anderson's (2003) work-flexibility hypotheses, i.e. that timing and flexibility of child-care work may be just as important as the level of child-care itself.

Since this model was developed fairly recently, direct empirical research on it has been sparse. However, Anderson et al (2003) offer one simple testable implications of the theory (which are outlined below and will be tested in Section 4) and some statistical evidence which points in that direction. They conjecture that high-school dropouts have fewer job options and they tend to be limited to shift-work which is paid by the hour: therefore quantity of hours matters more than the timing, and work done outside of standard office hours should be equally valuable. They offer statistics to show that high school dropouts are significantly more likely to work weekends and have greater variability in work start and stop times - therefore they should experience the smallest child penalty.

At the other end of the spectrum, college graduates should face a smaller penalty than high school graduates because they are more likely to have jobs with flexible schedules. If one views desirable job amenities as normal goods then college graduates who are likely to earn more can 'afford' more of such amenities. Moreover, their education makes them more productive and this gives them higher bargaining power when negotiating the terms of their contracts with employers. Golden (2001) finds that having a Bachelor's degree or Master's degree increases the likelihood of having a flexible daily schedule by 48 or 62 percentage points respectively, compared to only 16 percentage points for a high school diploma. College graduates will also have more control over job location - Anderson et al (2003) report that 38% of college graduates work at home as some part of their job, compared to only 8% of high school graduates. Moreover, since college graduates have more productive human capital they can also substitute standard office time with greater effective effort. Lastly, high school graduates are the most likely to have administrative or clerical jobs which will require their presence during standard office hours - they are unable to substitute other time or increased effort and will suffer the highest child penalty.

Section 4: Empirical Study

This Section presents results from my own empirical investigation which utilises new data to explore the six hypotheses discussed in previous sections: unobserved heterogeneity, human capital differences, compensating differentials, the work-effort explanation, employer discrimination, and the work-flexibility hypothesis. Sections 4.1 and 4.2 offer details of the data and empirical approach employed. I begin to present regression results in Section 4.3 where I explore several nested models which encompass the first 4 hypotheses (because they are directly testable). Sections 4.4-4.7 attempt to answer certain questions or explore certain hypotheses which the past literature has been either unable to explore or unable to reach a firm conclusion on. They are:

Section 4.4: Does the child penalty vary by marital status and why?

Section 4.5: Is there support for the work-flexibility hypothesis?

Section 4.6: Is there support for the employer discrimination hypothesis?

Section 4.7: Are the regression results subject to sample selectivity bias?

Data

I use a longitudinal dataset from the British Household Panel Survey containing individual-level data on work, family, and time use characteristics of 3800 women over 11 years (41800 observations of person-years). This is a restricted sample of women who are aged between 20 and 60, who are not full-time students. I believe this period covers an age-range that captures both post-education labour market experience and marital and fertility transitions which are needed for panel estimation. My data has the advantage of being quite recent, spanning observations from 1991 to 2002, so it captures current trends and will flag relevant issues. Most previous studies of the child penalty in Britain have used the National Child Development Study which follows the same cohort of women born in 1971, meaning less variation in the ages and (possibly) values and behaviour. The use of the comprehensive BHPS data-set affords us a heretofore untapped opportunity to relate information on household, job, time use and opinion characteristics to the market earning power of women.

In all our estimations, the dependent variable is the natural log of hourly wage in the respondent's current job, while the primary independent variable of interest is the number of children reported by the respondent. Person-years were eliminated where either variable appeared to be an outlier or where information on any key explanatory variable was missing. A major disadvantage of our data is that it does not contain information on women's actual labour market experience, so we must use Mincer's (1974) transformation of the worker's age as a proxy for her potential experience in the form of x = age-schooling-6, which assumes that a worker begins full-time work immediately upon completing full-time education[3]. However a significant advantage of our data is that it contains information on the respondents' time use especially in terms of household work, allowing us to explore the work-effort explanation.

Table 1 shows summary statistics for the pooled cross-section. For each variable, statistics are shown for all women as well as mothers and non-mothers separately. Standard deviations for variables measured continuously are shown in brackets. A few differences are worthy of note: mothers are much more likely than non-mothers to be non-white, married, part-time workers who do the majority of household chores, while non-mothers tend to be older and white, working in larger firms, during the day, in managerial positions.

Empirical Approach

For all models except the first Gross model, I use fixed effects estimations: to analyse our data with person-years as the unit of analysis.

Yit = ß0 + ?ßkXkit + eit

eit = ai + ut + vit

Regression coefficients are denoted by ß while k indexes measured independent variables, i indexes individuals, and t indexes time periods. ß0 denotes the intercept while eit is the error term consisting of a cross-sectional person-specific component ai, a time specific component ut, and a purely random component or error vit.

Except where otherwise noted, all tables showing regression results (tables 3-9) present only the coefficient associated with the total number of children a woman has. The Huber-White method and Prais-winsten estimations have been used to correct for heteroskedastic and serially correlated errors. As we move down the rows of the table, control variables are progressively added in order explore the first 4 hypotheses. Since each model is nested in the subsequent model, the order in which explanatory variables are added has important consequences for our interpretations of the validity of each hypothesis. I determined the order according to each model's previous empirical support - the human capital model is well established in the literature and so it was estimated first, the work-effort hypothesis is the least researched and the evidence has been weak so it is tested last.

ln (Wage) = ai + ß0 + ß1 number of children + ß2 married + ß3 divorced + ß4 education + ß5 experience + ß6 experience2 + ß7 weekly-hours + ß8 part-time + ß9 child- care + ß10 firm-size + ß11 manager + ß12 day-work + ß13 union ß14 overtime + ß15 cooking + ß16 cleaning + ß17 babysitting

Preliminary Investigation

Table 3 presents estimates of the child penalty for each of the above 6 nested models. Row (1) shows that our gross OLS model estimates a statistically significant penalty of 10%. However, there is a strong possibility of omitted variable bias if we fail to control for the time-constant unmeasured characteristics (ai) which may have additive effects on wages, such as family preferences, cognitive ability, present-orientation, future plans, and tastes for affluence. Since some types of individual heterogeneity which affect earnings are also likely to be correlated with other regressors such as education and marital status, we would need to use Fixed effects for consistency - but it is extremely inefficient when there are variables varying only a little over time, such as marriage and education. Consequently I conducted the Hausman test to evaluate whether random-effects models might be appropriate, but in each case the result indicated a need for fixed-effects formulations.

Moving from row (1) to row (2) of Table 3 allows us to compare results from the gross OLS model and the Fixed-effects model. The Lagrange Multiplier rejects the hypothesis that all individual effects are equal, providing evidence of significant heterogeneity bias. The Fixed-Effects model estimates a wage penalty of 13% for each child, while the OLS model shows a slightly smaller penalty of 10%. This is a striking result as most previous studies have found higher penalties for OLS models. The child penalty is partially masked in the raw data by the characteristics which cause mothers to be observed receiving higher wages than childless women. Thus, we have evidence suggesting that women who become mothers are wage-wise positively selected, but these premia are wiped out by the detrimental effects of actual motherhood. This stands in stark contrast to the 'unobserved heterogeneity' hypothesis because it appears mothers are actually rewarded (not penalised) for the unobserved characteristics which lead to having children, resulting in higher wages. Hereafter, except where otherwise noted, I refer to models which control for time and persons-specific fixed effects.

Adding marital status to the unobserved heterogeneity model increases the wage penalty slightly (by -0.008). An inspection of the full regression results in Appendix A shows that being currently married and having ever been married have a (jointly) significant positive effect on earnings: this confirms that there is a marriage premium and that the dummies for being currently married and divorced act as suppressors in the estimation. Note that these models include marital status additively so the coefficients indicate the average effect of marriage across child statuses - in Table 5 I explore how marriage interacts with the presence of children to affect earnings.

As expected, controlling for schooling and potential experience reduces the penalty significantly (by nearly 28%), offering strong support for the 'human capital' model. However we are still left with a large child penalty of 11.5%. I next explore the 'compensating differentials' hypothesis by including additional regressors which control for part-time work, managerial duties, weekly work hours, firm size etc. I find very strong support for it: the child penalty falls by 64% to only 4.1% when job characteristics are included. This implies that a significant portion of the child penalty is due to sorting of mothers into worse-paid occupations and positions. In order to explore the work-effort hypothesis, the final model includes variables which control for the proportion of the total household chores a woman performs. This practically eliminates the child penalty, rendering the coefficient on children to be statistically insignificant at the 10% level. As we progressively include controls, the child penalty becomes less significant, so we can infer that mothers tend to sift into worse-paid situations in terms of human capital, jobs, and household environments. Moreover we can conclude that even if on their own none of the hypotheses can account for the child penalty fully, the human capital, compensating differentials and work-effort hypotheses can be combined into one composite model which completely explains the penalty.

A Check on monotonicity

Table 4 presents a check on whether non-monotonic relationships are being blurred by measuring children as a continuous variable counting the total number of children. Three dummy variables are used to measure children in terms of one child, two children, and three or more children. Moving from OLS to Fixed Effects results in a bigger difference in coefficients for women with 2 children and 3 or more children: heterogeneity bias is a more serious problem in their case compared to women with one child. Given that effects are relatively monotonic for each model, we can justify trading off slightly imprecise results for increased simplicity by continuing to measure number of children as a continuous variable.

A check on Endogeneity

Since having children is usually planned, it is possible that a woman with lower wages might choose to have more children because she faces a lower opportunity cost of time spent in child-rearing, and because she may believe children will offer greater satisfaction than her thus-far-unimpressive career. This would lead to the coefficient for number of children to be biased away from zero such that we would overestimate the child penalty. However, Performing the Durbin-Wu-Hausman test using a dummy for 'having ever been married' as an instrument did not reject exogeneity of total number of children at a 5% significance level.

Waldfogel (1995) was the first to point out the potential endogeneity of part-time work: mothers with lower wages may decide to switch from full-time work to part-time working. However there I find no statistical evidence that part-time working is correlated with the wage equation error: using a dummy for 'being currently married' as an instrument, the Durbin-Wu-Hausman test cannot reject exogeneity of part-time work at a 5% significance level. Thus I did not need to use an Instrumental Variables regression to correct for possible endogeneity.

Does the child penalty vary by marital status?

Most previous research on the motherhood wage penalty has entered the number of children and marital status additively, but I use interaction terms to examine whether the child penalty varies by mothers' marital status. The Compensating Differentials model would suggest that single and divorced mothers should bear a greater penalty because they face greater pressure to trade off lower wages for certain mother-friendly amenities in her job: for example, a single mother may have no choice but to work part-time or work at night since she has to care for her children during the day because she has no partner. Additionally, the work-effort hypothesis would suggest that single and divorced mothers should face a larger penalty because the lack of a husband to share the household responsibilities would leave them with less energy for work. Married mothers who are fortunate to have another adult to share child-rearing responsibilities may be able to work longer hours, take over-time, or bring their work home with them - leading to a smaller penalty.

The human capital model predicts that married mothers should face a larger penalty because husbands' wages make it financially feasible for them to take time out of employment to focus on child-rearing (Budig and England 2001). Single and divorced mothers do not have the financial security of an additional adult earner in the household cannot afford to take such career interruptions, and as a result they will accumulate more human capital and bear a smaller penalty. [4] Table 5 offers estimates of the child penalty for single, married and divorced mothers separately - allowing us to evaluate which of the above outlined effects of the different models will dominate.

Controlling for person-fixed effects has different effects on the child penalties for single, married and divorced mothers. For never-married mothers, the penalty falls from moving from model 1 to model 2 suggesting that, in their case only, the unobserved characteristics which increases the likelihood of having children also lower their earnings. One possible explanation is the present-orientation characteristic discussed in Section 2.1: it would increase the likelihood of having children out of wedlock and also lower self-discipline and organisation in their career. In each model (except Model 2)[5] single mothers suffer a larger penalty than married mothers- indicating that the effects of the work-effort and compensating differentials hypotheses dominate those of the human capital model.

However we find that curiously, divorced women face a smaller penalty than both married mothers and single mothers. One explanation is that they may still benefit from the institutional support structure of marriage: for example they could have joint custody with their ex-husbands, or have in-laws who can care for their children on evenings/weekends. This may diminish the burden of their child-care responsibilities in terms of effort and time, and would also reduce the pressure and incentive to trade off lower wages for a mother-friendly job. This would mean that in the case of divorced mothers, the effects of the work-effort and compensating differentials models are less important, and the effects of the human capital model dominate.

Is there support for the work-effort and work-flexibility hypotheses?

Since younger children require more physical care in terms of diapering, holding, feeding etc, and are also more likely to wake their mothers up at night, mothers of young children are likely to be more exhausted and less productive at work than mothers of older children. Bielby and Bielby (1988) found that mothers of pre-school children report less work effort while on the job compared to other mothers. However Anderson (2003) points out that older children may equally strain their mothers' resources but in a different way by demanding time: shorter school days and extra-curricular activities may create a conflict with their mothers' work schedules. Thus a wage penalty which tends towards zero as children grow older would support only the work effort explanation, while a penalty that remains fairly persistent would allow support for the work-flexibility hypothesis also. Since our dataset only contains a dummy for being responsible for a child under the age of 12, Table 6 presents estimates for women who have children younger and older than 12.

After controlling for fixed effects, the coefficient on children for mothers with older children seems to be positive, indicating a child premium. However this is because they are usually older than mothers with young children and their increased experience accounts for higher wages. Upon controlling for potential experience, we see that in column 4 the coefficient returns to being significantly negative. Table 6 clearly indicates that mothers with younger children face significant child penalties while mothers with older children do not. This supports the work effort hypothesis since younger children require more energy to care for. Our results also accord with the work-flexibility hypothesis because we observe a smaller but still significant penalty for mothers of older children (who present demands on a mother's resources in terms of time). Particularly striking is the fact that the penalty disappears in model 5.2 where dummy variable for working during standard day office-hours is included, offering support for the idea that scheduling conflicts may explain some of the penalty. However we should not rely too much on this last interpretation - as discussed in section 3.6, flexible scheduling tends to be accessible only to those at the higher end of the income distribution so it is possible that day-time working is endogenous to wages.

In Table 7 we apply Anderson's (2003) suggestion for testing the work-flexibility hypothesis by observing how it changes across education levels: if the hypothesis holds true, high school dropouts should face the smallest penalty, and high school graduates should face the largest. As expected, we find that women with no formal qualifications suffer the lowest penalty. In fact, once we control for their human capital in model 4, the penalty completely disappears. This is probably because they mostly partake in shift work which allows them greater flexibility in deciding the time of day they work. Also as expected college graduates face a smaller penalty than high school graduates - this accords with Anderson's prediction that their greater education will allow them to substitute higher 'effective effort' in the place of some standard office hours. Finally, high school graduates consistently face the largest penalty in each model - this is because they are the most likely to have jobs requiring them to work during standard office hours, making them more susceptible to work-schedule conflicts.

Is there support for the employer discrimination hypothesis?

Column (2) of Table 8 offers evidence that self-employed mothers experience no penalty in any of the models, providing support for the employer discrimination hypothesis as it is the only explanation which has different implications for self-employed and paid-employed mothers. Unlike paid employees, self-employed women are their own bosses and so cannot face any discrimination in hiring, training and promotion.

However, discrimination is not the only or even the most likely explanation for our findings. Carr (1996) argues that self-employment offers women a flexible work strategy which makes it easier to balance competing work and family responsibilities. Features such as on-site childcare, flexible hours, short commutes may be more readily available to the self-employed who have greater control over the location, timing, intensity and pace of work (Budig 2006). In our sample, only 52% of self-employed women work during standard office hours, compared to 66% of paid employees. Moreover, 42% of self-employed women can work at home, compared to 6% of paid employees. In this case, self-employed mothers may face a smaller penalty because various convenient features of their jobs reduce the conflict between work and family needs. Ultimately, without being able to directly measure employer discrimination, our results are inconclusive and our interpretations are simply conjectures.

Are these results susceptible to Sample Selection Bias?

Our sample only includes women for whom at least two wage observations were noted in the BHPS waves 1-11. Consequently we are concerned that the missing wage information of women who do not participate in the labour market may cause selection bias i.e. the coefficients we have obtained in Table 3 may not be applicable to all mothers (working and non-working). Almost all of the previous studies on the motherhood wage penalty fail to check for sample selectivity bias; in this section we check whether our results are robust by estimating a Heckman Selectivity-corrected model[6]. Heckman (1979) likened the bias that results from using non-randomly selected samples when estimating behavioural relationships as a form of "omitted variables" bias.He wrote that if one were to estimate a 'selection equation' to explore the effects of certain observed variables on individuals' participation decisions, then the residuals would contain vital information about the unmeasured characteristics which affect these decisions and could therefore be used to construct a selection bias control factor (lambda). When lambda is included as an additional explanatory variable in the original equation, its coefficient reflects the effects of all unobserved characteristics which are related to participation.

I apply the above-outlined procedure to our study of the effect of motherhood on women's wages. In the first stage a participation probit is used to estimate the probability of a woman choosing to enter the labour market as a function of the original control variables and additional identifying variables which are assumed to affect the probability of working but not to influence the wages on offer once in work[7]. I use a probit model because the error term of this model is normally distributed, so it satisfies one of the critical assumptions underlying the Heckman procedure. The specification of our first-stage probit takes the form:

Prob (P = 1 | Z) = F (Z?)

where P is a dummy which equals 1 if the woman participated (i.e. is employed) or 0 if she does not participate, Z is a vector of explanatory variables, ? is a vector of unknown parameters, and F is the cumulative distribution function of the standard normal distribution. To see the probit regression estimates (reporting marginal effects) please see Appendix B.

Bearing in mind that the wage equation is w* = X ß + u where w * denotes an underlying wage offer (not observed if the woman chooses not to participate), the conditional expectation of wages given the woman works is:

E [w | P=1] = X ß + E [u | X, P=1]

Therefore if we make the assumption that the error terms are jointly normal, we can arrive at : E[w | X, P=1] = X ß + ? su ? (Z?)

where ? is the correlation between unobserved determinants of wage offers u and unobserved determinants of propensity to work (? equals 0 if there is no sample selectivity). su is the standard deviation of u, and ? is the inverse Mills ratio evaluated at Z?. Since su > 0, the coefficient on ? can only equal zero when ? = 0, so testing the null hypothesis that the coefficient on ? is zero allows us to very easily test for sample selection bias.

Table 9 presents results for the estimator derived from the above procedure which is a limited information maximum likelihood (LIML) estimator.[8] Puhani (2000) found through Monte Carlo simulations that the full information maximum likelihood estimator gives better statistical properties in asymptotic theory, but due to the large size of our sample we do not have to be too worried about this. I have used the bootstrapping method to correct standard errors since the variance-covariance matrix generated by estimation of the second stage is inconsistent. For all models we find the Heckman selectivity-corrected estimates of the child penalty to be larger than the Fixed-effects estimates: this suggests that sample selectivity was causing the returns to children to be biased towards 0. We can see that the coefficient on lambda has a negative sign in all models - this implies that the error terms from the selection and primary equations are negatively correlated, offering evidence that the unobserved factors which make participation in the labour market more likely tend to be associated with lower wages. Initially the coefficient on lambda is significantly different from zero, confirming the presence of sample selection bias. However as we move down the table and progressively add control variables to the regression it grows smaller and (once we control for heterogeneity and marital status) becomes statistically insignificant. Therefore even though Fixed Effects estimations underestimate the child penalty in every model, we can justify their use because we find no evidence of significant selection bias in the final three models which have been used to explore the three main hypotheses.

Section 5: Conclusion

In many developed countries a significant child penalty exists for the wages of mothers compared to non-mothers (Korenman and Neumark 1992, Waldfogel 1995;, Budig and England 2001, and Anderson, Binder and Kraus 2003, Molina and Montuenga 2009). Moreover, there is evidence to suggest that this family gap in wages has not diminished over the years (Avellar and Smock 2003). In this paper, we use panel data for 3800 British women to consider each of the offered explanations. A gross penalty of approximately 10% is observed for the average mother. The unobserved heterogeneity hypothesis is completely rejected for British data - in fact we find that controlling for individual-specific fixed effects actually increases the penalty to 13%. This implies that women who become mothers are actually positively selected wage-wise but these premia are wiped out by the effects of actual motherhood.

We find strong support for the human capital model, compensating differentials model and work-effort model. For the average British woman differences in education/experience, job characteristics and household responsibilities can explain 32.5%, 39.7% and 27.8% respectively of the penalty, eliminating the total observed family gap in wages. The size of this child penalty varies across marital statuses, education levels, and employment types, but is relatively large among women with younger children and increase with the number of children present in the household. Importantly, this paper finds that being married has a beneficial effect of reducing the child penalty. Single mothers experience the largest and most persistent penalty because they must bear the burden of housework and childcare alone; they also face the greatest pressure to accept lower wages in exchange for mother-friendly characteristics of jobs. This is a serious concern for British society since the institution of marriage is on the decline and the occurrence of single mothers is growing.

Our findings have several policy implications - for the sake of brevity we will discuss those implications which have not been brought to light by previous literature already. Firstly, they have highlighted the need to ease the strain on mother's (particularly single ones) resources in terms of energy and time but in a manner that does not dis-incentivise their labour force participation. In this respect there is a great deal that we can learn from our neighbours on the continent. The French government has developed many public crèches, day care centres and after school facilities to enable mothers to work full-time (Blossfeld and Hakim 1997). Similarly, Italy requires universal enrolment of children in pre-school starting at age three (see Silvera and Lemiere 2000), thus encouraging mothers to continue to engage in paid employment during the period of family formation.

This paper finds strong, albeit indirect, evidence in support of Anderson's (2003) work-flexibility hypothesis that children place certain demands on their mother's time, causing work schedule conflicts which may be responsible for a portion of the lower earnings she experiences. This underscores a need for public policies which encourage flexible work-scheduling in both the public and private sector. In this respect, policy may need to focus primarily on the issue of accessibility: flexible schedules need to be made accessible to all workers not just the educationally or occupationally elite. Moreover, it must be emphasised that such policies should not result in the penalisation of employees who adopt flexible schedules, either directly through lower pay (working through a compensating wage differential) or indirectly through missed promotions.

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  1. Maternity leave also imposes costs on employers - including that of continued health insurance coverage in the US, which Baum (2003) estimates can be as much as US$250 per employee on leave. Considerable costs arise due to employee absenteeism: when a mother takes maternity leave the employer must continue production without a replacement, which requires the remaining employees to exert greater effort which results in lower staff morale. Alternatively, the firm must bear the cost of finding, hiring and training a temporary replacement that will have lower firm-specific human capital and therefore be less productive. Klontz (1993) calculates the total cost of mandated maternity leave may be US$1995 per employee on leave. If employers choose to pass some of this cost on to the relevant employees, mothers will receive lower wages as their labour demand curve will shift to the left.
  2. It is important to note that using person-fixed effects modelling does not ensure removal of all bias: an important limitation is that if the unmeasured characteristic interacts with another control variable in affecting wages, the model will not eliminate bias. For example, a woman's career ambition is likely to negatively affect the number of children and positively influence wages. However it will likely also have a positive effect on experience, creating a steeper wage trajectory rather than having a simple additive effect on wages - so the coefficient on children may still be biased.
  3. This transformation does not account for any time taken out of employment for child-rearing reasons. However, I believe that due to the generous universal maternity leave system in place in the UK there will be limited variation in leave taking behaviour for child-birth. Moreover, since the empirical support for the human capital model has been overwhelming, the primary focus of this paper is to explore the remaining five hypotheses for which the evidence has been weaker.
  4. We must bear in mind that the theoretical predictions of the human capital model may be ambiguous for British women because of the generous welfare state provided by the UK government. Single mothers may find that after paying for the cost of childcare, their remaining salary is barely more than the unemployment and child benefits they could receive by staying at home, and so they may choose to leave the labour market altogether. If this is true the human capital model would predict that some single mothers will also take career interruptions and this will reduce the difference in penalty compared to married mothers. Since our dataset does not contain measures on government benefits received, we cannot test for this.
  5. Never-married mothers appear to have accumulated more human capital than women who have been married: Consulting summary statistics confirms that never-married mothers have more years of education (12.97) than married mothers (12.77) and divorced mothers (12.87). So in model 2 it falsely appears that they do not suffer a penalty. Upon controlling for human capital in model 3, it becomes clear that never-married mothers actually face the highest child penalty.
  6. Heckman (1979) developed the Heckman correction (also known as the two-stage method, Heckman's lambda or the Heckit method) which is a statistical method which allows the researcher to correct for selection bias. The basic procedure is outlined on the next page, but for full details please see Heckman's original paper 'Sample Selection Bias as a Specification Error', Econometrica, Vol 47, No. 1 (Jan 1979), pp 153-161.
  7. The additional variables used in the first stage participation probit (which I have tested to ensure they do not directly affect wages) include measures of current health, spouse's overtime hours, financial expectations for the coming year, and dummies for holding certain opinions and values namely 'family suffers if woman works', 'husband should earn money while wife should stay at home', and 'working makes woman independent'.
  8. Puhani (2000) give results from monte carlo simulations which show that Heckman's LIML estimator can be very inefficient when there is a high correlation between the error terms of the selection and outcome equations - moreover it can be unrobust when there is high correlation between the regressors of the two equations because the inverse mills ratio is almost linear over wide ranges of its argument. However it does have the appealing large-sample property of consistency, and after initial exploratory work I could find no evidence of strong correlation therefore I chose to use Heckman's LIML over sub-sample OLS, Two-Part method, or the Full Information Maximum likelihood estimators.

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