Mind the gap—German motherhood risks in figures and game theory issues

ORIGINAL PAPER

Mind the gap—German motherhood risks in figuresand game theory issues

Christina Boll

Published online: 5 April 2011# Springer-Verlag 2011

Abstract After childbirth, while parents are delighted at public cash transfers likethe German ‘Elterngeld’ (parental leave benefit), the decline in mothers’ earningscapacity is an awkward issue that tends to hover in the background. This paper aimsfirstly to make a contribution to quantifying West German mothers’ foregone grossearnings that stem from intermittent labor market participation, due to the birth oftheir first child. Secondly, it discusses behavioral outcomes of the resulting implicitchild costs in a dynamic bargaining model of household decisions. The regressionresults of a Mincer-type wage equation, with German Socio-Economic Panel Data(West) for the period 1984–2005 and correcting for sample selection (Two-stepHeckman), indicate considerable wage penalties due to birth-related employmentwithdrawal. On the closure of the fecund window, mothers suffer gross hourly wagecuts of up to 25%, compared to their equally educated, non-stop full-time employedcounterparts, and the total of annualized losses amounts to as much as 201,000Euros. Although foregone earnings do not matter as much in stable partnerships,they turn out to be a veritable asymmetric specialization risk that can prevent womenfrom having children, if divorce seems sufficiently probable.

Keywords Cooperative bargaining .Wage loss . Fertility

JEL Classifications C71 . J31 . J13

1 Introduction

Everybody knows that children enrich our lives and that they cost a lot of money.But whose money? Whereas explicit costs related to nurturing, clothing and

Int Econ Econ Policy (2011) 8:363–382DOI 10.1007/s10368-011-0188-x

C. Boll (*)Hamburg Institute of International Economics (HWWI), Heimhuder Str. 71,20148 Hamburg, Germanye-mail: [email protected]: www.hwwi.org

educating children can be estimated easily, calculating the implicit costs, such as theincome loss due to birth-related labor market discontinuities, is a far morechallenging task. The large body of theoretical research on human capital decisionsin a multi-period household model context is accompanied by a profound lack ofquantitative data. Nevertheless, manifold evidence justifies the assumption that thoseimplicit child-related costs play a specific role in individual fertility and labor supplydecisions. In Western Germany, the overall fertility rate declined between 1997 and2008 from 1.44 to 1.37, whereas during the same period, it rose continuously in theEastern part of Germany from 1.04 to 1.40. The overall German rate in 2008amounted to 1.38 (Statistisches Bundesamt 2010a). Furthermore, postponing the firstchild is far more pronounced in Western Germany, as the mothers bear their firstchild at an average age of 29, whereas their East German counterparts average27 years (Statistisches Bundesamt 2010b). Last but not least, only in WesternGermany, is childlessness positively correlated to mothers’ level of education andhence their level of losses (Statistisches Bundesamt 2009). Given that long labormarket withdrawals often emerge in contexts where job and family are notreconcilable, income losses should be considered as a specific risk of motherhood,especially in Western Germany.

The aim of this paper is to quantify these wage losses and to discuss their possiblebehavioral outcomes, especially with respect to time use and fertility decisions. Inthis context, the paper reveals the crucial challenges for economic policy that have tobe faced, in order simultaneously to raise birth rates and female labor participation.

The paper is organized as follows In Section 2, the underlying theoretical argumentis outlined, and some relevant papers reviewed, especially those using German data.Section 3 deals with the empirical results relating to birth-related income losses. Tothis end, there is first an analysis of the data used, before describing the econometricmodel, as well as the regression and simulation results. Section 4 addresses the issueof how to convert the results of Section 3 into a quantified specialization risk, andfurther isolates three important determinants of its quantity. A brief conclusioncompletes the paper (Section 5).

2 Basic theoretical argument—the bargaining approach

The subject of family economics has a long tradition. With his model of timeallocation in the household context, Gary S. Becker established the research area of‘New Home Economics’ (Becker 1965). In this model, the single household acts as aconsumer, producer, and insurance community that protects its members againstvarious ‘vicissitudes of life’ (Ott 19951).2 Owing to economies of scale in the use ofcollective goods and comparative advantages in time use, combined with

1 p. 81.2 The expressions ‘partnership’, ‘household’, ‘connection’, ‘commitment’, ‘liaison’ etc. are usedsynonymously in this paper, since the decisive issue is that of having a common household.

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interpersonally transferable goods, the maximization of individual household utilityis achieved through the maximized specialization of household partners.3

At least three developments coincided with the transition of gender roles. Firstly,the educational level of females caught up with that of their male counterparts, and,secondly, due to technological progress in household production, the gains ofspecialization diminished rapidly. Thirdly, at the same time and possibly as a result,divorce rates increased in most western countries, creating asymmetric risks forpartners coping with the traditional division of labor. The decision to specializetherefore resembles the classic prisoner’s dilemma. In the case of cooperation(keeping the connection viable), both partners benefit from specialization in terms ofgreater household welfare (win-win situation). However, in the case of dissolution asthe end of cooperation, the market-oriented partner continues to reap the returns ofhis/her non-stop market employment career, whereas the care-oriented partner facesan abrupt deterioration in economic prospects. The efficiency gains from marriageemerge particularly in the first few years, when the children are young and theadvantages of specialization are relatively high (Becker 1976). During that period,the partner who specializes in household-related work contributes a large share ofhousehold welfare by refraining from investing in his own market-oriented humancapital. In the cooperative scenario, this input is reimbursed by the market-orientedpartner in terms of continued alimentation of the spouse in the later life course whenthe woman has stepped out of her fecund window and the children have grown upand finally left the family home. By contrast, in the non-cooperative scenario, sinceconnections are assumed to be unstable, the end of the fecund window not onlydenotes the beginning of the reimbursement phase of the male spouse, but alsomarks a point of risk-turnaround in the marriage.

Dynamic bargaining models deal with the cross-period effects of time allocationdecisions in the framework of collective (cooperative or non-cooperative) decisionmaking. The first Nash-bargaining model of household behavior was presented byManser and Brown (1980) and McElroy and Horney (1981). In these papers, under-investment in child rearing is considered as an outcome of marriage-specific riskslike divorce or the loss of intra-marriage bargaining power. The figures below arebased on Ott (1992).4 In the Ott-model, the conflict payment equals the maximumutility of one partner that is obtainable in the event of a commitment breakdown. Theconflict payment is part of the following cooperative Nash solution:

maxxN ¼ ½UmðxÞ � Dm�»½U f ðxÞDf �:In this specification, parameter x denotes a vector of household goods produced at

a price vector p and which are subject to the periodic bargaining activities ofpartners. Furthermore, partners bargain over the time allocation of household andmarket-related work (and leisure, if any). In this context, they face commonrestrictions, namely a budget constraint (consumption expenditures may not exceed

3 Interestingly, the theory of female endowment advantage, with respect to household work, relies on theassumption of compatibility between pregnancy and nursing, and household tasks (Becker 1981, p. 38).4 The multiplicative conjunction of marital gains indicates interdependent individual utilities and serves asan incentive for both partners to maximize total household output. Individual utilities are assumed to beintertemporally additive. See Ott (1995), p. 80-91 for a complete formulation of the model.

Mind the gap—German motherhood risks in figures and game theory issues 365

family income Y (Y=x´ p)), and the time constraint of a 24-hour day. Um denotes themarital utility of the male, and Uf that of the female partner. The conflict payment(threat point) of a partner, Di( p, Y i), equals his or her maximum individually derivedutility that is attainable with Y i as his/her single income at current prices ( p):

Dið p; Y iÞ ¼ maxxUiðxÞ; upon condition that Y i ¼ x0p:

Each partner enters into cooperation, only if his or her utility from marriageexceeds the utility that would be derived individually:

ðUmðxÞ > Dm;U f ðxÞ > Df Þ:Individual out-of-marriage utility does not matter in the unitary model, because

the relationship is stable by definition. Therefore, a shift in out-of-marriage optionsdoes not alter the intra-marriage distribution rule. By contrast, in the bargainingmodel, the partner with increased external options benefits from augmentedbargaining power, resulting in a more favorable distribution of household-specificgoods. Thus, in dynamic bargaining models, the decision to concentrate onhousehold-related time allocation today (hereafter labeled as ‘caring’) induces aloss of market-oriented human capital and therefore, via reduced income-earningcapacity, a decline in intra-marriage bargaining power in the ensuring periods. Fromthe caring spouse’s point of view, the deterioration of his/her bargaining power mayoutweigh the overall gain in household utility through the increase in householdproduction. In a two-period model, compared with his or her utility beforespecialization (in Period P1), it may be that the caring spouse is worse offafterwards (in Period P2). As a rational individual, he or she foresees thisconstellation and thus refuses to agree on the deal in Period P1. Because of anincomplete specialization of partners, in dynamic bargaining models, overallhousehold welfare turns out to be sub-optimal. The context is illustrated in Fig. 1.5

F1 denotes the household production possibility frontier before specialization(before childbirth) as the sum of utility pairs that are achievable with given income Yat given prices p. The household indifference curves IND1 and IND2 represent utilitypairs that guarantee constant household utility, whereas the utility level of IND2

exceeds that of IND1. Before childbirth, point A emerges as the maximumachievable household utility that coincides with the given intra-marital distributionrule. From point A, Um

1 as the marital utility of the male and U f1 that of the female

partner, are derived. As is clearly evident, each partner is better off in the alliancethan out of it, since Um

1 exceeds Dm and U f1 exceeds D f.

I assume that the birth of the first child marks the beginning of a new period(Period P2). I further assume that the spouses agree that the female specializes incaring, because of a lack of external care facilities. I thirdly assume that the birth ofthe child induces a household net welfare gain which is indicated by an outwardsshift of the household production possibility frontier (F2). In this case, the dottedarea in Fig. 1 denotes all Pareto-improvements derived from the imagined newsituation. Because of the assumption of exogenous preferences, an unchangeddistribution rule in the unitary model, point B emerges as the new tangential point of

5 The depictions in Figs. 1 and 2 are based on Ott (1995), p. 90.

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F2 and IND2. Given that the post-birth utility of each partner exceeds the pre-birthlevel (Um

2 > Um1 ; U

f2 > U f

1 ), both partners would be willing to agree on thespecialization deal, so that they will have a child.

Things look different if a termination of the alliance is taken into consideration(see Fig. 2):

As in Fig. 1, the marital utility levels of both partners exceed their individualutility levels in Period P1. Correspondingly, the birth of a child causes the householdproduction possibility frontier to shift from F1 to F2, yielding a higher householdutility level. However, the deterioration of female out-of-marriage options in PeriodP2 that results from her specialization-decision in Period P1 (as indicated by thesharply reduced single utility Df

2) alters the intra-marital distribution rule in PeriodP2 to the detriment of the woman (demonstrated by the change in the slope ofIND2). Compared to her utility level in Period P1, the woman turns out to be worseoff in Period P2. While the male partner is better off in two respects (because of bothan increase in outside options and of intra-marriage bargaining power), the female

Fig. 1 Household utility de-rived from household speciali-zation of the female partner inthe unitary model withexogenous preferences

Fig. 2 Household utility derivedfrom household specialization ofthe female partner in the dy-namic bargaining model withendogenous preferences


partner will refuse to agree on the deal from a purely economic point of view. If so,the partners’ utility levels freeze at point A, they will not have a child, and thepotential welfare gains will not be realized.

Is there empirical evidence of the underlying assumption of devaluating humancapital in the context of labor force intermittencies? Mincer and Polachek (1974) andMincer and Ofek (1982) conducted relevant pioneer work on this issue. Based on‘National Longitudinal Survey’ panel data of married women, Mincer and Ofek(1982) found severe human capital depreciation rates during out-of-labor-force spellsand noticeable rebound effects after labor market re-entry. With ‘British HouseholdPanel Survey’ panel data for the period 1991–2004, Jenkins (2008) demonstratedthat women’s risk of income losses in the context of marital splits is aggravated inthe event of a lack of labor market integration. He showed that the size of lossesincurred has declined over time, mainly due to increased female employment rates.Nevertheless, the income drop suffered by women is still much more severe than thatof men, and, over a five-year horizon after a marital split, the average income ofseparated wives remains 10% below the pre-split level, with employed women faringmuch better, and unemployed women without a new partner faring worst.

There is also some empirical evidence based on German data. Pioneer work has beendone by Helberger (1984) and Galler (1991). Licht and Steiner (1991a, 1991b, 1992)reported a higher wage premium of work experience for men than for women. Ziefle(2004) showed that staying with the same employer only marginally lessens wagelosses after a return to the labor market. Görlich and de Grip (2007) stated that, aftercontrolling for gender, time-outs in so-called ‘female’ occupations cause less humancapital depreciation than those in commonly male-dominated jobs. Beblo and Wolf(2000, 2002, 2003) found that the market value of previous work experience declinesmore rapidly if it is followed by a time-out, rather than by a part-time spell, and thatthe wages of men are less sensitive to labor market interruption than those of women.

The study presented in this paper supplements the existing strands of literature,investigating the specific wage effects of certain form and timings of full-timeemployment interruption. With respect to the different forms, I distinguish betweenpart-time versus out-of-labor-force time, the latter occurring as registered unem-ployment, a break of up to10 years after a preceding birth event (birth-related time-out), or an unspecified break.

3 The quantity of birth-related wage losses

3.1 Data

In order to quantify birth-related income losses, the respective data and panel datafrom the German Socio-Economic-Panel (GSOEP), waves 1984–2005, were used.The GSOEP commenced in 1984 and is a wide-ranging, representative longitudinalstudy of private households, conducted at the German Institute for EconomicResearch, DIW, in Berlin. Every year, more than 10,000 households and nearly19,000 individuals are sampled, consisting of Germans living in the Old and NewGerman States, foreigners, and recent immigrants to Germany. The employmentsample for the empirical investigation outlined in this paper consists of 1,610 West

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German women aged 16–55 with 6,276 observations in total. I deploy an UnbalancedPanel and take only complete (free of missing information) biographies into account.The data for East German or foreign women are excluded, since their employmentpatterns do not conform to the Western German ones. The wage sample (as part of theemployment sample) consists of 1,038 women with 3,254 observations and isfurthermore restricted to dependently employed women (blue or white collar workers,civil servants) with completed education at the time of the interview.

3.2 The econometric model and regression results

With respect to the wage regression, a comprehensive set of human-capital-relatedvariables was used, supplemented by various workplace and work-setting variables.With regard to the model specification, ordinary least squares, fixed effects andrandom effects estimations were used.

Due to the (only) five-year time horizon for wage information (waves 2001–2005), in conjunction with the property of the within estimator of using onlyintrapersonal information, the fixed effects model failed to predict the wage impactof long-lasting employment spells. With respect to unobserved heterogeneity and thefact that there is far more cross-sectional than longitudinal information in theunderlying data set, the random effects specification suits the data better and wasthus chosen.6 The linear multiple regression framework is specified in the followingform (with reference to Licht and Steiner 1991b):

lnwit ¼ a0 þ ai þ b0lit þXm

j¼1bjSCHji þ

Xmþn

j¼mþ1bjEXPjit

þXmþnþk

j¼mþnþ1bjCONTRjit

þ "itði ¼ 1; 2; . . . ;N; t ¼ 1; 2; . . . ;TÞ

whereat

wit real gross hourly wage rate of person i at time tα0 constant (’Grand Mean’)αi unobserved individual effects1 it inverse of Mill’s RatioSCHji set of m compulsory school, post-school and vocational training

variablesEXPjit set of n professional experience variablesCONTRjit set of k control variablesεit disturbance termβ0, βj parameters to be estimated.

The real gross hourly wage rate of individual i at time t, wit, is a function of his/her time-invariant level of education (SCHji), his professional experience (EXPjit andthe magnitude of several control variables at time t (CONTRjit. ai denotesunobservable wage-relevant characteristics that are potentially correlated with the

6 More specifically, I estimated numerous fixed and random effects model specifications and calculatedthe resulting wage losses based on the regression results. The findings indicate that calculations based onfixed effects estimations vastly overestimate wage losses, whereas random effects estimations lead torather conservative simulation results at the lower end of the loss range.


explanatory variables (e. g. preferences with regard to labor market participation).1 it, the ‘Select’-variable, specifies the inverse of the Mill’s Ratio that was obtainedfrom a Probit estimation (Greene 2000), and, in order to control for sample selection,imputed into the wage equation (two-step Heckman 1979). The employmentequation has the following form:

d»

it ¼ zitg þ uit; dit ¼1 if d

»

it > 0

0 if d»

it � 0

(

d»it is a latent variable and measures the inclination of individual i at time t to be

(dependently) employed. dit denotes an observable dichotomous variable thatamounts to 1 in the of dependent employment and to zero otherwise. Vector zitconsists of various socio-economic variables which affect the woman’s reservationwage. uit denotes the disturbance term, and γ the parameter vector in question,indicating the impact of a distinct explanatory variable on the likelihood of(dependent) employment.7 Tables 1 and 2 depict both the descriptive statistics andregression results.

The average log of hourly wages, including fringe benefits, corresponds to anaverage hourly wage rate of €12.74, with a standard deviation of €1.55 andminimum (maximum) wage of €1.21 (€80.45). Without fringe benefits, the averagewage rate amounts to €11.95, with a standard deviation of €1.51 and minimum(maximum) wage of €1.12 (€71.27). Table 2 presents the wage and employmentregression. As the estimated parameters of the employment equation variables referto their impact on a latent variable, they cannot not be interpreted easily. Therefore,marginal effects are chosen instead.8 Compared to a vocational training degree, auniversity degree not only increases the likelihood of obtaining employment, butalso yields considerable remuneration benefits in terms of a 16% wage premium.The parameters of variables referring to the household context of the woman, forexample, the number and age of children, exhibit the expected shape. That is,determinants which increase the reservation wage restrict the likelihood ofemployment. With regard to job biography, the estimates reveal a certain pathdependency of employment and unemployment, respectively. Previous unemploy-ment tends to lead to current unemployment and vice versa. With respect toprofessional experience, all variables refer to the end of the preceding year, theirparameters indicating the current returns from previously accumulated humancapital.9 For instance, the job market rewards full-time employment in terms of a2.8% wage premium and even a 4.3% supplement (2.8+1.5) in the case ofuninterrupted activity since entering the labor market, both with respect to the first

7 The estimated employment propensity refers only to the domestic background of the individual, not tothe job conditions; neither is there an estimation of re-employment propensity which is responsive to theprevious work situation.8 The marginal effect of the explaining variable j, δPr(y=1|x)/δxj, illustrates the effect of an infinitesimalvariation or, with regard to dummies, of a switch from value “0” to value “1” on employment propensity.9 For example, if the preceding year was the first of a full-time spell, it is designated as a current full-timeyear. By contrast, if the full-time period ended in the year before last, that year belongs to previous full-time employment, whereas the last year is designated as current part-time, out-of-labor-force time orregistered joblessness. One single employment status was assigned to each year, depending on the reportedmonthly status frequencies.

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Table 1 Descriptive statistics

Variable (Reference in brackets; D = Dummy) Number ofobservations

Mean Standard-deviation

Min Max

Explained variable in employment equationi

Dependently employedii 6,276 .5188018 .4996862 0 1

Explained variable in wage equation (in €)iii

Log of real gross hourly wage withfringe benefits

3,254 2.544895 .4352205 .1945588 4.39

Log of real gross hourly wage withoutfringe benefits

3,254 2.480366 .4135072 .1100355 4.28

Schooling and Vocational Training

Low level of schoolingD: no compulsoryschool degree

6,276 .3355641 .4722249 0 1

(Moderate level of schoolingD: Realschule) 6,276 .3961122 .4891272 0 1

Higher education entrance qualificationD 6,276 .2683238 .4431223 0 1

No vocational degreeD 6,276 .2178139 .4127931 0 1

(Moderate vocational degreeD: 6,276 .6698534 .4703032 0 1

Apprenticeship, Training, ProfessionalSchool)University degreeD

6,276 .1123327 .3158005 0 1

Professional Experience (in years)

Tenure 6,276 3.392447 5.326808 0 37

Current full-time 6,276 2.664914 5.58918 0 37

Current uninterrupted full-time 6,276 1.646112 4.818772 0 35

Previous full-time beforeout-of-labor-force spell

6,276 3.746176 4.935741 0 39

Previous full-time before part-time 6,276 .8231358 3.145747 0 30

Current part-time 6,276 1.639579 3.812555 0 34

Previous part-time 6,276 1.898662 3.650848 0 25

Out-of-labor-force spell (current orprevious type)

6,276 4.581899 6.280722 0 36

Current out-of-labor-force spell 6,276 1.533461 4.32968 0 36

Current birth-related out-of-labor-force spell 6,276 .4362651 1.479286 0 10

Previous out-of-labor-force spell 6,276 3.048438 5.049133 0 32

Unemployment (current or previous type) 6,276 .4141173 1.223066 0 16

Current (registered) unemployment 6,276 .0482792 .406005 0 9

Previous (registered) unemployment 6,276 .3658381 1.097192 0 15

Workplace and work setting related control variables

Agriculture and forestryD 6,276 .0071702 .0843795 0 1

Mining and energyD 6,276 .0035054 .0591074 0 1

ConstructionD 6,276 .0116316 .1072294 0 1

TradeD 6,276 .1159975 .3202474 0 1

TransportationD 6,276 .0160931 .1258435 0 1

Banking, insurance, other private servicesD 6,276 .4115679 .4921568 0 1

(Manufacturing) 6,276 .1089866 .3116473 0 1

Civil ServiceD 6,276 -.4520395 1 .137591 • 1


year. The wage premium diminishes over time, since previous human capitaldepreciates. Part-time jobs do not yield significant wage growth, probably becauseof the limited promotion and training opportunities. Employment breaks, particularlyif they are birth-motivated, induce wage cuts at the time of re-entry that amount to12.3% for the first time-out year (however, the penalty decreases with increasingtime-out duration).10

Table 1 (continued)

Variable (Reference in brackets; D = Dummy) Number ofobservations

Mean Standard-deviation

Min Max

Occupational prestige# 6,276 43.0854 37.40649 • 216

Civil servantD 6,276 .0470045 .2116653 0 1

White collar workerD 6,276 .4507648 .4976096 0 1

(Blue collar workerD) 6,276 .1073932 .3096372 0 1

Firm size 20–199 employeesD 6,276 -.7267368 1 .277719 • 1

Firm size 200–1,999 employeesD 6,276 -.8608987 1 .133732 • 1

Firm size 2,000 minimumD 6,276 -.8368388 1 .16201 • 1

(Firm size 19 employees maximum)D 6,276 -.9063098 1 .076878 • 1

Weekly working hours## 6,276 21.05296 18.25826 0 80

Regional Job crush ratio### 6,276 9.80 5.54 3.20 44

Baden-WürttembergD 6,276 .1383047 .345247 0 1

Socio-economic control variables

Age 6,276 37.25032 9.338553 17 55

Number of children in household 6,276 .7123964 .9338158 0 6

Youngest child in household age 0-1D 6,276 .0495539 .2170387 0 1

Youngest child in household age 2-4 D 6,276 .1188655 .323656 0 1




Health deficiency D 6,276 .0581581 .2340607 0 1

Help requiring person in household D 6,276 .0226259 .1487194 0 1

Married/cohabiting with partner D 6,276 .6011791 .4896948 0 1

Monthly net non-wage household income

per capita, in 100 € 6,276 2.966601 3.85996 0 51.75

Monthly net labor income of partner

per capita, in 100 € 6,276 4.641409 4.523627 0 43.46

i as far as not indicated differently, the results refer to the Employment sample; ii 1 = employed, 0 = notemployed; iii results refer to Wage sample; • not applicable: as several women of the employment samplewere not employed in the interval 2001-2005, some job-related variables for these individuals may not beinterpreted meaningfully; #Prestige score; ##in hours; ###unemployed persons per vacant job; DataSource: GSOEP (West) 1984-2005, own calculations; see text for sample selection information

10 The wage penalties of joblessness resemble those of an otherwise (non-birth) motivated time-out, but theypersist longer. Indeed, the joblessness parameters are not statistically significant. To shorten the analysis, Irefrain from outlining the parameters of workplace-related variables, most of which are highly significant.

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Table 2 Regression results

Explained variable: Wage equation Employment equation

Real gross hourly wage rate withproportional fringe benefits (log)

Employment statusi

Explaining variable (in years, if notlabeled as D = Dummy or otherwise;references: see Table 1)

GLS Random Effects Maximum Likelihood

Coefficient Std. dev. Marginal effect+ Std. dev.

Schooling and Vocational Training

Low level of schoolingD -0.089 (0.028)*** -.0161146 (.0187383)

Higher education entrance qualificationD 0.121 (0.033)*** -.1324789 (.0222846)

No vocational degreeD -0.062 (0.034)* -.1786794 (.0200796)

University degreeD 0.163 (0.043)*** .1722132 (.0265177)

Professional Experience

Tenure .0487871 (.0024544)

Current full-time 0.028 (0.006)***

Current full-time squared/100 -0.046 (0.000)*

Current uninterrupted full-time 0.015 (0.007)**

Current uninterrupted full-time sq./100 -0.048 (0.000)

Previous full-time beforeout-of-labor-force

0.008 (0.002)***

Previous full-time before part-time 0.016 (0.003)***

Current part-time -0.003 (0.003)

Previous part-time 0.010 (0.003)***

OLF spell (current or previous type) -.0234816 (.0017915)

Current time-out -0.047 (0.016)***

Current time-out squared 0.002 (0.001)**

Current birth-related time-out -0.076 (0.038)**

Current birth-related time-out squared 0.018 (0.006)***

Previous time-out -0.004 (0.003)

Unemployment (current or previous type) -.0397241 (.0065424)

Current (registered) unemployment -0.045 (0.024)*

Previous (registered) unemployment -0.016 (0.012)

Workplace and work setting related control variables

Agriculture and forestryD -0.108 (0.098)

Mining and energyD 0.054 (0.096)

ConstructionD -0.064 (0.055)

TradeD -0.127 (0.028)***

TransportationD -0.108 (0.055)**

Banking, insurance, other private servicesD -0.021 (0.025)

Civil ServiceD 0.053 (0.021)**

Occupational prestige# 0.002 (0.000)***

Civil servantD 0.121 (0.047)**

White collar workerD 0.149 (0.023)***

Firm size 20-199 employeesD 0.110 (0.023)***

Firm size 200-1,999 employeesD 0.172 (0.028)***

Firm size 2,000 minimumD 0.186 (0.028)***

Weekly working hours## -0.014 (0.001)***


Table 2 (continued)

Explained variable: Wage equation Employment equation

Real gross hourly wage rate withproportional fringe benefits (log)

Employment statusi

Explaining variable (in years, if notlabeled as D = Dummy or otherwise;references: see Table 1)

GLS Random Effects Maximum Likelihood

Coefficient Std. dev. Marginal effect+ Std. dev.

Regional Job crush ratio### 0.002 (0.01) -.0027708 (.0014834)

Baden-Württemberg -.0543233 (.0227468)

Socio-economic control variables

Age .0087143 (.0013135)

Number of children in household -.0442861 (.0148191)

Youngest child in household age 0-1D -.4916809 (.023042)

Youngest child in household age 2-4 D -.3135247 (.0306148)




Health deficiency D -.155613 (.0354777)

Help requiring person in household D -.0910423 (.056389)

Married/cohabiting with partner D -.0524218 (.0228794)

Monthly net non-wage householdincome per capita, in 100 €

-.0636424 (.0048433)

Monthly net non-wage householdincome per capita, in 100 €, squared

.0017055 (.000257)

Monthly net labor income of partnerper capita, in 100 €

-.0273282 (.0043205)

Monthly net labor income of partnerper capita, in 100 €, squared

.0009201 (.0002168)

Select 0.042 (0.013)***

Constant 2.390 (0.055)*** Coeff.: 0.490 (0.122)***

Number of observations 3,255 6,276

+ The marginal effect of the explaining variable j, δPr(y=1|x)/δxj, illustrates the effect of an infinitesimal variation(metric variables) respectively the effect of a switch from value “0” to value “1” (dummy variables) on employmentpropensity

* significant at 10%; ** significant at 5%; *** significant at 1%; i 1 = employed, 0 = not employed; # Prestige score;## in hours; ### unemployed persons per vacant job; Data Source: GSOEP (West) 1984-2005, own calculations

Test statistics of wage equation estimation:

R2 within/between/overall = 0.1394/0.3755/0.3582

Random effects u_i~Gaussian

corr (u_i, X)=0 (assumed)

Wald chi2 (35)=982.97; Prob>chi2 =0.0000

LM Test statistics (H0: Var(u)=0): chi2 (1)=990.29; Prob>chi2 =0.0000

Hausman Test statistics (H0: difference in coefficients not systematic): chi2 (31)=217.05; Prob>chi2 =0.0000

Test statistics of employment equation estimation:

Pseudo R2 (Mc Fadden, 1973)=0.3424

Log likelihood=-2857.8323(0 failures and 1 success completely determined)

Wald-Test (chi2 -distributed Likelihood Ratio-Value, number of explaining variables in brackets): LR chi2 (23)=2975.84; Prob>chi2 =0.0000

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3.3 Results on simulated wage losses

Wage simulations are conducted, so as to illustrate the wage losses that are related toa distinct hypothetical employment profile. For this purpose, several intermittentemployment patterns were constructed. They differ in the timing and duration of theout-of-labor-force spell, as well as of the succeeding part-time spell. I compare thewage profile of the mother, which is associated with a distinct hypothetical patternwith the wage profile of an uninterrupted full-time employed woman with the sameeducational level (‘reference woman’). The corresponding wage loss comprises thegap in earnings between the mother and the reference woman. In detail, I specify atri-annual out-of-labor-force spell, followed by a tri-annual part-time spell as a‘Primary School Pattern’, since the mother reduces full-time employment until theprimary school enrolment of her child. A second pattern labeled ‘KindergartenPattern’ denotes a one-year out-of-labor-force spell after giving birth, combined with2 years of part-time subsequent employment. The labor market intermittency due tothe first birth starts respectively at the ages (of the mother) of 28, 32 or 36 years. Iuse three types of vocational education: with/without vocational degree, and with/without university degree.11 With respect to the remaining attributes (e. g. industry,firm size or the ‘Select’-variable) the education-specific average was used.12 Thesimulations abstract from the disturbance term and depict an ideal-typical wageprofile, based on the estimated regression coefficients.

The wage loss is calculated both in terms of an hourly wage gap and an aggregatewage sum lost. Both the hourly wage gap and the total of lost wages refer to an ageof 45. This arises from the frequencies of biographic events in the underlyingsample, which restrict the extrapolation of regression results. On the assumption thatthe rate of real wage growth (which the study excluded), equals the discount rate, thetransformation of losses into their present values is dispensable.

The following Fig. 3 depicts potential hourly wages, as they occur in the case ofcontinuous full-time employment (reference wages). By contrast, wages in the caseof intermittent employment are shown as being considerably lower.

Firstly, the wage gap rises with an increasing educational level. As in the veryfirst years of a professional career, investments in human capital are high and, sincegraduates enter the labor market relatively late, graduate mothers’ opportunity costsof childbirth are particularly high during that time—consisting, to a large extent, of afailure to gain returns from foregone investments. On the other hand, according totheir late labor market entrance and their comparatively high basic wage rate,graduate mothers refraining from market work suffer only modest human capitaldepreciation. As for poorly educated women, they start their professional careerearly in life, so that, at the time of employment break, a relatively large amount ofjob-related human capital that has been generated up to this time, is subject todepreciation.

11 No compulsory school degree plus no vocational degree is labeled “low education”, intermediatesecondary school plus vocational training is denoted “medium education” and matriculation standard plusuniversity degree, as “higher education”.12 As mentioned above, since graduates are under-represented amongst employment sample mothers, thisleads to an overestimation of their postnatal re-employment propensities, by underestimating the resultingwage losses of graduate women.


Secondly, the hourly wage loss is higher, the longer the out-of-labor-force spell.Although Germany actually seeks to improve institutional care facilities, the returnto full-time employment when the child reaches school age (Primary School Pattern)remains a considerable challenge. The finding that losses are quite sensitive tointerruption duration, reveals substantial scope of action for policy makers.

Thirdly, hourly wage gaps increase with an increasing age of the mother on thefirst birth. Although the spread per time unit decreases over time, as wage growth

Fig. 3 Gross hourly wage rates of reference woman and intermittently employed woman, both aged 45,subject to education, timing and duration of withdrawal

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decelerates, the shortening time span to catch up reference wages, functions in theopposite direction and outweighs the first effect mentioned above. This holds forboth patterns and all educational levels.

As Fig. 4 below illustrates, not only hourly, but also aggregate losses decrease,when withdrawal spells are reduced (from the Primary School to the KindergartenPattern).

The annualized wage losses have been aggregated into an overall lost wage sumfrom the time of withdrawal up to the age of 45. This is referred to as the ‘care bill’,since it equals the total of lost (gross) earnings due to child care. The care bill isdivided into three components—lost earnings during the out-of-labor-force timespell itself, losses during the succeeding part-time interval and, last but not least,losses during the subsequent phase that covers the time span from the mother’s re-entry into full-time employment up to the age of 45. However, moderately educatedwomen, who have their first child at 28 or 32, suffer a higher wage loss thangraduates. In comparison to the latter, moderately educated women’s disadvantagesin terms of formal qualifications are almost fully offset by their professionalexperience advantage, due to their earlier labor market entrance. Hence, the wagelevel of moderately educated, continuously employed women, comes very close tothat of the graduate women. Additionally, returning from a family break, the drop inwages turns out to be smaller for highly, than for moderately educated women, withhigher losses of the latter as a consequence. At the age of 36, the earlier decelerationof moderately qualified womens’ wage growth accounts for comparatively lowerwage losses with respect to graduate women.

Furthermore, the abovementioned loss components are differently responsive to avariation in birth timing. While direct losses during out-of-labor-force (OLF) spellsand during succeeding part-time spells increase through postponing the first birth,the loss after returning to full-time work up to the age of 45, hereafter referred to asconsequential costs, decreases. As a result, the overall wage loss decreases throughpostponement, with the single exception of graduates switching from childbearing atage 28 to age 32.

4 Wage losses as a specialization risk in the bargaining context

This section addresses the question as to how the calculated wage losses may entail aspecialization risk in the context of the ‘Ott model’ (1992). The simple message ofthe ‘Ott-model’ is the following. Anticipated asymmetric specialization risks causethe female labor supply to increase and the propensity to have children to decrease.At first sight, the model thus simultaneously explains two common phenomena: thehigh employment rates of mothers and declining birth rates. However, this does nothold for graduate women. I now demonstrate which modifications of the model arenecessary to capture the birth risk more comprehensively, to provide a betterunderstanding of observed fertility.

In the ‘Ott-framework’, specialization risk is conceptualized as an intrapersonalloss of utility that arises from a loss in income between periods P1 and P2. As aconsequence, with the underlying catching-up of wages in the Kindergarten Pattern,the disadvantage of specialization covers only half a dozen of years, particularly if


Fig. 4 Gross wage sum lost by the intermittently employed woman up to age 45, dependent on educationand age at first birth*, split into OLF-, part-time and subsequent losses

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women have their children early. Furthermore, according to the logic of the model, itturns out that graduate women who, in most cases, offset foregone income fasterthan less educated women, have the comparatively highest propensity to specialize.This contradicts the empirical evidence, since the share of childless women ishighest amongst graduates. Therefore, departing from risk-conceptions that relyexclusively on past earnings, the paper presented here focuses on a morecomprehensive loss definition. Deviating from the ‘Ott-model’, not the differenceto previously earned, but the gap to potentially earned wages at each point in time,define the specialization risk in question. Potentially earned wages are those of theequally educated, but continuously full-time employed woman (reference woman).Thus, specialization risks are not simply restricted to human capital depreciation, butalso comprise foregone investments as a notable component of implicit child rearingcosts. Therefore, the birth-related specialization risk outlasts the recovery of formerwages. To this end, the applied risk concept of potential wages readily indicates theutility loss of mothers, even in the context of intrapersonal cross-period incomebalancing. The magnitude of existing wage gaps at age 45, gives rise to theassumption that, by enlarging the time horizon until retirement, the upward trend ofwage losses will continue. This process is intensified, given that foregone old-agepensions due to omitted pension scheme contributions further jeopardize women’sperspectives for building up capital.

Another crucial point of the ‘Ott-model’ relates to the male conflict payment, ashis maximum individually-derived utility outside the alliance. The assumption that itremains unchanged over time, contradicts the fact that the partner who specializes inmarket work, benefits from a steadily increased income over the course of his life.The growing earnings are related to a likewise growing derived utility inside andoutside the alliance. Thus, the male partner is in a lead position that ensurespersisting gender asymmetries in income distribution over time, even if the femalepartner catches up on previously earned wages.

In the two-period ‘Ott-model’, specialization risks become far more severe inPeriod P2. In this phase, around her 46th birthday, the woman usually exits herfecund window. Persisting wage losses so far must be considered as largelyirreversible. As the woman has already returned to full-time work, the short-runmonthly earnings range has been exhausted, and public transfer payments like theGerman parental leave benefit (‘Elterngeld’) have terminated. In such phases,financial support from the domestic partner is at risk, because of his diminishingincentives to maintain the domestic deal. To sum up, persisting gross hourly wagedifferentials at age 45 may be considered as a specialization risk in the narrow sense.From a more comprehensive point of view, the total consequential cost afterreturning to full-time employment may be seen as a specialization risk in a broadersense, if one considers the fact that, with her re-entry decision, the mother signals thedispensability of her child-raising services.

As mentioned above, the mother’s education, as well as the timing and durationof the birth-related employment break, affect the magnitude of computed losses.Because both hourly wage differentials and consequential costs, are higher for thePrimary School Pattern, compared to the Kindergarten Pattern, the willingness tospecialize—in terms of venturing into motherhood—is likely to increase withimproving institutional care that enables women to take short leaves. With respect to


the timing of withdrawal, the results are ambiguous. The hourly wage loss is higher,the later in life the first birth occurs. By contrast, the consequential costs decreasethrough postponing birth. Thus, from an hourly point of view, an incentive topostpone contrasts with an incentive to “prepone” with regard to the total losses.How should one interpret these contradictory results? The cost-minimizing timingdecision relates to the question of which stage of life is regarded as critical forspecialization, from the individual perspective. If terminating the partnership isexpected at the end of the fecund span, both household partners have to bear theincome losses occurring until then. As the hourly wage gap at the time of labormarket re-entry is minimized with an early birth, in this case, bringing the first birthforward appears to be rational. Otherwise, if the partnership is seen as unstable at anearlier date, the woman risks bearing the entire burden of total losses herself. In thisscenario, postponing the first birth would be a rational strategy.

With regard to the educational level, the hourly wage gap increases with increasedschooling and training or through gaining university degrees. From this perspective,graduate women face the highest specialization risks. This is exacerbated by the factthat, since graduate women often are married to graduate men, the prenatal distributionof the partners’ labor income is quite balanced. To this extent, the bargaining powerand external options of the partners are balanced as well. In such a situation, the birth-related income loss experienced solely by the woman is particularly utility-damaging.With regard to the consequential costs, the moderately educated woman bears thehighest burden, if the first birth takes place at age 28, after which she changes placeswith the graduate woman. Since the average age of the first motherhood for Germanwomen is currently roughly at 30, the graduate woman faces the highest specializationrisk, even with respect to consequential costs.

5 Conclusion

This paper argues that, after childbirth, while parents enjoy leave benefits like theGerman ‘Elterngeld’, the woman should rather be concerned with her long-run incomecapacity than with the short-run household cash situation. As the results of the studyindicate, this turns out to be necessary, in order to circumvent a medium-termdeterioration of the woman’s income prospects. The latter occurs rather radically themoment the mother attempts to return to the labor market, when substantial wagelosses in the context of first motherhood become obvious. At the age of 45, the grosshourly wage gap of the woman with intermittent employment amounts to €4.21,roughly one third of the sampled average gross hourly wage rate with fringe benefits(€12.74). This applies, if a graduate woman chooses to take a tri-annual out-of-labor-force spell after the first birth at the age of 36, succeeded by a tri-annual part-time spell.Furthermore, the overall sum of lost wages up to age 45 amounts to €181,466. This isapproximately 34% of the gross wages that West German graduate women earn overthe course of their professional career until the age of 45.

As the regression results and subsequent simulations illustrate, losses increasewith rising educational levels, as well as with an increasing duration of employmentinterruption. As to the timing of first birth, the hourly wage gap promotes birthsearly in life, whereas, from the perspective of subsequent costs (as a component of

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the overall lost wage) postponing is profitable. If one keeps in mind that the averagemarriage duration was 14 years in 2008, the subsequent costs are decisive to thetiming decision.

The calculated losses underline the economic risk of giving birth. To this end, thestudy provides evidence of the economic rationality of childlessness or, at least, ofpostponing the first birth. This is especially true for women in the Western part ofGermany, where reconciling one’s professional career is still in its infancy, withrespect to children below 3 and above 6 years of age.

With regard to the challenges for economic policy, the findings suggest that theessence of the matter is to enable both parents to combine business and family life.There is empirical evidence that countries with an improved reconcilability in thisrespect, succeed twofold, with increased female employment rates and at least adecelerated decrease in birth rates (Adserà 2005). Thus, with respect to Germany, whatexactly is needed? Far more so than another upgrade in pecuniary child-related rewards,a significantly improved institutional setting is essential. Hence, policy makers mustconcentrate on establishing appropriate employment incentives via the tax and transfersystem and through providing a high-quality and sufficiently broad institutional childcare system. At the firm level, family-friendly working schedules, which also suitmanagerial positions, are necessary. In the context of scarce, highly skilled personnel,one should bear in mind that in competitive markets, foregone wages reflect foregoneproductivity. Therefore, reducing asymmetric specialization risks is a worthy policyobjective, from both the micro and macroeconomic perspectives.

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Mind the gap—German motherhood risks in figures and game theory issues